ELECTRICAL MACHINES. For ELECTRICAL ENGINEERING

Transcription

1 ELECTRICAL MACHINES For ELECTRICAL ENGINEERING

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3 ELECTRICAL MACHINES SYLLABUS DC Machines Types, Winding, Generator characteristics, Armature reaction and commutation, Starting & speed control of Motors; three phase induction motors principles, Types, performance characteristics and applications Transformers principles, equivalent circuit, voltage regulation, Transformer losses, efficiency, three phase Transformer Induction Motors Introduction, equivalent circuit, phasor diagram, characteristics, Crawling & Cogging and double Squirrel Cage Motor Synchronous Machine Introduction, circuit model of Synchronous Machines, Hunting and Damper Winding in Synchronous Machine ANALYSIS OF GATE PAPERS Exam Year 1 Mark Ques. 2 Mark Ques. Total Set Set Set Set Set Set Set Set Set

4 Topics 1. DC MACHINES CONTENTS Page No 1.1 D.C. Generators Types of Generators E.M.F. Equation of a Generator Iron Loss in Armature Total Loss in A D.C. Generator Armature Reaction and Commutation Parallel Operation of Shunt Generators Characteristics of D.C. Generators Compound Wound Generator D.C. Motor Motor Characteristics Performance Curves Speed Control of D.C. Motors Speed Control of Series Motors Electric Braking Testing Of D.C. Machines TRANSFORMERS 2.1 Introduction Transformer Construction Principle of Transformer Action Equivalent Circuit of A Transformer Open Circuited and Short Circuit Tests Voltage Regulation of A Transformer Transformer Losses Transformer Efficiency Transformers Tests Auto-Transformers Three Phase Transformer INDUCTION MOTORS 3.1 Introduction Losses and Efficiency Induction Motor Phasor Diagram Equivalent Circuit Rotor Circuit Model Torque-Slip Characteristics Power-Slip Characteristics 34

5 3.8 Operating Characteristics of Induction Motors Induction Motor Stability Determination of Equivalent Circuit Parameters Circle Diagram Power Factor Control of 3 Phase Induction Motors Starting Of Polyphase Induction Motors Methods of Starting Wound-Rotor Motors Induction Generator Crawling Cogging or Magnetic Locking Double Squirrel Cage Motor SYNCHRONOUS MACHINES 4.1 Introduction Circuit Model of Synchronous Machine Characteristics of Synchronous Machine Short-Circuit Ratio (SCR) Potier Method Operating Characteristics Power Flow (Transfer) Equations Capability Curve of Synchronous Generator Salient-Pole Synchronous Machine Two-Reaction Model Power-Angle Characteristic Determination of Xd And Xq Slip Test Parallel Operation of Synchronous Generators Hunting in Synchronous Machines Damper Winding Special Machines GATE QUESTIONS ASSIGNMENT QUESTIONS 118

6 1 DC MACHINES 1.1 D.C. GENERATORS Generator principle: An electric generator is a machine which converts mechanical energy (or power) into electric energy (or power). The energy conversion is based on the principal of the production of dynamically (or motionally) induced e.m.f. Whenever a conductor cuts magnetic flux, dynamically induced e.m.f. is produced in it according to Faraday s Laws of Electromagnetic Induction. This e.m.f. causes a current to flow if the conductor is closed. An actual generator consists of the following essential parts: 1. Magnetic Frame oryoke 2. Pole Cores and Pole Shoes 3. Pole Coils or Filed Coils 4. Armature Core 5. Armature Winding or Conductors 6. Commutator 7. Brushes and Bearings 1) Yoke: The outer frame or yoke serves double purpose: (i) It provides mechanical support for the poles and acts as a protecting cover for the whole machine and (ii) It carries the magnetic flux produced by the poles. 2) Poles Cores and Pole Shoes: The pole shoes serve two purposes (i) They spread the flux in the air gap and also, beings of larger cross section, reduces the reluctance of the magnetic path (ii) They support the exciting coils (or filed coils) 3) Armature Core: It houses the armature conductors or coils, its most important function is to provide a path of very low reluctance to the flux through the armature. 4) Commutator: The commutator is to facilities collection of current from the armature conductors. Converts the alternative current induced in the armature conductors into unidirectional current in the external load circuit. 5) Armature Winding i) Pole pitch It is equal to the number of armature conductors (or armature slots) per pole. If there are 48 conductors and 4 poles, the pole pitch is 48/4 = 12 ii) Coil-span or Coil-pitch (Ys) If the pole span or coil pitch is equal to the pole pitch then winding is called full-pitched. iii) Pitch of a Winding (Y) Y = YB - YF for lap winding = YB + YF for wave winding Where YB - Back Pitch YF- Front Pitch iv) Commutator Pitch (YC) 1

