ELECTRICAL MACHINES 1

Transcription

1 ELECTRICAL MACHINES 1

2 EI2201 ELECTRICAL MACHINES L T P C (Common to EIE & ICE) AIM To impart basic knowledge on Electrical machines, principles and its behavior. OBJECTIVES At the end of this course, student would have been exposed to: 1.Theory of structures, operating principle, characteristics, and applications of D.C and A.C rotating machines and transformers in detail. 2. Introductory knowledge on Special Machines. UNIT I D.C. MACHINES 12 Construction of D.C. Machines - Principle and theory of operation of D.C. generator - EMF equation - Characteristics of D.C. generators - Armature reaction Commutation - Principle of operation of D.C. motor - Voltage equation - Torque equation - Types of D.C. motors and their characteristics Starters - Speed control of D.C. motors - Applications. UNIT II TRANSFORMERS 9 Principle - Theory of ideal transformer - EMF equation - Construction details of shell and core type transformers - Tests on transformers - Equivalent circuit - Phasor diagram - Regulation and efficiency of a transformer - Introduction to three - phase transformer connections. UNIT III SYNCHRONOUS MACHINES 8 Principle of alternators:- Construction details, Equation of induced EMF and Vector diagram -Synchronous motor:- Starting methods, Torque, V curves, Speed control and Hunting. UNIT IV INDUCTION MACHINES 9 Induction motor:- Construction and principle of operation, Classification of induction motor, Torque equation, Condition for maximum torque, Equivalent Circuit, Starting methods and Speed control of induction motors. UNIT V SPECIAL MACHINES 7 Types of single phase motor Double revolving field theory Cross field theory Capacitor start capacitor run motors Shaded pole motor Repulsion type motor Universal motor Hysteresis motor - Permanent magnet synchronous motor Switched reluctance motor Brushless D.C motor. L = 45 TOTAL: 45 PERIODS TEXT BOOKS: 1. Nagrath, I.J., and Kothari, D.P., Electrical Machines, Tata McGraw - Hill, Fitzgerald A.E, Kingsley C., Umans, S. and Umans S.D., Electric Machinery, McGraw- Hill, Singapore, REFERENCES: 1. Theraja, B.L., A Text book of Electrical Technology, Vol.II, S.C Chand and Co., New Delhi, Del Toro, V., Electrical Engineering Fundamentals, Prentice Hall of India, New Delhi, Cotton, H., Advanced Electrical Technology, Sir Isaac Pitman and Sons Ltd., London,

3 Chapter 1 Alternators TABLE OF CONTENTS 1.1 Construction of DC Machine Principle and theory of DC Generator E.M.F Equation of DC Generator Power Flow in DC Generator Types of DC Generators Methods of Armature Reaction Methods of Improving Commutation-E.M.F. Commutation Generator types & Characteristics DC Motor Starting of D.C shunt motor Speed control of shunt motor Series motor Applications of DC motor 37 Chapter 2 TRANSFORMERS 2.1 Introduction Basics of Transformer Transformer Construction Equivalent Circuit of Transformer Phasor Diagram and Voltage Regulation Voltage Regulation Losses and Efficiency of Transformer Transformers in Three Phase Systems 65 Chapter 3 SYNCHRONOUS MACHINES 3.1 Introduction Concept of slip rings and brush assembly Construction of synchronous generator(stator and rotor) Working principle of synchronous generator E.m.f. Equation of an alternator 68 3

4 3.6 Armature reaction Concepts of synchronous reactance and impedance voltage regulation of an alternator Blondel's two reaction theory Direct and quadrature axis synchronous reactance Details analysis of phasor diagram for synchronous gen Determination of xd and xq using slip test Introduction to synchronization of alternators Phasor diagram Synchronous Motor Types Construction of three phase synchronous motor Principle of working of 3-phase synchronous motor Methods of starting synchronous motor Behaviour of synchronous motor on loading Analysis of phasor diagram V-Curves and inverted v-curves Expression for back e.m.f or induced e.m.f. Per phase in s.m Power flow in synchronous motor Salient pole synchronous motor Hunting in synchronous motor Synchronization with infinite bus bar Synchronous condensers Applications of three phase synchronous motor Comparison of synchronous and induction motor Synchronous induction motor 144 Chapter 4 INDUCTION MACHINES 4.1 Introduction Rotating Magnetic field Construction of Three phase induction motor Working principle Slip of the induction motor 156 4

5 4.6 Torque Equation Relationship between P 2r, Pc, Pm Need of Starter Torque-slip characteristic Losses in induction motor Power flow in an induction motor Necessity of Starter Types of Starter Speed Control of Three Phase Induction Motor 169 Chapter 5 SPECIAL MACHINES 5.1 Introduction Types of Single Phase AC Motors Construction of Single Phase Induction motor Working Principle and Operation of Single phase Induction motor Cross field Theory Starting of Single Phase induction Motor Shaded Pole Motor Universal Motor Repulsion Motor Brush Less DC Motor Permanent Magnet Synchronous Motor Reluctance Motor Hysteresis Motor 198 5

6 UNIT I D.C. MACHINES UNIT I D.C. MACHINES 12 Construction of D.C. Machines - Principle and theory of operation of D.C. generator - EMF equation - Characteristics of D.C. generators - Armature reaction Commutation - Principle of operation of D.C. motor - Voltage equation - Torque equation - Types of D.C. motors and their characteristics Starters - Speed control of D.C. motors - Applications. 1.1 Construction of DC Machine: Figure 1.1.Cross section of DC Machine The DC Generator has the following important parts: (a) Yoke (b) Pole of Generator (c) Field Winding (d) Armature of DC Generator (e) Commutator (f) Brushes and Bearing (a) Yoke : The ring shaped body of the DC machine frame which makes the magnetic path for the magnetic fluxes from the main poles and inter poles is called Yoke. it serves two purposes for an DC machines, (i) It provides mechanical support to the magnetic pole shoes and protecting cover of a machine. (ii) It carries and acting as the path for the magnetic field flux produced by field windings. In small Rating DC generator, yoke are made of cast iron. In the case of large Machines,where weight of the machine also in concern, cast steel or rolled steel is used. The nature of Cast iron(0.8 Wb/sq.m) is cheaper in cost but heavier than Cast steel(1.5 Wb/sq.m). Yokes are formed in the form of Cylindrical shape with the help rectangular sheet and the edges are welded together at the bottom. (b) Pole of Generator :The poles or Pole shoes are fabricated steel and it is welded to the frame by means of bolts. Pole shoes are generally laminated to reduce the Eddy current Losses in DC Machine. The thickness of the lamination is in the range of 0.04 to The pole shoes are shaped as shown in the diagram to get air gap at the tips. Inter-poles are smaller in size and additional poles located in between the main poles. It is also laminated and connected with yoke through bolts. The inter poles are also called as commutating poles to improve Commutation and Improves the efficiency of a DC machine by reducing Armature reaction. 6

7 (c)field Winding: The field winding made in the form of a concentric coil wound around the main poles. It is wounded to carry the excitation current and produce the main field flux in the machine. Thus the poles are energized by separate supply or on its own output. There are two types of windings are generally employed in a DC generator are,(i) shunt winding, large number of turns of small thickness of copper conductors used. The resistance of shunt winding always larger than the armature winding resistance. (ii) series winding, a few turns of heavy cross section conductor is used. The resistance of series windings is low and is comparable to armature resistance. Some machines may have both the windings on the poles with their fluxes opposing or aiding each other. (d)armature Winding: The armature coils are wounded on the surface of slotted armature.to avoid the conductors flying outside during armature rotation,the armature windings are formed and covered with tape and fixed into the open slots on the armature. In a small machines, the winding can be done through hands.in the case of large machines slot segments are used to prevent the coils flying outside during rotation. The end portion of the windings are short circuited with commutator end. The armature design should be done to balance and reduce the centrifugal forces at the high operating speeds. Compensating winding windings are required to reduce the effect of Armature reaction and it is presented only in large rating machines. (e) Commutator: Commutator is very important element in DC machines, which made of copper segments together with mica/micanite insulating material to separate each segment.the diagram of Commutator is as shown in figure 1.2. The commutator is an rigid and solid assembly of insulated copper strips and can rotate at high speeds. Each segment of Commutator is provided with a riser in which the ends of the armature coils get connected. The surface of the commutator is Concentric and Smooth one to collect current form it with the help of brushes. Figure 1.2.Commutator of DC Machine (f) Brush, brush holders and Bearings: A brush is an device which conducts current between stationary wires and moving parts, most commonly in a rotating shaft. Brushes are fixed above the surface of commutator to collect current from its segments. Mainly graphite and Carbon materials are used as brush material. The type of the brush selection depends on the peripheral speed of the commutator and the working voltage. 7

8 Figure 1.3.Brushes of a DC Machine The brushes are designed to press on the commutator with the help of tension springs. This is to provide proper contact between the brushes and the commutator during high speeds of operation. Brushes jumping over the segments provides poor armature current collection and it is prevented the brushes are made up of graphite (with added copper). In a Small machines ball bearings are employed at both ends. For larger machines well designed roller bearings are used at the driving end. The bearings are housed inside prevent moisture and dust entering it.the bearing must always be lubricated properly for smooth operation and long life of generator. 1.2 Principle and theory of DC Generator In 1831, Michael Faraday, gave two laws of electromagnetism called Faraday s law of electro magnetic induction. This law explains the working principle of DC generators. It explains the relationship between electric circuit and magnetic field.. According to faraday s first law, there is any change in magnetic field of a coil, the Emf is induced in the coil. This is called induced Emf.When the coil or circuit is closed, the current will flow through the circuit it is named as induced current. According to Faraday s Second Law, the magnitude of induced in a coil is directly proportional to the amount of rate of change of flux linkages with the coil. Consider a magnet moving above the surface a coil and assume two instants at time t 1 and time t 2. Flux linkage with the coil at time, t 1 = NΦ 1 Wb Flux linkage with the coil at time, t 2 = NΦ 2 wb Resultant or change in flux = NΦ where Φ = Φ 2 Φ 1 The rate of change of flux linkage or Induced Emf e = NΦ / t The rate of change of flux linkage E= NdΦ/dt.1.1 According to lenz law, E= -NdΦ/dt 1.2 The direction of the current and magnetic field is determined by Fleming Right Hand Rule. The principle of DC generator explained through Single Loop or winding placed in a magnetic field. Figure 1.4.Single Loop DC Generator In the figure 1.4 the single winding with rectangular shape is placed between two different poles of a magnet. Let s us consider, the single conductor is in the position ABCD without any rotation there is no induced enf in it,because no rate of change of flux will occur. The same conductor starts rotating inside the constant magnetic field with its axis,it cuts the magnetic field.due to this the emf is induced in the conductor.the loop is opened and connect it with a split rings and brushes as shown in the figure 1.5. Split ring are helping 8

9 brushes to take current outside to supply the external load terminals are connected with two carbon brushes. Working principle of dc generator Figure 1.5.Single Loop DC Generator with load In the first half of the revolution,it is seen that the current flows through the direction ABLMCD i.e. brush X in contact with segment a. In the next half revolution, the direction of the induced current in the coil is reversed,but the position of the segments a and b are also reversed so it results that brush X comes in touch with that segment b. Hence, the current in the load resistance again flows follows the same path. The output wave form of the current through the load circuit is is purely sinusoidal and the current is unidirectional. 1.3 E.M.F Equation of DC Generator: Let Φ = flux/pole in weber Z = total number of armture conductors = No.of slots x No.of conductors/slot P = No.of generator poles A = No.of parallel paths in armature N = armature rotation in revolutions per minute (r.p.m) E = e.m.f induced in any parallel path in armature Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e E. Average e.m.f generated /conductor = dφ/dt volt (n=1) flux cut/conductor in one revolution dφ = ΦP Wb No.of revolutions/second = N/60 Time for one revolution, dt = 60/N second Hence, according to Faraday's Laws of Electroagnetic Induction, E.M.F generated /conductor is dφ/dt =ΦPN/ therefore,the generated emf of DC generator with Z no of conductors and A parallel path is E g = ΦPNZ/60A volts 1.4 For a simplex wave-wound generator, No.of parallel paths A = 2 No.of conductors (in series) in one path = Z/2 E.M.F. generated/path is E g = ΦPNZ/60*2= ΦPNZ/

10 For a simplex lap-wound generator No.of parallel paths A = P No.of conductors (in series) in one path = Z/P E.M.F.generated/path E g = ΦPNZ/60*P= E g = ΦNZ/ Power Flow in DC Generator: The Power flow in the DC generator is explained in the diagram Figure 1.6.Power flow diagram of DC Generator From the diagram we understand that, the mechanical power input of DC generator is converted in to Electrical power as a Output. The total input energy should not be converted as Electrical power output, because different types of Losses are presented in it. 1.5 Types of DC Generators Energy can be converted from one form to other form A generator does the same it converts mechanical energy to electrical energy. Mechanical energy can be created by using water turbines, steam turbines, internal combustion engines etc. And a generator converts this mechanical energy to electrical energy. Generators can be broadly classified as AC generators and DC generators. Here lets take a look the the types of DC generators. DC generators are classified based on their method of excitation. So on this basis there are two types of DC generators:- 1. Separately excited DC generator 2. Self excited DC generator Self excited DC generator can again be classified as 1) DC Series generator 2) DC Shunt generator and 3) DC Compound generator. Let s take a brief look at how all these differ Separately excited DC generator As you can guess from the name itself, this dc generator has a field magnet winding which is excited using a separate voltage source (like battery). You can see the representation 10

11 in the below image. The output voltage depends on the speed of rotation of armature and field current. The higher the speed of rotation and current the higher the output e.m.f Figure 1.7 Separately excited DC generator Note: Separately excited DC generators are rarely used in practice Self Excited DC Generator These are generators in which the field winding is excited by the output of the generator itself. As described before there are three types of self excited dc generators they are 1) Series 2) Shunt and 3) Compound. A series DC generator is shown below in fig 1.8 in which the armature winding is connected in series with the field winding so that the field current flows through the load as well as the field winding.field winding is a low resistance,thick wire of few turns. Series generators are also rarely used Figure 1.8 Self excited DC Series generator A shunt DC generator is shown in figure 1.9, in which the field winding is wired parallel to armature winding so that the voltage across both are same. The field winding has high 11

12 resistance and more number of turns so that only a part of armature current passes through field winding and the rest passes through load. Figure 1.9 Self excited DC Shunt generator A compound generator is shown in figure below. It has two field findings namely R sh and R se. They are basically shunt winding (R sh ) and series winding (R se ). Compound generator is of two types 1) Short shunt and 2) Long shunt Figure 1.10 Self excited DC Compound generator Short shunt:- Here the shunt field winding is wired parallel to armature and series field winding is connected in series to the load. It is shown in fig (1) Long shunt:- Here the shunt field winding is parallel to both armature and series field winding (Rse is wired in series to the armature). It is shown in figure (2) 12

13 So you have got a basic idea about the types of DC generators! Now you may know that these generators are used only for special industrial purposes where there is huge demand for DC production. Otherwise electrical energy is produced by AC generators and is transmitted from one place to other as AC itself. When a DC power is required, we usually convert AC to DC using rectifiers. 1.6 Methods of Armature Reaction In a d.c. generator, the purpose of field winding is to produce magnetic field (called main flux) whereas the purpose of armature winding is to carry armature current. Although the armature winding is not provided for the purpose of producing a magnetic field, nevertheless the current in the armature winding will also produce magnetic flux (called armature flux). The armature flux distorts and weakens the main flux posing problems for the proper operation of the d.c. generator. The action of armature flux on the main flux is called armature reaction. It was hinted that current in the coil is reversed as the coil passes a brush. This phenomenon is termed as commutation. The criterion for good commutation is that it should be sparkless. In order to have sparkless commutation, the brushes should lie along magnetic neutral axis.so far we have assumed that the only flux acting in a d.c. machine is that due to the main poles called main flux. However, current flowing through armature conductors also creates a magnetic flux (called armature flux) that distorts and weakens the flux coming from the poles. This distortion and field weakening takes place in both generators and motors. The action of armature flux on the main flux is known as armature reaction. The phenomenon of armature reaction in a d.c. generator is shown in Fig. (1.11). Only one pole is shown for clarity. When the generator is on no-load, a smal1 current flowing in the armature does not appreciably affect the main flux Φ1 coming from the pole [See Fig 1.11 (i)]. When the generator is loaded, the current flowing through armature conductors sets up flux Φ 1. Fig. (1.11 ) (ii) shows flux due to armature current alone. By superimposing Φ 1 and Φ 2, we obtain the resulting flux Φ 3 as shown in Fig. (1.11 ) (iii). Referring to Fig (1.11 ) (iii), it is clear that flux density at; the trailing pole tip (point B) is increased while at the leading pole tip (point A) it is decreased. This unequal field distribution produces the following two effects: (i)the main flux is distorted.(ii) Due to higher flux density at pole tip B, saturation sets in. Consequently, the increase in flux at pole tip B is less than the decrease in flux under pole tip A. Flux Φ3 at full load is, therefore, less than flux Φ1 at no load. As we shall see, the weakening of flux due to armature reaction depends upon the position of brushes. Figure 1.11 armature reactions in a DC generator 13

14 1.6.1Geometrical and Magnetic Neutral Axes (i) The geometrical neutral axis (G.N.A.) is the axis that bisects the angle between the centre line of adjacent poles [See Fig (i)]. Clearly, it is the axis of symmetry between two adjacent poles. Figure 1.12 geometrical neutral axis and magnetic neutral axis of DC generator (ii) The magnetic neutral axis (M. N. A.) is the axis drawn perpendicular to the mean direction of the flux passing through the centre of the armature. Clearly, no e.m.f. is produced in the armature conductors along this axis because then they cut no flux. With no current in the armature conductors, the M.N.A. coincides with G, N. A. as shown in Fig. [1.12(ii)]. In order to achieve spark less commutation, the brushes must lie along M.N.A. 1.7 Methods of Improving Commutation-E.M.F. Commutation In this method, an arrangement is made to neutralize the reactance voltage by producing a reversing voltage in the coil undergoing commutation. The reversing voltage acts in opposition to the reactance voltage and neutralizes it to some extent. If the reversing voltage is equal to the reactance voltage, the effect of the latter is completely wiped out and we get sparkless commutation. The reversing voltage may be produced in the following two ways: (i) By brush shifting (ii) By using interpoles or compoles By Brush Shifting In this method, the brushes are given sufficient forward lead (for a generator) to bring the short-circuited coil (i.e., coil undergoing commutation) under the influence of the next pole of opposite polarity. Since the short-circuited coil is now in the reversing field, the reversing voltage produced cancels the reactance voltage. This method suffers from the following drawbacks:(a) The reactance voltage depends upon armature current. Therefore, the brush shift will depend on the magnitude of armature current which keeps on changing. This necessitates frequent shifting of brushes. (b) The greater the armature current, the greater must be the forward lead for a generator. This increases the demagnetizing effect of armature reaction and further weakens the main field By Using Inter poles or Com poles The best method of neutralizing reactance voltage is by, using interpoles or compoles. The best way to produce reversing voltage to neutralize the reactance voltage is by using interpoles or compoles. These are small poles fixed to the yoke and spaced mid-way between the main poles (See Fig. 1.13). They are wound with comparatively few turns and connected in series with the armature so that they carry armature current. Their polarity is the same as the next main pole ahead in the direction of rotation for a generator (See Fig. 1.13). Connections for a d.c. generator with interpoles is shown in Fig. (1.13). 14

15 Figure 1.13 Inter poles and its connections in a DC generator Functions of Interpoles The machines fitted with inter poles have their brushes set on geometrical neutral axis (no lead). The inter poles perform the following two functions: (i) As their polarity is the same as the main pole ahead (for a generator), they induce an e.m.f. in the coil (undergoing commutation) which opposes reactance voltage. This leads to sparkless commutation. The e.m.f. induced by compoles is known as commutating or reversing e.m.f. Since the interpoles carry the armature current and the reactance voltage is also proportional to armature current, the neutralization of reactance voltage is automatic. (ii) The m.m.f. of the compoles neutralizes the cross-magnetizing effect of armature reaction in small region in the space between the main poles. It is because the two m.m.f.s oppose each other in this region. Fig shows the circuit diagram of a shunt generator with commutating winding and compensating winding. Both these windings are connected in series with the armature and so they carry the armature current. However, the functions they perform must be understood clearly. The main function of commutating winding is to produce reversing (or commutating) e.m.f. in order to cancel the reactance voltage. In addition to this, the m.m.f. of the commutating winding neutralizes the cross magnetizing ampere-turns in the space between the main poles. The compensating winding neutralizes the cross-magnetizing effect of armature reaction under the pole faces. Figure 1.14 shunt generator with commutating winding 1.8 Generator types & Characteristics D.C generators may be classified as (i) separately excited generator, (ii) shunt generator, and (iii) series generator and (iv) compound generator. 15

16 In a separately excited generator field winding is energised from a separate voltage source in order to produce flux in the machine. So long the machine operates in unsaturated condition the flux produced will be proportional to the field current. In order to implement shunt connection, the field winding is connected in parallel with the armature. It will be shown that subject to fulfillment of certain conditions, the machine may have sufficient field current developed on its own by virtue of its shunt connection. In series d.c machine, there is one field winding wound over the main poles with fewer turns and large cross sectional area. Series winding is meant to be connected in series with the armature and naturally to be designed for rated armature current. Obviously there will be practically no voltage or very small voltage due to residual field under no load condition (I a = 0). However, field gets strengthened as load will develop rated voltage across the armature with reverse polarity, is connected and terminal voltage increases. Variation in load resistance causes the terminal voltage to vary. Terminal voltage will start falling, when saturation sets in and armature reaction effect becomes pronounced at large load current. Hence, series generators are not used for delivering power at constant voltage. Series generator found application in boosting up voltage in d.c transmission system. A compound generator has two separate field coils wound over the field poles. The coil having large number of turns and thinner cross sectional area is called the shunt field coil and the other coil having few number of turns and large cross sectional area is called the series field coil. Series coil is generally connected in series with the armature while the shunt field coil is connected in parallel with the armature. If series coil is left alone without any connection, then it becomes a shunt machine with the other coil connected in parallel. Placement of field coils for shunt, series and compound generators are shown in figure Will develop rated voltage across the armature with reverse polarity. Figure 1.15 field coils for shunt, series and compound generators Characteristics of a separately excited generator No load or Open circuit characteristic In this type of generator field winding is excited from a separate source, hence field current is independent of armature terminal voltage as shown on figure The generator is driven by a prime mover at rated speed, say n rps. With switch S in opened condition, field is excited via a potential divider connection from a separate d.c source and field current is gradually increased. The field current will establish the flux per pole Φ. The voltmeter V connected across the armature terminals of the machine will record the generated emf (E G = pnφz/a=knφ). Remember pz/a is a constant (k) of the machine. As field current is increased, E G will increase. E G versus I f plot at constant speed n is shown in figure (38.3a). 16

17 Figure 1.16 Schematic diagram of separately excited DC generator It may be noted that even when there is no field current, a small voltage (OD) is generated due to residual flux. If field current is increased, Φ increases linearly initially and O.C.C follows a straight line. However, when saturation sets in, φ practically becomes constant and hence E g too becomes constant. In other words, O.C.C follows the B-H characteristic, hence this characteristic is sometimes also called the magnetisation characteristic of the machine. It is important to note that if O.C.C is known at a certain speed n l, O.C.C at another speed n 2 can easily be predicted. It is because for a constant field current, ratio of the generated voltages becomes the ratio of the speeds as shown below and the characteristics of No load or Open circuit characteristic and Load characterisitcs as shown in the figure 1.17 Figure 1.17 O.C.C and Load characteristics of separately excited DC generator Therefore points on O.C.C at n 2 can be obtained by multiplying ordinates of O.C.C at n 1 with the ratio n 2 /n 1 O.C.C at two different speeds are shown in the following figure

18 Figure 1.18 O.C.C characteristics with different speed values of separately excited DC generator Load characteristic of separately excited generator Load characteristic essentially describes how the terminal voltage of the armature of a generator changes for varying armature current I a. First at rated speed, rated voltage is generated across the armature terminals with no load resistance connected across it (i.e., with S opened) by adjusting the field current. So for I a = 0, V = E oo should be the first point on the load characteristic. Now with S is closed and by decreasing R L from infinitely large value, we can increase I aa gradually and note the voltmeter reading. Voltmeter reads the terminal voltage and is expected to decrease due to various drops such as armature resistance drop and brush voltage drop. In an uncompensated generator, armature reaction effect causes additional voltage drop. While noting down the readings of the ammeter A2 and the voltmeter V, one must see that the speed remains constant at rated value. Hence the load characteristic will be drooping in nature as shown in figure Characteristics of a shunt generator We have seen in the previous section that one needs a separate d.c supply to generate d.c voltage. Is it possible to generate d.c voltage without using another d.c source? The answer is yes and for obvious reason such a generator is called self excited generator. Field coil (F1, F2) along with a series external resistance is connected in parallel with the armature terminals (A1, A2) of the machine as shown in figure (1.19). Let us first qualitatively explain how such connection can produce sufficient voltage. Suppose there exists some residual field. Therefore, if the generator is driven at rated speed, we should expect a small voltage (knφ res ) to be induced across the armature. But this small voltage will be directly applied across the field circuit since it is connected in parallel with the armature. Hence a small field current flows producing additional flux. If it so happens that this additional flux aids the already existing residual flux, total flux now becomes more generating more voltage. This more voltage will drive more field current generating more voltage. Both field current and armature generated voltage grow cumulatively. This growth of voltage and the final value to which it will settle down can be understood by referring to figure where two plots have been shown. One corresponds to the O.C.C at rated speed and obtained by connecting the generator in separately excited fashion as detailed in the preceding section. The other one is the V-I characteristic of the field circuit which is a straight line passing through origin and its slope represents the total field circuit resistance. 18

19 Figure 1.19 Schematic diagram of DC Shunt generator Figure 1.20 O.C.C characteristics DC shunt generator Initially voltage induced due to residual flux is obtained from O.C.C and given by Od. The field current thus produced can be obtained from field circuit resistance line and given by Op. In this way voltage build up process continues along the stair case. The final stable operating point (M) will be the point of intersection between the O.C.C and the field resistance line. If field circuit resistance is increased, final voltage decreases as point of intersection shifts toward left. The field circuit resistance line which is tangential to the O.C.C is called the critical field resistance. If the field circuit resistance is more than the critical value, the machine will fail to excite and no voltage will be induced. Suppose a shunt generator has built up voltage at a certain speed. If the speed of the prime mover is reduced without changing R f, the developed voltage will be less as because the O.C.C at lower speed will come down If speed is further reduced to a certain critical speed (n crir ), the present field resistance line will become tangential to the O.C.C at n cr For any speed below n cr, no voltage built up is possible in a shunt generator. A shunt generator driven by a prime mover, can not built up voltage if it fails to comply any of the conditions listed below. 1. The machine must have some residual field. To ensure this one can at the beginning excite the field separately with some constant current. Now removal of this current will leave some amount of residual field. 2. Field winding connection should be such that the residual flux is strengthened by the field current in the coil. If due to this, no voltage is being built up, reverse the field terminal connection. 3. Total field circuit resistance must be less than the critical field resistance. 19

20 Load characteristic of shunt generator With switch S in open condition, the generator is practically under no load condition as field current is pretty small. In other words, E oo and I aa = 0 is the first point in the load characteristic. To load the machine S is closed and the load resistances decreased so that it delivers load current I L.The drop in the terminal voltage will be caused by the usual I a r a drop, brush voltage drop and armature reaction effect. Apart from these, in shunt generator, as terminal voltage decreases, field current hence excited motor, here I L I a In fact, for shunt generator, I aa = I L - I f So increase of I L will mean increase of I aa Remember in shunt f generator, field current is decided by the terminal voltage by virtue of its parallel connection with the armature. Figure 1.21 shows the plot of terminal voltage versus armature current which is called the load characteristic. Figure 1.21 O.C.C and Load characteristics DC shunt generator Compound generator As introduced earlier, compound machines have both series and shunt field coils. On each pole these two coils are placed as shown in figure Series field coil has low resistance, fewer numbers of turns with large cross sectional area and connected either in series with the armature or in series with the line. On the other hand shunt field coil has large number of turns, higher resistance, small cross sectional area and either connected in parallel across the armature or connected in parallel across the series combination of the armature and the series field. Depending on how the field coils are connected, compound motors are classified as short shunt and long shunt types as shown in figures 1.22(a) and (b) Figure 1.22.(a)Short shunt Compound generator 20

21 Figure 1.22.(b)Long shunt Compound generator Series field coil may be connected in such a way that the mmf produced by it aids the shunt field mmf-then the machine is said to be cumulative compound machine, otherwise if the series field mmf acts in opposition with the shunt field mmf then the machine is said to be differential compound machine. In a compound generator, series field coil current is load dependent. Therefore, for a cumulatively compound generator, with the increase of load, flux per pole increases. This in turn increases the generated emf and terminal voltage. Unlike a shunt motor, depending on the strength of the series field mmf, terminal voltage at full load current may be same or more than the no load voltage. When the terminal voltage at rated current is same that at no load condition, then it is called a level compound generator. If however, terminal voltage at rated current is more than the voltage at no load, it is called a over compound generator. The load characteristic of a cumulative compound generator will naturally be above the load characteristic of a shunt generator as depicted in figure At load current higher than the rated current, terminal voltage starts decreasing due to saturation, armature reaction effect and more drop in armature and series field resistances. Figure 1.23Load characteristics of DC generators To understand the usefulness of the series coil in a compound machine let us undertake the following simple calculations. Suppose as a shunt generator (series coil not connected) 300 AT/pole is necessary to get no load terminal voltage of 220 V. Let the terminal voltage becomes 210 V at rated armature current of 20 A. To restore the terminal voltage to 220 V, shunt excitation needs to be raised such that AT/pole required is 380 at 20 A of rated current. As a level compound generator, the extra AT ( = 80) will be provided by series field. Therefore, number of series turns per pole will be 80/20 = 4. Thus in a compound generator series field will automatically provide the extra AT to arrest the drop in terminal voltage which otherwise is inevitable for a shunt generator. For the differentially compounded generator where series field mmf opposes the shunt field mmf the terminal voltage decreases fast with the increase in the load current. 1.9 DC Motor DC motor converts electrical energy into mechanical energy. When a current carrying conductor is placed in a magnetic field, a force acts on the conductor and conductor moves in the direction of force. When the DC machine is connected to DC supply a current passes through the armature winding. 21

22 Figure 1.24 DC Motor Construction The construction of DC motor is as shown in the figure When conductors of armature winding carry outward current under north and incoming current under south pole then those conductors experience a force in clockwise direction according to fleming s left hand rule. Due to this force, conductors move in clockwise direction. The direction of current is reversed by commutator, which causes the moving conductor coming under different pole to carry reverse current. This causes the force on the conductor to be again in the same direction as flux and current both change direction simultaneously. Thus armature conductors always experience force in same direction Back EMF When the armature of a DC motor rotates, an emf is induced in armature conductors known as back emf which opposes the applied voltage. If R a is armature resistance then V =E b +I a R a. where I a is armature current and V is applied voltage Back emf makes a dc motor self-regulating. When speed is low then back emf will less and armature current will be large Speed Regulation The back emf in armature is since P, Z and A are constant for a machine then For a shunt motor Φ is constant then 22

23 For a series motor is proportional to Ia where No is speed at no load in RPM and N f is speed at full load in RPM Power Equation and Torque The voltage equation for motor is By multiplying Ia in this equation by Ia we get is a power equation, V I a is input power, E b I is power developed in armature and I a 2 R a represents power losses in armature. So mechanical power developed by the motor is P m = input power losses Differentiate the Eq. P m with respect to I a we get For maximum power output But so In any motor mechanical power developed in armature is maximum when back emf is half of applied voltage Power Flow and Losses Electrical Losses in Core/Iron Parts In the iron part of machine some electrical losses occur in the form of hysteresis and eddy current losses. Hysteresis losses occur due to magnetic reversals caused by the rotating armature. Hysteresis losses are directly proportional to the number of magnetic reversal per second. hysteresis loss Pn = n (Bmax) x f V watts 23

24 these losses occur in armature core and teeth of the dc machine. To reduce the hysteresis loss armature core is made of silicon steel. When armature core rotates in magnetic fields of poles which induce emf in armature core and yoke. Due to this induced emf eddy currents circulate in armature core, the eddy current losses mainly depend on thickness of material. `P e = K Bmax f 2 V t 2 watt To minimize eddy current losses the armature core is made of laminated stampings. Hysteresis and eddy current losses are known as core losses and are about 20% to 30% of full load losses Mechanical Losses Due to friction of bearings, air friction or windage some losses occur in dc machines. These are known as mechanical losses. The brush friction losses are quite large. These losses are about 10% to 20% of full load losses Losses and Efficiency In electrical machines, the efficiency is always less then one. It means that the output is less than the input For any machine, efficiency=output/input In electrical machine input power is sum of output power and power loss i.e. Power (Input) = Power (Output) + Power loss The various machine losses may be classified as electrical losses and mechanical losses Electrical Losses DC Machines In DC machines electrical losses occur in several parts of machine. The maximum electrical losses occur due to I 2 R losses because a large current flows through various machine windings. In addition to I 2 R losses there is brush contact loss at the contacts between the brushes and commutator. These losses are known as copper losses and amount to 40% to 60% of the full load losses Torque In a DC motor, output power is converted to torque. If at a wheel of radius r metre as shown in figure, a force F acts on circumference then Torque T = F. r work done per revolution = F. 2π r joules work done per second = F. 2π r. n where, n =N/60 and N is speed of rotation in RPM. 24

25 Figure 1.25 DC Motor wheel with radius r Now power developed, P = work done per second or P = F r. 2π n or P = T. ω where, T = Torque, and ω = angular velocity. where ω = 2π n=2π N/60 Power developed in armature is E b. I a So, E b I a = T. ω Since Z, P and A are constant so T α Φ I a For DC shunt motor Φ is constant so T α Ia and for dc series motor Φ α I a, so T α I a Power Flow for DC Motor 1.10 Starting of D.C shunt motor Problems of starting with full voltage We know armature current in a d.c motor is given by 25

26 At the instant of starting, rotor speed n = 0, hence starting armature current is I ast =.V/R a Since, armature resistance is quite small, starting current may be quite high (many times larger than the rated current). A large machine, characterized by large rotor inertia (J), will pick up speed rather slowly. Thus the level of high starting current may be maintained for quite some time so as to cause serious damage to the brush/commutator and to the armature winding. Also the source should be capable of supplying this burst of large current. The other loads already connected to the same source, would experience a dip in the terminal voltage, every time a D.C motor is attempted to start with full voltage. This dip in supply voltage is caused due to sudden rise in voltage drop in the source's internal resistance. The duration for which this drop in voltage will persist once again depends on inertia (size) of the motor. Hence, for small D.C motors extra precaution may not be necessary during starting as large starting current will very quickly die down because of fast rise in the back emf. However, for large motor, a starter is to be used during starting. To limit the starting current, a suitable external resistance R ext. is connected in series (Figure 1.26(a)) with the armature so that I ast =V/R ext +r a At the time of starting, to have sufficient starting torque, field current is maximized by keeping the external field resistance R f to zero value. As the motor picks up speed, the value of R ext is gradually decreased to zero so that during running no external resistance remains in the armature circuit. But each time one has to restart the motor, the external armature resistance must be set to maximum value by moving the jockey manually. Imagine, the motor to be running with R ext = 0 (Figure 1.26(b)). Figure 1.26 DC shunt Motor with external resistance Now if the supply goes off (due to some problem in the supply side or due to load shedding), motor will come to a stop. All on a sudden, let us imagine, supply is restored. This is then nothing but full voltage starting. In other words, one should be constantly alert to set the resistance to maximum value whenever the motor comes to a stop. This is one major limitation of a simple rheostatic starter Three-point starter A 3-point starter is extensively used to start a D.C shunt motor. It not only overcomes the difficulty of a plain resistance starter, but also provides additional protective features such as over load protection and no volt protection. The diagram of a 3-point starter connected to a shunt motor is shown in figure Although, the circuit looks a bit clumsy at a first glance, the basic working principle is same as that of plain resistance starter. The starter is shown enclosed within the dotted rectangular box having three terminals marked as A, L and F for external connections. Terminal A is connected to one armature terminal Al of the motor. Terminal F is connected to one field terminal F1 of the motor and terminal L is connected to one supply terminal as shown. F2 terminal of field coil is connected to A2 through an external variable field resistance and the common point connected to supply (-ve). The external armatures resistances consist of several resistances connected in series and are shown in the form of an arc. The junctions of the resistances are 26

27 brought out as terminals (called studs) and marked as 1, 2,.12. Just beneath the resistances, a continuous copper strip also in the form of an arc is present. There is a handle which can be moved in the clockwise direction against the spring tension. The spring tension keeps the handle in the OFF position when no one attempts to move it. Now let us trace the circuit from terminal L (supply + ve). The wire from L passes through a small electro magnet called OLRC, (the function of which we shall discuss a little later) and enters through the handle shown by dashed lines. Near the end of the handle two copper strips are firmly connected with the wire. The furthest strip is shown circular shaped and the other strip is shown to be rectangular. When the handle is moved to the right, the circular strip of the handle will make contacts with resistance terminals 1, 2 etc. progressively. On the other hand, the rectangular strip will make contact with the continuous arc copper strip. The other end of this strip is brought as terminal F after going through an electromagnet coil (called NVRC). Terminal F is finally connected to motor field terminal Fl. Figure 1.27 construction of Three point Starter Working principle Initially the handle is in the OFF position. Neither armature nor the field of the motor gets supply. Now the handle is moved to stud number 1. In this position armature and all the resistances in series gets connected to the supply. Field coil gets full supply as the rectangular strip makes contact with arc copper strip. As the machine picks up speed handle is moved further to stud number 2. In this position the external resistance in the armature circuit is less as the first resistance is left out. Field however, continues to get full voltage by virtue of the continuous arc strip. Continuing in this way, all resistances will be left out when stud number 12 (ON) is reached. In this position, the electromagnet (NVRC) will attract the soft iron piece attached to the handle. Even if the operator removes his hand from the handle, it will still remain in the ON position as spring restoring force will be balanced by the force of attraction between NVRC and the soft iron piece of the handle. The no volt release coil (NVRC) carries same current as that of the field coil. In case supply voltage goes off, field coil current will decrease to zero. Hence NVRC will be deenergised and will not be able to exert any force on the soft iron piece of the handle. Restoring force of the spring will bring the handle back in the OFF position. The starter also provides over load protection for the motor. The other electromagnet, OLRC overload release coil along with a soft iron piece kept under it, is used to achieve this. The current flowing through OLRC is the line current I drawn by the motor. As the motor is L 27

28 loaded, I a hence I L increases. Therefore, I L is a measure of loading of the motor. Suppose we want that the motor should not be over loaded beyond rated current. Now gap between the electromagnet and the soft iron piece is so adjusted that for I L I rated, the iron piece will not be pulled up. However, if I L I rated force of attraction will be sufficient to pull up iron piece. This upward movement of the iron piece of OLRC is utilized to de-energize NVRC. To the iron a copper strip ( shaped in figure) is attached. During over loading condition, this copper strip will also move up and put a short circuit between two terminals B and C. Carefully note that B and C are nothing but the two ends of the NVRC. In other words, when over load occurs a short circuit path is created across the NVRC. Hence NVRC will not carry any current now and gets deenergised. The moment it gets deenergised, spring action will bring the handle in the OFF position thereby disconnecting the motor from the supply. Three point starter has one disadvantage. If we want to run the machine at higher speed (above rated speed) by field weakening (i.e., by reducing field current), the strength of NVRC magnet may become so weak that it will fail to hold the handle in the ON position and the spring action will bring it back in the OFF position. Thus we find that a false disconnection of the motor takes place even when there is neither over load nor any sudden disruption of supply Two Point Starter The starte for a series motor is shown in the figure 1.28.the line current passes through holding coil, thus providing the energy required to hold the arm at the zero resistance point.this starter protects the motor against over speed damage in the event of removal load.whether intentionally or not removal of the load from the motor will cause high motor speed and possible damage.when the load is removed,the line current is reduced the strength of the holding magnets,there by releasing the arm.the protection offered by the starter is referred to as no-load release Figure 1.28 construction of Two point Starter Where the removal of load is remote,the no voltage release type of starter may be used.the advantages of this type of starter are similar to the four point starter. The four point starter can be used to start series motors provided the ratings of the starting resistor are not exceeded. The F terminal is disregarded in this application. A motor should never be disconnected from the line by forcing the arm of the starter to off position. this will cause burning of the first contact because of the breaking of the field circuit and resulting discharge of the magnetic field. A disconnect or other appropriate device should be used to connect of disconnect motor Four Point starter 28

29 The 4 point starter like in the case of a 3 point starter also acts as a protective device that helps in safeguarding the armature of the shunt or compound excited dc motor against the high starting current produced in the absence of back emf at starting. The 4 point starter has a lot of constructional and functional similarity to a three point starter, but this special device has an additional point and a coil in its construction, which naturally brings about some difference in its functionality, though the basic operational characteristic remains the same. Now to go into the details of operation of 4 point starter, let s have a look at its constructional diagram, and figure out its point of difference with a 3 point starter. Construction and Operation of four point Starter A 4 point starter as the name suggests has 4 main operational points, namely 1. L Line terminal. (Connected to positive of supply.) 2. A Armature terminal. (Connected to the armature winding.) 3. F Field terminal. (Connected to the field winding.) Like in the case of the 3 point starter, and in addition to it there is 4. A 4th point N. (Connected to the No Voltage Coil) Figure 1.29construction of Four point Starter The construction of Four point starter as shown in the figure 1.29.The remarkable difference in case of a 4 point starter is that the No Voltage Coil is connected independently across the supply through the fourth terminal called N in addition to the L, F and A. As a direct consequence of that, any change in the field supply current does not bring about any difference in the performance of the No Voltage Coil. Thus it must be ensured that No Voltage Coil always produce a force which is strong enough to hold the handle in its RUN position, against force of the spring, under all the operational conditions. Such a current is adjusted through No Voltage Coil with the help of fixed resistance R connected in series with the NVC using fourth point N as shown in the figure above. Apart from this above mentioned fact, the 4 point and 3 point starters are similar in all other ways like possessing is a variable resistance, integrated into number of sections as shown in the figure above. The contact points of these sections are called studs and are shown separately as OFF, 1, 2, 3, 4, 5, RUN, over which the handle is free to be maneuvered manually to regulate the starting current with gathering speed. 29

30 Now to understand its way of operating lets have a closer look at the diagram given above. Considering that supply is given and the handle is taken stud No. 1, then the circuit is complete and line current that starts flowing through the starter. In this situation we can see that the current will be divided into 3 parts, flowing through 3 different points. (i) 1 part flows through the starting resistance (R 1 + R 2 + R 3..) and then to the armature. (ii) A 2nd part flowing through the field winding F. (iii) A 3rd part flowing through the No Voltage Coil in series with the protective resistance R. So the point to be noted here is that with this particular arrangement any change in the shunt field circuit does not bring about any change in the No Voltage Coil as the two circuits are independent of each other. This essentially means that the electromagnet pull subjected upon the soft iron bar of the handle by the No Voltage Coil at all points of time should be high enough to keep the handle at its RUN position, or rather prevent the spring force from restoring the handle at its original OFF position, irrespective of how the field rheostat is adjusted. This marks the operational difference between a 4 point starter and a 3 point starter. As otherwise both are almost similar and are used for limiting the starting current to a shunt field or compound excited dc motor, and thus act as a protective device Speed control of shunt motor We know that the speed of shunt motor is given by: where, V a is the voltage applied across the armature and Φ is the flux per pole and is proportional to the field current I f. As explained earlier, armature current I a is decided by the mechanical load present on the shaft. Therefore, by varying V a and I f we can vary n. For fixed supply voltage and the motor connected as shunt we can vary V a by controlling an external resistance connected in series with the armature. I f of course can be varied by controlling external field resistance R f connected with the field circuit. Thus for.shunt motor we have essentially two methods for controlling speed, namely by: 1. varying armature resistance. 2. varying field resistance Speed control by varying armature resistance The inherent armature resistance r a being small, speed n versus armature current I a characteristic will be a straight line with a small negative slope as shown in figure In the discussion to follow we shall not disturb the field current from its rated value. At no load (i.e., I a = 0) speed is highest and Note that for shunt motor voltage applied to the field and armature circuit are same and equal to the supply voltage V. However, as the motor is loaded, I a r a drop increases making speed a 30

31 little less than the no load speed n 0. For a well-designed shunt motor this drop in speed is small and about 3 to 5% with respect to no load speed. This drop in speed from no load to full load condition expressed as a percentage of no load speed is called the inherent speed regulation of the motor. Figure 1.30 Speed Vs Armature current and torque characteristics It is for this reason, a d.c shunt motor is said to be practically a constant speed motor (with no external armature resistance connected) since speed drops by a small amount from no load to full load condition. Since Te=kI a Φ, for constant φ operation, T e becomes simply proportional to I a. Therefore, speed vs. torque characteristic is also similar to speed vs. armature current characteristic as shown in figure Speed control by varying field current In this method field circuit resistance is varied to control the speed of a d.c shunt motor. Let us rewrite.the basic equation to understand the method. If we vary I f, flux Φ will change, hence speed will vary. To change I f, an external resistance is connected in series with the field windings. The field coil produces rated flux when no external resistance is connected and rated voltage is applied across field coil. It should be understood that we can only decrease flux from its rated value by adding external resistance. Thus the speed of the motor will rise as we decrease the field current and speed control above the base speed will be achieved. So from the initial steady condition, we have If load torque remains constant and flux is reduced to 1φ, new armature current in the steady state is obtained from Therefore new armature current is 31

32 But the fraction,φ/φ 1 >1; hence new armature current will be greater than the rated armature current and the motor will be overloaded. This method therefore, will be suitable for a load whose torque demand decreases with the rise in speed keeping the output power constant as shown in figure Obviously this method is based on flux weakening of the main field. Therefore at higher speed main flux may become so weakened, that armature reaction effect will be more pronounced causing problem in commutation. Figure 1.31 Constant power and torque characteristics Speed control by armature voltage variation In this method of speed control, armature is supplied from a separate variable d.c voltage source, while the field is separately excited with fixed rated voltage as shown in figure Here the armature resistance and field current are not varied. Since the no load speed n 0 =V a /KΦ, the speed versus I a characteristic will shift parallely as shown in figure 1.33 for different values of V a. Figure 1.32 Speed control by controlling Armature voltages Figure 1.33 family of n Vs Armature current characteristics As flux remains constant, this method is suitable for constant torque loads. In a way armature voltage control method is similar to that of armature resistance control method except that the 32

33 former one is much superior as no extra power loss takes place in the armature circuit. Armature voltage control method is adopted for controlling speed from base speed down to very small speed as one should not apply across the armature a voltage which is higher than the rated voltage Ward Leonard method: combination of V a and I f control In this scheme, both field and armature control are integrated as shown in figure 1.34,1.35. Arrangement for field control is rather simple. One has to simply connect an appropriate rheostat in the field circuit for this purpose. However, in the pre power electronic era, obtaining a variable d.c supply was not easy and a separately excited d.c generator was used to supply the motor armature. Obviously to run this generator, a prime mover is required. A 3-phase induction motor is used as the prime mover which is supplied from a 3-phase supply. By controlling the field current of the generator, the generated emf, hence V a can be varied. The potential divider connection uses two rheostats in parallel to facilitate reversal of generator field current. First the induction motor is started with generator field current zero (by adjusting the jockey positions of the rheostats). Field supply of the motor is switched on with motor field rheostat set to zero. The applied voltage to the motor V a, can now be gradually increased to the rated value by slowly increasing the generator field current. In this scheme, no starter is required for the d.c motor as the applied voltage to the armature is gradually increased. To control the speed of the d.c motor below base speed by armature voltage, excitation of the d.c generator is varied, while to control the speed above base speed field current of the d.c motor is varied maintaining constant V a. Reversal of direction of rotation of the motor can be obtained by adjusting jockeys of the generator field rheostats. Although, wide range smooth speed control is achieved, the cost involved is rather high as we require one additional d.c generator and a 3-phase induction motor of simialr rating as that of the d.c motor whose speed is intended to be controlled. In present day, variable d.c supply can easily be obtained from a.c supply by using controlled rectifiers thus avoiding the use of additional induction motor and generator set to implement Ward leonard method. Figure 1.34 Ward Leonard speed control using shunt motor Figure 1.35 Ward Leonard speed control using three phase induction motor 33

34 1.12 Series motor In this motor the field winding is connected in series with the armature and the combination is supplied with d.c voltage as depicted in figure Unlike a shunt motor, here field current is not independent of armature current. In fact, field and armature currents are equal i.e., I f = I a. Now torque produced in a d.c motor is: T ΦI a Ι f I a I a 2 before saturation sets in i.e., Φ I a I a after saturation sets in at large I a Figure 1.36 DC series motor Since torque is proportional to the square of the armature current, starting torque of a series motor is quite high compared to a similarly rated d.c shunt motor Characteristics of series motor Torque vs. armature current characteristic Since T I 2 a in the linear zone and T I a in the saturation zone, the T vs. I a characteristic is as shown in figure 1.37 speed vs. armature current From the KVL equation of the motor, the relation between speed and armature current can be obtained as follows: The relationship is inverse in nature making speed dangerously high as Ia 0. Remember that the value of I a, is a measure of degree of loading. Therefore, a series motor should never be operated under no load condition. Unlike a shunt motor, a series motor has no finite no load speed. Speed versus armature current characteristic is shown in figure

35 Figure 1.37 T vs. I a, Speed versus armature current and speed vs. torque characteristic DC series motor speed vs. torque characteristic Since T Ia in the linear zone, the relationship between speed and torque is k'' and k' represent appropriate constants to take into account the proportionality that exist between current, torque and flux in the linear zone. This relation is also inverse in nature indicating once again that at light load or no load T 0condition; series motor speed approaches a dangerously high value. The characteristic is shown in figure For this reason, a series motor is never connected to mechanical load through belt drive. If belt snaps, the motor becomes unloaded and as a consequence speed goes up unrestricted causing mechanical damages to the motor Speed control of series motor Speed control below base speed For constant load torque, steady armature current remains constant, hence flux also remains constant. Since the machine resistance r as +r is quite small, the back emf E b is approximately equal to the armature terminal voltage V a. Therefore, speed is proportional to V a. If V a is reduced, speed too will be reduced. This V a can be controlled either by connecting external resistance in series or by changing the supply voltage. Series-parallel connection of motors If for a drive two or more (even number) of identical motors are used (as in traction), the motors may be suitably connected to have different applied voltages across the motors for controlling speed. In series connection of the motors shown in figure 1.38, the applied voltage across each motor is V/2 while in parallel connection shown in figure 1.39, the applied voltage across each motor is V. The back emf in the former case will be approximately half than that in the latter case. For same armature current in both the cases (which means flux per pole is same), speed will be half in series connection compared to parallel connection. Figure 1.38 motors connected in series 35

36 Figure 1.39 motors connected in Parallel Speed control above base speed Flux or field current control is adopted to control speed above the base speed. In a series motor, independent control of field current is not so obvious as armature and field coils are in series. However, this can be achieved by the following methods: 1. Using a diverter resistance connected across the field coil. Figure 1.40 Field control with diverter In this method shown in figure 1.40, a portion of the armature current is diverted through the diverter resistance. So field current is now not equal to the armature current; in fact it is less than the armature current. Flux weakening thus caused, raises the speed of the motor. 2. Changing number of turns of field coil provided with tapings. Figure 1.41 Field control with tappings In this case shown figure 1.41, armature and field currents are same. However provision is kept to change the number of turns of the field coil. When number of turns changes, field mmf N se I f changes, changing the flux hence speed of the motor. 3. Connecting field coils wound over each pole in series or in. parallel. Figure 1.42 coils in series 36

37 Generally the field terminals of a d.c machine are brought out after connecting the field coils (wound over each pole) in series. Consider a 4 pole series motor where there will be 4 individual coils placed over the poles. If the terminals of the individual coils are brought out, then there exist several options for connecting them. The four coils could be connected in series as in figure 1.42; the 4 coils could be connected in parallel or parallel combination of 2 in series and other 2 in series as shown in figure For series connection of the coils (figure 1.42) flux produced is proportional to I a and for series-parallel connection as shown in figure Figure 1.42 series-parallel connection of coils flux produced is proportional to 2aI. Therefore, for same armature current I a, flux will be doubled in the second case and naturally speed will be approximately doubled as back emf in both the cases is close to supply voltage V. Thus control of speed in the ratio of 1:2 is possible for series parallel connection Applications of DC motor DC Series Motors (a). Electric Traction 1. High starting torque and reduced torque at high speeds. 2. Large tractive effort, so a number of motors in series. 3. High, Weight/Power ratio 4. Motors robust in construction. (b) Hoists, cranes, excavations, electric vehicles, streetcars, battery powered portable tools, automotive starter motors : all because of high starting torque. (c) Drive fan load 1.Torque requirement increases with the square of speed. (d) Battery Operated Vehicles 1.Cars and other battery powered vehicles have traction characteristics. 2. Speed control can be carried out by thyristers. DC Shunt Motors (a) Constant speed applications. Applications where a wide range of speed control is employed e.g. in lathes, in paper industry etc. (c) As a separately excited motor when field winding is disconnected from armature and connected to an external voltage source. DC Compound Motors (a) Rolling Mills : To improve characteristic and have higher starting torque for the lower rolling motor of the twin-drive. Cummulative compound motors are better suited than shunt motors. In conjunction with flywheel, they can take sudden temporary loads and are ideal for rolling mills and coal-cutting machines. (b) Punching Press. (c) Milling Machine. 37

38 (d) Traction Motors : Only where supply voltage is likely to vary considerably. (e) Hoisting and Lowering of Loads (along with regenerative braking). (f) to (v) were for cumulatively compounded motor. (g) Differential compound motors find only rare application as in research and experimental work. Two mark Questions and Answers 1. Write down the emf equation for d.c generator. E = (фnz / 60)(P/A) V Where P= number of poles Z= Total number of conductors A= number of parallel paths Ф= flux per pole N= speed in rpm 2. Why the armature core in D.C machines is constructed with laminated steel sheets instead of solid steel? Steel sheets offer low reluctance path for the magnetic field, laminated sheets reduce eddy current loss 3. Why is commutator employed in d.c machines? Conduct electricity between armature and fixed brushes Converts alternating emf into unidirectional emf and vice versa 4. What is meant by selective commutation? The use of more than one pair of brushes in wave winding does not divide the armature coil sides into more than two parallel paths, but current collected from the armature i divided between the brushes of like polarity. In case of slight differences in contact resistance the current collected by individual brushes may be different and is called selective commutation 5. Define critical field resistance in dc shunt generator. Critical field resistance is defined as the resistance of the field circuit, which will cause the shunt generator just to build up its emf at a specified field 6. Define the term armature reaction in dc machines. The interaction between the flux set up by the current carrying armature conductors with the main field flux is defined as armature reaction 7. What are the two unwanted effects of armature reaction? Cross magnetizing effect / Distorting effect Demagnetising effect 8. Name the two methods of improving commutation. (ii) Emf commutation. (iii) Resistance commutation. 9. Define the term commutation in dc machines. The changes that take place in winding elements during the period of short circuit by a brush is called commutation. 10. How will you change the direction of rotation of a D.C motor? Either the direction of the main field or the direction of current through the armature conductors is to be reserved. 11. Enumerate the factors on which the speed of a dc motor depends. The speed of dc motor depends on three factors. 38

39 Flux in the air gap. Resistance of the armature circuit. Voltage applied to the armature 12. List the different methods of speed control employed for dc series motor. Field diverter method. Regrouping of field coil. Tapped field control. Armature resistance control. Armature voltage control for single motor. Series parallel control for multiple identical motors 13. Give the voltage expression of DC motor. V=E + I R 14. List the characteristics of DC Motor Torque and armature current characteristics (electrical characteristics) Speed and armature current characteristics. Speed and torque characteristics. 15. Explain why DC series motor is suitable for traction purposes. Series motor exerts torque proportional to the square of armature current and it has good accelerating torque and has a relatively huge starting torque. 16. What is the necessity of starter in DC motors? When motor is at rest there is no back emf developed in armature. If full supply voltage is given across stationery armature, it will draw very large current, as armature r3esistance is very small. This excessive current will blow out fuses and it will damage the commutator and brushes. To avoid this starter is used in dc motors, which limits the starting current to safe value 17. Write the applications of different types of DC motors. Shunt motor: For driving constant speed line shafting lathes. Centrifugal pumps, blowers and fans Reciprocating pumps. Series motor: For traction work Electric locomotives Cranes and hoists, trolley cars. Compound motor: Heavy planers Elevators, for shears and punches 18. List out the various methods that are used to control the speed of DC motor Flux control method. Armature control method. Voltage control method. Multiple voltage control Ward Leonard system 39

40 UNIT II TRANSFORMERS 9 Principle - Theory of ideal transformer - EMF equation - Construction details of shell and core type transformers - Tests on transformers - Equivalent circuit - Phasor diagram - Regulation and efficiency of a transformer - Introduction to three - phase transformer connections. 2.1 Introduction The transformer is a device that transfers electrical energy from one electrical circuit to another electrical circuit. The two circuits may be operating at different voltage levels but always work at the same frequency. Basically transformer is an electro-magnetic energy conversion device. It is commonly used in electrical power system and distribution systems. In this unit, we will first get an understanding of the physical principle of operation and construction of transformer. Thereafter, we will study in detail the operation of transformer at load. In particular, we will consider the representation of the transformer using equivalent circuits for estimating voltage and efficiency at various loads. Apart from ac power system, transformers are used for communication, instrumentation and control. In this unit, you will be introduced to the salient features of instrument transformers. This unit ends by considering the use of three phase transformers, and basics of thee phase bank of single-phase transformers. 2.2 Basics of Transformer In its simplest form a single-phase transformer consists of two windings, wound on an iron core one of the windings is connected to an ac source of supply f. The source supplies a current to this winding (called primary winding) which in turn produces a flux in the iron core. This flux is alternating in nature (Refer Figure 4.1). If the supplied voltage has a frequency f, the flux in the core also alternates at a frequency f. the alternating flux linking with the second winding, induces a voltage E 2 in the second winding (called secondary winding). [Note that this alternating flux linking with primary winding will also induce a voltage in the primary winding, denoted as E 1. Applied voltage V 1 is very nearly equal to E 1 ]. If the number of turns in the primary and secondary windings is N 1 and N 2 respectively, we shall see later in this unit that E 2 /E 1 =N 2 /N 1 E 2. The load is connected across the secondary winding, between the terminals a1, a2. Thus, the load can be supplied at a voltage higher or lower than the supply voltage, depending upon the ratio N 2 /N Basic arrangements of Transformer When a load is connected across the secondary winding it carries a current I 2, called load current. The primary current correspondingly increases to provide for the load current, in addition to the small no load current. The transfer of power from the primary side (or source) to the secondary side (or load) is through the mutual flux and core. There is no direct electrical connection between the primary and secondary sides. In an actual transformer, when the iron core carries alternating flux, there is a power loss in the core called core loss, 40

41 iron loss or no load loss. Further, the primary and secondary windings have a resistance, and the currents in primary and secondary windings give rise to I 2 R losses in transformer windings, also called copper losses. The losses lead to production of heat in the transformers, and a consequent temperature rise. Therefore, in transformer, cooling methods are adopted to ensure that the temperature remains within limit so that no damage is done to windings insulation and material EMF Equation of a Transformer In the Figure 2.1 of a single-phase transformer, the primary winding has been shown connected to a source of constant sinusoidal voltage of frequency f in Hz and the secondary terminals are kept open.the primary winding of N1 turns draws a small amount of alternating current of instantaneous value i0, called the exciting current. This current establishes flux Φ in the core (+ve direction marked on diagram). The strong coupling enables all of the flux ΦΦ to be confined to the core (i.e. there is no leakage of flux). Consequently, the flux linkage of primary winding is λ 1 = N 1 Φ... (4.1) and the flux linkage λ 2 of the secondary winding is λ 2 = N 2 Φ... (4.2) The time rate of change of these flux linkages induces emf in the windings given by As per Lenz s law, the positive direction of the induced emf opposes the positive current direction and is shown by (+) and ( ) polarity marked on the diagram. Assuming the ideal case of the windings possessing zero resistance, as per KVL, we can write v1 = e1... (4.5) Thus, both e1 and Φ must be sinusoidal of frequency f Hz, the same as that of the voltage source. (Consequently, e2 is also of same frequency and hence the definition of transformer should incorporate the same frequency concept). Let Φ = Φ m sin ωt... (4.5a) Where, ω = 2π f, and Φ m is the peak (maximum) value of the flux. From Eq. (4.3), where, E m1 = ω N 1 Φ m From Eq. (4.4) Similarly, where, E m2 = ω N 2 Φ m m 41

42 Eqs. (4.6a) and (4.6b) indicate that both E 1 and E 2 lag Φ (Eq. (4.5a)) by 90. RMS Value of Induced emf The RMS values of the induced emf in the primary and secondary windings, E 1, E 2 are given by The turns ratio is denoted by k and has no unit as it is a ratio. If k < 1, the secondary-voltage is less than the primary voltage and the transformer is called a step-down transformer. If k > 1, secondary voltage is more than the primary voltage (step up transformer). 2.3 Transformer Construction Core-type and Shell-type Construction Depending upon the manner in which the primary and secondary windings are placed on the core, and the shape of the core, there are two types of transformers, called (a) core type, and (b) shell type. In core type transformers, the windings are placed in the form of concentric cylindrical coils placed around the vertical limbs of the core. The low-voltage (LV) as well as the high-voltage (HV) winding are made in two halves, and placed on the two limbs of core. The LV winding is placed next to the core for economy in insulation cost. Figure 2.2(a) shows the cross-section of the arrangement. In the shell type transformer, the primary and secondary windings are wound over the central limb of a three-limb core as shown in Figure 2.2(b). The HV and LV windings are split into a number of sections, and the sections are interleaved or sandwiched i.e. the sections of the HV and LV windings are placed alternately. Core The core is built-up of thin steel laminations insulated from each other. This helps in reducing the eddy current losses in the core, and also helps in construction of the transformer. The steel used for core is of high silicon content, sometimes heat treated to produce a high permeability and low hysterisis loss. The material commonly used for core is CRGO (Cold Rolled Grain Oriented) steel. Conductor material used for windings is mostly copper. However, for small distribution transformer aluminium is also sometimes used. The conductors, core and whole windings are insulated using various insulating materials depending upon the voltage. 42

43 Figure 4.2 Windings and Core in Core Type and Shell-Type Transformer Insulating Oil In oil-immersed transformer, the iron core together with windings is immersed in insulating oil. The insulating oil provides better insulation, protects insulation from moisture and transfers the heat produced in core and windings to the atmosphere. The transformer oil should posses the following quantities : (a) High dielectric strength, (b) Low viscosity and high purity, (c) High flash point, and (d) Free from sludge Tank and Conservator The transformer tank contains core wound with windings and the insulating oil. In large transformers small expansion tank is also connected with main tank is known as conservator. Conservator provides space when insulating oil expands due to heating. The transformer tank is provided with tubes on the outside, to permits circulation of oil, which aides in cooling. Some additional devices like breather and Buchholz relay are connected with main tank.buchholz relay is placed between main tank and conservator. It protect the transformer under extreme heating of transformer winding. Breather protects the insulating oil from moisture when the cool transformer sucks air inside. The silica gel filled breather absorbes moisture when air enters the tank. Some other necessary parts are connected with main tank like, Bushings, Cable Boxes, Temperature gauge, Oil gauge, Tappings, etc. 2.4 Equivalent Circuit of Transformer The performance of a transformer at no load and at load is influenced by mutual flux, the leakage fluxes, the winding resistances and the iron losses. For the purpose of performance evaluation, the effect of these is represented on an electrical circuit, in the form of resistances and reactances. Such an electrical circuit is called equivalent circuit. In this section, we will develop the equivalent circuit of a single-phase transformer in the following steps : (a) Equivalent circuit of an ideal transformer at no load (b) Equivalent circuit of an ideal transformer on load (c) Equivalent circuit at load (d) Equivalent circuit referred to primary side (e) Approximate equivalent circuit Equivalent Circuit of an Ideal Transformer at No Load Under certain conditions, the transformer can be treated as an ideal transformer. 43

44 The assumptions necessary to treat it as an ideal transformer are : (a) Primary and secondary windings have zero resistance. This means that ohmic loss (I 2 R loss), and resistive voltage drops in windings are zero. (b) There is no leakage flux, i.e. the entire flux is mutual flux that links both the primary and secondary windings. (c) Permeability of the core is infinite this means that the magnetizing current needed for establishing the flux is zero. (d) Core loss (hysteresis as well as eddy current losses) are zero. We have earlier learnt that : (k is a constant, known as voltage transformation ratio or turns ratio). For an ideal transformer, V 1 = E 1 and E 2 = V 2.therefore Even at no load, a transformer draws some active power from the source to provide the following losses in the core : (a) eddy-current loss, and (b) hysteresis loss. The current responsible for the active power is nearly in phase with V 1 (applied voltage) and is known as core-loss current. A transformer when connected to supply, draws a current to produce the flux in the core. At no-load, this flux lags nearly by 90o behind the applied voltage V 1. The magnetizing current, denoted by I m is in phase with the flux Φ and thus, lags behind the applied voltage by nearly 90. The phasor sum of the core loss component of current I c and the magnetizing current I m is equal to the no-load current I 0. I 0 =I 0 cos Φ 0 and I m =I 0 sin Φ 0 Core loss = P 0 = V 1 I 0 (cos Φ 0 ) where Φ 0 is the phase angle between V 1 and I 0, and, (cos Φ 0 ) is the no load power factor. The phase relationship between applied voltage V 1, no-load current I 0, and its components Ic, Im is shown in Figure 2.3(a). Figure 2.3 Phasor Diagram at No load and Equivalent circuit of Transformer 44

45 In the form of equivalent circuit, this can be represented as Figure 2.3(b), in which R c is a resistance representing core loss and X m is an inductive reactance (called magnetizing reactance). Note that the current in the resistance is in phase with V 1 and X m being an inductive reactance, the current I m in this branch lags V 1 by 90o as shown in the phasor diagram of Figure 2.3(a). This implies that the primary winding resistance and leakage reactance are neglected. Similarly, in the secondary winding of transformer mutually induced emf is antiphase with V 1 and its magnitude is proportional to the rate of change of flux and the number of secondary turns. (You will learn about the concept of leakage reactance when you study about the equivalent circuit at load). The equivalent circuit parameters R c and X m can also be expressed as conductance and susceptance G c, B m such that Equivalent Circuit of an Ideal Transformer on Load Under certain conditions the transformer can be treated as an ideal transformer. The idealizing assumptions are listed below : (a) Both primary and secondary windings have zero resistance. This means, no ohmic power loss and no resistive voltage drop. (b) No leakage flux, i.e. all the flux produced is confined to the core and links both the windings (c) Infinite permeability of the core. This means no zero magnetizing current is needed to establish the requisite amount of flux in the core, i.e. I m = 0. (d) Core-loss (hysteresis as well as eddy-current loss) is zero, i.e. I c = 0. Assumptions (a), (b) and (d) mean that copper losses, and iron losses being zero, the efficiency of the transformer is 100%. Since I m = I c = 0, I 0 = 0. As per earlier derived equation Figure 2.4 Transformer on load where, V 1 is supply voltage and V 2 is voltage across load terminals.when load is applied, let the impedance of load be Z L, as shown in Figure 2.4. Sinusoidal current i 2 flows through the secondary.therefore, secondary winding creates an mmf F 2 = N 2 i 2 which opposes the flux Φ. 45

46 But mutual flux Φ is invariant with respect to load (otherwise v 1 = e 1 balance is disturbed). As a result, the primary winding starts drawing a current i1 from the source so as to create mmf F 1 = N 1 i 1 which at all times cancels out the load-caused mmf N 2 i 2 so that Φ is maintained constant independent of the magnitude of the load current which flows in the secondary winding. This implies that for higher load, more power will be drawn from the supply. Thus, (Instantaneous power into primary) = (Instantaneous power out of secondary)in terms of rms values,i.e. VA output = VA input, i.e. V 1 I 1 = V 2 I 2 Since The circuit representation of Figure 2.4, can be simplified by referring the load impedance and secondary current to the primary side. From Figure 2.4, we see that Where Z L be the load impedance referred to the primary side. From V 2 = I 2 Z L we can also easily obtain V 2 = I 2 Z L, where secondary terminal voltage referred to primary side, and is secondary current referred to primary side. In the ideal transformer, I 1 = I 2 and V1 =V Equivalent Circuit of a Real Transformer In real conditions, in addition to the mutual flux which links both the primary and secondary windings transformer, has a component of flux, which links either the primary winding or the secondary, but not both. This component is called leakage flux. The flux which links only with primary is called primary leakage flux, and the flux which links only with secondary is called secondary leakage flux. Figure 2.4 shows schematically the mutual and the leakage flux. From our knowledge of magnetic circuits, we know that a flux lining with a winding is the cause of inductance of the winding (Inductance = Flux linkage per ampere). Since in a 46

47 transformer the flux is alternating, its flux linkage gives rise to an induced voltage in the winding. Thus, primary leakage flux (which is proportional to I 1 ) causes an induced voltage, which acts as a voltage drop. Similarly for the secondary leakage flux. The effect of these induced EMFs are, therefore, represented as inductive leakage reactance X l1, X l2. X l1 and X l2 are called leakage reactance s of the primary and secondary respectively. These are also denoted as X 1, X 2. The windings of the transformer have resistance R 1, R 2. These resistances cause a voltage drop I 1 R 1 and I 2 R 2, as also ohmic loss I 1 2 R 1 and I 2 2 R 2 To sum up, in a Real Transformer, (a) Both the primary and secondary windings possess resistance. As a result, the value of actual impressed voltage across the transformer is the voltage V1 less the drop across the resistance R1. Moreover, the copper loss in the primary winding is (I 1 2 R 1 ) and in the secondary winding (I 2 2 R 2 ). (b) A Real Transformer has some leakage flux, as shown in the Figure 2.4. These fluxes, as discussed earlier, lead to self-reactances X l1, and X l2 for the two windings respectively. (c) The magnetizing current cannot be zero. Its value is determined by the mutual flux Φm. The mutual flux also determines core-loss taking place in the iron parts of the transformer. The value of Io does not depend on load and hence the iron-loss or core-loss is constant which is not zero. Considering the effects of resistances and leakage reactances, a transformer can be visualized as shown in Figure 2.5. Figure 2.5 Exact Equivalent Circuit of Real Transformer Equivalent Circuit Referred to Primary Side We will now refer the impedance R 2 + j X l2 to the primary side i.e. to the left hand side of the ideal transformer. We have seen earlier that a load impedance Z L can be referred to primary side as Z L ' where, Similarly Z 2 = R 2 + j X l2 can be referred to the primary side as where Z 2 ' is said to be the secondary winding impedance referred to the primary side. Equating real and imaginary parts 47

48 R 2 ' is the secondary winding resistance referred to primary, and X 2 ' is the secondary winding eakage reactance referred to primary side. Figure 4.6 can now be modified (i.e. referring the secondary resistance and reactance to the primary side) to get the equivalent circuit shown in Figure 2.6. Figure 2.6 Exact Circuit with Secondary Parameters Referred to Primary Side The secondary terminal voltage V2 and secondary current I2 can also be referred to the primary side using the relations. 2.5 Phasor Diagram and Voltage Regulation The phasor diagram or vector diagram of a transformer for the no load case was discussed before. The phasor diagram for a loaded transformer depends on, whether the resistances and reactances of the primary and secondary winding have been considered or neglected Phasor Diagram at Load without Winding Resistance and Reactance The starting point of all phasor diagrams is the mutual flux phasor. The induced voltage in the two windings lag behind the flux phasor by 90. Now we will proceed to obtain the phasor diagram for three specific load power factors, viz., (a) pure resistive load (b) inductive or lagging pf load, and (c) capacitive or leading pf load. Resistance Load The phasor diagram neglecting winding resistance and reactance is given in Figure 2.7.E 1, E 2 lag behind Im by 90. The load current I 2 being at unity power factor is in phase with E 2. Corresponding to the load current the primary draws an additional current I 2 ' (in addition to no load current). The magnitude of I 2 ' is 48

49 times the magnitude of I 2. Phase position of I 2 ' is opposite to that of I 2, so that the ampere turns of secondary and primary can balance each other. 2.7 Phasor diagram of Resistive Load The primary current I will be phasor sum of I 2 ' and no load current I 0. Φ 0 : Phase angle of at no-load Φ 1 : Phase angle at load (between current I 1 and V 1 ). For Inductive Load For an inductive load (i.e. R L + j X L ), the load current (i.e. secondary winding current) I 2 will lag the secondary voltage E 2 by an angle Φ 2. I 2 ' is in direct opposition to I 2 in the phasor diagram. The primary current I 1 is the phasor sum of I 0 and I 2 '. Once again Φ 0 is the phase angle of the no load current and Φ 1 is the phase angle of input current. The phasor diagram is shown in Figure 2.8. Phasor diagram for a capacitive load (leading power factor), i.e. R L j X L can be similarly drawn, as shown in Figure Phasor Diagram for Inductive Load (Neglecting Winding Resistance and Reactance) 2.9 Phasor Diagram for Capacitive Load (Neglecting Winding Resistance and Reactance) 49