7 It is the distance between the segments to which the ends of a coil are connected. v) Single-layer Winding: It is the winding in which one conductor or one coil side is placed in each armature slot. Such a winding is not much used. vi) Two-layer Winding: In this type of winding, there are two conductors or coil sides per slot arrangement in two layers. Usually, one side of ever coil lies in the upper half of one slot and other side lies in the lower half of some other slot at a distance of approximately one pitch away. vii)multiplex Winding: In such windings, there are several sets of completely closed and independent windings. If there is only one set of closed winding, it is called simplex wave winding. If there are two such windings on the same armature, it is called duplex winding LAP AND WAVE WINDINGS i) Simplex Lap-winding DC Machines 5. Resultant pitch YR is even, being the arithmetical difference of two odd numbers, i.e., YR = YB - YF. 6. The number of slots for a 2 layer winding is equal to the number of coils (i.e. half the number of coils sides). The number of commutator segments is also the same. 7. The number of parallel paths in the armature = mp where m is the multiplicity of the winding and P the number of poles. (a) If YB> YF i.e. YB = YF + 2, then we get a progressive or right handed winding I.e. a winding which progressive in the clockwise direction as seen from the commutator end. In this case, obviously, YC = +1. (b) Hence, it is obvious that Z YF 1 P for progressive Z YB 1 P Z YF 1 winding and P for Z YB 1 P retrogressive winding 1. The back and front pitches are odd and of opposite sign. But they cannot be equal. They differ by 2 or some multiple thereof. 2. Both YB and YF should be nearly equal to a pole pitch. YB YF 3. The average pitch YA. It 2 Z equals pole pitch = P 4. Compotator pitch YC = 1. (In general, YC = m) ii) Simplex Wave Winding YB back pitch nearly equal to pole YF front pitch pitch YB YF YA = average pitch; 2 1. Both pitches YB and YF are odd and of the same sign. 2. Back and front pitches are nearly equal to the pole pitch and may be equal or differ by 2, in which case, they are respectively one more or one less than the average pitch. 3. Resultant pitch YR = YF + YB 4. Commutator pitch, YC = YA (in lap winding YC = 1) 2

8 Also, YA = No.of Commutator bars 1 No.of pair of poles 5. The average pitch which must be an integer is given by Z +1 Z ± 2 Y 2 A = = P P/2 No. of Commuatorbars ± 1 = No. of pair of poles DUMMY OR IDLE COILS These dummy coils do not influence the electrical characteristics of the winding because they are not connected to the commutator. They are there simply to provide mechanical balance for the armature because an armature having some slots without windings would be out of balance mechanically USES OF LAP & WAVE WINDINGS The advantage of the wave winding is that, for a given number of poles and armature conductors, it gives more e.m.f. than the lap winding. Another advantage is that in wave winding, equalizing connections are not necessary whereas in a lap winding they definitely are. However, when large currents are required, it is necessary to use lap winding, because it gives more parallel paths. Hence, lap winding is suitable for comparatively lowvoltage but high-current generators whereas wave-winding is used for highvoltage, low current machines. 1.2 TYPES OF GENERATORS Generators are usually classified according to the way in which fields are excited. Generators may be divided into (a) separately-excited generators and (b) selfexcited generators. a) Separately-excited generators are those whose field magnets are DC Machines energized from an independent external source of d.c. current. b) Self-excited generators are those whose field magnets are energized by the current produced by the generators themselves. Due to residual magnetism, there is always present some flux in the poles. When the armature is rotated, some e.m.f. and hence some induced current is produced which is partly or fully passed through the field coils thereby strengthening the residual pole flux. There are three types of self-excited generators. i) Shunt wound The field windings are connected across or in parallel with the armature conductors and have the full voltage of the generator applied across them. ii) Series Wound In this case, the field windings are joined in series with the armature conductors. As they carry full load current, they consist of relatively few turns of thick wire or strips. Such generators are rarely used except for special purposes i.e. as boosters etc. iii) Compound Wound It is a combination of a few series and a few shunt windings and can be either short-shunt or long-shunt 3

9 DC Machines In general generated e.m.f. Eg ZN P = volt 60 A Where A = 2-for simplex wave-winding = P-for simplex lap-winding 1 2N P Eg=. Z 2 60 A Z P volt in rad / s 2 A E K N volts where Nis in r.p.s. g a 1.4 IRON LOSS IN ARMATURE (i) Hysteresis Loss (Wh) This loss is due to the reversal of magnetisation of the armature core. The loss depends upon the volume and grade of iron, maximum value of flux density Bmax and frequency of magnetic reversals. 1.6 W B f V watts h max V volume of thecorein m Steinmetz hysteresiscoefficien t. 3 BRUSH CONTACT DROP It is the voltage drop over brush contact resistance when current passes from commutator segments to brushes. 0.5 V for metal-graphite brushes. 2.0 V for carbon brushes 1.3 E.M.F. EQUATION OF A GENERATOR Average e.m.f. generated/conductor = d volt ( n 1) dt Now, flux cut/conductor in one revolution d P Wb No. of revolutions/second = N/60 Time for one revolution, dt = 60/N second Hence, according to Faraday s Laws of Electron magnetic Induction, E.M.F. generated/ conductor d PN volt dt 60 (ii) Eddy Current Loss (We) When the armature core rotates, it also cuts the magnetic flux. Hence, an e.m.f. is induced in the body of the core according to the laws of electromagnetic induction. This e.m.f. though small, sets up large current in the body of the core due to its small resistance. This current is known as eddy current. The power loss due to the flow of this current known as eddy loss. In order reduce this loss the core is built up of thin laminations, which are stacked core laminations are insulated from each other by a thin coating of varnish W KB f t V watt e Where, max Bmax = maximum flux density f = frequency of magnetic reversals t = thickness of each lamination V = volume of armature core. 1.5 TOTAL LOSS IN A D.C. GENERATOR 4

10 DC Machines c) Mechanical Losses i) friction loss at bearings and commutator. ii) air-friction or windage loss of rotating armature. d) Stray Losses Usually, magnetic and mechanical losses are collectively known as stray Losses. These are also known as rotational losses for obvious reasons. COMMUTATION Improving commutation i.e. of making current reversal in the short-circuited coil as sparkles as possible 1) Resistance Commutation This method of improving commutation consists of replacing low-resistance Cu brushes by comparatively highresistance carbon brushes. 2) E.M.F Commutation In this method, arrangement is made to neutralize the reactance voltage by producing reversing e.m.f. in the shortcircuited coil under commutation. i) either by giving the brushes a forward lead sufficient enough to bring the short-circuited coil under the influence of next pole of opposite polarity ii) by using interpoles. a) Copper Losses i) Armature copper loss = I 2 R a a ii) Field copper loss. iii) The loss due to brush contact resistance. b) Magnetic Losses i) hysteresis loss. ii) eddy current loss, W B f h e 1.6 max W B f 2 2 max These losses are practically constant for shunt & compound-wound generators. 1.6 ARMATURE REACTION AND COMMUTATION By armature reaction is meant the effect of magnetic field set up by armature current on the distribution of flux under main poles of a generator. The armature magnetic field has two effects: i) It demagnetizes or weakens the main flux ii) It cross-magnetises or distorts it. 5

11 DC Machines Total number of turns in these angles 2 = m ZI 360 Demagnetising amp-turns per pair of 2 poles = m ZI 360 Demagnetising amp-turns/pole = m ZI 360 m ATd per pole = ZI CROSS-MAGNETIZING AT PER POLE The conductors lying between angles AOD and BOC constitute what are known as distorting or cross-magnetising conductors DEMAGNETIZING AT PER POLE Since armature demagnetizing ampereturns are neutralized by adding extra ampere-turns to the main field winding, Total number of armature conductors in 4 angles AOC and BOD is m Z 360 Total armature-conductors/pole both cross and demagnetising = Z / P Demagnetising conductors/pole 2 = Z. m (found above) 360 Cross-magnetising conductors/pole Z 2m 1 2m = Z Z P 360 p 360 Cross-magnetisingamp-conductors/ 1 2m pole = ZI P 360 Cross-magnetising amp-turns/pole 1 m = ZI 2P m ATc/pole = ZI 2P 360 6