50 2.5.2 Phasor Diagram at Load with Winding Resistance and Reactance Since the basics of phasor diagram with resistive, inductive and capacitive loads have already been considered in Figures 2.7, 2.8, 2.9, respectively, we now restrict ourselves to the more commonly occurring load i.e. inductive along with resistance, which has a lagging power factor.for drawing this diagram, we must remember that 2.6 Voltage Regulation A transformer is interposed in between the load and the supply terminals in such cases. There are additional drops inside the transformer due to the load currents. While input voltage is the responsibility of the supply provider, the voltage at the load is the one which the user has to worry about. If undue voltage drop is permitted to occur inside the transformer the load voltage becomes too low and affects its performance. It is therefore necessary to quantify the drop that takes place inside a transformer when certain load current, at any power factor, is drawn from its output leads. This drop is termed as the voltage regulation and is expressed as a ratio of the terminal voltage (the absolute value per se is not too important). The voltage regulation can be defined in two ways - Regulation Down and Regulation Up Regulation down: This is defined as the change in terminal voltage when a load current at any power factor is applied, expressed as a fraction of the no-load terminal voltage. Expressed in symbolic form we have, Regulation = V nl V l \ V nl V nl and V l are no-load and load terminal voltages. This is the definition normally used in the case of the transformers, the no-load voltage being the one given by the power supply provider on which the user has no say. Hence no-load voltage is taken as the reference. Regulation up: Here again the regulation is expressed as the ratio of the change in the terminal voltage when a load at a given power factor is thrown off, and the on load voltage. This definition if expressed in symbolic form results in Regulation = V nl V l \ V l V nl is the no-load terminal voltage. V l is load voltage. Normally full load regulation is of interest as the part load regulation is going to be lower. Voltage regulation is generally expressed as a percentage. Percent voltage regulation (% VR) Note that E 2, V 2 are magnitudes, and not phasor or complex quantities. Also note that voltage regulation depends not only on load current, but also on its power factor. Using approximate equivalent circuit referred to primary or secondary, we can obtain the voltage regulation. From approximate equivalent circuit referred to the secondary side and phasor diagram for the circuit. where r eq =r 2 + r 1 ' (referred to secondary) 1 x e =x 2 + x 1 ' (+ sign applies lagging power factor load and sign applies to leading pf load). 50

51 % Voltage regulation = (% resistive drop) cos Φ 2 (% reactive drop) sin Φ Losses and Efficiency of Transformer A transformer does t contain any rotating part so it is free from friction and windage losses. In transformer the losses occur in iron parts as well as in copper coils. In iron core the losses are sum of hysteresis and eddy current losses. The hysteresis losses are P h α f 2 B x max and eddy current loss is equal to Pe α f 2 B max. Where f is frequency B max is maximum flux density. We know that the maximum flux density is directly proportional to applied voltage so if the applied voltage is constant then the flux density is constant and the hysteresis losses are proportional to f and eddy current losses are proportional to f Iron Losses or Core Losses To minimize hysteresis loss in transformer, we use Cold Rolled Grain Oriented (CRGO) silicon steel to build up the iron core. Eddy Current Loss When the primary winding variable flux links with iron core then it induces some EMF on the surface of core. The magnitude of EMF is different at various points in core. So, there is current between different points in Iron Core having unequal potential. These currents are known at eddy currents. I 2 R loss in iron core is known as eddy current loss. These losses depends on thickness of core. To minimize the eddy current losses we use the Iron Core which is made of laminated sheet stampings. The thickness of stamping is around 0.5 mm. Determination of Iron or Core Losses Practically we can determine the iron losses by performing the open circuit test. Open Circuit Test We perform open circuit test in low voltage winding in transformer keeping the high voltage winding open. The circuit is connected as shown in Figure 4.12(a). The instruments are connected on the LV side. The advantage of performing the test from LV side is that the test can be performed at rated voltage. When we apply rated voltage then watt meter shows iron losses [There is some copper loss but this is negligible when compared to iron loss]. The ammeter shows no load current I 0 which is very small [2-5 % of rated current]. Thus, the drops in R 1 and X l1 can be neglected. We have W 0 = iron loss I 0 = no load current 2.10 Open Circuit Test 51

52 So I e =I 0 cos Φ 0 and I m =I 0 sin Φ 0. Under no load conditions the PF is very low (near to 0) in lagging region. By using the above data we can draw the equivalent parameter shown in Figure Where 2.10 No Load Equivalent Circuit from Open Circuit Test Copper Losses In a transformer the primary and secondary winding currents increase with increases in load. Due to these currents there is some I2 R losses. These are known as copper losses or ohmic losses. The total I 2 R loss in both windings at rated or full load current is equal to I 1 2 R 1+ I 2 2 R 2. I 1 '= I 1 2 R 01 Similarly, it can be shown that Copper loss= I 2 2 R 02 Here I 1 and I 2 are primary and secondary current. R 1 is primary winding resistance and R 2 is secondary winding resistance. R 01 is total resistance of winding referred to primary R 02 is total resistance of windings referred to secondary. By performing short circuit test we find out copper loss experimentally. Short Circuit Test It s an indirect method to find out the copper losses. To perform this test, we apply a reduced voltage to the primary winding through instruments keeping LV winding short circuited. The connections are shown in Figure We need to apply only 5-10% of rated voltage to primary to circulated rated current in the primary and secondary winding. The applied voltage is adjusted so that the ammeter shows rated current of the winding. Under this condition, the watt-meter reading shows the copper losses of the transformer. Because of low value of applied voltage, iron losses, are very small and can be neglected. As applied voltage is very small, small voltage across the excitation branch produces very small percentage of exciting current in comparison to its full load current and can therefore, 52

53 be safely ignored. As a result, equivalent circuit with secondary short circuited can be represented as Figure Short circuit test fo Transformer Figure 2.12 Transformer Equivalent Circuit with Secondary Short Circuited At a rated current watt meter shows full load copper loss. We have V s = applied voltage, I s = rated current,w s = copper loss then, equivalent resistance and equivalent impedance So we calculate equivalent reactance These R eq and X eq are equivalent resistance and reactance of both windings referred in HV side. These are known as equivalent circuit resistance and reactance Efficiency of Single Phase Transformer Generally we define the efficiency of any machine as a ratio of output power to the input power, i.e. efficiency 53

54 In a transformer, if P i is the iron loss, and P c is the copper loss at full load (when the load current is equal to the rated current of the transformer, the total losses in the transformer are P i + P c. In any transformer, copper losses are variable and iron losses are fixed. When the load on the transformer is (x *full load), the copper loss will be total x 2 P c and total losses =P i + x 2 P c. P c is full load copper loss and x is the ratio of load current to the full load current. If the output power of the transformer is x V 2 I 2 cos Φ, then efficiency (η) becomes, The efficiency varies with load. So, we can find the condition under which the η is maximum. For maximum efficiency, Solving this, we get P i = x 2 P c or iron loss = copper loss The copper loss varies with load current I 2 so when the copper losses are equal to the iron losses for a particular load then efficiency (η) of the transformer is maximum. This is called condition for maximum efficiency. The maximum efficiency, Now, we determine the load at which the maximum efficiency occurs. From the condition of maximum efficiency, we have P i = x 2 P c Thus, the load at which efficiency is maximum occurs, is given by All Day Efficiency (Energy Efficiency) In electrical power system, we are interested to find out the all day efficiency of any transformer because the load at transformer is varying in the different time duration of the day. So all day efficiency is defined as the ratio of total energy output of transformer to the total energy input in 24 hours. 54

55 Where kwh is kilowatt hour. 2.8 Transformers in Three Phase Systems For a proper understanding of this section you will need to revise your knowledge of balanced three phase systems. In particular, you should know (a) the relations between line and phase quantities in star connected and delta connected balanced three phase circuits; (b) expressions for three phase power and volt-amperes; and (c) equivalence relations between star-connected and delta-connected balanced systems Three-phase Bank of Single-phase Transformers Electric power is generated, transmitted and distributed in three-phase form. Even where single-phase power is required, as in homes and small establishments, these are merely tapped off from a basic three-phase system. Transformers are, therefore, required to interconnect three phase systems at different voltage levels. This can be done using three single-phase transformers, constituting what is often called a transformer bank. The primary windings of three identical single-phase transformers can usually be connected either in star or in delta to form a three-phase system. Similarly, the secondary windings can also be connected in star or delta. We have, therefore, four methods of interconnection of primary/secondary, viz., star/star, star/delta, delta/star and delta/delta. 55

56 Let the primary to secondary turns ratio of each single-phase transformer be k. We will identify these transformers by the letters A, B and C. Transformers A will be assumed to have primary terminals A1, A2 and secondary terminals a1, a2, transformers B has terminals B1, B2 and b1, b2 and similarly for transformer C. We will also designate the three phase line terminals on the primary by A, B, C and the secondary line terminals by a, b, c. Further, we will suppose that in all the transformers the winding sense is such that on adopting a dot convention, dots would have to be marked next to primary and secondary terminals having the suffix 1. The four types of transformers connection would be as shown in Figure The ratios of the primary and secondary line voltages is shown in this diagram, where k is the transformation ratio of one phase Three-phase Transformers Instead of a bank of three separate single-phase transformers, each having its own separate iron-core, a single transformer can be designed to serve the same function. Such a single unit, called a three-phase transformer, has three primary windings and three secondary windings. These primary and secondary windings can be connected in star or in delta. The onnections and voltage relations of Figure 4.16 apply in this case also. Such a transformer differs from the single-phase transformers in the design of the iron-core. In the single-phase transformer bank the fluxes associated with a particular phase utilize an ironcore which serves only that phase, whereas in the three-phase transformer the iron-core couples different phases together. Because of this sharing of the iron-core by the three phases, such transformers can be built more economically. A three-phase transformer is always cheaper than three single-phase transformers used for the same purpose, weighs less and occupies less floor space. Despite the above advantages, three single-phase transformers may be preferred if the conditions of operation are such that provision must be made for replacement. When using single-phase transformers it might be sufficient to provide just one single-phase transformer as a spare. If a three-phase transformer is used another three-phase Despite the above advantages, three single-phase transformers may be preferred if the conditions of operation are such that provision must be made for replacement. When using single-phase transformers it might be sufficient to provide just one single-phase transformer as a spare. If a three-phase transformer is used another three-phase transformer will be needed as a spare. While a threephase transformer is cheaper than three single-phase transformers, it is much more expensive than one single-phase transformer. Secondly, there might exist situations like hydroelectric projects in remote locations, where it is not feasible to transport and install a heavy three-phase transformer and the use of three lighter single-phase transformers becomes the only feasible solution. Two mark Questions and Answers 1. Define voltage regulator of a transformer. (N/D-03) (M/J-06) (N/D-08) (M/J-09) 56

57 When a transformer is loaded with a constant primary voltage, the secondary voltage decreases for lagging power factor load, and increases for leading pf load because of its internal resistance and leakage reactance.the change in secondary terminal voltage from no load to full load expressed as a percentage of no loads or full load voltage is termed as regulation. % Regulation down = (0V 2 -V 2 ) x 100/0V 2 % Regulation up = (0V 2 -V 2 ) x 100/V 2 2. Draw the typical equivalent circuit of a single phase transformer. (N/D-03) (N/D-07) The equivalent circuit diagram for a single phase transformer referred to primary side is shown in Fig. 3. What is in ideal transformer? (A/M-04) 1. The primary and secondary winding having no resistance. 2. No leakage flux. 3. No losses. 4. The core has infinite permeability so that the magnetizing current is needed to establish the require amount of flux % efficiency. The transformer having above hypothetical properties it referred as ideal transformer. 4. Define all day efficiency of a transformer. (A/M-04) (N/D-04) (N/D-05) (N/D-06) All day efficiency or energy efficiency is computed on the basis of energy consumed during a certain time period, usually a day of 24 hrs. All day efficiency = Output in Kwh Input in Kwh 5. State the different losses which occur in transformer. (N/D-04) 1. Core or iron loss. (It includes both hysteresis loss and eddy current loss). 2. Copper loss 57

58 6. What is the condition for maximum efficiency and regulation of a transformer? (A/M-05) (M/J-06) Condition for maximum efficiency is Copper loss = Iron loss 7. List the various application of an auto transformer. (A/M-05) To give small boost to a distribution cable to correct for the voltage drop. As induction motor starters. As furnace transformers As interconnecting transformers In control equipment for single phase and 3 phase elective locomotives. 8. What is the application of equivalent circuit of single phase transformer? (N/D-04) To simplify calculations the transformer represented by its equivalent circuit 9. What is dielectric loss in a transformer? (N/D-06) The dielectric loss occurs in transformer due to insulation material particularly in oil and solid insulation. 10. What are the components of magnetic losses in transformer and on what factors do they depend? (M/J-07) The magnetic losses are hysteresis loss and eddy current loss. These losses depend on flux density and frequency. It is a constant loss. 11. Write down equations for volt ampere transferred inductively and volt ampere conductively in an auto transformer. (M/J-07) Volt ampere transferred inductively = S ti =V 2 (I 2 -I 1 ) Volt ampere transferred conductively = S tc =V 2 I Compare core and shell type transformers. (A/M-08) In core type, the windings surround the core considerably and in shell type the core surround the winding. 13. Why the efficiency of transformer more than that of other rotating machines? (A/M- 08) 1. In transformer electrical energy is converted into electrical energy 2. There in no moving part in transformer hence no mechanical losses. Therefore the transformer has more efficiency than that of rotating machines. 58

59 14. Why the transformer rating expressed in KVA? (N/D-08) Copper loss of a transformer depends on current and iron loss on voltage. Hence total losses depend on Volt- Ampere and not on the power factor. That is why the rating of transformers is in kva and not in kw. 15. What are the advantages of auto transformer as compared to two winding transformer? (M/J-09) 1. Smaller in size 2. Lower cost 3. Better efficiency 4. Less exciting current 5. Better voltage regulation 59

60 UNIT III SYNCHRONOUS MACHINES 8 Principle of alternators:- Construction details, Equation of induced EMF and Vector diagram -Synchronous motor:- Starting methods, Torque, V curves, Speed control and Hunting. 3.1 INTRODUCTION It is known that the electric supply used, now a days for commercial as well as domestic purposes, is of alternating type.similar to d.c. machines, the a.c. machines associated with alternating voltages, are also classified as generators and motors.the machines generating a.c. e.m.f. are called alternators or synchronous generators. While the machine accepting input from a.c. supply to produce mechanical output are called synchronous motors. Both these machines work at a specific constant speed called synchronous speed and hence in general called synchronous machines.all the modern power stations consists of large capacity three phase alternators. In this chapter, the construction, working principle and the e.m.f. equation of three phase alternator is discussed. Difference between D.C. Generator and Alternator It is seen that in case of a d.c. generator, basically the nature of the induced e.m.f. in the armature conductors is of alternating type. By using commutator and brush assembly it is converted to d.c. and made available to the external circuit. If commutator is dropped from a d.c. generator and induced e.m.f. is tapped from an armature directly outside, the nature of such e.m.f. will be alternating. Such a machine without commutator, providing an a.c. e.m.f. to the external circuit is called an alternator. The obvious question is how is it possible to collect an e.m.f. from the rotating armature without commutator? Note : So the arrangement which is used to collect an induced e.m.f. from the rotating armature and make it available to the stationary circuit is called slip ring and brush assembly. 3.2 CONCEPT OF SLIP RINGS AND BRUSH ASSEMBLY Whenever there is a need of developing a contact between rotating element and the stationary circuit without conversion of an e.m.f. from a.c. to d.c., the slip rings and brush assembly can be used.in case of three phase alternators, the armature consist of three phase winding and an a.c. e.m.f. gets induced in these windings. After connecting windings in star or delta, the three ends of the windings are brought out. Across these terminals three phase supply is available. But the armature i.e. these terminals are rotating and hence stationary load cannot be connected directly to them. Hence slip rings, made up of conducting material are mounted on the shaft. Each terminal of winding is connected to an individual slip ring, permanently. Hence three phase supply is now available across the rotating slip rings. The brushes are resting on the slip rings, just making contact. Note : The brushes are stationary. Hence as brushes make contact with the slip rings, the three phase supply is now available across the brushes which are stationary. Hence any stationary load can then by connected across these stationary terminals available from the brushes. The schematic arrangement is shown in the Fig Not only the induced e.m.f. can be taken out from the rotating winding check outside but an induced e.m.f. can be injected to the rotating winding from outside with the help of slip ring 60

61 and brush assembly. The external voltage can be applied across the brushes, which gets applied across the rotating due to the springs.now the induced e.m.f. is basically the effect of the relative motion present between an armature and the field. Such a relative motion is achieved by rotating armature with the help of prime mover, in case of a d.c. generator. As armature is connected to commutator in a d.c. generator, armature must be rotating member while field as a stationary. But in case of alternators it is possible to have, 1) The rotating armature and stationary field. 2) The rotating field and stationary armature. Fig. 3.1 Arrangement of slip rings Note : But practically most of the alternators prefer rotating field type construction with stationary armature due to certain advantages. Advantages of Rotating Field Over Rotating Armature The various advantages of rotating field can be stated as, 1) As everywhere a.c. is used, the generation level of a.c. voltage may be higher as 11 KV to 33 KV. This gets induced in the armature. For stationary armature large space can be provided to accommodate large number of conductors and the insulations. 2) It is always better to protect high voltage winding from the centrifugal forces caused due to the rotation. So high voltage armature is generally kept stationary. This avoids the interaction of mechanical and electrical stresses. 3) It is easier to collect larger currents at very high voltage from a stationary member than from the slip ring and brush assembly. The voltage required to be supplied to the field is very low (110 V to 220 V d.c.) and hence can be easily supplied with the help of slip ring and brush assembly by keeping it rotating. 4) The problem of sparking at the slip rings can be avoided by keeping field rotating which is low voltage circuit and high voltage armature as stationary. 5) Due to low voltage level on the field side, the insulation required is less and hence field system has very low inertia. It is always better to rotate low inertia system than high inertia, as efforts required to rotate low inertia system are always less. 61

62 6) Rotating field makes the overall construction very simple. With simple, robust mechanical construction and low inertia of rotor, it can be driven at high speeds. So greater output can obtained from an alternator of given size. 7) If field is rotating, to excite it be external d.c. supply two slip rings are enough. Once each for positive and negative terminals. As against this, in three phase rotating armature the minimum number of slip rings required are three and can not be easily insulated due to high voltage levels. 8) The ventilation arrangement for high voltage side can be improved if it is kept stationary. Due to all these reasons the most of the alternators in practice use rotating field type of arrangement. For small voltage rating alternators rotating armature arrangement may be used. 3.3 CONSTRUTION OF SYNCHRONOUS GENERATOR (STATOR AND ROTOR) Most of the alternators prefer rotating field type of the construction. In case of alternators the winding terminology is slightly different than in case of d.c. generators. In alternators the stationary winding is called 'Stator' while the rotating winding is called 'Rotor' Note : so most of alternator have stator as armature and rotor as field, in practice.constructional details of rotating field type of alternator are discussed below Stator The stator is a stationary armature. This consists of a core and the slots to hold the armature winding similar to the armature of a d.c. generator. The stator core uses a laminated construction. It is built up of special steel stampings insulated from each other with varnish or paper. The laminated construction is basically to keep down eddy current losses. Generally choice of material is steel to keep down hysteresis losses. Fig. 3.2 Section of an alternator stator The entire core is fabricated in a frame made of steel plates. The core has slots on its periphery for housing the armature conductors. Frame does not carry any flux and serves as the support to the core. Ventilation is maintained with the help of holes cast in the frame. The section of an alternators stator is shown in the Fig Rotor There are two types of rotors used in alternators, 1) Salient pole type, and 2) Smooth cylindrical type. Salient Pole Type 62

63 This is also called projected pole type as all the poles are projected out from the surface of the rotor. The poles are built up of thick steel laminations. The poles are bolted to the rotor as shown in the Fig The pole face has been given a specific shape. The field winding is provided on the pole shoe. These rotors have large diameter and small axial length. The limiting factor fore the size of the rotor is the centrifugal force acting on the rotating member of the machine. As mechanical strength of salient pole type is less, this is preferred for low speed alternators ranging from 125 r.p.m. to 500 r.p.m. The prime movers used to drive such rotor are generally water turbines and I.C. engines. Fig.3.3 Salient pole type rotor Smooth Cylindrical Type This is also called non-salient type or non-projected pole type or round rotor construction. The Fig. 3.4 shows smooth cylindrical type of rotor. Fig. 3.4 Smooth cylindrical rotor The rotor consists of small solid steel cylinder, having number of slots to accommodate the field coil. The slots are covered at the top with the help of steel or manganese wedges. The unslotted portions of the cylinder itself act as the poles. The poles are not projecting out and the surface of the rotor is smooth which maintains uniform air gap between stator and the rotor. These rotors have small diameters and large axial lengths. This is to keep peripheral speed within limits. The main advantage of this type is that these are mechanically very strong and thus preferred for high speed alternators ranging between 1500 to 3000 r.p.m. Such high speed alternators are called 'turboalternators'. The prime movers used to drive such type of rotors are generally steam turbines, electric motors. Difference between Salient and Cylindrical Type of Rotor: 63

64 3.3.3 Excitation System The synchronous machines whether alternator or motor are necessarily separately excited machines. Such machines always require d.c. excitation for their operation. The field systems are provided with direct current which is supplied by a d.c. source at 125 to 600 V. In many cases the exciting current is obtained from a d.c. generator which is mounted on the same shaft of that of alternator. Thus excitation systems are of prime importance. Many of the conventional system involves slip rings, brushes and commutators. Brushless Excitation System With the increase in rating of alternator, the supply of necessary magnetic field becomes difficult as the current values may reach upto 4000 A. If we use conventional excitation systems such as a d.c. generator whose output is supplied to the alternator field through brushes and slip rings then problems are invariable associated with slip rings commutators and brushes regarding cooling and maintenance. Thus modern excitation systems are developed which minimizes thees problems by avoiding the use of brushes. Such excitation system is called brushless excitation system which is shown in the Fig. 3.5 Fig. 3.5 Brushless Excitation system 64

65 It consists of silicon diode rectifier which is mounted on the same shaft of alternator and will directly provide necessary excitation to the field. The power required for rectifiers is provided by an a.c. excitor which is having stationary field but rotating armature.the field of an excitor is supplied through a magnetic amplifier which will control and regulate the output voltage of the alternator since the feedback of output voltage of alternator is taken and given to the magnetic amplifier. The system can be made self-contained if the excitation power for the magnetic amplifier is obtained from the main shaft. The performance and design of the overall system can be optimized by selecting proper frequency and voltage for a.c. excitor. The additional advantage that can be obtained with this system is that it is not necessary to make arrangement for space excitors, generators-field circuit breakers and field rheostats Methods of Ventilation 1)Natural of Ventilation: A fan is attached to either ends of the machine. The ventilation medium is nothing but an atmospheric air which is forced over the machine parts, carrying away the heat. This circulation is possible with or without ventilating ducts. The ventilating ducts if provided may be either axial or radial. 2) Closed Circuit Ventilation System: An atmospheric air may contain injurious elements like dust, moisture, and acidic fumes etc. which are harmful for the insulation of the winding. Hence for large capacity machined closed circuit system is preferred for ventilation. The ventilating medium used is generally hydrogen. The hydrogen circulated over the machine parts is cooled with the help of water cooled heat exchangers. Hydrogen provides very effective cooling than air which increases the rating of the machine upto 30 to 40% for the same size. All modern alternators use closed circuit ventilation with the help of hydrogen as a ventilation medium. 3.4 Working Principle of Synchronous Generator The alternators work on the principle of electromagnetic induction. When is a relative motion between the conductors and the flux, e.m.f. gets induced in the conductors. The d.c. generators also work on the same principle. The only difference in practical alternator and a d.c. generator is that in an alternator the conductors are stationary and field is rotating. But for understanding purpose we can always consider relative motion of conductors with respect to the flux produced by the field winding.consider a relative motion of a single conductor under the magnetic field produced by two stationary poles. The magnetic axis of the two poles produced by field is vertical, shown dotted in the Fig.3.6. Fig. 3.6 Two pole alternator 65

66 Let conductor starts rotating from position 1. At this instant, the entire velocity component is parallel to the flux lines. Hence there is no cutting of flux lines by the conductor. So dφ/dt at this instant is zero and hence induced e.m.f. in the conductor is also zero.as the conductor moves from position 1 towards position 2, the part of the velocity component becomes perpendicular to the flux lines and proportional to that, e.m.f. gets induced in the conductor. The magnitude of such an induced e.m.f. increases as the conductor moves from position 1 towards 2. At position 2, the entire velocity component is perpendicular to the flux lines. Hence there exists maximum cutting of the flux lines. And at this instant, the induced e.m.f. in the conductor is at its maximum. As the position of conductor changes from 2 towards 3, the velocity component perpendicular to the flux starts decreasing and hence induced e.m.f. magnitude also starts decreasing. At position 3, again the entire velocity component is parallel to the flux lines and hence at this instant induced e.m.f. in the conductor is zero. As the conductor moves from 3 towards 4, the velocity component perpendicular to the flux lines again starts increasing. But the direction of velocity component now is opposite to the direction of velocity component existing during the movement of the conductor from position 1 to 2. Hence an induced e.m.f. in the conductor increases but in the opposite direction.at position 4, it achieves maxima in the opposite direction, as the entire velocity component becomes perpendicular to the flux lines.again from position 4 to 1, induced e.m.f. decreased and finally at position 1, again becomes zero. This cycle continues as conductor rotates at a certain speed. So if we plot the magnitudes of the induced e.m.f. against the time, we get an alternating nature of the induced e.m.f. as shown in the Fig Fig.3.7 Alternating nature of the induced e.m.f Mechanical and Electrical Angle We have seen that for 2 pole alternator, one mechanical revolution corresponds to one electrical cycle of an induced e.m.f. Now consider 4 pole alternator i.e. the field winding is designed to produce 4 poles. Due to 4 poles, the magnetic axis exists diagonally shown dotted in the Fig

67 Fig.3.8 Mechanical and Electrical Angle. Now in position 1 of the conductor, the velocity component is parallel to the flux lines while in position 2, there is gathering of flux lines and entire velocity component is perpendicular to the flux lines. So at position 1, the induced e.m.f. in the conductors is zero while at position 2, it is maximum. Similarly as conductor rotates, the induced e.m.f. will be maximum at position 4, 6 and 8 and will be minimum at position 3, 5 and 7. So during one complete revolution of the conductor, induced e.m.f. will experience four times maxima, twice in either direction and four times zero. This is because of the distribution of flux lies due to existence of four poles.so if we plot the nature of the induced e.m.f; for one revolution of the conductor, we get the two electrical cycles of the induced e.m.f., as shown in the Fig. 3.9 Fig.3.9 Mechanical and Electrical Angle. Note : Thus the degrees electrical of the induced e.m.f. i.e. number of cycles of the induced e.m.f. depends on the number of poles of an alternator. So for a four pole alternator we can write, 360 o mechanical = 720 o electrical. From this we can establish the general relation between degrees mechanical and degrees electrical as, 360 o mechanical = 360 o x (p/2) electrical Where P = Number of poles 67

68 3.4.2 Frequency of induced E.M.F. Let, P = Number of poles N = Speed of the rotor in r.p.m f = Frequency of the induced e.m.f. From this discussion above in section 1.1, we can write, One mechanical revolution of rotor = P/2 cycles of e.m.f. electrically. Thus there are P/2 cycles per revolution. As speed is N r.p.m., in one second, rotor will complete (N/60) revolutions. But cycles/sec = frequency = f. Frequency f = (No.of cycles per revolution) x (No.of revolution per second)... f = (P/2) x (N/60) So there exists a fixed relationship between three quantities, the number of poles P, the speed of the rotor N in r.p.m. and f the frequency of an induced e.m.f. in Hz (Hertz). Note : Such a machine bearing a fixed relationship between P, N and f is called synchronous machine and hence alternators are also called synchronous generators Synchronous speed (N s ) From the above expression, it is clear that for fixed number of poles, alternator has to be rotated at a particular speed to keep the frequency of the generated e.m.f. constant at the required value. Such a speed is called synchronous speed of the alternator denoted as N s. Where, f = Required frequency. In our nation, the frequency of an alternating e.m.f. is standard equal to 50 Hz. To get 50 Hz frequency, for different number of poles, alternator must be driven at different speeds called synchronous speeds. Following table gives the values of the synchronous speeds for the alternators having different number of poles. From the table, it can be seen that minimum number of poles for an alternator can be two hence maximum value of synchronous speed possible in our nation i.e. for frequency of 50 Hz is 3000 r.p.m 3.5 E.M.F. Equation of an Alternator Let, Φ = Flux per pole, in Wb P = Number of poles 68

69 N s = Synchronous speed in r.p.m. f = Frequency of induced e.m.f. in Hz Z = Total number of conductors Z ph = Conductors per phase connected in series Z ph = Z/3 as number of phases = 3. Consider a single conductor placed in a slot. The average value of e.m.f. induced in a conductor = dφ/dt. For one revolution of a conductor, e avg per conductor = (Flux cut in one revolution)/(time taken for one revolution) Total flux cut in one revolution is Φ x P Time taken for one revolution is 60/N s seconds. e avg per conductor = ΦP / (60/N s ) = Φ (PN s /60)... (1) But f = PN s /6120 PN s /60 = 2f Substituting in (1), e avg per conductor = 2 f Φ volts Assume full pitch winding for simplicity i.e. this conductor is connected to a conductor which is 180 o electrical apart. So there two e.m.f.s will try to set up a current in the same direction i.e. the two e.m.f. are helping each other and hence resultant e.m.f. per turn will be twice the e.m.f. induced in a conductor.... e.m.f. per turn = 2 x (e.m.f. per conductor) = 2 x (2 f Φ) = 4 f Φ volts Fig.3.10 Single turn in generator. Let T ph be the total number of turn per phase connected in series. Assuming concentrated winding, we can say that all are placed in single slot per pole per phase. So induced e.m.f.s in all turns will be in phase as placed in single slot. Hence net e.m.f. per phase will be algebraic sum of the e.m.f.s per turn.... Average E ph = T ph x (Average e.m.f. per turn)... Average Eph = T ph x 4 f Φ 69

70 But in a.c. circuits R.M.S. value of an alternating quantity is used for the analysis. The form factor is 1.11 of sinusoidal e.m.f. K f = (R.M.S.)/Average = for sinusoidal R.M.S. value of E ph = K x Average value E = 4.44 x f Φ T ph volts... (2) Note : This is the basic e.m.f. equation for an induced e.m.f. per phase for full pitch, concentrated type of winding. Where T ph = Number of turns per phase. T ph = Z ph /2... as 2 conductors constitute 1 turn But as mentioned earlier, the winding used for the alternators is distributed and short pitch hence e.m.f. induced slightly gets affected. Let us see now the effect of distributed and short pitch type of winding on the e.m.f. equation Pitch Factor or Coil Span Factor (Kc) In practice short pitch coils are preferred. So coil is form by connecting one coil side to another which is less than one pole pitch away. So actual span is less than 180 o. The coil is generally shorted by one or two slots. Note : The angle by which coil are short pitched is called angle or short pitched is called angle of short pitch denoted as 'α'. Where α is the angle by which coils are short pitched. As coils are shorted in terms of number of slots i.e. either by one slot, two slots and so on and slot angle is β then angle of short pitch is always a multiple of the slot angle β. Fig.3.11 Short pitched coil.... α = β x Number of slots by which coils are short pitched. Or α = 180 o -Actual coil span of the coils. This is shown in the Fig Now let E be the induced e.m.f. in each coil side. If coil is full pitch coil, the induced e.m.f. in each coil side help each other. Coil connections are such that both will try to set up a current in the same direction in the external circuit. Hence the resultant e.m.f. across a coil will be algebraic sum of the two.... E R = E + E = 2E... for full pitch 70

71 Fig.3.12 Full pitched coil. Now the coil is short pitched by angle 'α', the two e.m.f. in two coil sides no longer remains in phase from external circuit point of view. Hence the resultant e.m.f. is also no longer remains algebraic sum of the two but becomes a phasor sum of the two as shown in the Fig. 3. Fig.3.13Phasor sum of two emfs. Obviously E R in such a case will be less than what it is in case of full pitch coil. From the geometry of the Fig. 3, we can write, AC is perpendicular drawn on OB bisecting OB.... l (OC) = l (CB) = E R /2 BOA = α/2... cos (α/2) = OC/OA = E R /2E... E R = 2 E cos (α/2)... For short pitch This is the resultant e.m.f. in case of a short pitch coil which depends on the angle of short pitch 'α'. Note : Now the factor by which, induced e.m.f. gets reduced due to short pitching is called pitch factor or coil span factor denoted by K c. It is defined as the ratio of resultant e.m.f. when coil is short pitch to the resultant e.m.f. when coil is full pitched. It is always less than one. Where α = Angle of short pitch Distribution Factor (Kd) 71

72 Similar to full pitch coils, concentrated winding is also rare in practice. Attempt is made to use all the slots available under a pole for the winding which makes the nature of the induced e.m.f. more sinusoidal. Such a winding is called distributed winding. Consider 18 slots, 2 pole alternator. So slots per pole i.e. n = 9. m = Slots per pole per phase = 3 β = 180 o /9 = 20 o Let E = Induced e.m.f. per coil and there are 3 coils per phase. In concentrated type all the coil sides will be placed in one slot under a pole. So induced e.m.f. in all the coils will achieve maxima and minima at the same time i.e. all of them will be in phase. Hence resultant e.m.f. after connecting coils in series will be algebraic sum of all the e.m.f.s. as all are in phase. As against this, in distributed type, coil sides will be distributed, one each in the 3 slots per phase available under a pole as shown in the Fig. 3.14(a). Fig.3.14 Distributed and Phase difference betweeninduced emf. Thought the magnitude of e.m.f. in each coil will be same as 'E', as each slot contributes phase difference of β o i.e. 20 o in this case, there will exist a phase difference of β o with respect to each other as shown in the Fig. 1(b). Hence resultant e.m.f. will be phasor sum of all of them as shown in the the Fig. 2. So due to distributed winding resultant e.m.f. decreases. Fig.3.14 Phase sum of induced emf Note : The factor by which there is a reduction in the e.m.f. due to distribution of coils is called distribution factor denoted as K d. Let us see the derivation for its expression. In general let there be 'n' slots per pole and 'm' slots per pole per phase. So there will be 'm' coils distributed under a pole per phase, connected in series. Let E be the induced e.m.f. per coil. Then all the 'm' e.m.f.s induced in the coils will have successive phase angle difference of β = 180 o /n. While finding out the phasor sum of all of them, phasor diagram will approach a shape of a 'm' equal sided polygon circumscribed by a semicircle of radius 'R'.This is shown in the Fig AB, BC, CD etc, represents e.m.f. per coil. All the ends joined at 'O' which is center of the circumscribing semicircle of raduis 'R'. 72

73 Fig Phasor sum of 'm' e.m.f.s Angle subtended by each phasor at the origin 'O' is β o. This can be proved as below. All the triangles OAB, OBC... are similar and isosceles, as AB = BC = CD =... = E. Comparing (3) and (4), y = β OAB = OBA = OBC =... = x AOB = BOC =... = y say Now in OAB, 2x + y = 180 while OBA + OBC + β = 180 o... (3) i.e. 2x + β = 180 o So AOB = BOC = COD =... = β If 'M' is the last point of the last phasor, AOM = m x β = mβ and AM = E R = Resultant of all the e.m.f.s. Consider a OAB separately as shown in the Fig. 4. Let OF be the perpendicular drawn on AB bisecting angle at apex 'O' as β/2. Fig. 3.16angle of OAB 73

74 l (AB) = E l (AF) = E/2 and l (OA) = R... sin (β/2) = AF/OA = (E/2)/R... E = 2R sin (β/2)... (5) Now consider OAM as shown in the Fig.. 3 and OG is the perpendicular drawn from 'O' on its base bisecting OAM.... AOG = GOM = (mβ)/2... l (AM) = E... l (AG) = E/2 = 2 (OA) sin (mβ/2) Arithmetic sum of e.m.f.s = Arc AB = OA x (mβ) Note : The angle (mβ/2) in the denominator must be in radians. The above formula is used to calculate distribution factor when phase spread is and the winding is uniformly distributed Generalized Expression for E.M.F. Equation of an Alternator Considering full pitch, concentrated winding. E ph = 4.44 f Φ T ph Volts. Generalized expression for e.m.f. equation can be written as For full pitch coil, K c = 1. For concentrated winding K d = 1. Note : For short pitch and distributed winding K c and K d are always less than unity. Example 1 : An armature of a three phase alternators has 120 slots. The alternator has 8 poles. Calculate its distribution factor. Solution : n = Slots/Pole = 120/8 = 15 m = slots/pole/phase = n/3 = 15/3 = 5 74