12 1.6.3 COMPENSATING WINDINGS DC Machines Their function is to neutralize the cross magnetizing effect of armature reaction. In the absence of compensating windings, the flux will be suddenly shifting backward and forward with every chance in load. No. of armature conductors/pole = P Z No. of Z armature turns/pole = 2P No. of armature-turns immediately under one pole Z Pole arc Z 0.7 (approx.) 2P Pole pitch 2P No. of armature amp-turns/pole for compensating winding ZI armatureamp turn / pole 2P COMMUTATION This reversal of current takes place along magnetic neutral axis or brush axis i.e. when the brush spans and hence short circuits that particular coil undergoing reversal of current through it. This process by which current in the short-circuited coil is reversed while it crosses the M.N.A. is called commutation. The brief period during which coil remains short-circuited is known as commutation period Tc. So, we conclude that sparking at the brushes, which results in poor commutation is due to the inability of the current in the short-circuited coil to reverse completely by the end of short-circuit period. 7

13 1.6.5 VALUE OF REACTANCE VOLTAGE DC Machines INTERPOLES Self- induced or reactance voltage 2I L if commutation is linear Tc 2I 1.11L if commutation issin usodial T c They carry full armature current. Their polarity, in the case of a generator, is the same as that of the main pole ahead in the direction of rotation. They induce an e.m.f. in the coil (under commutation) which helps the reversal of current. The e.m.f. induced by the Compoles is known as commutating or reversing e.m.f. The commutating e.m.f neutralizes the reactance e.m.f. thereby making commutation sparkles. With interpoles, sparkles commutation can be obtained up to 20 to 30% overload with fixed brush position EQUALIZING CONNECTIONS Hence, the function of equalizer rings is to avoid unequal distribution of current at the brushes thereby helping to get sparkles commutation. Equalizer rings are not used in wave-wound armatures, because there is no imbalance in the e.m.f. of the two parallel paths METHODS OF IMPROVING COMMUTATION Improving commutation i.e. of making current reversal in the short-circuited coil as sparkles as possible 1) Resistance Commutation This method of improving commutation consists of replacing low-resistance Cu brushes by comparatively highresistance carbon brushes. 2) E.M.F Commutation In this method, arrangement is made to neutralize the reactance voltage by producing reversing e.m.f. in the shortcircuited coil under commutation. i) either by giving the brushes a forward lead sufficient enough to bring the short-circuited coil under the influence of next pole of opposite polarity ii) by using interpoles. 1.7 PARALLEL OPERATION OF SHUNT GENERATORS Desirable for the following reasons: (i) Continuity of Service (ii) Efficiency (iii)maintenance and Repair (iv) Addition to Plant Two generators of different kw ratings automatically share a load in proportion to their ratings, then their external characteristics 8

14 DC Machines Then E1V E2 V I1 and I2 R1 R2 I E V R K N V R.. I E V R K N V R Paralleled generators with different power ratings but the same voltage regulation will divide any oncoming bus load in direct proportion to their respective power ratings. 1.8 CHARACTERISTICS OF D.C. GENERATORS 1. No-load saturation Characteristic (E0/If) It is also known as magnetic Characteristic or Open- circuit Characteristic (O.C.C.). 2. Internal or Total Characteristic (E/Ia) It gives the relation between the e.m.f. E actually induces in the armature (after allowing for the demagnetising effect of armature reaction) and the armature current I. 3. External Characteristic (V/I) It is also referred to as performance characteristic or sometimes voltageregulating curve. It gives relation between that terminal voltage V and the load current I CRITICAL RESISTANCE FOR SHUNT GENERATOR Every point on this curve is such that volt/ampere = R.If R is increased so much that the resistance line does not cut the O.C.C. at all (like OT), then obviously the machine will fall to excite i.e. there will be no build up of the voltage. If the resistance line just lies along the slope, then with that value of field resistance, the machine will just excite. The value of the resistance represented by the tangent to the curve is known as critical resistance Rc for a given speed. 9