75 β = 180 o /n = 180 o /5 = 12 o = Example 2: In a 4 pole, 3 phase alternator, armature has 36 slots. It is using an armature winding which is short pitched by one slot. Calculate its coil span factor. Solution : n = Slots/pole = 36/4 = 9 β = 180 o / = 20 o Now coil is shorted by 1 slot i.e. by 20 o to full pitch distance.... α = Angle of short pitch = 20 o... K c = cos (α/2) = cos (10) = Line Value of Induced E.M.F If the armature winding of three phase alternator is start connected, then the value of induced e.m.f. across the terminals is 3E ph where E ph is induced e.m.f. per phase.while if it is delta connected line value of e.m.f. is same as E ph.this is shown in the Fig. 3.17(a) and (b). Fig Line value of induced emf with different connections Practically most of the alternators are star connected due to following reasons: 1. Neutral point can be earthed from safety point of view. 2. For the same phase voltage, available across the terminal is more than delta connection. 3. For the same terminal voltage, the phase voltage in star is 1/ 3 times line value. This reduces strains on the insulation of the armature winding. Example 3 : An alternator runs at 250 r.p.m. and generates an e.m.f. at 50 Hz. There are 216 slots each containing 5 conductors. The winding is distributed and full pitch. All the conductors of each phase are in series and flux per pole is 30 mwb which is sinusoidally 75

76 distributed. If the winding is star connected, determine the value of induced e.m.f. available across the terminals. Solution : N s = 250 r.p.m., f = 50 Hz N s = 120f/P = (120 x 50)/P... P = n = Slots/Pole = 216/24 = 9... m = n/3 = 3 β = 180 o /9 = 20 o = K c = 1 as full pitch coils. Total no. of conductors Z = 216 x 5 = Z ph = Z/3 = 1080/3 = 360 T ph = Z ph / conductors 1 turn = 360/2 = E ph = 4.44 K c K d f Φ T ph. = 4.44 x 1 x x 30 x 10-3 x 50 x 180 = V E line = 3 E ph... star connection = 3 x = V. Example 4 : A 3 phase, 16 pole, star connected alternators has 144 slots on the armature periphery. Each slot contains 10 conductors. It is driven at 375 r.p.m. The line value of e.m.f. available across the terminals is observed to be kv. Find the frequency of the induced e.m.f. and flux per pole. Solution : P = 16, N s = 375 r.p.m. Slots = 144, Conductors / slots = 10 E line = kv Ns = 120f/P = (120 x f)/16... f = 50 Hz Assuming full pitch winding, K c = 1... n = Slots/pole = 144/16 = 9... m = n/3 = 3 76

77 ... β = 180 o /9 = 20 o = Total conductors = Slots x condutors/slot i.e. Z = 144 x 10 = Z ph = Z/3 = 1440/3 = 480 T ph = Z ph /2 = 480/2 = 240 E ph = E line / 3 = 2.657/ 3 = kv Now E ph = 4.44 K c K d f Φ T ph x 10-3 = 4.44 x 1 x x Φ x 50 x Φ = 0.03 Wb = 30 mwb 3.6 Armature Reaction When the load is connected to the alternator, the armature winding of the alternator carries a current. Every current carrying conductor produces its own flux so armature of the alternator also produces its own flux, when carrying a current. So there are two fluxes present in the air gap, one due to armature current while second is produced by the filed winding called main flux. The flux produced by the armature is called armature flux. Note : So effect of the armature flux on the main flux affecting its value and the distribution is called armature reaction. The effect of the armature flux not only depends on the magnitude of the current flowing through the armature winding but also depends on the nature of the power factor of the load connected to the alternator.now we will study the effect of nature of the load power factor on the armature reaction Unity Power Factor Load Consider a purely resistive load connected to the alternator, having unity power factor. As induced e.m.f. E ph drives a current of I aph and load power factor is unity, E ph and I ph are in phase with each other. If Φ f is the main flux produced by the field winding responsible for producing E ph then E ph lags Φ f by 90 o.now current through armature I a, produces the armature flux say Φ a. So flux Φ a and I a are always in the same direction.this relation between Fig Armature reaction for unity power factor 77

78 It can be seen from the phasor diagram that there exists a phase difference of 90 o between the armature flux and the main flux. The waveforms for the two fluxes are also shown in the Fig From the waveforms it can be seen that the two fluxes oppose each other on the left half of each pole while assist each other on the right half of each pole. Hence average flux in the air gap remains constant but its distribution gets distrorted. Note : Hence such distorting effect of armature reaction under unity p.f. condition of the load is called cross magnetising effect of armature reaction.due to such distortion of the flux, there is small drop in the terminal voltage of the alternator Zero Lagging Power Factor Load Consider a purely inductive load connected to the alternator having zero lagging power factor. This indicates that I aph driven by E ph lags E ph by 90 o which is the power factor angle Φ.Induced e.m.f. E ph lags main flux Φ f by 90 o while Φ a is in the same direction as that of I a. So the phasor diagram and the waveforms are shown in the Fig It can be seen from the phasor diagram that the armature flux and the main flux are exactly in opposite direction to each other. Note : So armature flux tries to cancel the main flux. Such an effect of armature reaction is called demagnetising effect of the armature reaction.as this effect causes reduction in the main flux, the terminal voltage drops. This drop in the terminal voltage is more than the drop corresponding to the unity p.f. load. Fig Armature reaction for zero lagging p.f. load Zero Leading Power Factor Load Consider a purely capacitive load connected to the alternator having zero leading power factor. This means that armature current I aph driven by E ph, leads E ph by 90 o, which is the power factor angle Φ. Induced e.m.f. E ph lags Φ f by 90 o while I aph and Φ a are always in the same direction. The phasor diagram and the waveforms are shown in the Fig Fig Armature reaction for zero leading p.f. load 78

79 It can be seen from the phasor diagram and waveforms shown in the Fig. 2, the armature flux and the main field flux are in the same direction i.e. they are helping each other. This results into the addition in main flux. Note : Such an effect of armature reaction due to which armature flux assists field flux is called magnetising effect of the armature reaction.as this effect adds the flux to the main flux, greater e.m.f. gets induced in the armature. Hence there is increase in the terminal voltage for leading power factor loads. For intermediate power factor loads i.e. between zero lagging and zero leading the armature reaction is partly cross magnetising and partly demagnetising for lagging power factor loads or partly magnetising for leading power factor loads Armature Reaction Reactance (X ar ) In all the conditions of the load power factors, there is change in the terminal voltage due to the armature reaction. Mainly the practical loads are inductive in nature, due to demagnetising effect of armature reaction, there is reduction in the terminal voltage. Now this drop in the voltage due to the interaction of armature and main flux. This drop is not across any physical element.but to quantify the voltage drop due to the armature reaction, armature winding is assumed to have a fictitious reactance. This fictitious reactance of the armature is called armature reaction reactance denoted as X ar Ω/ph. And the drop due to armature reaction can be accounted as the voltage drop across this reactance as I ar X ar. Note : The value of this reactance changes as the load power factor changes, as armature reaction depends on the load power factor. 3.7 Concepts of Synchronous Reactance and Impedance The sum of fictitious armature reaction reactance accounted for considering armature reaction effect and the leakage reactance of the armature called synchronous reactance of the alternator demoted as X s. So X s = X L + X ar Ω/ph As both X L and X ar are ohmic values per phase, synchronous reactance is also specified as ohms per phase.now from this, it is possible to define an impedance of the armature winding. Such an impedance obtained by combining per phase values of synchronous reactance and armature resistance is called synchronous impedance of the alternator denoted as Z s. So Z s = R a + j X s Ω/ph Z s = (R a 2 + j (Xs) 2 For getting a standard frequency, alternator is to be driven at synchronous speed. So word synchronous used in specifying the reactance and impedance is referred to the working speed of the alternator. Generally impedance of the winding is constant but in case of alternator, synchronous reactance depends on the load and its power factor condition, hence synchronous impedance also varies with the load and its power factor conditions. 3.8 Voltage Regulation of an Alternator Under the load condition, the terminal voltage of alternator is less than the induced e.m.f. E ph. So if load is disconnected, V ph will change from V ph to E ph, if flux and speed is maintained constant. This is because when load is disconnected, I a is zero hence there are no 79

80 voltage drops and no armature flux to cause armature reaction. This change in the terminal voltage is significant in defining the voltage regulation. Note : The voltage regulation of an alternator is defined as the change in its terminal voltage when full load is removed, keeping field excitation and speed constant, divided by the rated terminal voltage., So if, V ph = Rated terminal voltage E ph = No load induced e.m.f. the voltage regulation is defined as, The value of the regulation not only depends on the load current but also on the power factor of the load. For lagging and unity p.f. conditions there is always drop in the terminal voltage hence regulation values are always positive. While for leading capacitive load conditions, the terminal voltage increases as load current increases. Hence regulation is negative in such cases. The relationship between load current and the terminal voltage is called load characteristics of an alternator. Such load characteristics for various load power factor conditions are shown in Fig Fig Load characteristics of an alternator KVA Rating of an Alternator The alternators are designed to supply a specific voltage to the various loads. This voltage is called its rated terminal voltage denoted as V L. The power drawn by the load depends on its power factor. Hence instead of specifying rating of an alternator in watts, it is specified in terms of the maximum apparent power which it can supply to the load. In three phase circuits, the apparent power is 3V L I L, measured in VA (volt amperes). This is generally expressed in kilo volt amperes and is called kva rating of an alternator where I L is the rated full load current which alternator can supply. So for a given rated voltage and kva rating of an alternator, its full load rated current can be decided. Consider 60 kva, 11 kv three phase alternator, In this case kva rating = to express the product in kilo volt amperes = 3 x 11 x 10 3 x I L x I L = 3.15 A 80

81 This is the rated full load current of an alternator. But load current is same as the armature current. So from kva rating, it is possible to determine full load armature current of an alternator which is important in predicating the full load regulation of an alternator for various power factor conditions. Similarly if load condition is different than the full load, the corresponding armature current can be determined from its full load value. Note : I a at half load = 1/2 x I a at full load. It reduces in the same proportion in which load condition reduces.hence regulation at any p.f. and at any load condition can be determined Regulation of Synchronous Generator The regulation of an alternator can be determined by various methods. In case of small capacity alternators it can be determined by direct loading test while for large capacity alternators it can be determined by synchronous impedance method.the synchronous impedance method has some short comings. Another method which is popularly used is ampere-turns method. But this method also has certain disadvantages. The disadvantages of these two methods are overcome in a method called zero power factor method. Another important theory which gives accurate results is called Blondel's two reaction theory. Thus there are following methods available to determine the voltage regulation of an alternator, 1. Direct loading method 2. Synchronous impedance method or E.M.F. method 3. Ampere-turns method or M.M.F. method 4. Zero power factor method or potier triangle method 5. ASA modified from of M.M.F. method 6. Two reaction theory a. Voltage Regulation by Direct Load The Fig shows the circuit diagram for conducting the direct loading test on the three phase alternator. The star connected armature is to be connected to a three phase load with the help of triple pole single throw (TPST) switch. The field winding is excited by separate d.c. supply. To control the flux i.e. the current through field winding, a rheostat is inserted in series with the field winding. The prime mover is shown which is driving the alternator at its synchronous speed. Procedure : The alternator is first driven at its synchronous speed N s by means of a prime mover. Now E ph α Φ... (From e.m.f. equation) By giving d.c. supply to the field winding, the field current is adjusted to adjust the flux so that rated voltage is available across the terminals. This can be observed on the voltmeter connected across the lines. The load is then connected by means of a TPST switch. The load is then increased so that ammeter reads rated value of current. This is full load condition of the alternator. Again adjust the voltage to its rated value by means of field excitation using a rheostat connected. The throw off the entire load by opening the TPST switch, without changing the speed and the field excitation. Observe the voltmeter reading. As load is thrown off, there is no armature current and associated drops. So the voltmeter reading in this situation indicates the value of internally induced e.m.f. called no load terminal voltage. 81

82 Fig Circuit diagram for direct loading test on alternator Convert both the reading to phase values. The rated voltage on full load is V ph while reading when load is thrown off is E ph. So by using the formula,the full load regulation of the alternator can be determined. The value of the regulation obtained by this method is accurate as a particular load at required p.f. is actually connected to the alternator to note down the readings. Note : But for high capacity alternators, that much full load cannot be simulated or directly connected to the alternator. Hence method is restricted only for small capacity alternators. Example: While supplying a full load, running at synchronous speed, the terminal voltage of an alternator is observed to be 1100 V. When the load is thrown off, keeping field excitation and speed constant, the terminal voltage is observed to be 1266 V. Assuming star connected alternator, calculate its regulation on full load. Solution : On full load, terminal voltage is 1100 V. So V L = 1100 V... V ph = V L / 3 = V When load is thrown off, V L = 1266 V. But on no load, V L = E line... E line = 1266 V... E ph = 1266/ 3 = V b. Synchronous Impedance Method or E.M.F. Method 82

83 The method is also called E.M.F. method of determining the regulation. The method requires following data to calculate the regulation. 1. The armature resistance per phase (R a ). 2. Open circuit characteristics which is the graph of open circuit voltage against the fieldcurrent.this is possible by conducting open circuit test on the alternator. 3. Short circuit characteristics which is the graph of short circuit current against field current.thisis possible by conducting short circuit test on the alternator. Let us see, the circuit diagram to perform open circuit as well as short circuit test on the alternator. The alternator is coupled to a prime mover capable of driving the alternator at its synchronous speed. The armature is connected to the terminals of a switch. The other terminals of the switch are short circuited through an ammeter. The voltmeter is connected across the lines to measure the open circuit voltage of the alternator.the field winding is connected to a suitable d.c. supply with rheostat connected in series. The field excitation i.e. field current can be varied with the help of this rheostat. The circuit diagram is shown in the Fig Fig Circuit diagram for open circuit and short circuit test on alternator Open Circuit Test: Procedure to conduct this test is as follows: i) Start the prime mover and adjust the speed to the synchronous speed of the alternator. ii) Keeping rheostat in the field circuit maximum, switch on the d.c. supply. iii) T.P.S.T switch in the armature circuit is kept open iv) With the help of rheostat, field current is varied from its minimum value to the rated value. Due to this, flux increasing the induced e.m.f. Hence voltmeter reading, which is measuring line value of open circuit voltage increases. For various values of field current, voltmeter readings are observed. The observation for open circuit test are tabulated as below. Observation table for open circuit test : 83

84 From the above table, graph of (V oc ) ph against I f is plotted. Note: This is called open circuit characteristics of the alternator, called O.C.C. This is shown in the Fig Fig O.C.C. and S.C.C. of an alternator Short Circuit Test After completing the open circuit test observation, the field rheostat is brought to maximum position, reducing field current to a minimum value. The T.P.S.T switch is closed. As ammeter has negligible resistance, the armature gets short circuited. Then the field excitation is gradually increased till full load current is obtained through armature winding. This can be observed on the ammeter connected in the armature circuit. The graph of short circuit armature current against field current is plotted from the observation table of short circuit test. This graph is called short circuit characteristics, S.C.C. This is also shown in the Fig Observation table for short circuit test : The S.C.C. is a straight line graph passing through the origin while O.C.C. resembles B-H curve of a magnetic material. 84

85 Note : As S.C.C. is straight line graph, only one reading corresponding to full load armature current along with the origin is sufficient to draw the straight line. The synchronous impedance of the alternator changes as load condition changes. O.C.C. and S.C.C. can be used to determine Z s for any load and load p.f. conditions.in short circuit test, external load impedance is zero. The short circuit armature current is circulated against the impedance of the armature winding which is Z s. The voltage responsible for driving this short circuit current is internally induced e.m.f. This can be shown in the equivalent circuit drawn in the Fig. 3. Fig Equivalent circuit on short circuit From the equivalent circuit we can write, Z s = E ph / I asc. Now value of I asc is known, which can be observed on the alternator. But internally induced e.m.f. cannot be observed under short circuit condition. The voltmeter connected will read zero which is voltage across short circuit. To determine Z s it is necessary to determine value of E which is driving I asc against Z s. Now internally induced e.m.f. is proportional to the flux i.e. field current I f. equation E ph α Φ α I f... from e.m.f. So if the terminal of the alternator is opened without disturbing I f which was present at the time of short circuited condition, internally induced e.m.f. will remain same as E ph. But now current will be zero. Under this condition equivalent circuit will become as shown in the Fig Fig.3.26 Equivalent circuit It is clear now from the equivalent circuit that as I a = 0 the voltmeter reading (V oc ) ph will be equal to internally induced e.m.f. (E ph ). This is what we are interested in obtaining to calculate value of Z s. So expression for Z s can be modified as, 85

86 So O.C.C. and S.C.C. can be effectively to calculate Z s. The value of Z s is different for different values of I f as the graph of O.C.C. is non linear in nature.so suppose Z s at full load is required then, I asc = full load current. From S.C.C. determine I f required to drive this full load short circuit I a. This is equal to 'OA', as shown in the Fig.2.Now for this value of I f, (V oc ) ph can be obtained from O.C.C. Extend kine from point A, till it meets O.C.C. at point C. The corresponding (V oc ) ph value is available at point D. (V oc ) ph = OD While (I asc ) ph = OE General steps to determine Z s at any load condition are : i) Determine the value of (I asc ) ph for corresponding load condition. This can be determined from known full load current of the alternator. For half load, it is half of the full load value and so on. ii) S.C.C. gives relation between (I asc ) ph and I f. So for (I asc ) ph required, determine the corresponding value of I f from S.C.C. iii) Now for this same value of I f, extend the line on O.C.C. to get the value of (V oc ) ph. This is (V oc ) ph for same I f, required to drive the selected (I asc ) ph. iv) The ratio of (V oc ) ph and (I asc ) ph, for the same excitation gives the value of Z s at any load conditions.the graph of synchronous impedance against excitation current is also shown in the Fig. 2. Regulation Calculations From O.C.C. and S.C.C., Z s can be determined for any load condition. The armature resistance per phase (R a ) can be measured by different methods. One of the method is applying d.c. known voltage across the two terminals and measuring current. So value of R a per phase is known. So synchronous reactance per phase can be determined.no load induced e.m.f. per phase, E ph can be determined by the mathematical expression derived earlier where V ph = Phase value of rated voltage I a = Phase value of current depending on the load condition cosφ = p.f. of load Positive sign for lagging power factor while negative sign for leading power factor, R a and X s values are known from the various tests performed.the regulation then can be determined by using formula, Advantages and Limitations of Synchronous Impedance Method 86

87 The main advantages of this method is the value of synchronous impedance Z s for any load condition can be calculated. Hence regulation of the alternator at any load condition and load power factor can be determined. Actual load need not be connected to the alternator and hence method can be used for very high capacity alternators. The main limitation of this method is that the method gives large values of synchronous reactance. This leads to high values of percentage regulation than the actual results. Hence this method is called pessimistic method. c. M.M.F. Method of Determining Regulation This method of determining the regulation of an alternator is also called Ampere-turn method or Rothert's M.M.F. method. The method is based on the results of open circuit test and short circuit test on an alternator.for any synchronous generator i.e. alternator, it requires m.m.f. which is product of field current and turns of field winding for two separate purposes. 1. It must have an m.m.f. necessary to induce the rated terminal voltage on open circuit. 2. It must have an m.m.f. equal and opposite to that of armature reaction m.m.f. Note : In most of the cases as number of turns on the field winding is not known, the m.m.f. is calculate and expressed i terms of the field current itself. The field m.m.f. required to induce the rated terminal voltage on open circuit can be obtained from open circuit test results and open circuit characteristics. This is denoted as F O.We know that the synchronous impedance has two components, armature resistance and synchronous reactance. Now synchronous reactance also has two components, armature leakage reactance and armature reaction reactance. In short circuit test, field m.m.f. is necessary to overcome drop across armature resistance and leakage reactance and also to overcome effect of armature reaction. But drop across armature resistance and also to overcome effect of armature reaction. But drop across armature resistance and leakage reactance is very small and can be neglected. Thus in short circuit test, field m.m.f. circulates the full load current balancing the armature reaction effect. The value of ampere-turns required to circulate full load current can be obtained from short circuit characteristics. This is denoted as F AR.Under short circuit condition as resistance and leakage reactance of armature do not play any significant role, the armature reaction reactance is dominating and hence the power factor of such purely reactive circuit is zero lagging. Hence F AR gives demagnitising ampere turns. Thus the field m.m.f. is entirely used to overcome the armature reaction which is wholly demagntising in nature.the two components of total field m.m.f. which are F O and F AR are indicated in O.C.C. (open circuit characteristics) and S.C.C. (short circuit characteristics) as shown in the Fig If the alternator is supplying full load, then total field m.m.f. is the vector sum of its two components F O and F AR. This depends on the power factor of the load which alternator is supplying. The resultant field m.m.f. is denoted as F R. Let us consider the various power factors and the resultant F R. 87

88 Fig.3.27 O.C.C and S.C.C Zero lagging p.f. : As long as power factor is zero lagging, the armature reaction is completely demagnetising. Hence the resultant F R is the algebraic sum of the two components F O and F AR. Field m.m.f. is not only required to produce rated terminal voltage but also required to overcome completely demagnetising armature reaction effect. This is shown in the Fig Fig phasor diagram OA = F O AB = F AR demagnetizing OB = F R = F O + F AR Total field m.m.f. is greater than F O. Zero leading p.f When the power factor is zero leading then the armature reaction is totally magnetising and helps main flux to induce rated terminal voltage. Hence net field m.m.f. required is less than that required to induce rated voltage normally, as part of its function is done by magnetising armature reaction component. The net field m.m.f. is the algebraic difference between the two components F O and F AR. This is shown in the Fig OA = F O Fig AB = F AR magnetizing OB = F O - F AR = F R Total m.m.f. is less than F O Unity p.f 88

89 Under unity power factor condition, the armature reaction is cross magnetising and its effect is to distort the main flux. Thus and F are at right angles to each other and hence resultant m.m.f. is the vector sum of F O and F AR. This is shown in the Fig OA = F O Fig AB = F AR cross magnetizing General Case Now consider that the load power factor is cos Φ. In such case, the resultant m.m.f. is to be determined by vector addition of F O and F AR.cosΦ, lagging p.f. : When the load p.f. is cosφ lagging, the phase current I aph lags V ph by angle Φ. The component F O is at right angles to V ph while F AR is in phase with the current I aph. This is because the armature current I aph decides the armature reaction. The armature reaction F AR due to current I aph is to be overcome by field m.m.f. Hence while Finding resultant field m.m.f., - F AR should be added to vectorially. This is because resultant field m.m.f. tries to counterbalance armature reaction to produce rated terminal voltage. The phasor diagram is shown in the Fig From the phasor diagram the various magnitude are, OA = F O, AB = F AR, OB = F R Fig phasor diagram Consider triangle OCB which is right angle triangle. The F AR is split into two parts as, AC = F AR sinφ and BC = F AR cosφ... ( F R ) 2 = (F O + F AR sinφ ) 2 + (F AR cosφ) 2... (1) From this relation (1), F R can be determined. leading p.f When the load p.f. is cosφ leading, the phase current I aph leads V ph by Φ. The component F O is at right angles to V ph and F AR is in phase with I aph. The resultant F R can be obtained by adding - F AR to F O. The phasor diagram is shown in the Fig

90 Fig.3.32 phasor Diagram From the phasor diagram, various magnitudes are, AC = F AR sinφ and BC = F AR cosφ OA = F O, AB = F AR and OB = F R Consider triangle OCB which is right angles triangle.... (OB) 2 = (OC) 2 + (BC) 2... ( F R ) 2 = (F O - F AR sinφ ) 2 + (F AR cosφ)... (2) Fig 3.33 Various Values of F O, F AR and F O From the relation (2), F R can be obtained. Using relations (1) and (2), resultant field m.m.f. F R for any p.f. load condition can be obtained.once F R is known, obtain corresponding voltage which is induced e.m.f. E ph, required to get rated terminal voltage V ph. This is possible from open circuit characteristics drawn. Once E ph is known then the regulation can be obtained as, Note : To obtain E ph corresponding to F R, O.C.C. must be drawn to the scale, from the open circuit test readings. This ampere-turn method gives the regulation of an alternator which is lower than the actually observed. Hence the method is called optimistic method. When the armature resistance is neglected then F O is field m.m.f. required to produce rated V ph at the output terminals. But if the effective armature resistance is given then F O is to be calculated from O.C.C. such that F O represents the excitation (field current) required a voltage of V ph + I aph R aph cosφ where 90

91 V ph = rated voltage per phase I aph = full load current per phase R a = armature resistance per phase cosφ = power factor of the load It can also be noted that, F R can be obtained using the cosine rule to the triangle formed by F O, F AR and F O as shown in the Fig Fig 3.34 Various Values of Cos Φ leading and lagging Using cosine rule to triangle OAB, Students can use equations 1, 2 or 3 to calculate F R. The angle between E o and V ph is denoted as δ and is called power angle. Neglecting R a. We can write, I a X s cosφ = E o sinδ P d = V ph I a cosφ = internal power of machine Note: This equation shows that the internal power of the machine is proportional to sin δ. d. Zero Power Factor (ZPF) Method This method is also called potier method. In the operation of any alternator, the armature resistance drop and armature leakage reactance drop IX L are actually e.m.f. quantities while the armature reaction is basically m.m.f. quantity. In the synchronous impedance all the quantities are treated as e.m.f. quantities as against this in M.M.F. method all are treated as m.m.f. quantities. Hence in both the methods, we are away from reality. Note : This method is based on the separation of armature leakage reactance and armature reaction effects. The armature leakage reactance X L is called Potier reactance in this method, hence method is also called potier reactance method.to determine armature leakage reactance and armature reaction m.m.f. separately, two tests are performed on the given alternator. The two tests are, 1. Open circuit test 2. Zero power factor test Open Circuit Test The experimental setup to perform this test is shown in the Fig

92 Fig 3.35 Experimental setup for Open Circuit Test The steps to perform open circuit test are, 1. The switch S is kept open. 2. The alternator is driven by its prime mover at its synchronous speed and same is maintained constant throughout the test. 3. The excitation is varied with the help of potential divider, from zero upto rated value in definite number of steps. The open circuit e.m.f. is measured with the help of voltmeter. The readings are tabulated. 4. A graph of I f and (V oc ) i.e. field current and open circuit voltage per phase is plotted to some scale. This is open circuit characteristics. Zero Power Factor Test To conduct zero power factor test, the switch S is kept closed. Due to this, a purely inductive load gets connected to an alternator through an ammeter. A purely inductive load has power factor of cos i.e. zero lagging hence the test is called zero power factor test.the machine speed is maintained constant at its synchronous value. The load current delivered by an alternator to purely inductive load is maintained constant at its rated full load value by varying excitation and by adjusting variable inductance of the inductive load. Note that, due to purely inductive load, an alternator will always operate at zero p.f. lagging. Note : In this test, there is no need to obtain number of points to obtain the curve. Only two points are enough to construct a curve called zero power factor saturation curve.this is the graph of terminal voltage against excitation when delivering full load zero power factor current. One point for this curve is zero terminal voltage (short circuit condition) and the field current required to deliver full load short circuit armature current. While other point is the field current required to obtain rated terminal voltage while delivering rated full load armature current. With the help of these two points the zero p.f. saturation curve can be obtained as, Fig 3.36 open circuit characteristics 92

93 1. Plot open circuit characteristics on graph as shown in the Fig Plot the excitation corresponding to zero terminal voltage i.e. short circuit full load zero p.f. armature current. This point is shown as A in the Fig. 1 which is on the x-axis. Another point is the rated voltage when alternator is delivering full load current at zero p.f. lagging. This point is P as shown in the Fig Draw the tangent to O.C.C. through origin which is line OB as shown dotted in the Fig. 1. This is called air line. 4. Draw the horizontal line PQ parallel and equal to OA. 5. From point Q draw the line parallel to the air line which intersects O.C.C. at point R. Join RQ and join PR. The triangle PQR is called potier triangle. 6. From point R, drop a perpendicular on PQ to meet at point S. 7. The zero p.f. full load saturation curve is now be constructed by moving a triangle PQR so that R remains always on O.C.C. and line PQ always remains horizontal. The doted triangle is shown in the Fig. 1. It must be noted that the potier triangle once obtained is constant for a given armature current and hence can be transferred as it is. 8. Through point A, draw line parallel to PR meeting O.C.C. at point B. From B, draw perpendicular on OA to meet it at point C. Triangles OAB and PQR are similar triangles. 9. The perpendicular RS gives the voltage drop due to the armature leakage reactance i.e. IX L. 10.The length PS gives field current necessary to overcome demagnetising effect of armature reaction at full load. 11. The length SQ represents field current required to induce an e.m.f. for balancing leakage reactance drop RS. These values can be obtained from any Potier triangle such as OAB, PQR and so on. So armature leakage reactance can be obtained as, This is nothing but the potier reactance. Use of Potier Reactance to Determine Regulation To determine regulation using Potier reactance, draw the phasor diagram using following procedure :Draw the rated terminal voltage V ph as a reference phasor. Depending upon at which power factor (cosφ) the regulation is to be predicted, draw the Current phasor I ph lagging or leading V ph by angle Φ.Draw I ph R aph voltage drop to V ph which is in phase with I ph. While the voltage drop I ph X Lph is to be drawn perpendicular to I ph R aph vector but leading I ph R aph at the extremely of V ph.the R aph is to be measured separately by passing a d.c. current and measuring voltage across armature winding. While X Lph is Potier reactance obtained by Potier method.phasor sum of V ph rated, I ph R aph and I ph X Lph gives the e.m.f. which is say E 1ph. 93

94 Fig 3.36 The complete phasor diagram Obtain the excitation corresponding to Ē 1ph from O.C.C. drawn. Let this excitation be F f1. This is excitation required to induce e.m.f. which does not consider the effect of armature reaction.the field current required to balance armature reaction can be obtained from Potier triangle, which is say F AR.... F AR = l (PS) = l (AC) =... The total excitation required is the vector sum of the F f1 and F AR. This can be obtained exactly similar to the procedure used in M.M.F. method.draw vector F f1 to some scale, leading E 1ph by 90 o. Add F AR to F f1 by drawing vector F AR in phase opposition to I ph. The total excitation to be supplied by field is given by F R.The complete phasor diagram is shown in the Fig. 3. Once the total excitation is known which is F R, the corresponding induced e.m.f. E ph can be obtained from O.C.C. This E ph lags F R by 90 o. The length CD represents voltage drop due to the armature reaction. Drawing perpendicular from A and B on current phasor meeting at points G and H respectively, we get triangle OHC as right angle triangle. Hence E 1ph can be determined analytically also.once E ph is known, the regulation of an alternator can be predicted as, This method takes into consideration the armature resistance an leakage reactance voltage drops as e.m.f. quantities and the effect of armature reaction as m.m.f. quantity. This is reality hence the results obtained by this method are nearer to the reality than those obtained by synchronous impedance method and ampere-turns method.the only drawback of this method is that the separate curve for every load condition is necessary to plot if potier triangles for various load conditions are required. 3.9 BLONDEL'S TWO REACTION THEORY (THEORY OF SALIENT POLE MACHINE) It is known that in case of nonsalient pole type alternators the air gap is uniform. Due to uniform air gap, the field flux as well as armature flux very sinusoidally in the air gap. In nonsalient rotor alternators, air gap length is constant and reactance is also constant. Due to this the m.m.f.s of armature and field act upon the same magnetic circuit all the time hence can be added vectorially. But in salient pole type alternators the length of the air gap varies and the reluctance also varies. Hence the armature flux and field flux cannot vary sinusoidally in the air gap. The reluctances of the magnetic circuits on which m.m.fs act are different in case of salient pole alternators.hence the armature and field m.m.f.s cannot be treated in a simple way as they can be in a nonsalient pole alternators.the theory which gives the method of analysis of the distributing effects caused by salient pole construction is called two reaction theory. Professor Andre Blondel has put forward the two reaction theory. Note : According to this theory the armature m.m.f. can be divided into two components as, 1. Components acting along the pole axis called direct axis 2. Component acting at right angles to the pole axis called quadrature axis. The component acting along direct axis can be magnetising or demagnetising. The component acting along quadrature axis is cross magnetising. These components produces the effects of different kinds. The Fig shows the stator m.m.f. wave and the flux distribution in the air gap along direct axis and quadrature axis of the pole. The relucatnce offered to the m.m.f. wave is 94

95 lowest when it is aligned with the field pole axis. This axis is called direct axis of pole i.e. d- axis. The relucatnce offered is highest when the m.m.f. wave is oriented at 90 to the field pole axis which is called quadrature axis i.e. q-axis. The air gap is least in the centre of the poles and progressively increases on moving away from the centre. Due to such shape of the poleshoes, the field winding wound on salient poles produces the m.m.f. wave which is nearly sinusoidal and it always acts along the pole axis which is direct axis.let F f be the m.m.f. wave produced by field winding, then it always acts along the direct axis. This m.m.f. is responsible to produce an excitation e.m.f. E f which lags F f by an angle 90 o. When armature carries current, it produces its own m.m.f. wave F AR. This can be resolved in two components, one acting along d-axis (cross-magnetising). Fig Flux distribution in air gap for salient pole machine imilarly armature current I a also can be divided into two components, one along direct axis and along quadrature axis. These components are denoted as, : F d = Component along direct axis F AR : } F q = Component along quadrature axis I d = Component along direct axis I a : } I q = Component along quadrature axis The positions of F AR, F d and F q in space are shown in the Fig The instant chosen to show these positions is such that the current in phase R is maximum positive and is lagging E f by angle Ψ. Fig M.M.F. wave positions in salient pole machine The phasor diagram corresponding to the positions considered is shown in the Fig The I a lags E f by angle Ψ.It can be observed that F d is produced by I d which is at 90 o to E f while 95

96 F q is produced by I q which is in phase with E f.the flux components of Φ AR which are Φ d and Φ q along the direct and quadrature axis respectively are also shown in the Fig.3. It can be denoted that the reactance offered to flux along direct axis is less than the reactance offered to flux along quadrature axis. Due to this, the flux Φ AR is no longer along F AR or I a. Depending upon the reluctances offered along the direct and quadrature axis, the flux Φ AR lags behind I a. Fig 3.39 Basic phasor diagram for salient pole machine 3.10 DIRECT AND QUADRATURE AXIS SYNCHRONOUS REACTANCE We know that, the armature reaction flux Φ AR has two components, Φ d along direct axis and Φ q along quadrature axis. These fluxes are proportional to the respective m.m.f. magnitudes and the permeance of the flux path oriented along the respective axes.... Φ d = P d F d where P d = permeance alomng the direct axis Permeance is the reciprocal of reluctance and indicates ease with which flux can travel along the path. But F d = m.m.f. = K ar I d in phase with I d The m.m.f. is always proportional to current. While K ar is the armature reaction coefficient.... Φ d = P d K ar I d Similarly Φ q = P q K ar I q As the reluctance along direct axis is less than that along quadrature axis, the permeance P d along direct axis is more than that along quadrature axis, (P d < P q ).Let E d and E q be the induced e.m.f.s due to the fluxes Φ d and Φ q respectively. Now E d lags Φ d by 90 o while E q lags Φ q by 90 o. where K e = e.m.f. constant of armature winding The resultant e.m.f. is the phasor sum of E f, E d and E q. Substituting expressions for Φ d and Φ q 96

97 Now X ard = Equivalent reactance corresponding to the d-axis component of armature reaction = K e P d K ar and X arq = Equivalent reactance corresponding to the q-axis component of armature reaction = K e P q K ar For a realistic alternator we know that the voltage equation is, where V t = terminal voltage X L = leakage reactance Substituting in expression for Ē R, where X d = d-axis synchronous reactance = X L + X ard...(2) and X q = q-axis synchronous reactance = X L + X arq...(3) It can be seen from the above equation that the terminal voltage V t is nothing but the voltage left after deducing ohmic drop I a R a, the reactive drop I d X d in quadrature with I d and the reactive drop I q X q in quadrature with I d, from the total e.m.f. E f.the phasor diagram corresponding to the equation (1) can be shown as in the Fig. 1. The current I a lags terminal voltage V t by Φ. Then add I a R a in phase with I a to V t. The drop I d X d leads I d by 90 o as in case purely reactive circuit current lags voltage by 90 o i.e. voltage leads current by 90 o. Similarly the drop I q X q leads X q by 90 o. The total e.m.f. is E f DETAILS ANALYSIS OF PHASOR DIAGRAM FOR SYNCHRONOUS GEN In the phasor diagram shown in the Fig. 3.40, the angles Ψ and δ are not known, through V t, I a and Φ values are known. Hence the location of E f is also unknown. The components of I a, I d and I q cannot be determined which are required to sketch the phasor diagram. Fig 3.40 Basic phasor diagram 97

98 Let us find out some geometrical relationships between the various quantities which are involved in the phasor diagram. For this, let us draw the phasor diagram including all the components in detail. We know from the phasor diagram shown in the Fig. 4 that, I d = I a sin Ψ... (4) I q = I a cos Ψ...(5) cosψ = I q /I a...(6) The drop I a R a has two components which are, I d R d = drop due to R a in phase with I d I q R a = drop due to R a in phase with I q The I d X d and I q R q can be drawn leading I d and I q by 90 o respectively. The detail phasor diagram is shown in the Fig Fig Phasor diagram for lagging p.f. In the phasor diagram, OF = E f OG = V t GH = I d R a and H A = I q R a GA = I a R a AE = I d X d and EF = I q X a Now DAC is drawn perpendicular to the current phasor I a and CB is drawn perpendicular to AE. The triangle ABC is right angle triangle, But from equations (6), cosψ = I q /I a Thus point C can be located. Hence the direction of E f is also known.now triangle ODC is also right angle triangle, Now OD = OI + ID = V t cos Φ + I a R a and CD = AC + AD = I a X q + V t sinφ 98

99 As I a X q is known, the angle Ψ can be calculated from equation (10). As Φ is known we can write, δ = Ψ - Φ for lagging p.f. Hence magnitude of E f can be obtained by using equation (11). Note : In the above relations, Φ is taken positive for lagging p.f. For leading p.f., Φ must be taken negative DETERMINATION OF Xd AND Xq USING SLIP TEST The method used to determine X q and X d, the direct and quadrature axis reactance is called slip test.in an alternatore we apply excitation to the field winding and voltage gets induced in the armature. But in the slip test, a three phase supply is applied to the armature, having voltage must less than the rated voltage while the field winding circuit is kept open. The circuit diagram is shown in the Fig Fig.3.42 Circuit diagram for slip test The alternator is run at a speed close to synchronous but little less than synchronous value.the three phase currents drawn by the armature from a three phase supply produce a rotating flux. Thus the armature m.m.f. wave is rotating at synchronous speed as shown in the Fig Fig Rotating armature m.m.f. Note that the armature is stationary, but the flux and hence m.m.f. wave produced by three phase armature currents is rotating. This is similar to the rotating magnetic field existing in an induction motor. The rotor is made to rotate at a speed little less than the synchronous speed. Thus armature m.m.f. having synchronous speed, moves slowly past the filed poles at a slip speed (n s -n) 99

100 where n is actual speed of rotor. This causes an e.m.f. to be induced in the field circuit.when the stator m.m.f. is aligned with the d-axis of field poles then flux Φ d per poles is set up and the effective reactance offered by the alternator is X d.when the stator m.m.f. is aligned with the q-axis of field poles then flux Φ q per pole is set up and the effective reactance offered by the alternator is X q.as the air gap is nonuniform, the reatance offered also varies and hence current drawn the armature also varies cyclically at twice the slip frequency.the r.m.s. current is minimum when machine reactance is X d and it is maximum when machine reactance is X q. As the reactance offered varies due to nonuniform air gap, the voltage drops also varies cyclically. Hence the impedance of the alternator also varies cyclically. The terminal voltage also varies cyclically. The voltage at terminals is maximum when current and various drops are minimum while voltage at terminals is minimum when current and various drops are maximum. The waveforms of voltage induced in rotor, terminal voltage and current drawn by armature are shown in the Fig It can observed that rotor field is aligned with the armature m.m.f., its flux linkage are maximum, but the rate of change of flux is zero. Hence voltage induced in field goes through zero at this instant. This is the position where alternator offers reactance X d. While when rate of change of flux associated with rotor is maximum, voltage induced in field goes through its maximum. This is the position where alternator offers reactance X q. The reactances can be calculated as 100

101 Fig Current and voltage wave forms in slip test 3.13 Introduction to Synchronization of Alternators In utility systems there will be such thousands of generators which then have to be operated in parallel so that they will get interconnected by thousands of kilometers of transmission lines and will supply electrical energy to the loads which are scattered over areas of thousand kilometers. The reasons for interconnecting these systems are continuity of service, economics in plant investment and operating costs.when number of generators are operating at the same voltage and are required to be interconnected electrically, bus bars are used as the common electrical component. Bus bars are nothing but copper rods which operate at constant voltage.the process of switching of an alternator to another alternator or with a common bus bar without any interruption is called synchronization. Alternately it can also be defined as the process of connecting the two alternators in parallel without any interruption. The synchronous machine which is to be synchronized is normally called an incoming machine. If any alternators is connected to a bus bar which has many other alternators already connected, no matter what power it is supplying then alternator is said to be connected to infinite bus bar. An infinite bus bar is one of whose frequency and phase e.m.f. remains unaffected by changes in condition of any one machine connected to it. Thus they are nothing but constant frequency and constant voltage bus bars. The system can be efficiently analysed if it is connected to infinite bus bar Many important features about the 101

102 behaviour of the synchronous machine can be obtained from analysis of a single machine connected to an infinite bus bar.in case of synchronous machines, stator carries the armature winding which is having small resistance. Under stationary conditions e.m.f. induced in stator winding is zero. So if such an alternator at stationary conditions is connected to bus bar, there is always danger of short circuit. So it is not a practice to connect a stationary to live bus bars Necessary Conditions for Synchronization To have effective synchronization without any interruption there are certain conditions to be fulfilled. These conditions are ; i) The terminal voltage of the incoming machine must be same as that of bus bar voltage. ii) The frequency must be same as that of the incoming machine as well as that of the bus bar. This necessitates that speed must be properly adjusted (f = PN/120). iii) With respect to the external load, the phase of alternator voltage must be identical with that of the bus bar voltage. Alternately we can say that phase sequence for the two voltages must be same. Note ; The violence of any of the above conditions may cause a circulating current and power surges which are accompanied by undesirable electromechanical oscillations of the rotor. The above conditions can be satisfied by using a voltmeter, synchronizing lamps or synchroscope. The use of voltmeter will satisfy the first conditions. Preferably the same voltmeter is used for measuring both the voltages. Bu using synchronizing lamps conditions (ii) and (iii) will be fulfilled. A synchroscope is a special device used for synchronizing the machines more accurately. It will satisfy both the conditions provided that a phase sequence indicator is used with it Synchronization of Single Phase Alternators In case of single phase alternators, synchronization is done generally by lamp methods. It can be done by two ways : a) Lamp dark method b) Lamps bright Method. Lamps Dark Method In this method the lamps are arranged as shown in Fig The alternator to be synchronized (which is also called incoming alternator) consists of two lamps connected across the switch terminals of the same phase. 102

103 Fig Dark lamp method The voltage for the two alternators is measured with the help of a voltmeter. The lamps are connected in such a way that the polarity and the frequency for the two machines can be checked. No resultant voltage will appear across the switch terminals if the frequency of the two alternators is exactly same as their voltage are in exact phase opposition. Thus under this case lamps will not glow. The voltages for both the machines are having same maximum and r.m.s. values and are in exact phase opposition thus resultant voltage is zero in local circuit. This is represented in the Fig.3.46 Fig Resultant Voltage It can be seen that with unequal frequencies of the two alternators, the two lamps will become alternately bright and dark. The light beat will be produced whose number is equal to the difference in frequencies for the two machines.the resultant voltage appearing across the lamp will be difference of the two voltages at any instant resulting in a waveform shown in the Fig Since number of cycle completed by two machines in any given time are not same the light beat is produced which is shown in the Fig Fig 3.47 Volatge waveform Whenever the two voltage are in exact phase opposition (i.e. angle between them is 180 o ) then resultant voltage E R is zero. If the switch is not closed at this instant the voltage across lamp will go on rising and synchronization will not appear proper.the alternate darkness and brightness of the lamp will not indicate whether the incoming alternator is running fast or slow. For the exact synchronization the speed of incoming alternator is adjusted in such a way that the light beats are produced at a very slow speed and the alternators are 103

104 synchronized during the middle of the dark period where resultant voltage E R will be zero. The word middle is used as the lamp will not glow even though there is sufficient voltage across it. So it becomes difficult to know the correct instant of zero voltage. Lamps Bright Method Since it is very difficult to judge the correct instant of zero voltage in Lamps dark method, this method is introduced which is shown in the Fig The lamps remain maximum bright when there is no difference in voltages for the two machines. This is more sharp and accurate method of synchronization because the lamps are much more sensitive to changes in voltage at their maximum brightness than when they are dark. Fig Bright lamp method Sycnhronization Of Three Phase Alternators Fig Setup for Synchronization of Alternators The conditions to be satisfied for synchronization of three phase alternators are same as that for single phase alternators. But instead of saying that voltages must act in phase opposition, the phase sequence must be same i.e. phase must be connected in proper order of R, Y, B. Typical setup for synchronization of alternators is shown in the Fig In synchronizing three phase alternators, three lamps are connected as shown in the Fig.3.50, so that it can be use to indicate whether the incoming machine is running slow or fast. With symmetrical connection of lamps, they would dark out or glow up simultaneously provided that phase sequence is same for incoming machine and bus bar.consider the two alternators A and B to be synchronized. The alternator A is already running at synchronous speed and its excitation is so adjusted that it builds up the rated voltage. The alternator A is connected to 104

105 the bus bars of constant voltage and frequency. The alternator B is to be connected to bus bar i.e. it is to be synchronized with alternator A. The process or synchronization can be explained as below : Step 1 : Start the prime mover of machine. Adjust its speed to a synchronous speed of machine B. This will rotate the rotor of alternator B. This will rotate the rotor of alternator B at synchronous speed. Step 2 : The switch S 4 is then closed. By adjusting the rheostat R x the excitation to the field is adjusted so that induced e.m.f. of B is equal to the induced e.m.f. of A. This can be verified by voltmeter. Step 3 : To satisfy remaining conditions, the three lamps pairs are used which are L 1, L 2 and L 3 as shown in the Fig These are connected in such a way that pair L 1 is straight connected while the pairs L 2 and L 3 are cross connected to understand the connection, the pairs are again shown in the Fig Fig synchronozing lamps Fig Now two supplies are supplying lamp pairs, E RYB i.e. voltage supply of bus bar while E R'Y'B' i.e. supply generated by alternator B. The switch S 3 is still open.let the three bus bar voltages be represented by phasors OR, OY, OB rotating at angular speed of ω 1 rad/s. The incoming alternator voltage are represented by phasors OR', OY', OB' rotating at angular speed of ω 2 rad/s.the phasor E RR', joining the tips R and R' is voltage across lamp pair L 1. Similarly E YB, and E BY, are voltages across lamps L 2 and L 3 respectively.if there is difference between the two frequencies due to difference in speeds of the twp alternators, the lamps will become dark and bright in a sequence. This sequence tells whether incoming 105

106 alternator frequency is less or greater than machine A.The sequence L 1, L 2, L 3 tells that machine B is faster as the voltage star R'Y'B' will appear to rotate anticlockwise with respect to bus bar voltage RYB at a speed corresponding to difference between their frequencies shown in the Fig The sequence L 3, L 2, L 1 tells that the machine B is slower because voltage star R'Y'B' will appear to rotate clockwise with respect to bus bar voltage RYB. The prime mover speed can be adjusted accordingly to match the frequencies. Fig difference between their frequencies The synchronization is done at the moment when lamp L 1 is in the middle of dark period. If the lamps pair becoming dark and bright simultaneously, it indicates incorrect phase sequence which can be correct by interchanging any two leads either of the incoming machine or of bus bars. Note ; For high voltage alternators it is not possible to use the lamps directly. In such cases lams are connected through potential transformers.in this method when lamp L 1 is dark the other two lamp pairs L 2 and L 3 and equally bright. So this method of synchronization is called ''Lamps bright and dark'' method Synchronization by Sycnhronscope It can be seen that the previous method is not accurate since it requires correct sense of judgement of the operator. Hence to avoid the personal judgement, the machines are synchronized by accurate device known as synchroscope.it consists of a rotating pointer which indicates the exact moment of closing the synchronizing switch. If the pointer rotates in anticlockwise direction, it indicates that incoming machine is running slow whereas clockwise rotation of pointer indicates that incoming machine is running faster. The rotation of pointer is proportional to the difference in the two frequencies. The pointer should rotate at a very low speed in the direction of arrow marked fast as shown in the Fig

107 Fig Synchronization by Sycnhronscope When the rotating pointer reaches the vertical position at slow speed, the switch must be closed. The pointer will oscillate about some mean position instead of rotating if difference in frequencies is large. In such cases the speed of incoming machine is adjusted properly.the connections for synchroscope are shown in Fig. 1. Any two bus bars lines are connected to its terminals while its other terminals are connected to corresponding lines of incoming machine. The phase sequence from bus bars and from machine must be same. It can be checked with the help of phase sequence indicator. The voltmeter is used to check the equality of voltage of bus bars and incoming machine. The synchronization procedure is already explained before. Note : The use of lamps and synchroscope together is a best method of synchronization. Now a days automatic synchronizing devices are also available which will perform the entire process of synchronization automatically without the help of shift engineer. But such schemes are more complicated and may take larger time than required by a shift engineer Sycnhronizing Current After proper synchronization of the alternators, they will run in synchronism. A synchronizing torque will be developed if any of the alternator drops out of synchronism and will bring it back to the synchronism.consider the two alternators shown in the Fig which are in exact synchronism. Due to this they are having same terminal p.d. and with reference to their local circuit they are in exact phase opposition. So there will not be any circulating current in the local circuit. The e.m.f. E 1 of alternator 1 is in exact phase opposition to that of alternator E 2. Fig two alternators in parallel 107

108 With respect to external load, the e.m.f.s of the two alternators are in the same direction although they are in phase opposition with reference to local circuit. There will be no resultant voltage in the local circuit.now assume that speed of alternator 2 is changed such that its e.m.f. E 2 falls by an angle α. But E 1 and E 2 are equal in magnitude. The resultant voltage in this case will cause a current in the local circuit which is called synchronizing current. This circulating current is given by, I SY = E r /Z s where Z s = Synchronous impedance of winding of alternator The phase angle of I SY is given by an angle θ which can be computed as tanθ = X s /R a where X s is synchronous reactance and R a is armature resistance. This angle is almost 90 o. Fig phasor diagram two alternators in parallel Thus I SY lags E r by almost 90 o and approximately in phase with E 1. This current is generating current with respect to alternator 1 since it is in the same direction as that of e.m.f. of alternator 1 while it will be motoring current for alternator 2 as it is in the opposite direction as that of e.m.f. of alternator 2. This current I SY will produce a synchronizing torque which will try to retard alternator 1 whereas accelerate the alternator 2.The power output of alternator 1 supplies power input to alternator 2 and copper losses in the local path formed by armatures of two alternators.power output of alternator 1 = E 1 I SY cosφ 1 This power is approximately equal to E 1 I SY as Φ 1 is small and is almost in phase with E 1. This power is called synchronizing power. Similarly power input to alternator 2 is E 2 I SY cosφ 2 which is equal to E 2 I SY as Φ 2 is also small. E 1 I SY = E 2 I SY + Cu losses in the local circuit Let E 1 = E 2 = E Let the magnitude of resultant e.m.f. be E r which is given by, But α is small.... sin α/2 = α/2 E r = 2 E (α/2) = αe... ( θ = 90 o, sin θ = 1) The electrical angle α is expressed in radians. X s is synchronous reactance of each machine Now, synchronizing power per phase, P SY = E 1. I SY = E. I SY 108

109 If R a is not assumed as negligible then will not be so the above expression can be written in exact form as, For 3 phases, total synchronizing power is given by, The above expression is valid for two alternators connected in parallel and operating at no load.now let us consider the case of alternator connected to infinite bus bar (the concept of infinite bus bar is explained later) then the above expression for synchronizing power is still valid with the changes of reactance of only one alternators.... E r = α E If R a is neglected, The exact expression is, For 3 phases, total synchronizing power Now assuming that E 2 has advanced in phase shown in the Fig. 2(b). The synchronizing current I SY in this case will be generating current for machine 2 and motoring current for machine 1. This will again produce a torque which will try to accelerate alternator 1 and try to retard alternator 2. Note : Hence if synchronism between the two machines is lost then synchronizing current will flow in the local circuit which will produce a synchronizing torque. This torque will tend to accelerate the lagging machine while will try to retard the leading machine. In case of machines which are loaded this current is superimposed on the load current. 109

110 Effect of change in Excitation In case of alternators a field rheostat may be used to change the excitation or its field current. If alternators are running in parallel, a change in the field current will not change the active power shared significantly but will change the operating power factor. With change in the excitation the armature current will change which will change the active power by a small amount. Let us consider the effect of change in excitation on alternator with and without load. Alternator on No Load Consider two alternators on no load and working in parallel. If their excitations are adjusted properly then the e.m.f.s E 1 and E 2 will be equal. Thus will not be any current in local circuit.now say excitation of alternator 1 is increased then magnitude of E 1 will be more than that of. This will cause resultant voltage Ē r = Ē 1 - Ē 2 that will appear in the local circuit. This can be shown in the phasor diagram shown in the Fig. 1. Fig phasor diagram for Alternator on No Load This resulting voltage will set up a synchronizing current I SY in the local circuit and since the synchronizing impedances are mainly reactive, this current lags E r by approximately 90 o.for alternator 1, I SY lags behind E 1 by 90 o. This lagging current will produce demagnetizing effect and will try to reduce the generated e.m.f. Alternately for other alternator, I SY leads E 2 by 90 o. There will be leading current which will produce magnetizing effect and the field will be strengthened which will try to increase the generated e.m.f. Thus E 1 will be reduced whereas E 2 will be increased. Hence the circulating current will try to make the two generated e.m.f.s equal at no load whereas the power angle will remain at zero degrees. From the Fig Fig equivalent circuit 110

111 Alternator on Load Consider again two alternators running in parallel with each alternator supplying one half of active power and one half of reactive power. Each alternator supplies a load current of I such that total load current is 2I. It is assumed that E 1 = E 2 while the operating power factor is cos Φ and terminal voltage V. The power triangles for both the alternators can be represented as shown in the Fig where both active and reactive powers divided equally giving apparent power triangles same. Fig Load sharing From the circuit diagram it can be seen that I SY current is vectorially added to the load current of alternator no 2. Now the load currents will be changed to I 1 and I 2 with change in power factors. The new power factor are cosφ 1 and cosφ 2. This is shown in the Fig

112 Fig Load sharing with various power factors It can be seen that from the Fig. 4 that cosφ 1 is reduced whereas cosφ 2 is increased. The armature currents for the two machines are changed but their active components are not changed. Thus changes in KW loading of the two alternators is negligible but reactive power KVAR 1 from first alternator is increased whereas KVAR 2 supplied by second alternator is decreased which can be seen from power triangles Phasor Diagram The effect of change in excitation on the performance of the alternators can be explained with the help of phasor diagram shown in the Fig Again the two alternators are working in parallel. If now excitation of alternator 1 is increased so that its induced e.m.f. E 1 is increased to E 1 ' which will try to increase the terminal voltage V. But the terminal voltage V can be kept constant by decreasing the excitation of other alternator. The increase in E 1 and decrease in E 2 are adjusted in such a way that E sin δ remains constant. The difference between E' 1 and E' 2 give rise to circulating current I SY. This current must be added to I 1 and subtracted from I 2 which will give new armature currents I' 1 and I' 2.Induced e.m.f. are given by, Fig Phasor diagram for alternator for effect of change in excitation 112

113 It can be seen that there is increase in magnitude of I' 1 but its active component I' 1 cosφ 1. is unaltered. Similarly I' 2 is decreased in magnitude but its active component I' 2 cosφ 2. is unaffected. Thus the load current, terminal voltage and load power factors are unchanged.form the Fig it is clear that the alternator 1 operated at a proof p.f. which delivers greater reactive power than alternator 2 operating at a better p.f. Since the mechanical power input to the two alternators is not distributed, the active power output is remaining same. Thus change in excitation causes only the KVAR sharing of the two alternators without distributing kw sharing of the two machines.thus the load current, the load terminal voltage and the load power factor remain unchanged but armature currents, induced e.m.f.s and operating power factors remain unchanged but armature currents, induced e.m.f.s and operating power factors for each of the alternator is changed. Note : By varying the field excitation with the help of rheostats the distribution of reactive power shared by the alternators and their terminal voltage can be controlled Division of Load Between Two Alternators The division of load between the two alternators can be calculated as follows.from the Fig.3.61 it can be seen that Substituting the above values in equation 1 From the Fig. 6 it can also be seen that Subtracting above two equations, 113

114 Fig Division of Load Between Two Alternators Note : When two e.m.f.s are unequal in magnitude the second term of above equation represents the circulating current under loaded conditions. At no load (i.e. Z = ) the circulating current is given by, Effect of Change in Input or Mechanical Torque For any alternator its driving torque can be changed by controlling the gate opening in case of hydrogenerators or by controlling the throttle opening in case of turbogenerators. Again we will consider two cases that are alternator with and without load respectively Alternator on No Load Suppose that two alternators are running in parallel without any load in them. The excitations for two alternators are adjusted in such a way that the induced e.m.f.s. are equal in magnitude. The resultant voltage in the local circuit will be zero. With respect to external circuit the two e.m.f.s are in phase whereas in local circuit they are in opposition.now the driving torque of alternator 1 is increased. This increment in torque will try to accelerate the alternator 1 and its induced e.m.f. E 1 will lead e.m.f. E 2. This will give rise to resultant voltage E r. This voltage Ē = Ē 1 - Ē 2 circulates current I SY in local circuit which is given by 114

115 This current lags behind E r by angle of approximately 90 o if the resistance of the armatures of the two alternators are neglected. This is represented in following phasor diagram shown in Fig This circulating current I SY is almost in phase with E 1 and in phase opposition with E 2. Now here the synchronizing power will come into play. The alternator 1 produces a power E 1 I SY cosφ 1 which is positive as Φ 1 < 90 o while alternator 2 generates a power E 2 I SY cosφ 2 which is negative as Φ 2 > 90 o. Alternately we can say that alternator 1 experience a generating action which will try to retard it and alternator 2 receives the power produced by alternator 1. Hence it will experience a motoring action which will tend to accelerate it. Thus there will be automatic synchronizing action will retard the faster machine and accelerate the slower machine and synchronism is maintained.it can be seen that the autosynchronizing action is on account of Z 1 and Z 2 considered mainly reactive. If Z 1 and Z 2 are purely resistive then I SY will be in phase of E r. Then power for both the machines is positive and both will experience generating action. So there would not be synchronizing power will tend to accelerate the slower machine. Note : Thus reactance mainly causes auto synchronization but it is bad for voltage regulation. Fig Phasor diagram Alternator on Load Again we will consider two alternators which are loaded and running in parallel. The sharing of load between these alternators is governed by speed-load characteristics of their prime mover. In the Fig the two alternators are shown driven by prime movers 1 and 2. Fig Two Alternators with two primemovers 115

116 In Fig the lines 1 and 2 represent the speed load characteristics of prime movers 1 and 2. For clarity and simplicity the slopes are exaggerated. Fig Speed -Load characteristic. Horizontal line ab represents total load of 2P with load on each alternator as P. The frequency of bus bar is f.now if by governer setting, the torque of prime mover 1 is increased, its speed will be increased which will shift its speed-load curve upwards. This is shown by dotted line 1'. Then original operating points a and b are now shifted to c and d. This will give new operating conditions which will increase load on alternator 1 from P to P 1 and decrease load on alternator 2 from P to P 2 with P 1 + P 2 = 2P. From the Fig.3 it can be seen that frequency has increased from f to f'. Now, if it is desired to maintain the frequency constant then the input to prime mover 2 must be reduced which will shift its speed-load curve download shown by dotted line 2' The operating points c and d now shift to new points x and y. The horizontal line xy indicates that the load on alternator 1 is further increased from P 1 and P' 1 and that on alternator 2 is reduced from P 2 to P' 2 such that the relation P' 1 + P' 2 = 2P is maintained. Thus the load sharing between the alternators and the frequency can be controlled by changing the mechanical torque input to the alternators. By controlling the gate opening of water turbines or the throttle opening of steam turbines, the speed-load characteristics of prime movers can be shifted up and down. To consider what happens internally in the two alternators, let us consider the phasor diagram. 116

117 Fig.3.65 phasor diagram The two alternators are running in parallel with their excitations constant. The armature currents I 1 and I 2 are also equal so that total load current is 2I 1 or 2I 2. The terminal voltage V is constant. Each alternator is sharing a load equal to Now when mechanical torque of alternator 1 is increased, its output will also increase. But E 1, V and X s are constant. So to increase power angle must be increased from δ to δ 1 so new E 1 will be ahead of previous position. The alternator 1 shares greater load than P. Therefore for constant load of 2P the load on alternator 2 must be less than P. This will make new E 2 to fall back from its previous position. Due to the different positions of E 1 and E 2, resulting voltage AB appears in the local circuit which will send a circulating current I SY lagging behind the voltage by 90 o. This current I SY must be added to I 1 and subtracted from I 2.The alternator 1 carries increased current I' 1 and alternator 2 carries decreased current I' 2 but total load current remains same (Ī = Ī' 1 + Ī' 2 ). The power factor of alternator 1 is improved from cosφ to cosφ 1 whereas it is reduced from cosφ to cosφ 2 for alternator 2. But the load power factor remains unaffected.thus increase in mechanical torque in case of alternator will increase armature current and improve the power factor. The alternator will share increased load whose driving torque is increased whereas the other alternator which is in parallel is relieved from the load whereas the reactive power distribution remains unaffected.to consider the effect of change in input on corresponding power triangles of the two alternators we will assume that the two alternators are turbo alternators whose prime mover are supplied with steam.now the excitations for the two alternators are kept constant where steam supply i.e. power input to prime mover of alternator 1 is increased. The two alternators are running in synchronism. So machine 1 cannot overrun machine 2. The increased power input for alternator 1 makes it possible for carrying more load. This will make rotor fort machine 1 advancing its angular position by an angle δ. The resultant e.m.f. E r is produced in the local circuit which will setup a circulating current I SY which lags E r by 90 o and almost in phase with E 1. The power per phase fort alternator 1 is increased by an amount E 1 I SY whereas it is decreased by same amount for alternator 2. This current I SY has no appreaciable reactive component and it will not disturb the reactive power distribution but active power output of alternator 1 will increase and that of 2 will decrease. This is shown in Fig Fig.3.66 phasor diagram and load sharing Note : The change in input to the prime mover will change the distribution of load between the alternators. 117

118 3.15 SYNCHRONOUS MOTOR Introduction If a three phase supply is given to the stator of a three phase alternator, it can work as a motor. As is is driven at synchronous speed, it is called synchronous generator. So if alternator is run as a motor. It will rotate at a synchronous speed. Such a device which converts an electrical energy into a mechanical energy running at synchronous speed is called synchronous motor. Synchronous motor works only at synchronous speed and cannot work at a speed other than the synchronous speed. Its speed is constant irrespective of load, no doubt, its speed changes for an instant at the time of loading Types The two types of synchronous motor are, 1. Three phase synchronous motors 2. Single phase synchronous motor The single phase synchronous motor are further classified as reluctance motor and hysteresis motor. The three phase synchronous motor works on the concept of rotating magnetic field. The field produced by stationary three phase winding, which rotates in space is called rotating magnetic field. Its speed is always synchronous and given by, Ns = 120f/P Where P = Number of poles for which winding is wound f = Frequency of the supply Construction of Three Phase Synchronous Motor Similar to d.c. machine where there is no constructional difference between a generator and motor, There is no difference between the construction of synchronous motor and the alternator, both being the synchronous machines. The synchronous motor construction is basically similar to rotating field type alternator. It consists of two parts i) Stator : Consisting of a three phase star or delta connected winding. This is excited by a three phase a.c. supply. ii) Rotor : Rotor is a field winding, the construction of which can be salient (projected pole) or non salient (cylindrical) type. Practically most of the synchronous motors use salient i.e. projected pole type construction. The field winding is excited by a separate d.c. supply through slip rings. 118

119 Fig.3.67 Schematic representation of three phase synchronous motor 3.18 Principle of Working of 3-Phase Synchronous Motor Synchronous motor works on the principle of the magnetic locking. When two unlike poles are brought near each other, if the magnets are strong, there exists a tremendous force of attraction between those two poles. In such condition the two magnets are said to be magnetically locked. If now one of the two magnets is rotated, the other also rotates in the same direction, with the same speed due to the force of attraction i.e. due to magnetic locking condition. The principle is shown schematically in the Fig Fig.3.68 Schematic representation of principle of motor So to have the magnetic locking condition, there must exist two unlike poles and magnetic axes of two must be brought very close to each other. Let us see the application of this principle in case of synchronous motor. Consider a three phase synchronous motor, whose stator is wound for 2 poles. The two magnetic fields are produced in the synchronous motor by exciting both the windings, stator and rotor with three phase a.c. supply and d.c. supply respectively. When three phase winding is excited by a three phase a.c. supply the the flux produced by the three phase winding is always of rotating type, which is already discussed in the previous post. Such a magnetic flux rotates in space at a speed called synchronous speed. This magnetic field is called rotating magnetic field. The rotating magnetic field creates the effect similar to the physical rotation of magnets in space with a synchronous speed. So stator of the synchronous motor produces one magnet which is as good as rotating in space with the synchronous speed. The synchronous speed of a stator rotating magnetic field depends on the supply frequency and the number of poles for which stator winding is wound. if the frequency of the a.c. supply is f Hz and stator is wound for P number of poles, then the speed of the rotating magnetic field is synchronous given by, N s = 120f/P r.p.m. In this case, as stator is wound for say 2 poles, with 50 Hz supply, the speed of the rotating magnetic field will be 3000 r.p.m. This effect is similar to the physical rotation of two poles with a speed of N s r.p.m. For simplicity of understanding let us assume that the stator poles are N 1 and S 1 which are rotating at a speed of N s. The direction of rotation of rotating magnetic field is say clockwise. When the field winding on rotor is excited by a d.c. supply, it also produces two poles, assuming rotor construction to be two pole, salient type. Let these poles be N 2 and S 2. Now one magnet is rotating at N s having poles N 1 and S 1 while at start rotor is stationary i.e. second magnet is stationary having poles N 2 and S 2. If somehow the unlike poles N 1 and S 2 or S 1 and N 2 are brought near each other, the magnetic locking may get established between stator and rotor poles. As stator poles are rotating due to magnetic locking rotor will also rotate in the same direction as that of stator poles i.e. in the direction of rotating magnetic field, with the same speed i.e N s. Hence synchronous motor rotates at one and only one speed i.e. synchronous speed. But this all depends 119

120 on existence of magnetic locking between stator and rotor poles. Practically it is not possible for stator poles to pull the rotor poles from their stationary position into magnetic locking condition. Hence synchronous motors are not self-starting. Let us see the reason behind this in detail Why synchronous Motor Is Not Self Starting Consider the rotating magnetic field as equivalent to physical rotation of two stator poles N 1 and S 1. Consider an instant when two poles are at such a position where stator magnetic axis is vertical, along A-B as shown in the Fig. 3.68(a). At this instant, rotor poles are arbitrarily positioned as shown in the Fig. 1. At this instant, rotor is stationary and unlike poles will try to attract each other. Due to this rotor will be subjected to an instantaneous torque in anticlockwise direction as shown in the Fig. 1(a). Now stator poles are rotating very fast i.e. at a speed N s r.p.m. Due to inertia, before rotor hardly rotates in the direction of anticlockwise torque, to which it is subjected, the stator poles change their positions. Consider an instant half a period latter where stator poles are exactly reversed but due to inertia rotor is unable to rotate from its initial position. This is shown in the Fig. 3.68(b). Fig Direction of Rotation of motor At this instant, due to the unlike poles trying to attract each other, the rotor will be subjected to a torque in clockwise direction. This will tend to rotate rotor in the direction of rotating magnetic field. But before this happen, stator poles again change their position reversing the direction of the torque exerted on the rotor. Key Point : As a result, the average torque exerted on the rotor is zero. And hence the synchronous motor is not self-starting. Note: The question is obvious that will happen if by chance the rotor position is in such a way that the unlike rotor and stator poles are facing each other? But owing to the large inertia of the rotor, the rotor fails to rotate along with the stator poles. Hence again the difference of position of magnetic axes gets created and rotor gets subjected to quickly reversing torque. This is because the speed with which rotating magnetic field is rotating is so high that it is unable to rotate the rotor from its initial position, due to the inertia of the rotor. So under any case, whatever may be the starting position of the rotor, synchronous motor is not self-starting Procedure to Start a Synchronous Motor 120

121 Now suppose the rotor is rotated by some external means at a speed almost equal to synchronous speed. And then the rotor is excited to produce its poles. At a certain instant now, the stator and rotor unlike poles will face each other such that their magnetic axes are near each other. Then the force of attraction between the two, pulls both of them into the magnetic locking condition. Once magnetic locking is established, the rotor and stator poles continue to occupy the same relative positions. Due to this, rotor continuously experiences a unidirectional torque in the direction of the rotating magnetic field. Hence rotor rotates at synchronous speed and said to be in synchronism with rotating magnetic field. The external device used to rotate rotor near synchronous speed can be removed once synchronism is established. The rotor then continues its rotation at N s due to magnetic locking. This is the reason why synchronous motor runs only at synchronous speed and does not rotate at any speed other than the synchronous. This operation is shown in the Fig 3.69(a) and (b). Fig Unidirectional torque experienced by rotor It is necessary to keep field winding i.e. rotor excited from d.c. supply to maintain the magnetic locking, as long as motor is operating. So a general procedure to start a synchronous motor can be stated as 1. Give a three a.c. supply to a three phase winding. This will produce rotating magnetic field rotating at synchronous speed N s r.p.m. 2. Then drive the rotor by some external means like diesel engine in the direction of rotating magnetic field, at a speed very near or equal to synchronous speed. 3. Switch on the d.c. supply given to the rotor which will produce rotor poles. now there are twp fields one is rotating magnetic field produced by stator while the other is produced by rotor which is physically rotated almost at the same speed as that of rotating magnetic field. 4. At a particular instant, both the fields get magnetically locked. The stator field pulls rotor field into synchronism. Then the external device used to rotate rotor can be removed. But rotor will continue to rotate at the same speed as that of rotating magnetic field i.e. N s due to magnetic locking. Key Point : So the essence of the discussion is that to start the synchronous motor, it needs some device to rotate the rotor at a speed very near or equal to the synchronous speed Methods of Starting Synchronous Motor As seen earlier, synchronous motor is not self-starting. It is necessary to rotate the rotor at a speed very near to synchronous speed. This is possible by various method in practice. The various methods to start the synchronous motor are, 1. Using pony motors 121

122 2. Using damper winding 3. As a slip ring induction motor 4. Using small d.c. machine coupled to it Using pony motors In this method, the rotor is brought to the synchronous speed with the help of some external device like small induction motor. Such an external device is called 'pony motor'. Once the rotor attains the synchronous speed, the d.c. excitation to the rotor is switched on. Once the synchronism is established pony motor is decoupled. The motor then continues to rotate as synchronous motor Using Damper Winding In a synchronous motor, in addition to the normal field winding, the additional winding consisting of copper bars placed in the slots in the pole faces. The bars are short circuited with the help of end rings. Such an additional winding on the rotor is called damper winding. This winding as short circuited, acts as a squirrel cage rotor winding of an induction motor. The schematic representation of such damper winding is shown in the Fig Fig.3.70 Starting as a squirrel cage I.M. Once the rotor is excited by a three phase supply, the motors starts rotating as an induction motor at sub synchronous speed. Then d.c. supply is given to the field winding. At a particular instant motor gets pulled into synchronism and starts rotating at a synchronous speed. As rotor rotates at synchronous speed, the relative motion between damper winding and the rotating magnetic field is zero. Hence when motor is running as synchronous motor, there can not be any induced e.m.f. in the damper winding. So damper winding is active only at start, to run the motor as an induction motor at start. Afterwards it is out of the circuit. As damper winding is short circuited and motor gets started as induction motor, it draws high current at start so induction motor starters like stardelta, autotransformer etc. used to start the synchronous motor as an induction motor As a Slip Ring Induction Motor The above method of starting synchronous motor as a squirrel cage induction motor does not provide high starting torque. So to achieve this, instead of shorting the damper winding, it is designed to a form a three phase star or delta connected winding. The three ends of this winding are brought out through slip rings. An external rheostat then can be introduced in series with the rotor circuit. So when stator is excited, the motor starts as a slip ring induction motor and due to resistance added in the rotor provides high starting torque. The resistance is then gradually cut off, as motor gathers speed. When motor attains speed near synchronous. d.c. excitation is provided to 122

123 the rotor, then motors gets pulled into synchronism ans starts rotating at synchronous speed. The damper winding is shorted by shorting the slip rings. The initial resistance added in the rotor not only provides high starting torque but also limits high inrush of starting current. Hence it acts as a motor resistance starter. The synchronous motor started by this method is called a slip ring induction motor is shown in the Fig Fig Starting as a slip ring I.M. It can be observed from the Fig. 1(b) that the same three phase rotor winding acts as a normal rotor winding by shorting two of the phases. From the positive terminal, current 'I' flows in one of the phases, which divides into two other phases at start point as 1/2 through each, when switch is thrown on d.c. supply side Using Small D.C. Machine Many a times, a large synchronous motor are provided with a coupled d.c. machine. This machine is used as a d.c. motor to rotate the synchronous motor at a synchronous speed. Then the excitation to the rotor is provided. Once motor starts running as a synchronous motor, the same d.c. machine acts as a d.c. generator called exciter. The field of the synchronous motor is then excited by this exciter itself Behaviour of Synchronous Motor on Loading When a d.c. motor or an induction motor is loaded, the speed of the motors drops. This is because the load torque demand increases then the torque produced by the motor. Hence motor draws more current to produce more torque to satisfy the load but its speed reduces. In case of synchronous motor speed always remains constant equal to the synchronous speed, irrespective of load condition. It is interesting to study how synchronous motor reacts to changes in the load condition. In a d.c. motor, armature develops an e.m.f.after motoring action starts, which opposes supply voltage, called back e.m.f. E b. Hence if R a the armature resistance and V is the supply voltage, we have established the relation for the armature current as, I a = (V- E b ) / R a... for a d.c. motor where E b = ΦPNZ / 60A...for a d.c. motor 123

124 In case of synchronous motor also, once rotor starts rotating at synchronous speed, the stationary stator (armature) conductors cut the flux produced by rotor. The only difference is conductors are stationary and flux is rotating. Due to this there is an induced e.m.f. in the stator which according to Lenz's law opposes the supply voltage. This induced e.m.f. is called back e.m.f. in case of synchronous motor. It is obtained as E bph i.e. back e.m.f. per phase. This gets generated as the principle of alternator and hence alternating in nature and its magnitude can be calculated by the equation, or E bph α Φ As speed is always synchronous, the frequency is constant and hence magnitude of such back e.m.f. can be controlled by changing the flux Φ produced by the rotor. So back e.m.f. in case of synchronous motor depends on the excitation given to the field winding and not on the speed, as speed is always constant. As stator construction is similar to the armature of a three phase alternator, the impedance of the stator is called synchronous impedance of synchronous motor consisting of R a as the stator winding resistance and X s as the synchronous reactance. All the values are generally expressed on per phase basis. Z s = R a + jx s Ω per phase So similar to the d.c. motor, we can write voltage equation for a synchronous motor as, The difference is that this equation is vector equation as each quantity is alternating and has different phase. So addition is to be performed vectorially to obtain the result. where V ph is the supply voltage per phase. The magnitude of E bph is adjusted almost equal to V ph, on no load by controlling flux produced by rotor i.e. field winding. Fig Magnetic locking under no load condition 124

125 Ideal Condition on No Load The ideal condition on no load can be assumed by neglecting various losses in the motor. V ph = E bph Under this condition, the magnetic locking between stator and rotor is in such a way that the magnetic axes of both, coincide with each other as shown in the Fig As this is possible only under no losses condition, is said to be ideal in case of synchronous motor. As magnitude of E bph and V ph is same and opposes the phasor diagram for this condition can be shown as in the Fig Fig Phasor diagram on no load losses In practice this is impossible. Motor has to supply mechanical losses and iron losses alongwith small copper losses. Let us see how it can be explained in case of synchronous motor Synchronous Motor on No Load (With Losses) We have seen that E bph and V ph are magnitudewise same, which is adjusted by controlling field current, in turn controlling the flux. Now due to the various losses practically present on no load, the magnetic locking exists between stator and rotor but in such a way that there exists a small angle difference between the axes of two magnetic fields as shown in the Fig Fig Magnetic locking under practical condition So the rotor axis falls back with respect to stator axis by angle 'δ' as shown in the Fig.3 This angle decides the amount of current required to produce the torque to supply various losses. Hence this angle is called load angle, power angle, coupling angle, torque angle or angle of retardation and denoted as δ as mentioned earlier. The magnetic locking still exists between the two and rotor rotates at synchronous speed alongwith rotating magnetic field maintaining angle difference between the axes of two fields, as shown in the Fig. 3.74(b). The flux lines between the two get stretched due to such retardation of rotor axis with respect to stator. Now 125

126 though E bph = V ph, E bph will not be located in exact opposition with V ph, but will get displaced from its initial position by angle'δ' as shown in the Fig. 3.75(a). Fig. 3.75(a) Phasor diagram for no load condition with losses Hence the vector difference between the two, E bph and V ph is not zero but give rise to a phasor 'OB' as shown. This resultant decides the amount of current I aph to be drawn to produce the torque which meets the various losses present in the synchronous motor. Under no load condition, δ is very small and hence E Rph is also very small. So current drawn by the motor is also very small on no load which is the case in all the various type of motors Synchronous Motor on Load As the load on the synchronous motor increases, there is no change in its speed. But what gets affected is the load angle 'δ' i.e. the angle by which rotor axis retards with respect to stator axis. Hence as load increases, δ increases but speed remains synchronous. As δ increases, though E bph and V ph magnitudes are same, displacement of E bph from its ideal position increases. Fig.3.76 phasor diagram for motor on load So from the above discussion it is clear that on no load, current drawn by the motor is very small. This is because the stator and the rotor magnetic axes are almost matching transformer each other i.e. load angle δ is very small. As load increases, rotor magnetic axis starts retarding with respect to stator axis i.e. load angle δ increases maintaining the magnetic locking condition. And hence in case of the synchronous motor load affects the angle δ without affecting the speed. As δ increases, the magnitude of E Rph increases which shows that motor draws more current from the supply. This satisfies the increased load torque demand. So torque produced in the synchronous motor depends on the load angle 'δ' for small values of and to be precise depends on 'sinδ'. The load angle 'δ' is measured in degrees electrical. As 126

127 angle δ increases, the magnetic flux lines producing the force of attraction between the two get more and more stretched. This weakens the force maintaining the magnetic locking, though torque produced by the motor increases. As δ reaches upto 90 o electrical i.e. half a pole pitch, the stretched flux lines get broken and hence magnetic locking between the stator and rotor no longer exists. The motor comes out of synchronism. So torque produced at δ equal to 90 o electrical is the maximum torque, a synchronous motor can produce, maintaining magnetic locking i.e. synchronism. Such s torque is called pull out torque. The relationship between torque produced and load angle is shown in the Fig Analysis of Phasor Diagram Fig Torque angle characteristic Consider a phasor diagram with normal excitation i.e. such a current through field winding which will produce flux that will adjust magnitude of E bph same as V ph. Let δ be the load angle corresponding to the load on the motor. So from the exact opposing position of E bph with respect to V ph. E bph gets displaced by angle δ. Vector difference of E bph and V ph, gives the phasor which represents I a Z s, called E Rph. Now Z s = R a + j X s Ω where R a = Resistance of stator per phase X s = Synchronous reactance of stator per phase i.e. θ = tan -1 (X s /R a ) And Z s = (R a 2 + R s 2 ) Ω This angle 'θ' is called internal machine angle or an impedance angle. The significant of 'θ' is that it tells us that phasor I aph lags behind E Rph i.e. I a Z s by angle θ. Current always lags in case of inductive impedance with respect to voltage drop across that impedance. So phasor I aph can be shown lagging with respect to E Rph by angle θ. Practically R a is very small compared to X a and hence θ tends to 90 o. Note : The power factor at which motor is running, gets decided by the angle between V ph and I aph shown. This angle is denoted as Φ and called power factor angle. 127

128 and cos Φ = Power factor at which motor is working. The nature of this p.f. is lagging if Iaph lags V ph by angle Φ. While it is leading if Iaph leads V ph by angle Φ. Phasor diagram indicating all the details is shown in the Fig.3.78 Fig Phasor diagram under normal working condition Operation of S.M. at constant Load Variable Excitation We have seen previously that when load changes, for constant excitation, current drawn by the motor increases. But if excitation i.e. field current is changed keeping load constant, the synchronous motor reacts by by changing its power factor of operation. This is most interesting feature of synchronous motor. Let us see the details of such operation. Consider a synchronous motor operating at a certain load. The corresponding load angle is δ. At start, consider normal behaviour of the synchronous motor, where excitation is adjusted to get E b = V i.e. induced e.m.f. is equal to applied voltage. Such an excitation is called Normal Excitation of the motor. Motor is drawing certain current from the supply and power input to the motor is say P in. The power factor of the motor is lagging in nature as shown in the Fig. 3.79(a). Now when excitation is changed, changes but there is hardly any change in the losses of the motor. So the power input also remains same for constant load demanding same power output. Now P in = 3 V L I L cos Φ = 3 (V ph I ph cos Φ) Most of the times, the voltage applied to the motor is constant. Hence for constant power input as V ph is constant, 'I ph cos Φ' remains constant. Note: So far this entire operation of variable excitation it is necessary to remember that the cosine component of armature current, I a cosφ remains constant. So motor adjusts its cos Φ i.e. p.f. nature and value so that I a cos Φ remains constant when excitation of the motor is changed keeping load constant. This is the reason why synchronous motor reacts by changing its power factor to variable excitation conditions. a. Under Excitation When the excitation is adjusted in such a way that the magnitude of induced e.m.f. is less than the applied voltage (E b < V) the excitation is called Under Excitation. Due to this, E R increases in magnitude. This means for constant Z s, current drawn by the motor increases. But E R phase shifts in such a way that, phasor I a also shifts (as E R ^ I a = θ) to keep I a cos Φ component constant. This is shown in the Fig. 3.79(b). So in under excited condition, current 128

129 drawn by the motor increases. The p.f. cos Φ decreases and becomes more and more lagging in nature. Fig Constant load variable excitation operation b. Over Excitation The excitation to the field winding for which the induced e.m.f. becomes greater than applied voltage (E b < V), is called over excitation. Due to increased magnitude of E b, E R also increases in magnitude. But the phase of E R also changes. Now = E R ^ I a = θ is constant, hence I a also changes its phase. So Φ changes. The I a increases to keep I a cos Φ constant as shown in Fig.3.79(c). The phase of E R changes so that I a becomes leading with respect to V ph in over excited condition. So power factor of the motor becomes leading in nature. So overexcited synchronous motor works on leading power factor. So power factor decreases as over excitation increases but it becomes more and more leading in nature. c. Critical Excitation When the excitation is changed, the power factor changes. The excitation for which the power factor of the motor is unity (cos Φ = 1) is called critical excitation. Then I aph is in 129

130 phase with V ph. Now I a cos Φ must be constant, cos Φ = 1 is at its maximum hence motor has to draw minimum current from supply for unity power factor condition. So for critical excitation, cos Φ = 1 and current drawn by the motor is minimum compared to current drawn by the motor for various excitation conditions. This is shown in the Fig.3.79(d) V-Curves and Inverted V-Curves From the previous article, it is clear that if excitation is varied from very low (under excitation) to very high (over excitation) value, then current I a decreases, becomes minimum at unity p.f. and then again increases. But initial lagging current becomes unity and then becomes leading in nature. This can be shown as in the Fig Fig various values of I a and powerfactor Excitation can be increased by increasing the field current passing through the field winding of synchronous motor. If graph of armature current drawn by the motor (I a ) against field current (I f ) is plotted, then its shape looks like an english alphabet V. If such graphs are obtained at various load conditions we get family of curves, all looking like V. Such curves are called V-curves of synchronous motor. These are shown in the Fig. 3.81(a). As against this, if the power factor (cos Φ) is plotted against field current (I f ), then the shape of the graph looks like an inverted V. Such curves obtained by plotting p.f. against I f, at various load conditions are called Inverted V-curves of synchronous motor. These curves are shown in the Fig. 3.82(b). 130

131 Fig V-curves and Inverted V-curves Experimental Setup to Obtain V-Curves Fig shows an experimental setup to obtain V-curves and Inverted V-curves of synchronous motor. Stator is connected top three phase supply through wattmeters and ammeter. The two wattmeter method is used to measure input power of motor. The ammeter is reading line current which is same as armature (stator) current. Voltmeter is reading line voltage. Fig Experimental setup for V-curves A rheostat in a potential divider arrangement is used in the field circuit. By controlling the voltage by rheostat, the field current can be changed. Hence motor can be subjected to variable excitation condition to note down the readings. Observation Table: Now I L = I a, per phase value can be determined, from the stator winding connections. 131

132 I L = I aph for stator connection I L / 3 = I aph for delta connection The power factor can be obtained as The result table can be prepared as: The graph can be plotted from this result table. 1) I a Vs I f V-curve 2) cosφ Vs I f Inverted V-curve The entire procedure can be repeated for various load conditions to obtain family of V-curves and Inverted V-curves Expression for Back E.M.F or Induced E.M.F. per Phase in S.M. Case i) Under excitation, E bph < V ph. Z s = R a + j X s = Z s θ Ω θ = tan -1 (X s /R a ) E Rph ^ I aph = θ, I a lags always by angle θ. V ph = Phase voltage applied E Rph = Back e.m.f. induced per phase E Rph = I a x Z s V... per phase Let p.f. be cosφ, lagging as under excited, V ph ^ I aph = Φ Phasor diagram is shown in the Fig Fig Phasor diagram for under excited condition Applying cosine rule to OAB, (E bph ) 2 = (V ph ) 2 + (E Rph ) 2-2V ph E Rph x (V ph ^ E Rph ) but V ph ^ E Rph = x = θ - Φ 132

133 (E bph ) 2 = (V ph ) 2 + (E Rph ) 2-2V ph E Rph x (θ - Φ)...(1) where E Rph = I aph x Z s Applying sine rule to OAB, E bph /sinx = E Rph /sinδ So once E bph is calculated, load angle δ can be determined by using sine rule. Case ii) Over excitation, E bph > V ph p.f. is leading in nature. E Rph ^ I aph = θ V ph ^ I aph = Φ The phasor diagram is shown in the Fig Fig.3.84 Phasor diagram for overexcited condition Applying cosine rule to OAB, (E bph ) 2 = (V ph ) 2 + (E Rph ) 2-2V ph E Rph x cos(v ph ^ E Rph ) V ph ^ E Rph = θ + Φ... (E bph ) 2 = (V ph ) 2 + (E Rph ) 2-2 V ph E Rph cos(θ + Φ)...(3) But θ + Φ is generally greater than 90 o... cos (θ + Φ) becomes negative, hence for leading p.f., E bph > V ph. Applying sine rule to OAB, E bph /sin( E Rph ^ V ph ) = E Rph /sinδ Hence load angle δ can be calculated once E bph is known. Case iii) Critical excitation In this case E bph V ph, but p.f. of synchronous motor is unity.... cos = 1... Φ = 0 o i.e. V ph and I aph are in phase and E Rph ^ I aph = θ Phasor diagram is shown in the Fig Fig Phasor diagram for unity p.f. condition Applying cosine rule to OAB, (E bph ) 2 = (V ph ) 2 + (E Rph ) 2-2V ph E Rph cos θ...(5) 133

134 Applying sine rule to OAB, E bph /sinθ = E Rph /sinδ where E Rph = I aph x Zs V 3.24 Power Flow in Synchronous Motor Net input to the synchronous motor is the three phase input to the stator.... P in = 3 V L I L cosφ W where V L = Applied Line Voltage I L = Line current drawn by the motor cosφ = operating p.f. of synchronous motor or P in = 3 ([er phase power) = 3 x V ph I aph cosφ W Now in stator, due to its resistance R a per phase there are stator copper losses. Total stator copper losses = 3 x (I aph ) 2 x R a W... The remaining power is converted to the mechanical power, called gross mechanical power developed by the motor denoted as P m.... P m = P in - Stator copper losses Now P = T x ω... P m = T g x (2πN s /60) as speed is always N s This is the gross mechanical torque developed. In d.c. motor, electrical equivalent of gross mechanical power developed is E b x I a, similar in synchronous motor the electrical equivalent of gross mechanical power developed is given by, P m = 3 E bph x I aph x cos (E bph ^ I aph ) i) For lagging p.f., E bph ^ I aph = Φ δ ii) For leading p.f., E bph ^ I aph = Φ + δ iii) For unity p.f., 134

135 E bph ^ I aph = δ Note: While calculating angle between E bph and I aph from phasor diagram, it is necessary to reverse E bph phasor. After reversing E bph, as it is in opposition to V ph, angle between E bph and I aph must be determined. In general, Positive sign for leading p.f. Neglecting sign for lagging p.f. Net output of the motor then can be obtained by subtracting friction and windage i.e. mechanical losses from gross mechanical power developed.... P out = P m - mechanical losses. Where, T shaft = Shaft torque available to load. P out = Power available to load... Overall efficiency = P out /P in Alternative Expression for Power Developed by a Synchronous Motor Consider the phasor diagram of a synchronous motor running on leading power factor cosφ as shown in the Fig Fig 3.86 Phasor Diagram The line CD is drawn at an angle θ to AB. The lines AC and DE are perpendicular to CD and AE. and angle between AB = E bph and I aph is also ψ. The mechanical per phase power developed is given by, 135

136 In triangle OBD, BD = OB cosψ = I a Zs cosψ OD = OB sin ψ = Ia Zs sin Now BD = CD - BC = AE BC Substituting in (2), I a Zs cosψ = V ph cos (θ-δ) - E b cosθ All values are per phase values Substituting (3) in (1), This is the expression for the mechanical power developed interms of the load angle δ and the internal machine angle θ, for constant voltage V ph and constant E ph i.e. excitation Condition for Maximum Power Developed The value of δ for which the mechanical power developed is maximum can be obtained as, Note : Thus when R a is negligible, θ = 90 o corresponding torque is called pull out torque. for maximum power developed. The The Value of Maximum Power Developed 136

137 The value of maximum power developed can be obtained by substituting θ =δ in the equation of P m. When R a is negligible, θ = 90 o and cos (θ) = 0 hence,... R a = Z s cosθ and X s = Z s sinθ Substituting cosθ = R a /Z s in equation (6b) we get, Solving the above quadratic in E b we get, As E b is completely dependent on excitation, the equation (8) gives the excitation limits for any load for a synchronous motor. If the excitation exceeds this limit, the motor falls out of step Condition for Excitation When Motor Develops (P m ) R max Let us find excitation condition for maximum power developed. The excitation controls E b. Hence the condition of excitation can be obtained as, Assume load constant hence δ constant. but θ = δ for P m = (P m ) max Substitute cosθ = R a /Zs 137

138 This is the required condition of excitation. Note: Note that this is not maximum value of but this is the value of foe which power developed is maximum. The corresponding value of maximum power is, 3.25 Salient Pole Synchronous Motor The analysis of salient pole synchronous motor is based on the Blondel's two reaction. The direct and quadrature axis components of current and reactance are same as defined earlier for the synchronous generators. Thus, X d = Direct axis reactance X q = Quadrature axis reactance I d = Direct axis component of I a I q = Quadrature axis component of I a The complete phasor diagram of lagging p.f. is shown in the Fig Fig Phasor diagram for lagging p.f. From the phasor diagram it can be derived that, Note : For the proof of above results refer example 2. The complete phasor diagram of leading p.f. is shown in the Fig

139 Fig Phasor diagram for leading p.f. Note: Φ should be taken negative for the leading power factor for calculating other parameters. While the mechanical power developed per phase is given by, Total P m = 3 x P m 3.26 Hunting in Synchronous Motor It is seen that, when synchronous motor is on no load, the stator and rotor pole axes almost coincide with each other. When motor is loaded, the rotor axis falls back with respect to stator. The angle by which rotor retards is called load angle or angle of retardation δ. If the load connected to the motor is suddenly changed by a large amount, then rotor tries to retard to take its new equilibrium position. But due to inertia of the rotor, it cannot achieve its final position instantaneously. While achieving its new position due to inertia it passes beyond its final position corresponding to new load. This will produce more torque than what is demanded. This will try reduce the load angle and rotor swings in other direction. So there is periodic swinging of the rotor on both sides of the new equilibrium position, corresponding to the load. Such a swing is shown in the Fig Fig Hunting in synchronous motor Such oscillations of the rotor about its new equilibrium position, due to sudden application or removal of load is called swinging or hunting in synchronous motor. Due to such hunting, the load angle changes its value about its final value δ. As changes, for same excitation i.e. E bph 139

140 the current drawn by the motor also changes. Hence during hunting there are changes in the current drawn by the motor which may cause problem to the other appliances connected to the same line. The changes in armature current due to hunting is shown in the Fig Fig Current variations during hunting If such oscillations continue for longer period, there are large fluctuations in the current. If such variations synchronous with the natural period of oscillation of the rotor, the amplitude of the swing may become so great that motor may come out of synchronism. At this instant mechanical stresses on the rotor are sever and current drawn by the motor is also very large. So motor gets subjected to large mechanical and electrical stresses. Note : Hence hunting is not desirable phenomenon from motor point of view and must be prevented. Use of Damper Winding to Prevent Hunting It is mentioned earlier that in the slots provided in the pole faces, a short circuited winding is placed. This is called damper winding. When rotor starts oscillating i.e. when hunting starts a relative motion between damper winding and the rotating magnetic field is created. Due to this relative motion, e.m.f. gets induced in the damper winding. According to Lenz's law, the direction of induced e.m.f. is always so as to oppose the cause producing it. The cause is the hunting. So such induced e.m.f. oppose the hunting. The induced e.m.f. tries to damp the oscillations as quickly as possible. Thus hunting is minimised due to damper winding. The time required by the rotor to take its final equilibrium position after hunting is called as setting time of the rotor. If the load angle is plotted against time, the schematic representation of hunting can be obtained as shown in the Fig It is shown in the diagram that due to damper winding the setting time of the rotor reduces considreably. Fig.3.91 Effect of damper winding on hunting 3.27 Synchronization with Infinite Bus Bar 140

141 There is a specific procedure of connecting synchronous machine to infinite bus bars. Infinite bus bar is one which keeps constant voltage and frequency although load varies. The Fig shows a synchronous machine which is to be connected to the bus bars with the help of switch K. If the synchronous machine is running as a generator then its phase sequence should be some as that of bus bars. The machine speed and field current is adjusted in such a way so as to have the machine voltage same as that of bus bar voltage. The machine frequency should be nearly equal to bus bar frequency so that the machine speed is nearer to synchronous speed. Fig Synchronization with Infinite Bus Bar When the above conditions are satisfied, the instant of switching for synchronization should be determined. This can be determined by lamps dark method, Lamps bright and dark method or by using synchroscope. Once switch K is closed, the stator and rotor fields of the machine lock into each other and the machine then runs at synchronous speed. The real power exchange with the mains will be now governed by the loading conditions on the shaft while the reactive power exchange will be determined by field excitation. The same procedure is to be followed for synchronizing the synchronous motor to the infinite bus bars. The motor is run by an auxiliary device such as small dc or induction motor initially and then synchronized to the bus bars. As we know that the synchronous motors are not self-starting hence if switch K is closed when rotor is stationary, the average torque will be zero as the two fields run at synchronous speed relative to each other so the motor fails to start. They are made selfstarting by providing short circuited bars on the rotor which produce torque as produced in case of induction motors Synchronous Condensers When synchronous motor is over excited it takes leading p.f. current. If synchronous motor is on no load, where load angle δ is very small and it is over excited (E b > V) then power factor angle increases almost upto 90 o. And motor runs with almost zero leading power factor condition. This is shown in the phasor diagram Fig Fig Synchronous condenser 141

142 This characteristics is similar to a normal capacitor which takes leading power factor current. Hence over excited synchronous motor operating on no load condition is called as synchronous condenser or synchronous capacitor. This is the property due to which synchronous motor is used as a phase advancer or as power improvement device. Disadvantage of Low Power Factor In various industries, many machines are of induction motor type. The lighting and heating loads are supplied through transformers. The induction motors and transformers draw lagging current from the supply. Hence the overall power factor is very low and lagging in nature. The power is given by, P = VI cosφ... single phase... I = P/(VcosΦ) The supply voltage is constant and hence for supplying a fixed power P, the current is inversely proportional to the p.f. cosφ. Let P = KW is to be supplied with a voltage of 230 V then, Case i) cosφ = 0.8, I = (5 x10 3 )/(230 x 0.8) = A Case ii) cos = 0.6, I = (5 x10 3 )/(230 x 0.6) = A Thus as p.f. decreases, becomes low, the current drawn from the supply increases to supply same power to the load. But if p.f. maintained high, the current drawn from supply is less. The high current due to low p.f. has following disadvantages: 1. For higher current, conductor size required is more which increases the cost. 2. The p.f. is given by cosφ = Active power/ Apparent = (P in KW)/ (S i.e. KVA rating). Thus for fixed active power P, low p.f. demands large KVA rating alternators and transformers. This increases the cost. 3. Large current means more copper losses and poor efficiency. 4. Large current causes large voltage drops in transmission lines, alternators and other equipments. This results into poor regulation. To compensate such drop extra equipments is necessary which further increases the cost. Note : Hence power factor improvement is must practice. Hence the supply authorities encourage consumers to improve the p.f Use of Synchronous Condenser in Power Factor Improvement The low power factor increases the cost of generation, distribution and transmission of the electrical energy. Hence such low power factor needs to be corrected. Such power factor correction is possible by connecting synchronous motor across the supply and operating it on no load with over excitation. Now let V ph is the voltage applied and I 1ph is the current lagging V ph by angle Φ 1. This power factor Φ 1 is very low, lagging. The synchronous motor acting as a synchronous condenser is now connected across the same supply. This draws a leading current of I 2ph. The total current drawn from the supply is now phasor of I ph and I 2ph. This 142

143 total current I T now lags V ph by smaller angle Φ due to which effective power factor gets improved. This is shown in the Fig Fig Power factor correction by synchronous condenser This is how the synchronous motor as a synchronous condenser is used to improve power factor of the combined load Applications of Three Phase Synchronous Motor The important characteristics of the synchronous motor is its constant speed irrespective of the load conditions, and variable power factor operation. As seen earlier its power factor can be controlled by controlling its excitation. For over-excitation its power factor is leading in nature, which is very important from the power factor correction point of view. Due to constant speed characteristics, it is used in machine tools, motor generator sets, synchronous clocks, stroboscopic devices, timing devices, belt driven reciprocating compressors, fans and blowers, centrifugal pumps, vacuum pumps, pulp grinders, textile mills, paper mills line shafts, rolling mills, cement mills etc. The synchronous motors are often used as a power factor correction device, phase advancers and phase modifiers for voltage regulation of the transmission lines. This is possible because the excitation of the synchronous motor can be adjusted as per the requirement. The disadvantages of synchronous motor are their higher cost, necessity of frequent maintenance and a need of d.c. excitation source, auxiliary device or additional winding provision to make it self-starting. Overall their initial cost is very high Comparison of Synchronous and Induction Motor 143

144 3.31 Synchronous Induction Motor In the applications where high starting torque and constant speed are desired then synchronous induction motors can be used. It has the advantages of both synchronous and induction motors. The synchronous motor gives constant speed whereas induction motors can be started against full load torque. Consider a normal slip ring induction motor having three phase winding on the rotor as shown in the Fig Fig Synchronous Induction Motor The motor is connected to the exciter which gives d.c. supply to the motor through slip rings. One phase carries full d.c. current while the other two carries half of the full d.c. current as they are in parallel. Due to this d.c. excitation, permanent poles (N and S) are formed on the rotor. Initially it is run as an slip ring induction motor with the help of starting resistances. When the resistance is cut out the motor runs with a slip. Now the connections are changed and the exciter is connected in series with the rotor windings which will remain in the circuit permanently. As the motor is running as induction motor initially high starting torque (upto twice full load value) can be developed. When d.c. excitation is provided it is pulled into synchronism and starts running at constant speed. The synchronous induction motor provides constant speed, large starting torque, low starting current and power factor correction. It may be possible that the a.c. winding is put on the rotor and the d.c. excitation is provided on the stator. This simplifies control gear. It also gives better facilities for insulation which permits higher voltages and lower d.c. excitations. The d.c. winding must be designed in such a way as to give high m.m.f. with moderate d.c. excitation power. The excitation loss must be distributed evenly over the winding. The mmf distribution should be nearly sinusoidal. It should also provide damping against hunting and it should be satisfactorily started as induction motor. Fig Rotor current Variations 144

145 When the machine is running as an induction motor there are induced alternating currents in the rotor and it runs below synchronous speed. When the rotor carries d.c. currents in the rotor and it runs below synchronous speed. When the rotor carries d.c. currents the rotor field and hence the rotor must run at synchronous speed. This means that slip must be reduced to zero. But if there is any departure from this speed during normal operation then again induced currents are there in the rotor. The rotor is of low resistance so its windings act as damping winding. Hence no separate damping windings are required. When direct current excitation is provided a synchronizing torque is quickly set up. The magnitude of this torque is T m sinθ where θ is the angle between stator and rotor field. In addition to this induction motor torque is also present which is proportional to the slip (dθ/dt), so long as slip is small. There may also be constant load torque if it is started on load and finally it requires torque J(d 2 θ/d 2 t) to accelerate the rotor. It can be seen that θ<π as long as the synchronizing torque acts in opposite direction to that of load torque which tends to reduce the angular velocity dθ/dt of the slip motion. when π<θ<2π then synchronizing torque acts in conjuction with load torque to increase the slip i.e. nothing but angular velocity dθ/dt and the motor fails to synchronize. As the slip motion is irregular, the motor is subjected to mechanical strains. Also there may be oscillations in current and power factor. Hence it is desired that the motor should synchronize as quickly as possible after switching d.c. excitation. It requires that synchronizing torque should be sufficiently larger than load torque and it should be opposite of load torque. The angle obtained at the instant of switching d.c. excitation also affects pulling into step. Following figures shows oscillograms of rotor current on application of excitation for various values of θ. When the excitation is delayed beyond 60 o it is seen that the rotor fails to synchronize as the induction motor torque and the synchronizing torque work in conjuction and the torque will have pulsating value. Thus the motor can be pulled into the synchronism if excitation is applied at a position that the rotor will occupy when both stator and rotor fields are synchronized Performance Characteristics of Synchronous Induction Motors While studying the performance characteristics of synchronous induction motor, three different types of torques are to be considered. These are viz the starting torque which indicates capacity of motor to start against load, pull in torque which indicates the ability of the motor to maintain operation during change over from induction motor to synchronous motor, pull out torque which represents the running of motor synchronously at peak load. The first two torques are closely related with each other and are the characteristics of the machine running as induction motor. The pull out torque is characteristics when it is running running synchronously. The characteristics curves for synchronous induction motor operating at full load unity p.f. and at 0.8 p.f. leading is shown in the Fig Fig Characteristics Curves 145

146 When the load exceeds the synchronous pull out torque, the machine loses synchronism and runs as an induction motor with fluctuation in torque and slip due to d.c. excitation. With reduction in load torque the motor is automatically resynchronized Advantages, disadvantages and applications of Synchronism Induction Motor Advantages of Synchronous Induction Motor Following are the advantages of synchronous induction motor over salient pole synchronous motor. i) The synchronous induction motor can start and synchronize against more than full load torque which is not possible with salient pole synchronous motor which must be started against light load. ii) The exciter required for synchronous induction motor is of smaller capacity as the gap is not long as compared to normal salient pole motor. iii) The rotor winding in synchronous induction motor can function as providing excitation and required damping. So no separate damper winding is required. iv) No separate starting and control equipments are required. Disadvantages of Synchronous Induction Motor i) As the gap is small as compared to normal salient pole synchronous motor it will not give large overload capacity. ii) The variation of power factor is large as compared to normal synchronous motor. iii) The speed variation is not possible for synchronous induction motor as it runs at constant motor. Applications of Synchronous Induction Motor The applications where mechanical load is to be driven alongwith phase advancing properties of synchronous motors are to be used then use of synchronous induction motor is better option. Also the applications where in load torque is remaining nearly constant, this motor can be used. Two Marks Question and Answers 1. What are the causes of harmonics in the voltage and current waves of electrical machinery? The main causes of harmonics are, i) variation of airgap reluctance. ii) Distribution of stator winding. 2. Define coil span factor. The factor by which the induced emf gets reduced due to short pitching is called pitch factor or coil span factor denoted as K c. K = cos α c where, α is the angle of short pitch List the types of rotors of the synchronous generator. State their features. There are two types of synchronous generator namely salient type and cylindrical type rotor. In salient pole structure, the air gap is non uniform. These poles are mechanically weak and hence preferred for low speed alternators. Separate 146

147 damper winding is provided. In cylindrical type structure, the air gap is uniform. It is mechanically robust and hence preferred for high speed turbo alternators. Separate damper winding is not necessary. 4. Represent the power / power angle curve of a synchronous machine. Power Load angle 5. What is the speed range for which salient pole alternators are designed? Mention an application where such alternators are adopted? As mechanical strength of salient pole machine is less, this is preferred for low speed alternators ranging from 125 rpm to 500 rpm. These type of alternators are used in hydel power plants. 6. What are the functions of damping winding provided with alternator? Damper windings are provided with the alternator to reduce the oscillations. 7. What are the methods by which zero p.f. lagging curve can be obtained? In ZPF test the alternator is connected with inductive load. A pure inductive load has power factor of zero lagging hence the test is called zero power factor test. The machine speed is maintained constant at its synchronous value. The load current delivered by an alternator to purely inductive load is maintained constant at its rated full load value by varying excitation and by adjusting variable inductance of the inductive load. 8. Why the field system of an alternator made as a rotor? (Or) Why the armature is made stationary in alternator? The field system of an alternator is made rotating to avoid interaction of mechanical and electrical stresses. Also with rotating field system, it is easier to collect currents at very high voltages from stationary member. Due to low voltage on field side, the insulation required is less. The problem of sparking is avoided. The construction with rotating field is simple and only two slip rings are required to provide external dc supply. 9. Compare salient pole rotor and cylindrical pole rotor. Sl.No. Salient pole type Cylindrical type 1. Poles are projecting out from the surface Unslotted portion of the cylinder acts as poles hence poles are non projecting. 2. Airgap is non uniform Airgap is unifrom 3. Diameter is high and axial lengh is small. Small diameter and large axial length. 4. Mechanically weak and hence Mechanically robust and hence used for preferred for low speed alternators. high speed alternators. 147

148 10. What are the conditions of parallel operation of alternators? The conditions to be satisfied for parallel operation of alternators are, i) The terminal voltage of the incoming machine must be same as that of bus bar voltage. ii) The frequency must be same as that of the incoming machine as well as that of bus bar. iii) With respect to the external load, the phase of alternator voltage must be identical with that of the bus bar voltage. 11. What are the methods of reducing the space harmonics in a machine? i) Distribution of armature windings ii) Chording iii) Fractional slot windings 12.Explain distribution factor in synchronous generator. The factor by which there is a reduction of emf due to the distribution of coils is called distribution factor. m β sin 2 K d = where β is the slot angle and β m sin 2 m is number of slots per pole per phase. 13.What are the reasons for drop in voltage from no load to full load? The reasons for drop in voltage from no load to full load are, iv) Drop in armature resistance v) Armature leakage reactance vi) Reaction corresponding to armature reaction. 14.List the methods of ventilation. There are two types of ventilation namely, vii) Natural ventilation viii) Closed circuit ventilation system. 15.What is brushless excitation? It consists of silicon diode rectifiers which are mounted on the same shaft of alternator and will directly provide necessary excitation to the field. The problem of sparking is avoided in this type system. 16.Mention the advantages of short pitched coil. Because of short pitching the effective length of copper is reduced which leads to reduction of cost. 17. What are the methods to find the regulation of an alternator. There are four methods to find the regulation of an alternator. ix) Direct loading method x) EMF method xi) MMF method xii) ZPF method 148

149 xiii) ASA method 18.What do you mean by Synchronization of an Alternator? The process of connecting or switching of one alternator to the other alternator or to the infinite bus bar with out any interruption is called synchronization. 19.What is the necessity of Parallel Operation of an Alternator? To avoid the power shut down during maintenance or inspection by sharing the load to other units. To have the optimum utility of the alternators To have the good reliability of the supply To achieve the better efficiency by operating the alternators with full load. 20.What are the methods of Synchronizing Alternator? Dark lamp method Bright lamp method Synchroscope method 21.What is infinite bus bar? The bus bar whose frequency and phase emf remain unaffected by the changes in the condition of any one machine connected to it is called as infinite bus bar. 22.How it is identified that the phase sequence of an incoming Alternator is same as that of the bus bar? If the lamps are glowing with the same dark period or bright period, then the it can be considered as same phase sequence. If the lamps becoming dark and bright simultaneously it indicates the incorrect phase sequence. 23.Explain the term Alternator floating on bus bar. If the alternator is once connected in parallel with the bus bar after satisfying the condition then it is said to be in floating condition. UNIT 3 (Synchronous Motor) 1. Mention four applications of synchronous motor. i) Synthetic fiber drawing ii) Constant speed applications iii) Synchronous condenser 2. What are the inherent disadvantages of synchronous motor? i) It is not a self starting motor. ii) During under excited conditions, the power factor is very less. 3. What is the role of synchronous motor in a transmission line? How? By changing the excitation level, change in power factor is achieved. This Property is used in transmission line to improve the power factor of the transmission line. Give the expression for the gross mechanical power developed by synchronous motor. The gross mechanical power developed is denoted as P m and the expression is as follows. 149

150 2πN stg Pm = Where, N s is the synchronous speed, T g is the gross torque 60 Developed. 4. When is a synchronous motor said to be under excited? What will be the p.f. at this condition? When the excitation is adjusted in such a way that the magnitude of induced emf is less than the applied voltage, the excitation is called Under excitation. The power factor decreases and becomes more lagging in nature. 5. What is synchronous reactance? The leakage reactance X L and the armature reactance X a may be combined to give the synchronous reactance X s. X s = X L + X a. 6. What is hunting? When synchronous motor is on no load, the stator and rotor pole axes coincide with each other. When motor is loaded, the rotor pole axis falls back with respect to stator. If the load connected to motor is suddenly changed by a large amount, then rotor tries to retard to take its new equilibrium position. But due to inertia of rotor, it can not achieve equilibrium instantaneously. While achieving new position, it passes beyond its final position corresponding to new load. This will produce more torque than demanded. So, the load angle is reduced and rotor swings in other direction. Such oscillations of the rotor about its new equilibrium position due to sudden application or removal of load is called hunting. 7. Enlist the advantages and disadvantages of synchronous motor. Main disadvantage is it needs external starting arrangements. Regarding the advantage, it mainly improves the power factor by simply adjusting the excitation. 8. Why synchronous motor is not self starting? When a three phase supply is given to the stator, rotating magnetic field is produced. At one instant, due to unlike poles trying to attract each other, the rotor will be subjected to a torque in clockwise direction. At another instant, the like poles trying to repel each other, the rotor will be subjected to a torque in anticlockwise direction. As a result, the average torque exerted on the reotr is zero. And hence the synchronous motor is non self starting. 9. List the starting methods of synchronous motor. The starting methods are, i) Using pony motors ii) Using damper winding iii) As a slip ring induction motor iv) Using small dc machine coupled to it. 10. Define synchronous motor. The motor which rotates with always synchronous speed otherwise zero speed is known as synchronous motor. 150

151 11. What are V and inverted V curves? Why they called so? The variation of armature current in response to the field current is given by V curve. Since the variation looks like an English alphabet V, it is named as so. The variation of power factor in response to the change in field current is given by inverted V curve. Since the variation looks like an inverted V, it is named as so. 12. What is synchronous condenser? When synchronous motor is overexcited it takes leading power factor current. This characteristics is similar to a capacitor which always takes leading power factor current. Hence over excited synchronous motor operating on no load condition is called as synchronous condenser or synchronous capacitor. 13. List the disadvantages of low power factor. If the power factor is low, it results in large amount of current. The following are the disadvantages of having large current. i) For high current, conductor size required is more which increases the cost. ii) For fixed active power, low power factor demands large KVA rating alternators and transformers. This increases the cost. iii) The large amount of current leads to more copper lossed and poor efficiency. iv) Large current causes large voltage drops in transmission lines, alternators and other equipments. This results in poor regulation. 14. Compare synchronous motor and induction motor Synchronous motor is non self starting motor. By changing the field Excitation, the power factor can be varied. It can be used for power factor correction. Induction motor is a self starting motor. The field excitation cannot be changed. It cannot be used for power factor correction. 15. Discuss why the starting torque of a synchronous motor is zero? Due to inertia of the rotor it is not able to lock with the stator poles which is alternatively changing for the positive and negative half cycle. During that time the rotor rotates CW for some time and CCW for some time. So the average torque is zero. 19. Discuss how a synchronous motor can be used to control the power factor? By operating the motor in over excited condition, it takes the leading power factor current and at no load the power factor angle increases almost upto 90 degree. Hence to control the power factor the synchronous motor is over excited on no load condition which shows the characteristics of capacitor. 151

152 UNIT IV INDUCTION MACHINES 9 Induction motor:- Construction and principle of operation, Classification of induction motor, Torque equation, Condition for maximum torque, Equivalent Circuit, Starting methods and Speed control of induction motors. 4.1 Introduction An electric motor is device which connects an electrical energy in to mechanical energy. Generally it is classified A.C motor and D.C motors. The AC motor is further classified in to single phase and three phase induction motors. The important Quality of three phase induction motor is self-starting one and no need of starting device. It provides good speed regulation and robust construction. The working principle of three phase induction motor is based on the rotating magnetic field caused by mutual induction between stator and motor. So it is called rotating transformer, stator is primary and short circuited rotor is acting as secondary. 4.2 Rotating Magnetic field. The rotating magnetic field can be defined as the flux a field rotating continuously in a plane with constant amplitude and certain axis at a speed of synchronous speed (NS). In a three phase induction motor the rotating magnetic field is produced with the help of three phase AC supply applied to the set of stationary windings. Due to interaction of three fluxes, resultant flux produced with constant magnitude and its axis rotating in space without physical rotation of windings Production of R.M.F: A three phase windings in a stator of three phase induction motor is called stator. The stator winding may be connected Star (or) Delta. The three phase windings are displaced from each other by 120 and it is supplied by three phase A.C supply. The three phase currents flow simultaneously through the windings and are displaced from each other by 120 electrical each alternating phase current produces its own flux which is sinusoidal. φ R = φm Sin ( ω t ) = φ m sinθ φ Y = φm Sin ( ωt ) = φ m Sin (θ- 120 ) φ B = φm Sin ( ωt ) = φ m Sin (θ ) Let the flux φ R is taken as reference flux to find the resultant flux φ '. The resultant flux φ T = φ R + φ Y + φ B Waveform of three fluxes: Vector diagram o φ = φ m Sin θ = 0. R ' T Conclusion: (i) The resultant flux T φ is 1.5 times of maximum flux of an individual flux due to any phase 152

153 (ii) The resultant always keeps an rotating with a certain speed in space Speed of rotating magnetic field: Let f the frequency of A.C supply, P number of poles, For which winding in wound N Speed in R.P.M The relation between these three factors in deviced 120 f N S =. P For a fixed frequency whatever speed of RMF result called synchronous speed. In a phase sequence of R-Y-B, phase R leads y by 120and y leads by B by 120. So rotating magnetic field rotates form axis of R to axis of Y and then to axis of b and so on for clockwise direction rotation for Anticlockwise rotation, any two 8 th terminals are interchanged, the direction of RMF will be Anticlockwise. 4.3 Construction of Three phase induction motor Figure 4.1 Main parts of Induction motor The important parts of induction motor is as shown in the figure 4.1 Basically, two important parts are presented in an induction motor, 1. Stator the part at which three phase windings are implored and stationary 2. Rotor the part at which mechanical load connected through shaft and rotates : Stator Figure 4.2 Cross sectional view of Induction motor The stator is made up of silicon steed stampings. The thickness of each stamping is 0.4 to 0.5 mm and these stampings are slotted on its periphelly to carry stator winding. The stampings are stamped together to form the stator core. The core is fitted in a cast (or) fabricated steel frame and it laminated to reduce iron loss. The slots available in the stator core causes windings are called stator windings. The stator windings are three phase windings and it is 153

154 connected in star (or) delta. The windings are wounded with definite number of poles and it is excited by a three phase supply to produce rotating magnetic field. The radial duels are provided on the stator frame for cooling purposes of motor. There are six terminals are brought out from the stator of the motor to connect either star (or) delta Rotor: The rotor is made up of cast iron and it is cylindrical with slots on its periphery. The rotor is placed inside stator to provide the output of mechanical rotation. The rotor conduct (or) windings is placed in the rotor slots. There are two types of rotor constructions 1. Squirrel cage 2. Slip ring (or) wound Rotor Squirrel cage Rotor Figure 4.3 Squirrel cage Rotor of 3 phase induction motor The construction of squirrel cage rotor as shown in the figure 3.3.The rotor core is cylindrical and slotted at outer periphery. The rotor consists of copper (or) aluminium bars it s are called rotor conductors. The bars are permanently stored at both ends with the help of copper rings called end ring. The rotor windings (or) bars are shorted with brazed end rings to provide good mechanical strength. The rotor construction forms a closed electrical circuit (Short circuit) and looks like a cage, so it called squirrel cage rotor. The rotor resistance is very small and there is no position to add external resistance in the rotor circuit. So the construction of rotor is simple. To circulate air, during the operation of motor, fan blades are provided at the end of rotor core slip ring Rotor or wound rotor Figure 4.4 Slip ring Rotor construction of 3 phase induction motor In the type of rotor the three phase winding are employed in the slots of rotor with the connection of star or delta the winding are of distributed and wounded with same no of poles in the starter.the slots containing rotor winding,one end of winding in permanently connected to the slip ring. the slip ring are connected in same shaft of rotor and it is used to 154

155 add external resistance circuit to the internal circuit during the running condition, the slip ring are short circuit with the help of metal collar. At this time brushes are taken away from the slip rings Key points: The provision for adding external resistance to rotor circuit provides large starting torque and good control Difference between squirrel cage and phase wound rotor S.No squirrel cage rotor wound rotor or Slip ring rotor 1 Rotor consist of bars which are shorted at the ends with the helps of end rings 2 Rotor resistance in small because of its presently shorted.external resistance cannot be added Rotor consist of three phase winding with no of poles similarly to the starter winding Resistance can be added externally because rotor is also carrying winding 3 Construction is very simple Construction is complicated, due to the presence of slip ring brushless 4 Moderate starting torque is developed and torque is cannot be controlled Torque is controlled and it proudness high starting torque by adding external resistance 5 The rotor automatically adjusts itself for the same no of [poles as that of stator 6 Speed cannot be controlled by rotor resistance 7 Used for lathes, drilling machines,fans, blowers, printing machines Rotor must be wound for the same no of poles as that of stator Speed can be controlled by rotor resistance Used for lifts, cranes, elevator, compressor etc. 4.4 Working principle Induction motor works on the principle of electromagnetic induction. When a three phase supply in applied to the three phase stator winding of induction motor a rotating magnetic field is produced the speed of rotating magnetic field in synchronous speed N s rpm 120 f N s = where f-supply frequency,p- No of poles in stator winding P Let the direction of rotating magnetic field is clock wise as shown in the figure

156 Figure 4.5 Rotating magnetic fields in three phase induction motor At the instant rotor in stationary and stator flux R.M.F is rotating. The R.M.F is cutting by rotor conductor as R.M.F sweeps over the rotor conductors. Whenever conductor cuts the flux, the E.M.F gets induced in it. this is called electro-magnetic induction. The rotor is short circuited and it forms a closed circuit, induced E.M.F circulates current through rotor called rotor current. Any current carrying conductor produces its own flux, so rotor produces its flux called rotor flux. The direction can be easily determined using Fleming s right hand rule. There are two fluxes, one is R.M.F and another one is rotor flux. Both the flexes are inter acting each other on the left of rotor conductor, two fluxes are in same direction hence they added up to get high flux area. On right side, these two fluxes are cancel each other to produce low flux area. The flux lines are acted as stretched rubber band, where the high flux density area exerts a push on rotor conductor towards low flux. All rotor conductors are experiencing the force, so the whole rotor experiences a torque and starts rotating, in the directions of rotating magnetic field. Another explanation: According to lenz s law the direction of induced current in the rotor is opposing the cause of it. The cause of rotor current is induced E.M.F which is induced, because of relative motion present between the rotating magnetic field and the rotor conductor. Hence to oppose the relative motion, i.e, to reduce the relative speed the rotor experiences a torque in the same directions as that of E.M.F and tries to catch up the speed of rotating magnetic field N s - Speed of rotating magnetic field N- Speed of rotor i.e motor in rpm N s -N = relative speed between the two i.e. Rotating magnetic field and the rotor conductors can the rotating speed of rotor is equal to the speed of rotating magnetic field? When the rotor starts rotating and it tries to catch the speed of rotating magnetic field.if it catches the speed of RMF, the relative motion between rotor and rotating magnetic field will absent. If there is no relative motion, no induced emf and no rotor current and rotor flux.hence the rotor flux is not available, there is no torque produced in the motor. Due to this reason,the motor will stop. So always the rotor should rotate at a speed is slightly less than the synchronous speed is called sub synchronous speed and the motor is called asynchronous motor The difference between the rotor speed and rotating magnetic field is called slip speed of the motor N s -N = slip speed 4.5 Slip of the induction motor The slip in defined as the ratio of slip speed of induction motor (N s -N) and synchronous speed (N s ) N N S= s r Ns N N % S= s r x100 Ns The speed of rotor expressed as, N r = N s (1-S) when the motor at stand still condition at N r =o,s=1 at start 4.6 Torque Equation The torque produced in the induction motor depends on the following factors 1) The values of rotor current in running condition 156

157 2) The power factor of me rotor current in running condition Tαφ I 2 r cosφ 2 r 1 Where φ = flux produced by stator I 2r = rotor current in running condition cosφ 2r Power factor of rotor in running condition t the flux φ produced by stator is proportional to E 1 i.e. Stator voltage φα E1αE 2 ER Q = K E1 E2 SE I 2r Q r 2 = = 2 2 E1 R 2 + Sx2 Cos R 2 ( ) R 2 2 2r = 2 Z 2r R2 2 + ( Sx2) 3 Substitute 2,3,4 in 1 φ =E Tα E 2 2 SE 2 ( ) 2 R 2 + Sx2 Tα R SE 2R ( Sx2) 2 2 R 2 ( ) 2 R 2 + Sx2 NM N s N S = synchronous speed in rps = 60 T 2 KSE2 R2 = Where K = R 2 ( ) Sx2 T= From The power flow Diagram Rotor Efficiencyη r = 3 2πns Pout Efficiency of motor Pin 4.7 Relationship between P 2r, Pc, Pm: Let T= Torque developed by motor Gross mech power = P m T xω Where speed in rpm SE 2R 2 2 R ( Sx2) 2 3 2πns RotorOutpu t grossmechanicalpowerdevloped = RotorInput RotorInput Pm = P 2r Tx2πNr P m =

158 Next the input power P 2r is transferred from stator side to rotor through rotating magnetic field, whose speed is N s P 2r = T xω s Tx2πNs P 2r = 2 Dividing 3/2 60 Rotor colors P c = P 2r -P m = Tx2πNs 60 - Tx2πNr 60 Tx2π P c = (N s -N) = rotor copper loss Pc = P2 r Tx2π ( N N ) S 60 r Tx2πxNs = 60 Ns Nr Ns Pc = S P c SxP 2r P2r P 2 P c =P m P 2 P c =P m, (1-S)P 2 =P m Total rotor copper loss is slip times the rotor in put The gross mechanical power developed (1-S) times of rotor input P 2 = P c :P m is 1:S:1-S Pc S P2 I =, = Pm 1 S Pc S 4.8 Need of Starter The rotor current in the running condition is given by SE2 I 2 r 2 R 2 + ( Sx ) 2 during the starting condition the speed of the motor in zero and slip in maximum so the induced emf in rotor is very large.it circulated large current in rotor because rotor in short circuited if the rotor current in large, the stater also draws very high current from the supply. This is 5 to 7 times of full load current of motor.so need of starter is i ) to reduce heavy inrush of current at short and presenting damage of motor winding ii) to reduce the sudden inruse of current larges Large voltage drop in line and effecting other appliances in the same line the starter in advice used to limit high starting current by supplying reduced voltage to the motor at the timing starting types of Starters To reduce the value E 2 or by increasing the rotor resistance R 2 we can reduce the high value of rotor current The different types of starter 1) Stator resistance starter 2) Auto transformer starter 3) Star Delta starter 4) Rotor resistance starter 5) Direct on line starter Condition for maximum Torque. T α ØI 2r cosø 2r 2 158

159 3 2Πns 2 S E 2 R R 2+ S 2 ( ) 2 From the equation, torque depends only & slips of induction motor. The supply voltage E 2 and R 2,X 2,n s are constants in the induction motor. To obtain condition for maximum torque only variable S can be varied.so the equation can be differentiated with S dt =0 ds ( d( ks R 2 2 E 2 2 R ( S 2) )/ds=0 Whenever the load on induction motor changes, speed and slip also changes. The differentiation done with respect to S and u/v method. dt ` = ks E 2R ( 2 R S 2 ) 2 R + 2 S K 2 E 2R2 =0 ds ( R + S 2KS 2 E 2 2 R 2 X 2 2 (R 2 2 +S 2 X 2 2 )KE 2 2 R 2 =0 S2 X 2 2 -R 2 2 =0 2 S 2 = R2 S m = R2 2 X 2 X 2 S m in defined as the values of resistance & reactance per values where R 2 =SX 2 the torque in also maximum torque. Put S m = X R in the torque equation. 2 R K T= E 2 R X = K K E 2R2 2 = E R R2 X R X 2 X Torque-slip characteristic:- The curve obtained by plotting torque against slip from S=1 (at start) to S=0 (at synchronous speed) in called torque slip characteristics of the induction motor. The torque slip characteristics of the induction motor as shown in the figure ) Figure 4.6 torque slip characteristics of three phase induction motor 159

160 R 2 (figure from net) 2 ( 2 ) S 1) Low slip region Tα 2 R + S 2 In this region S is very small, so the tern (SX 2 ) 2 in so small as compared to R 2 2 that it can neglected, S Tα R2 α where R 2 2 & X 2 are constants S X 2 In this region torque is inversely proportional to the slip/ the curve in rectangular hyper bolo. When the load increases, Speed decreases and slips increase. Due to the high value of slip torque in decreasing and speed further drops. This problem makes the motor to reach stand still condition. The motor cannot continue to rotate at any point in this high slip region. Hence this region is called unstable region of operation. Figure 4.7 torque slip characteristics of three phase induction motor The torque slip characteristics has two parts, 1) Straight line called stable region of operation 2) Rectangular hyper bolo called unstable region of operation If load is increased beyond this limit. Motor slips are dominantly pushing motor in to high slip region. Due to such unstable conditions. Motor comes to stand still condition at a load. Hence T mi i e. maximum torque which motor can produce is also called break down torque (or) pull out torque. At S=1, N=.i e at start, motor produces a torque called starting torque and it is denoted as T s Losses in induction motor 1) constant losses 2) Variable losses 1) Constant losses: It is divided in two types a) Core losses(or) Iron losses b) Mechanical losses Core losses are divided is two types (i)eddy current losses (ii) Hysteresis losses The eddy current loss is minimized with the help of laminating of all parts of induction motor. The hysteresis loss is minimized by silicon steel sued to constant stator &rotor. these two types are purely depends on ferquancy.so the stator iron losses maximum, because stator receives three phase supply with constant frequency.in the case of rotor circuit the frequency of rotor f r = sf in very small hence the iron loss of rotor neglected. The mechanical losses include friction losses is bearing and winding losses. the friction losses are assumed almost constant and it is part of constant losses, because speed variation is induction motor not high. 160

161 2) Variable losses: It includes the copper losses in stator and rotor winding. Whenever the mechanical load changes, the current also change that is only if called variable losses Rotor copper; losses=3i 2 2 rr 2 Where I 2r =Rotor current/phase R 2 = Rotor resistance/phase 4.11 Power flow in an induction motor The various stages of power connections are called power flow in induction motor. The induction motor s constant electrical power in to mechanical out put the input power P in = 3 V L I L cosø Where V L -Line voltage,i L -Line current, P in -input power, CosØ-Power factor In put power is transferred to rotor due to mutual induction between stator &rotor excluding stator losses (core copper) The rotor input P 2r = P in stator losses (core& copper) The input of rotor is not fully connected as mechanical power, same part of the rotor in put power wasted in the rotor losses (core &^copper loss).the rotor core loss is neglected due to small volume of rotor frequency.so only rotor copper loss p cr is predominant The rotor copper losses P c =3I 2r 2 R 2 The mechanical power developed is wasted in the form of friction and winding losses when the load connected to the shaft. The output of motor P out =P m -mechanical losses 4.12 Necessity of Starter In a three phase induction motor, the magnitude of an induced e.m.f. in the rotor circuit depends on the slip of the induction motor. This induced e.m.f. effectively decides the magnitude of the rotor current. The rotor current in the running condition is given by But at start, the speed of the motor is zero and slip is s = 1 and maximum. So magnitude of rotor induced e.m.f. is very large at start. As rotor conductors are short circuited, the large induced e.m.f. circulates very high current through rotor at start.the condition is exactly similar to a transformer with short circuited secondary. Such a transformer when excited by a rated voltage, circulates very high current through short circuited secondary. As secondary current is large, the primary also draws very high current from the supply.similarly in a three phase induction motor, when rotor current is high consequently the stator draws a very high current from the supply. Similarly in a three phase induction motor, when rotor current is high, consequently the stator draws a very high current from the supply. This current can be of the order of 5 to 8 times the full load current, at start. Due to such heavy inrush current at start there is possibility of damage of the motor winding. Similarly such sudden inrush of current causes large line 161

162 voltage drop. Thus other appliances connected to the same line may be subjected to voltage spikes which may affect their working. To avoid such effects, it is necessary to limit the current drawn by the motor at start. The starter is a device which is basically used to limit high starting current by supplying reduced voltage to the motor at the limit of starting. Such a reduced voltage is applied only for short period and once rotor gets accelerated, full normal rated voltage is applied. Not only the starter limits the starting current but also provides the protection to the induction motor against overloading loading and low voltage situations. The protection against single phasing is also provided by the starter. The induction motor having rating below 5 HP can withstand starting currents hence such motors can be started directly on line. But such motors also need overload, single phasing and low voltage protection which is provided by a starter. Thus all the three phase induction motors need some or the other type of starter Types of Starter From the expression of rotor current it can be seen that the current at start can be controlled by reducing E 2 which is possible by supplying reduced voltage at start or by increasing the rotor resistance R 2 at start. The second method is possible only on case of slip ring induction motors. The various types of starters based on the above two methods of reducing the starting current are 1. Stator resistance starter 2. Autotransfomer starter 3. Star-delta starter 4. Rotor resistance starter 5. Direct on line starter Rotor Resistance Starter To limit the rotor current which consequently reduces the current drawn by the motor from the supply, the resistance can be inserted in the rotor circuit at start. This addition of the resistance in rotor in the form of 3 phase star connected rheostat. The arrangement is shown in the Fig Figure 4.8 Rotot Resitance Starter The external resistance is inserted in each phase of the rotor winding through slip ring and brush assembly. Initially maximum resistance is in the circuit. As motor gather speed, the resistance is gradually cut-off. The operation may be manual or automatic. We have seen that the starting torque is proportional to the rotor resistance. Hence important advantage of this method is not only the starting current is limited but starting torque of the motor also gets improved. 162

163 Note: The only limitation of the starter that it can be used only for slip ring induction motors as in squirrel cage motors the rotor is permanently short circuited. Calculation of Steps of Rotor Resistance Starter: The calculation of steps of rotor resistance starter is based on the assumptions that, 1. The motor starts against a constant torque 2. The rotor current fluctuates between two fixed values, a maximum and a minimum, denoted as I 2max and I 2min. The Fig. 3.9, shows a single phase of a three phase of a three phase rheostat to be inserted in the rotor. The starter has n steps, equally divided into the section AB. The contact point after each step is called stud. The total resistances upto each stud from the star point of star connected rotor as denoted as R 1, R 2,...R n-1. Figure 4.9: Steps of rotor resistance starter It consists of rotor resistance r 2 and the external resistances R x1, R x2...etc. At the time of reaching to the next step, current is maximum. Then motor gathers speed, slip reduces and hence while leaving a stud, the current is I 2min. Let E 2 = Standstill rotor e.m.f. per phase. When handle is moved to stud 1, the current is maximum and is given by, where s 1 = Slip at start = 1. While moving to stud 2, the current reduces to I 2min given by, where.just reaching to stud 2, the current again increases to I 2min as the part of external resistance R x1 gets cut-off. Hence at the last n th stud, the maximum current is, 163

164 Where s n = Slip under normal running condition. At n th stud no external resistance is in series with rotor. Where s n = Slip under normal running condition. At n th stud no external resistance is in series with rotor. From (1) and (2) we can write, Where K = Constant. From (1), R 1 = s 1 r 2 /s n. But s 1 = 1 at start Once R 1 is known, other resistances can be calculated. 164

165 From last expression of r 2, R 2 = KR 1 R 3 = K R 2 = KKR 1 = K 2 R 1 R 4 = K 3 R 1, r 2 = K n-1 R 1 where n = Number of starter studs. Thus the resistances of various sections can be obtained as, In this way the various steps of rotor resistance starter can be calculated Star - Delta Starter This is the cheapest starter of all and hence used very commonly for the induction motors. It uses tripple pole double throw (TPDT) switch. The switch connects the stator winding in star at start. Hence per phase voltage gets reduced by the factor 1/ 3. Due to this reduced voltage, the starting current is limited. When the switch is thrown on other side, the winding gets connected in delta, across the supply. So it gets normal rated voltage. The windings are connected in delta when motor gathers sufficient speed. The arrangement of star-delta starter is shown in the Fig The operation of the switch can be automatic by using relays which ensures that motor will not start with the switch in Run position. The cheapest of all and maintenance free operation are the two important advantages of this starter. While its limitations are, it is suitable for normal delta connected motors and the factor by which voltage changes is 1/ 3 which cannot be changed. Ratio of T st to T F.L : We have seen in case of autotransformer that if x is the factor by which the voltage is reduced then, Now the factor x in this type of starter is 1/ 3. Where I sc is the Starting phase current when delta connection with rated voltage and I F.L. is the Full load phase current when delta connection 165

166 Fig Star-delta starter Autotransformer Starter A three phase star connected autotransformer can be used to reduce the voltage applied to the stator. Such a starter is called an autotransformer starter. The schematic diagram of autotransformer starter is shown in the Fig It consists of a suitable change over switch. When the switch is in the start position, the stator winding is supplied with reduced voltage. This can be controlled by tappings provided with autotransformer. The reduction in applied voltage by the fractional percentage tappings x, used for an autotransformer is shown in the Fig When motor gathers 80% of the normal speed, the changeover switch is thrown into run position. Due to this, rated voltage gets applied to stator winding. The motor starts rotating with normal speed. Changing of switch is done automatically by using relays. The power loss is much less in this type of starting. It can be used for both star and delta connected motors. But it is expensive than stator resistance starter. Fig.4.11 Autotransformer starter 166

167 Fig.4.12 Use of autotransformer to reduce voltage at start Relation between T st and T F.L. Let x be the fractional percentage tappings used for an autotransformer to apply reduced voltage to the stator. So if, I sc = Starting motor current at rated voltage and I st = Starting motor current with starter, then on motor side But there exists a fixed ratio between starting current drawn from supply I st (supply) and starting motor current I st (motor) due to autotransformer, as shown in the Fig.3. Autotransformer ratio x = I st (supply)/ I st (motor) Substituting I st (motor) from equation (3), Now, T st α I st 2 (motor) α x 2 I sc 2 and T F.L. α (I F.L. ) 2 /s f Stator Resistance Starter: In order to apply the reduced voltage to the stator of the induction motor, three resistances are are added in series with each phase of the stator winding. Initially the resistances are kept maximum in the circuit. Due to its large voltage gets dropped across the 167

168 resistances. Hence a reduced voltage gets applied to the stator which reduces the high starting current. The schematic diagram showing stator resistances is shown in the Fig Fig Stator Resistance starter When the motor starts running, the resistances are gradually cut-off from the stator circuit. When the resistances are entirely removed from the stator circuit i.e. rheostats in RUN position then rated voltage gets applied to the stator. Motor runs with normal speed. The starter is simple in construction and cheap. It can be used for both star and delta connected stator. But there are large power losses due to resistances. Also the starting torque of the motor reduces due to reduced voltage applied to the stator. Relation between T st and T F.L : We know, P 2 = Tω s, where, T is torque produced and P 2 is the rotor input at N s. T α P 2 But, P 2 = P c /s, where, P c = Total copper loss = (3I 2 2r R 2 )/s T α I 2 2r /s But rotor current I 2r and stator current are related to each other through transformer action. T α I 2 1 /s Where I 1 = Stator current. At start, s = 1, T = T st and I 1 = I st When stator resistance starter is used, the factory by which stator voltage reduces is, say x < 1. The starting current is proportional to to this factor x. So if I sc is the normal current drawn under full rated voltage condition at start then, But, 168

169 where s f = Full load slip. Taking ratio of (8) and (9), Note: As x < 1, it can be seen that the starting torque reduces by the fraction x 2 due to the stator resistance starter Speed Control of Three Phase Induction Motor A three phase induction motor is practically a constant speed motor like a d.c. shunt motor. But the speed of d.c. shunt motor can be varied smoothly just by using simple rheostats. This maintains the speed regulation and efficiency of d.c. shunt motor. But in case of three phase induction motors it is very difficult to achieve smooth speed control. And if the speed control is achieved by some means, the performance of the induction motor in terms of its power factor, efficiency etc. gets adversely affected. For the induction motor we know that, From this expression it can be seen that the speed of induction motor can be changed either by changing its synchronous speed or by changing the slip s. Similarly torque produced in case of three phase induction motor is given by, N = N s (1 - s) So as the parameters like R 2, E 2 are changed then to keep the torque constant for constant load condition, motor reacts by change in its slip. Effectively it s speed changes. Thus speed of the induction motor can be controlled by basically two methods: 1. From stator side and 2. From rotor side Speed control from stator side includes following methods: a. Supply frequency control to control N s, called V / f control. b. Supply voltage control. c. Controlling number of stator poles to control N s. d. Adding rheostats in stator circuit. Speed control from rotor side includes following methods: a. Adding external resistance in the rotor circuit. b. Cascade control. c. Injecting slip frequency voltage into the rotor circuit Supply Frequency Control or V/F Control The synchronous speed is given by, 169

170 N s = 120f / P Thus by controlling the supply frequency smoothly, the synchronous speed can be controlled over a wide range. This gives smooth speed control of an induction motor. But the expression for the air gap flux is given by, This is according to the e.m.f. equation of a transformer where, K 1 = Stator winding constant T ph1 = Stator turns per phase V = Supply voltage f = Supply frequency It can be seen from this expression that if the supply frequency f is changed, the value of air gap flux also gets affected. This may result into saturation of stator and rotor cores. Such a saturation leads to the sharp increase in the (magnetisation) no load current of the motor. Hence it is necessary to maintain air gap flux constant when supply frequency f is changed. To achieve this, it can be seen from the above expression that along with f, V also must be changed so as to keep (V/f) ratio constant. This ensures constant air gap flux giving speed control without affecting the performance of the motor. Hence this method is called V / f control. AC input Constant V Constant f Converter DC Inverter AC input Variable V Variable f Fig 4.14 Electronic scheme for V/f control Stator of IM T T m f 1 >f f f 2 <f S=1 S m S=0 Fig 4.15 Torque-slip characteristics with variable f & (V/f) Hence in this method, the supply to the induction motor required is variable voltage variable frequency supply and can be achieved by an electronic scheme using converter and 170

171 inverter circuitry. The scheme is shown in the Fig. 1. The normal supply available is constant voltage constant frequency AC supply. The converter converts this supply into a DC supply. This DC supply is then given to the inverter. The inverter is a device which converts DC supply, to variable voltage variable frequency a.c. supply which is required to keep V/f ratio constant. By selecting the proper frequency and maintaining V/f constant, smooth speed control of the induction motor is possible. If f is the normal working frequency then the Fig shows the torque-slip characteristics for the frequency f 1 > f and f 2 < f i.e. for frequencies above and below the normal frequency. Another disadvantages of this method is that the supply obtained can not be used to supply other devices which require constant voltage. Hence an individual scheme for a separate motor is required which makes it costly Cascade Control This method is also called concatenation or tandem operation of the induction motors. In this method, two induction motors are mounted on the same shaft. One of the two motors must be of slip ring type which is called main motor. The second motor is called auxiliary motor. The arrangement is shown in the Fig The auxiliary motor can be slip ring type or squirrel cage type. Fig Cascade control pf two induction motor The stator of the main motor is connected to the three phase supply. While the supply of the auxiliary motor is derived at a slip frequency from the slip rings of the main motor. This is called cascading of the motors. If the torque produced by both act in the same direction, cascading is called cumulative cascading. If torques produced are in opposite direction, cascading is called differential cascading. Now let, P A = Number of poles of main motor P B = Number of poles of auxiliary motor f = Supply frequency N SA = 120f / P A N = Speed of the set The speed N is same for both the motors as motors are mounted on the same shaft. Now, s A = ( N SA - N)/N SA 171

172 f A = Frequency of rotor induced e.m.f. of motor A f A = s A f... as f r = s f The supply to motor B is at frequency f A, i.e. f B = f A Now on no load, the speed of the rotor B i.e. N is almost equal to its synchronous speed N SB. Key Point : Thus the speed N of the set is decided by the total number of poles equal to P A - P B. This is possible for cumulatively cascaded motors. If by interchanging any two terminals of motor B, the reversal of direction of rotating magnetic field of B is achieved then the set runs as differentially cascaded set. And in such a case effective number of poles are P A - P B.Thus in cascade control, four different speeds are possible as, a. With respect to synchronous speed of A independently, N s = 120f/P A b. With respect to synchronous speed of B independently with main motor is disconnected and B is directly connected to supply, N s = 120f/P B c. Running set as cumulatively cascaded with, N = 120f / (P A + P B ) d. Running set as differentially cascaded with, N = 120f / (P A - P B ) 172

173 This method is also rarely used due to following disadvantages: 1. It requires two motors which makes the set expensive. 2. Smooth speed control is not possible. 3. Operation is complicated. 4. The starting torque is not sufficient to start the set. 5. Set cannot be operated if P A = P B Controlling Number of Poles The method is called pole changing method of controlling the speed. In this method, it is possible to have one, two or four speeds in steps, by the changing the number of stator poles. A continuous smooth speed control is not possible by this method. The stator poles can be changed by following methods 1. Consequent poles method 2. Multiple stator winding method 3. Pole amplitude modulation method Consequent Poles Method: Fig Cascade control pf two induction motor In this method, connections of the stator winding are changes with the help of simple switching. Due to this, the number of stator poles get changed in the ratio 2 : 1. Hence either of the two synchronous speeds can be selected. Consider the pole formation due to single phase of a three phase winding, as shown in the Fig There are three tapping points to the stator winding. The supply is given to two of them and third is kept open. It can be seen that current in all the parts of stator coil is flowing in one direction only. Due to this, 8 poles get formed as shown in the Fig. 1. So synchronous speed possible with this arrangement with 50 Hz frequency is N s = 750 r.p.m. If now the two terminals to which supply was given either are joined together and supply is given between this common point and the open third terminal, the poles are formed as shown in the Fig

174 Fig.4.18 Pole winding Fig 4.19 pole winding It can be seen that the direction of current through remaining two. Thus upward direction is forming say S pole and downward say N. it can be observed that in this case only 4 poles are formed. So the synchronous speed possible is 1500 r.p.m. for 50 Hz frequency. Thus series/parallel arrangements of coils can produce the poles in the ratio 2 : 1. But the speed change is in step and smooth speed control is not possible. Similarly the method can be used only for the squirrel cage type motors as squirrel rotor adjusts itself to same number of poles as stator which is not the case in slip ring induction motor. Multiple Stator Windings Method: In this method instead of one winding, two separate stator winding are placed in the stator core. The windings are placed in the stator slots only but are electrically isolated from each other. Each winding is divided into coils to which, pole changing with consequent poles, facility is provided. Thus giving supply to one of the two windings and using switching arrangement, two speeds can be achieved. Same is true for other stator winding. So in all four different speeds can be obtained. The various limitations of this method are, 1. Can be applied to only squirrel cage motor. 2. Smooth speed control is not possible. Only step changes in speed are possible. 3. Two different stator windings are required to be wound which increases the cost of the motor. 4. Complicated from the design point of view. 174

175 Typical speed-torque characteristics of pole changing induction motor are shown in the Fig Pole Amplitude Modulation Method: Fig Multiple Stator Windings Method The basic disadvantage of other methods which is non-availability of smooth speed control is eliminated by this method. The ratio of two speeds in this method, need not be necessarily 2:1. The basic principle of this method is the modulation of two sinusoidally varying m.m.f. waves, with different number of poles. Consider sinusoidally distributed m.m.f. wave one phase of the stator as, Where P = Number of poles and θ = Mechanical angle This wave is modulated by another sinusoidal m.m.f. wave having P M number of poles, expressed as, The resultant m.m.f. wave after modulation is, Thus the resultant wave is equivalent to two m.m.f. waves having two separate number of poles as, P 1 = P - P M and P 2 = P + P M This is called suppressed carrier modulation. If we succeed in suppressing one of the two poles then there exists rotating magnetic field with number of poles as P 1 or P 2. And while suppressing, the method can be used such that the resultant number of poles retained is as required from the speed point of view. Now if the three stator windings are placed such that angle between their phase axes is (2π/3)r radians where r is an integer which is not divisible by 3 then the phase axes angle for modulated poles is given by, 175

176 Now to suppress one of the two poles, the angle between its phase axes must be multiple of 2π. So if r and n are selected so as to satisfy one of the above relations, then either P 1 or P 2 get suppressed and field corresponding to other pole exists. So speeds corresponding to P poles without modulation and corresponding to either P 1 or P 2 with modulation, can be achieved. The negative sign in equation (1), gives suppression of P 2 and existence of P 2 = P + P M while positive sign in equation (1), gives suppression P 2 of and existence of P 1 = P - P M poles. For example, stator has 8 poles while values of n and r are selected as 1 and 4 respectively. r is not divisible by 3.Let poles of modulation function P M are 2. From equation (1) we can see that, Thus P 1 gets suppressed and we get poles P 2 = P + P M = 10. So two speeds corresponding to P and P 2 can be obtained. Similarly if the poles of modulation function P M are 4 and n and r are selected as 1 and 2 then, In this case gets suppressed and we get poles P 1 = P - P M = 4. This method is advantages as it reduced the size to a great extent and hence cost of the machine. The limitation that it can be used only for squirrel cage motors still continues. Practically the rectangular wave is used for modulation. This is achieved by dividing stator coil into groups and then by dropping alternate group, other groups are connected in series opposition Supply Voltage Control We know that, T α (k s E 2 2 R 2 )/(R 2 2 +(s X 2 ) 2 ). Now E 2, the rotor induced e.m.f. at standstill depends on the supply voltage V.... E 2 α V Also for low slip region, which is operating region of the induction motor, (s X 2 ) 2 <<R 2 and hence can be neglected. 176

177 ... T α ( s E 2 2 R 2 )/R 2 2 ) α sv 2 for constant R 2 Now if supply voltage is reduced below rated value, as per above equation torque produced also decreases. But to supply the same load it is necessary to develope same torque hence value of slip increases so that torque produced remains same. Slip increases means motor reacts by running at lower speed, to decrease in supply voltage. So motor produces the required load torque at a lower speed. The speed-torque characteristics for the motor using supply voltage control are shown in the Fig Fig.4.21 Speed-torque curves for motor with voltage control But in this method, due to reduction in voltage, current drawn by the motor increases. Large change in voltage for small change in speed is required is the biggest disadvantage. Due to increased current, the motor may get overheated. Additional voltage changing equipment is necessary. Hence this method is rarely used in practice. Motors driving fan type of loads use this method of speed control. Due to reduced voltage, E 2 decreases, decreasing the value of maximum torque too. Two mark Questions and Answers 1. State the condition for maximum torque of a three phase induction motor. What is the maximum torque equal to? When the slip is maximum the torque of a three phase IM is maximum. The maximum torque is equal to s m E 2 2 R 2 R s 2 2 m X 2 2. A 3 ph, 4 pole, 50 Hz induction motor is running at 1440 rpm. Determine the slip speed and slip. N s N Slip speed = N s N; slip = 100 N s N s = 120f / p = (120) (50) / 4 = 1500 rpm. Slip speed = N s N = = 60 rpm. Slip = (60/1500) *100 = 4% 3. What is an induction generator? For the negative slip the induction motor runs faster than the synchronous speed. Now the induction motor runs as a generator and it is called as induction generator. 4. Mention the requirements of starting the two types of 3 phase induction motors. For SCIM minimum voltage should be supplied and for SRIM external rheostat should be connected. 177

178 5. Give the relationship between the following in a 3 phase induction motor: Rotor input and rotor output Starting torque and applied voltage P m = P 2 (1-s) which indicates the relationship between the rotor input and rotor output where P m denotes the gross mechanical power developed and P 2 denotes the rotor input. T st = 3 V 2 2 R 2 / ( 2πN s ( R X 2 2 ) which indicates the relation ship between the starting torque and applied voltage. 6. Draw the torque slip curves of double squirrel cage induction motor. T 7. What are the purposes that could be served by external resistors connected in the rotor circuit of phase would induction motor. To limit the starting current To increase the starting torque To control the speed. 8. How can the reversal of rotation of poly phase induction motor be attained? The reversal of rotation of poly phase induction motor is obtained by interchanging any two terminals of the three phase windings when connecting to the supply. 9. A 3 ph, 50 Hz induction motor runs at 960 rpm on full load. Find the number of poles and slip speed. Induction motor always runs nearer to synchronous speed. So, assume N s = 1000rpm. N s = 120f / p = 1000 p = (120) (50) / 1000 = 4. Slip speed = N s N = = 40 rpm. 10. Mention the losses occur in induction motor. Constant loss which includes hysterisis, eddy current loss and mechanical losses. Variable loss which includes the losses in the stator and rotor winding due to the current flowing in the winding. 11. Enlist four application of wound rotor induction motor. Cranes Hoists Pumps 178 S Outer cage Inner cage

179 Fans and blowers Chippers Conveyors Banbury mixers Ball and sag mill 12. What are the tests to be performed on induction motor to obtain data necessary to draw the circle diagram? No load test and blocked rotor test are performed to get the data necessary to draw the circle diagram. 13. List the salient characteristic features of double squirrel cage motor. High starting torque with low starting current No change in the performance under normal running condition. Constant speed characteristics 14. Point out the disadvantages of rotor rheostat control to obtain variable speed of induction motor. Large power loss due to the increase in resistance value. Due to large power loss efficiency is low. The speed above normal speed can not be obtained. Bulky and expensive Wide speed range is not possible. Because it needs large resistance which will be the cause to increase the losses. 15. What is the function of slip ring in 3 phase induction motor? The function of slip ring is used to connect the external stationary circuit to the rotor circuit of the induction motor. Here it is used to connect the external rheostat to the rotor of IM. 16. What is the effect of change in input voltage on starting torque of induction motor? If the input voltage is reduced the stator receives less voltage and hence the starting current is limited. 17. What is crawling and cogging in induction motor? Crawling is defined as the phenomenon which exhibits a tendency of IM to run at a stable speed as low as one seventh of their synchronous speed and is unable to pick up its normal speed. Due to magnetic locking between the stator and rotor teeth sometimes the motor is refused to start even with full supply voltage. This phenomenon is called cogging. 18. Write the advantages of slip ring induction motor. External resistance can be added in to the rotor circuit. High starting torque can be obtained Speed control by the rotor rheostat is possible. 179

180 Rotor resistance starter can be used. 19. Draw the equivalent circuit of induction motor. R 1 X 1 R 1 2 X 1 2 R 1 2 (1-s)/s V 1 R 0 X Explain the conditions for maximum torque under running condition. The torque depends on slip at which motor is running. So the only parameter which controls the torque is slip. So by differentiating the torque equation with respect to slip the condition for maximum torque can be achieved. That is slip is equal to the ratio between the rotor resistance and reactance. 21. What are the merits of inner and outer cage of double cage induction motor? Outer cage has high resistance and low reactance which is used to reduce the starting current. Inner cage has high reactance and low resistance which improves the performance of the motor. The starting torque will be increased. 22. Draw the power stages of an induction motor. Motor Input in Stator 23. Define slip. P 1 Stator Cu & Iron losses Rotor Input P 2 Rotor Cu Loss Gross Torque T g Friction &Windage losses Rotor Output P out The difference between the synchronous speed N s and the actual speed N of the rotor is known as slip. 24. Why the squirrel cage rotor is named so? The rotor bars are brazed or electrically welded to two heavy and short circuiting end rings which gives the pictorial representation of the squirrel s cage. That s why this motor is called as squirrel cage motor. 25. What are the principles involved in the starting of the rotor to rotate? Faraday s laws of electromagnetic induction.- By this principle an emf will be induced in the rotor conductors. Lenz s law By this law the rotor current is produced since the rotor conductors are short circuited. 26. Why the induction motor is called as rotating transformer. The induction motor is same as transformer in the principle of operation, i.e. mutual induction principle except the rotation. Similar to primary and secondary here 180

181 stator and rotor parts are available which involve in that principle of operation. That s why IM is called as rotating transformer. 27. Compare the squirrel cage and wound rotor IM. S.No Characteristics Slip Ring IM Squirrel Cage IM 1. Stator winding Three phase winding Three phase winding 2. Construction Complicated Very simple 3. Rotor Three phase winding Bars shorted with end rings 4. External resistance Can be added Can not be added 5. Slip rings and brushes Present Absent 6. Cost High Low 7. Starting torque High Moderate 8. Speed control By rotor resistance By rotor res. Not possible 9. Losses High Low 10. Efficiency Low High 11. Applications Lifts, hoists, cranes Laths, blowers, pumps 12. Usage Only 5% 95% 28. Why the IM is called as asynchronous motor? The speed of the rotor is not same as the speed of the synchronously revolving flux of the stator. That s why it is called as asynchronous motor. 29. What is synchronous induction motor? It is a motor which combines the advantage of synchronous and induction motor, which gives constant speed operation and high starting torque. 30. List the advantages and disadvantages of synchronous induction motor. Advantages: No separate damper winding is needed. Small capacity of the exciter is enough. It can be started and synchronized against more full load torque. No separate starting and control winding is needed. Disadvantages: Large variations in power factor. Wide speed range is not possible. No large over load capacity since the gap is small. 31. List the merits and demerits of induction generator. Merits: Synchronization is not required. Simple construction Most suitable for high speeds No danger of hunting. The voltage and frequency can be easily controlled with the help of the excitation supply and frequency. It delivers small power as it is short circuited. Demerits: It must be run in parallel with the synchronous machine. 181

182 The load is not deciding the power factor of induction generator but the power factor depends on slip. 32. List the applications of induction generator and synchronous induction motor. Induction generator: Braking purpose in railway. Synchronous induction motor: To drive the mechanical load with phase advancing properties. Can be used where the load torque is nearly constant. 33. What is the use of circle diagram? To derive the performance of an IM the circle diagram is used. The necessary data can be found from the no load test and blocked rotor test. 34. What are all the tests that have been conducted on 3 ph IM. No load and blocked rotor test Load test. Slip test. Define synchronous speed. The speed of rotating magnetic field in the stator is called as synchronous speed. It is denoted as N s. 120 f N S = p where F denotes the supply frequency and p denotes the number of poles. 37.Define synchronous watt. It is defined as the torque developed by the motor such that the power input to the rotor across the airgap is 1W while running at synchronous speed. 60 1Syn watt = N m. Where N s is the synchronous speed. 2πN s 38.Explain in brief the following terms with respect to induction motor: plugging, dynamic braking and regenerative braking. Plugging: An induction motor can be quickly stopped by simply inter changing any of its two stator leads. It reverses the direction of the revolving flux which produces a torque inn reverse direction that causes the speed to fall. Dynamic braking: For the slip ring induction motor it can be applied. By giving dc supply to the stator a constant magnetic field will be produced when the rotor is running. This will generates the emf in the rotor and that will be dissipated through the resistor. Regenerative braking: By operating the induction motor as induction generator the produced energy is fed back to the supply. This is called regenerative braking. 39. List the types of starters used for an IM. DOL starter For SCIM: Primary resistor started Auto transformer starter 182

183 Star delta starter For SRIM: Rotor rheostat starter. 40.What is the necessity of starter? If normal supply voltage is applied to the stationary motor, then as in the case of transformer very large initial current is taken atleast for a short while which is 5 to 7 times of their full load current. Hence to avoid this high value of initial current the starters are needed. 41.List the methods adopted to control the speed of an IM. From stator side: By changing the supply voltage By changing the supply frequency By changing the number of stator poles From rotor side: Rotor rheostat control Cascade operation By injecting an emf in the rotor circuit. 42.What are the merits and demerits of injecting emf method of speed control? Advantages: Wide speed range is possible Improved power factor. Demerit: It can be only applied for slip ring induction motors. 43.What is the method used to reduce the energy loss during starting? By means of Electronic starter, the energy loss is reduced during starting. 44.How do you achieve reduced voltage starting of IM? This is achieved by stator resistance starter, auto transformer starter and stardelta starter. In stator resistance starter, some amount of voltage is dropped across the starting resistance and the remaining voltage is supplied to the stator. In auto transformer starter, secondary of the transformer is connected with the stator and by adjusting the tapping reduced voltage is applied. In star-delta starter, the stator is connected with star connection during starting (V ph = V L / 3 and hence supplied with phase voltage). During running condition, motor is connected with the delta connection. 45. What is the name of the starter used for starting the slip ring IM? Rotor resistance starter is used for the starting of slip ring IM. There is a provision to change the value of rotor resistance in slip ring IM alone. This type of starter also improves the starting torque. 183

184 46. How much starting current is reduced in DOL starter? Write the expression for the ratio of starting torque to full load torque. For small rating motors only, DOL starter is used. So, there is no reduction in starting current i.e., I st = I sc. The expression for starting torque to full load torque is, T I T load torque; I st Starting current; I sc Short circuit current; S F Full load slip. 2 st st = S F FL I ; Where, T st Starting torque; T FL Full sc 47. How much starting current is reduced in stator resistance starter? Write the expression for the ratio of starting torque to full load torque. In stator resistance starter, the starting current is reduced by a factor X. Hence, I st = X I sc. The expression for starting torque to full load torque is, 2 T I X S T Starting current; I sc Short circuit current; S F Full load slip. X- reduction factor. st 2 st = F FL I ; Where, T st Starting torque; T FL Full load torque; I st sc 48. How much starting current is reduced in autotransformer starter? Write the expression for the ratio of starting torque to full load torque. In stator resistance starter, the starting current is reduced by a factor k. Hence, I st = k I sc. The expression for starting torque to full load torque is, 2 T I T Starting current; I sc Short circuit current; S F Full load slip. k- transformation ratio. st 2 st = k S F FL I ; Where, T st Starting torque; T FL Full load torque; I st sc 49. How much starting current is reduced in star-delta starter? Write the expression for the ratio of starting torque to full load torque. 1 In stator resistance starter, the starting current is reduced by a factor. 3 1 Hence, I st = Isc. The expression for starting torque to full load torque is, 3 2 T 1 I T Starting current; I sc Short circuit current; S F Full load slip. st st = S F FL 3 I ; Where, T st Starting torque; T FL Full load torque; I st sc 50. When an auto transformer becomes a star-delta starter? By comparing the torque expression for both the type of starters, if k = 57.7%, an autp transformer starter becomes a star-delta starter. k 2 = 1. So, 3 184

185 51. What are the factors to be considered while studying the starter? (a) Type of motor (b) Rating of motor (c)protection circuit 52. Very small motors can be start without using starters. Why? Very small motors will have low inertia and also the internal resistance of the motor is high. Hence the starting current of the small motor is less. 185

186 UNIT V SPECIAL MACHINES 7 Types of single phase motor Double revolving field theory Cross field theory Capacitor start -capacitor run motors Shaded pole motor Repulsion type motor Universal motor Hysteresis motor - Permanent magnet synchronous motor Switched reluctance motor Brushless D.C motor. 5.1 Introduction The single phase induction motor is not a self-starting one which is not to be available in Large power Rating. These type of motors are only fractional horse power motors and it is used in homes,fans, Washing machines,drillers,water pumps and Home Appliances. The Construction of motor is simple, when compare to Three Phase Induction Motor and less weight than the other. 5.2 Types of Single Phase AC Motors In single phase induction motor, there are three different types with same operating principle with less constructional modification. 1. Single phase induction motor 2. Single phase synchronous or constant speed motor 3. Single Phase universal or series motor (both AC and DC operated) Single Phase Induction Motor Almost of single phase induction motors are induction principle based and it is not self-starting motor. According to the starting methods it is divided in to four types. 1.Split Phase Induction motor 2. Capacitor start Induction motor 3. Capacitor start and run Induction motor 4. Shaded Pole induction motor Single Phase synchronous or constant speed motor In some applications like clocks CD drives,where the constant and silent operation required two types of single phase motors are used. 1. Reluctance type 2. Hysteresis type Single Phase universal or series motor These type of AC motor is operated both Single phase AC and DC supply and it is capable of producing high starting torque and rotates at high speed. This is used in Mixer grinders, vacuum cleaners, Hand Drillers, Sewing machines. 5.3 Construction of Single Phase Induction motor The construction of Single Phase Induction motor is similar to the three phase induction motor and the operating principle is same. Both stator and rotor poles and other parts are laminated but the rotor should not wounded and its slots are filled by copper or Aluminum bars (squirrel cage type ). The stator and rotor are properly designed to have minimum air gap between them over the area of stator. There is no direct contact between stator and rotor. The figure 5.1 shows the construction of single phase induction motor. Fig 5.1 Single phase induction motor construction 186

187 5.4 Working Principle and Operation of Single phase Induction motor The single phase induction motor is not a self-starting one and the stator is supplied single phase AC supply. The reason for this, the stator of the motor should not capable to produce rotating magnetic field, only it produces Alternating fluxes. This is explained in detail with the help of two theories in single phase induction motor. 1. Double field revolving (or)two fields Acting Theory 2. Cross field theory Double field revolving (or)two fields Acting Theory According to this theory,any alternating quantity can be resolved in to two rotating components and the components are rotating in opposite directions. The magnitude of the of each components are equal to the magnitude of the original one. When the distributed stator winding carries a sinusoidal current which is supplied from the single phase AC supply.it produces pulsating flux which is alternates with time, in the air gap of stator. This sinusoidal flux (Ф m ) is varying and it is divided in to two fluxes whose magnitude sum is equal to the half value of the alternating flux (Ф m /2). These two fluxes are rotating synchronously at the speed, N s =120f/P and rotates in opposite direction. This is shown in Figure 5.2. The first set of figures (Fig. 34.1a (i-iv)) show the resultant sum of the two rotating fluxes or fields, as the time axis (angle) is changing from =0θ to )180( π. Fig. 34.2b shows the alternating or pulsating flux (resultant) varying with time or angle. φ m \ φ m \ 2 2 φ m Fig 5.2 Alternating fluxes and its direction of rotation The flux or field rotating at N s, in the anticlockwise direction, i.e. the same direction, as that of the motor induces emf (voltage) in the rotor conductors. The rotor construction is squirrel cage type with bars short circuited via end rings. The current flowing in the rotor conductors, and torque produced by rotor conductors also in the same direction, which is termed as Forward torque(t f ). The other half of flux or field rotates at the same speed in the opposite (clockwise) direction, the torque produced by this field is Backward torque (t b ).These Two torques are in the opposite direction, and the resultant torque is the difference of the two torques produced T total = t f + t b. The two torques are equal and opposite, and the resultant torque is zero. So, there is no starting torque in a single-phase induction motor Torque speed characteristics The two torques produced and rotating opposite direction and the resultant torque is as shown in the figure

188 Fig 5.3 Torque Speed characteristics of single phase induction motor It can be seen that at start, the speed of rotor is zero and that torque value is also zero. Even the rotor is given an initial rotation in forward or reverse direction initially achieved by the respective torque it is not sufficient to continue. 5.5 Cross field Theory The single phase induction motor at stand still condition as shown in figure 5.4 Fig 5.4 Current direction and current induced in the rotor bars due to rotation The stator is excited by single phase AC supply and it produces stator flux Фs, the emf is induced in rotor due to transformer action and it circulates through rotor current. The direction of the rotor current as shown in the figure 5.4.When the flux Фs, acts in forward direction or upward direction and it is increased positively.so conductor experiences force from left to right.similarly the backward direction force acting in the rotor conductors,it experiences the force from right to left. The rotor sets up a flux Ф R which is at right angles to the stator flux Ф S in space, and hence it is called cross-field. The rotor flux always lags the stator flux by 90 in time. To produce a rotating field present in the stator divided in to two fields, and both are equal, and the rotating field has a constant magnitude. Whenever the slip increases the rate of change in flux in the rotor is less, so the magnitude of the cross field decreases. 5.6 Starting of Single Phase induction Motor The single-phase Induction Motor has no starting torque, but it has resultant torque, when it rotates at any other speed, other than that of synchronous speed. To make single phase induction motor has a self-starting one, an auxiliary winding is introduced in the stator, in 188

189 addition to the main winding, but placed at an angle of 90 (electrical). Now the starting torque is produced and he currents in the two (main and auxiliary) stator windings also must be at an angle of 90, to produce maximum starting torque. In this condition Single phase induction motor stator is acting as a balanced two-phase stator. Thus, rotating magnetic field is produced in such motor, giving rise to starting torque. When the motor is speed is reached almost 3/4 of the Synchronous speed,the starting or Auxiliary winding is disconnected form the circuit. S Fig 5.5 Split phase induction motor construction Resistance split phase induction motor The figure 5.5 shows the circuit diagram of Split phase induction motor. It consists two windings in the stator, 1.Starting or Auxiliary Winding 2.Running or Main Winding The Starting winding has high resistance and low reactance and main winding has low resistance and High reactance.both the windings are placed 90 degree(electrical) in the stator. The phasor diagram of Resistance split phase induction motor shown in the figure 5.6.The current (I st ) in the auxiliary winding lags the voltage by an angle θs, which is very small, but the current (I r ) in the main winding lags the voltage by an angle θr which is nearly 90. The phase angle between the two currents is (α=90 - θs), which should be minimum at least 30. This results only less amount of starting torque. The switch, S (centrifugal switch) is in series with the starting winding and It is automatically cuts out the auxiliary or starting winding, when the motor attains a speed 75% of full load speed. θs V θr α I st Fig 5.6 Phasor diagram of Resistance split phase I r induction motor I The torque-speed characteristics of the motor with/without auxiliary winding are shown in Fig Fig 5.7 Torque Speed characteristics of Resistance split phase induction motor The direction of rotation is reversed by reversing the terminals of any one of two windings, but not both, before connecting the motor to the supply terminals. This motor is used 189

190 for loads that require low or moderate torque in applications, such as fans, blowers, Centrifugal Pumps, Washing Machines. The power rating of the Motor is in the range of 0.25HP to 0.75HP Capacitor Start single phase Induction motor Fig 5.8 Capacitor Start single phase Induction motor The figure 5.8 shows the capacitor start induction motor. In this the capacitor is connected in series with starting winding to make the single phase induction motor as a self starting one by increasing the value of α (Phase Angle Between I st and I r ).The Phasor diagram as shown in the figure5.9 I st α<=90 θs θr I V Fig 5.9 Phasor Diagram of Capacitor Start single phase Induction motor The Phase displacement Between I st and I r approximately 90 during the starting condition. The starting leads the line voltage at an angle of θs.the motor reaches the speed 75% of its rated speed the centrifugal switch disconnects capacitor and starting winding. The torque speed characteristics of this type as shown in figure 5.10 Fig 5.10 Torque Speed characteristics of Capacitor Start single phase Induction motor The starting developed by the motor is 200 to 400% of the rated torque and the power factor is 0.5 to 0.7. It is used where the high starting requiring applications Compressors,Pumps, Refrigerators, Washing machines, Air conditioners. 190

191 5.6.3 Capacitor Run motor In this type the capacitor is permanently connected with starting winding and the centrifugal switch is not available. It improves the power factor of the circuit and the capacitor value is micro Farads Capacitor start Capacitor run Motor The figure5.11 shows the circuit of Capacitor start Capacitor run Motor. Aux or Starting winding I s I I rmain winding Fig 5.11 Schematic diagram of Capacitor Start and capacitor run motor In this motor,there are two capacitors use d. One is connected in Aux winding for starting, and another one connected in main winding for running prupose. The first capacitor is used only short period to start the motor after that it is disconnected with the help of Centrifugal switch. The second one is to be used for continuous duty, during running condition. The phasor diagram of two currents as shown in the figure α=>90 θs θr V I Fig 5.12Phasor diagram of Capacitor Start and capacitor run motor Currents The capacitor connected in running winding is used to improve the power factor during running condition and both the capacitors are connected in series to provide high starting Torque during starting Condition. The efficiency of the motor is very high. The torque speed characteristics of Capacitor start Capacitor run Motor as shown in the figure 5.13 Torque Start and Run winding (both capacitors are in) Run Wind and One capacitor 191

192 Fig 5.13 Phasor diagram of Capacitor Start and capacitor run motor Currents It is used where the high starting torque required applications Compressors, Pumps,Conveyors. 5.7 Shaded Pole Motor A Shaded Pole motor is also one of the type of single phase induction motor. The auxiliary winding, which is made of a copper ring, and it is called a shading coil. The current in the shading coil makes the phase of magnetic flux in that part of the pole in order to provide a rotating magnetic field. The direction of rotor rotation is from the un shaded side of the stator to the shaded part of the stator. The figure 5.14 shows the schematic diagram of shaded pole motor Basic principles of Shaded Pole Motor Alternating Flux The Flux produced due to shading band Fig 5.14 Fluxes produced in the Shaded Pole Induction Motor The fluxes are available in the shaded and un shaded area of the stator is shown in the figure 5.15.The shading-coil or ring in the stator displaces the axis of the shaded poles from the axis of the main poles. When single phase AC supply is applied to the stator, the Alternating flux in the main part of the stator pole induces voltage in the shading coil, which acts as a transformer secondary winding. According to Lenz law, The direction of current in shading coil is such as to oppose the cause producing it. The current in the secondary winding(shading Band) of a transformer is out of phase with the current in the primary winding (un shaded area) and the flux of the shading pole also out of phase with the flux in the main pole. Thus shaded coils supports to produce the rotating flux in the stator, hence the single phase Induction motor is converted into self-starting one using the Shading coil. Due to fixed of position of shading coils, the direction of rotation of such motors cannot be changed Advantages and Disadvantages of Shaded pole motors The various advantages of Shaded pole motors are 1.High reliable and Low cost and simple Construction 2.Robust and Rigged in construction The various Disadvantages of Shaded pole motors are 1.It produces very low starting torque 2.The efficiency of the motor is low 3.Copper Loss of the motor is high,due to shading coil is made of copper material Applications of Shaded pole motors It is used for the loads, where the low starting torque required applications like, toys, small fans, electric clocks, Motion Picture Projectors, hair dryers, ventilators and circulators. 5.8 Universal Motor A universal motor is a single-phase series motor, which is capable to run either on alternating current (ac) or direct current (dc). The characteristics of motor is similar for both ac and dc supply. The field winding of a universal motor is connected in series with the 192

193 armature windings through brushes. The universal Motor is as shown in the figure A Universal motor has a capacity to produce high starting torque and variable Torque speed characteristics. Universal motor runs dangerously at high speeds during no load Condition and the construction is similar to DC series motor construction. Fig 5.15 Schematic diagram of Universal Motor.A universal motor are divided in two types 1.Non-compensated with concentrated poles (low H.P) 2.Compensated with distributed field Non-Compensated motor The Non-compensated type,universal motor has 2 salient poles and all parts of a motor is laminated. The armature Contains Armature windings and it has laminated core. In the rotor, the slot type may be either straight or skewed slots. The armature winding are connected to the commutator through brushes. High resistance brushes are used in the motor to provide better commutation. The skew in the armature slots helps to reduce the magnetic hum and reducing the locking tendency of rotor, which is called magnetic locking Compensated type motor The compensated type universal motor consists of distributed field winding and the core of the stator is similar to split-phase induction motor. In the compensated type the motor has additional winding is called compensating winding and it helps to reduce the reactance voltage which is caused due to alternating flux. This happens in the motor, when the motor is excited with AC supply. The universal motor always develops unidirectional torque,whether the supply may be AC or DC. The direction of rotation can be changed in a non-compensated type, by changing the direction of flow of current in the armature or field winding. In compensated type, either reversing the armature leads or reversing field leads and shifting the brushes against the direction of rotation of motor Torque Speed characteristics of Universal motor The torque Speed characteristics of Uncompensated Universal motor is as shown in figure 5.16 Fig 5.16 Torque Speed characteristics of Uncompensated and Compensated type of Universal motor 193

194 The Torque-Speed characteristics of universal motor are similar to that of DC series motor. The Universal motor has varying speed characteristics with and without load. The speed of the motor is low at full loads and it is high and dangerous at no-loads. During no-load condition the speed of the motor is limited by its own frictional and windage losses Applications of Universal Motor Universal motors are used for domestic and industrial applications like Vacuum cleaners, Portable and Hand drills, Drink mixers, Electric Showers and Sewing machine 5.9 Repulsion Motor A repulsion motor is a type of electric motor for use on alternating current (AC). It was formerly used as a traction motor for electric trains but has been superseded by other types of motors and is now only of historical interest. Repulsion motors are classified under single phase motors. In repulsion motors the stator windings are connected directly to the AC power supply and the rotor is connected to a Commutator and brush assembly, similar to that of a direct current (DC) motor. Fig 5.17 Repulsion Motor A repulsion motor is similar to an a.c. series motor except that (i) brushes is not connected to supply but are short-circuited [See Fig.5.17)]. Consequently, currents are induced in the armature conductors by transformer action. (ii) the field structure has non-salient pole construction. By adjusting the position of short-circuited brushes on the commutator, the starting torque can be developed in the motor. The repulsion-induction motor is a combination of a repulsion motor and a squirrelcage induction motorrepulsion motors consist of a stator, rotor, commutator and brush assembly. The stator is mostly of non-salient pole type provided with slots. The rotor is connected to the commutator which is identical to the construction of DC armature. The windings of rotor are of distributed type. They may be either lap winding or wave winding. Repulsion motors consists of a commutator which may be of axial type or vertical type. Carbon brushes are used to conduct current through the armature.the principle difference between an AC series motor and repulsion motors is the way in which power is supplied to armature. In Ac series motor the armature receives voltage by conduction through the power supply. But In repulsion motors the armature is supplied by induction from the stator windings Principle of Operation: A repulsion-induction motor is a single-phase motor with conventional stator winding and two windings in the rotor. At start, the repulsion winding is predominant, but as the motor speed increases, the squirrel cage winding becomes predominant. Transition from repulsion to induction is smooth since no switching device is employed. This motor is ideally suited for applications where low voltage is a problem or high starting torque's are required. 194

195 5.9.2 The various types of motors which works under the repulsion principle are: Compensated repulsion motor Repulsion-start Induction-run motor Repulsion Induction motor Disadvantages of Repulsion Motor: Occurrence of sparks at brushes Commutator and brushes wear out quickly. This is primarily due to arcing and heat generated at brush assembly. The power factor is poor at low speeds. No load speed is very high and dangerous Application of Repulsion motors: Because of excellent starting and accelerating characteristics, repulsion-induction motors are ideal for: Value Operators Farm Motor Applications Hoists Floor Maintenance Machines Air Compressors Laundry Equipment Mining Equipment 5.10 Brush Less DC Motor Brushed DC motors depend on a mechanical system to transfer current, while AC and brushless DC motors use an electronic mechanism to control current. The brushed motors have a wound armature attached to the center with a permanent magnet bonded to a steel ring surrounding the rotor. As the brushes come into contact with the commutator the current passes through to the armature coils. AC induction motors and BLDC motors do not depend upon the mechanical system (brushes) to control current. The AC and BLDC motors pass current through the stator (electromagnet) which is connected to AC power directly or via a solid-state circuit. In AC induction motors the rotor turns in response to the "induction" of a rotating magnetic field within the stator, as the current passes. Rather than inducing the rotor in a brushless DC motor, permanent magnets are bonded directly to the rotor, as the current passes through the stator, the poles on the rotor rotate in relation to the electromagnetic poles created within the stator, creating motion Brushless DC Motor Construction Fig 5.18 Brushless DC Motor Construction sensor less and with sensor 195

196 The construction of BLDC motor as shown in the figure Brushless motors can be constructed in several different physical configurations: In the 'conventional' (also known as in runner) configuration, the permanent magnets are part of the rotor. Three stator windings surround the rotor. In the out runner (or external-rotor) configuration, the radial-relationship between the coils and magnets is reversed; the stator coils form the center (core) of the motor, while the permanent magnets spin within an overhanging rotor which surrounds the core. The flat or axial flux type, used where there are space or shape limitations, uses stator and rotor plates, mounted face to face. Out runners typically have more poles, set up in triplets to maintain the three groups of windings, and have a higher torque at low RPMs. In all brushless motors, the coils are stationary. There are two common electrical winding configurations; the delta configuration connects three windings to each other (series circuits) in a triangle-like circuit, and power is applied at each of the connections. The Wye (Y-shaped) configuration, sometimes called a star winding, connects all of the windings to a central point (parallel circuits) and power is applied to the remaining end of each winding.a motor with windings in delta configuration gives low torque at low speed, but can give higher top speed. Wye configuration gives high torque at low speed, but not as high top speed. The torque speed characteristics of a BLDC motor as shown in the figure 5.19 Figure 5.19 Torque-Speed Characteristics of BLDC Motor Efficiency The efficiency of a system is defined as the amount of output received, as a percentage of what was input into the system. Therefore, when we talk about the energy efficiency of brushless DC (BLDC) motors, we are saying that we can obtain a relatively high amount of mechanical power, in return for the electrical power that we use. DC motors utilize permanent magnets so none of their energy needs to be used in the creation of an electromagnet as in AC motors. The energy used by AC motors to create the electromagnet decreases the efficiency of the AC motor in comparison to the DC motors. At the same time, BLDC motors are considered more energy efficient than brushed DCmotors. This means for the same input power, a BLDC motor will convert more electrical power into mechanical power than a brushed motor, mostly due to absence of friction of brushes. The enhanced efficiency is greatest in the no-load and low-load region of the motor's performance curve. A BLDC motor, for the same mechanical work output, will usually be smaller than a brushed DC motor, and always smaller than an AC induction motor. The BLDC motor is smaller because its body has less heat to dissipate. From that standpoint, BLDC motors use less raw material to build, and are better for the environment Service and Maintenance: DC motor vs. BLDC motor Brushed motors are not only larger than their brushless counterparts, they also have a shorter service life. The brushes in the brushed motor are usually made of carbon or graphite compounds which wear during use. These brushes will require maintenance and replacement over time, so the motor will need to be accessible to ensure continued service. 196

197 As the brushes wear the not create dust but noise caused by the rubbing against the commutator. Brushless motors have longer service lives and are cleaner and quieter because they do not have parts the rub or wear during use. As the name implies, BLDC motors do not use brushes for commutation; instead, they are electronically commutated. BLDC motors have many advantages over brushed DC motors and induction motors. A few of these are: Better speed versus torque characteristics High dynamic response High efficiency Long operating life Noiseless operation Higher speed ranges Applications of BLDC motor BLDC motors are used in applications such as Appliances, Automotive, Aerospace, Consumer, Medical, Industrial Automation Equipment and Instrumentation Permanent Magnet Synchronous Motor Brushless AC electric motor is an electric motor driven by an AC electrical input, which lacks any form of commutator or slip ring. Generally the term 'brushless AC motor' will refer to a Permanent-Magnet Synchronous Motor (PMSM) or permanent-magnet motor (PMM), a synchronous motor which uses permanent magnets rather than windings in the rotor. The construction of PMSM as shown in the figure 5.20 Fig 5.20 Construction of Permanent-Magnet Synchronous Motor (PMSM) PMSMs are either axial flux, radial flux, transverse flux, or flux switching depending on the arrangement of components, with each topology having different tradeoffs among efficiency, size, weight, and operating speed. Alternative designs may use reluctance rather than magnets. Asynchronous induction motors are also brushless AC motors. The brushless DC motor is a brushless AC motor with integrated inverter and rectifier, sensor, and inverter control electronics Reluctance Motor It is a single-phase synchronous motor which does not require d.c. excitation to the rotor. Its operation is based upon the following principle: Whenever a piece of ferromagnetic material is located in a magnetic field; aforce is exerted on the material, tending to align the material so that reluctance of the magnetic path that passes through the material is minimum Construction Fig 5.21 Construction of Reluctance Motor 197