15 1.8.2 VOLTAGE BUILD UP OF A SHUNT GENERATOR There is always present some residual magnetism in the poles, hence a small e.m.f. is produced initially. This e.m.f. circulates a small current in the field circuit which increases the pole flux. When flux is increased, generated e.m.f. is increased which further increases the flux and so on. DC Machines 1.9 COMPOUND WOUND GENERATOR A shunt generator is unsuitable where constancy of terminal voltage is essential, because its terminal voltage decreases as the load on it increases. If the series filed amp turns are such as to produce the same voltage at rated load as at no load, then the generator is flat compounded. If the series filed amp turns are such that the rated load voltage, then the no load voltage, then generator is overcompounded. If rated load voltage is less than the no load voltage, then the generator is under compounded. Conditions necessary for build up voltage: 1. There must be some residual magnetism in the generator poles. 2. For the given direction of rotation. They should be so connected that the induced current reinforces the e.m.f. produced initially due to residual magnetism. 3. If excited on open circuit, its shunt field resistance should be less than the critical resistance Factors affecting voltage building: i) reversed shunt field connection ii) reversed rotation iii) reversed residual magnetism. Any effort to increase load current by further decreasing load resistance results in decreased load current (like OA) due to a very rapid decreases in terminal voltage. Voltage regulation: The voltage regulation of a d.c. generator is the change in voltage when the load is reduced from rated value to zero, expressed as percentage of the voltage. 1. Shunt generator with filed regulators are used for ordinary lighting and power supply purposes. 2. Series generators are not used for power supply because of their rising characteristic make then suitable for being used as boosters in certain types of distributed system particularly in railway service. 3. Compound generators The cumulatively compound generators is the most widely used d.c. generators because its external characteristic can be adjusted for compensating the voltage drop in the line resistance. The differential compound generators has an external characteristic similar to that of a shunt generator but with large demagnetization armature rection. Hence, it is widely used in arc welding where larger voltage drop is desirable with increases in current. 10

16 DC Machines 1.10 D.C. MOTOR Motor principle: An Electric motor is a machine which converts electric energy into mechanical energy. Its action is based on the principle that when a currentcarrying conductor is placed in a magnetic field, it experiences a mechanical force whose direction is given by Fleming s Lefthand Rule and whose magnitude is given by F = BIlNewton SIGNIFICANCE OF THE BACK E.M.F. When the motor armature rotates, the conductors also rotate and hence cut the flux. In accordance with the laws of electromagnetic induction, e.m.f. is induced in them whose direction, as found by Fleming s Right hand Rule, is in opposition to the applied voltage. Because of its opposing direction, it is referred to as counter e.m.f. or back e.m.f. Eb. ZN(P / A) volt E b SPEED REGULATION As the change in speed when the load on the motor is reduced from rated value to zero, expressed as percent of the rated load speed V IaRa KEb NK T I a a 1.11 MOTOR CHARACTERISTICS 1. Ta/Ia Characteristic. T a I a VOLTAGE EQUATION OF A MOTOR V = Eb + IaRa VIa = EbIa + I 2 a Ra Input power = developed Mechanical power + losees ARMATURE TORQUE OF A MOTOR Power developed = T a 2N watt Electrical power converted into mechanical powerin the armature =EbIa watt Ta 2N E b Ia Eb ZN (P / A) volt 1 P T a. ZI a N m 2 A SHAFT TORQUE (Tsh) Output in watts Tsh N m (Nin r.p.s.) 2N 2. N/Ia Characteristics. E N b 11

17 3. N/Ta or mechanical characteristic CHARACTERISTICS OF SHUNT MOTORS 1. Ta/Ia Characteristic Assuming to be practically constant T I. a a 2. N/Ia Characteristic DC Machines 1.12 PERFORMANCE CURVES a) Shunt Motor b) Series Motor 3. N/Ta Characteristic COMPOUND MOTORS COMPARISON OF SHUNT AND SERIES MOTORS a) Shunt Motors a) speed of a shunt motor is sufficiently constant. 12

18 Topics GATE QUESTIONS Page No 1. D.C MACHINES TRANSFORMERS THREE PHASE INDUCTION MACHINES SYNCHRONUS SINGLE PHASE INDUCTION OTORS, SPECIAL PURPOSE MACHINES & ELECTROMECHANICAL ENERGY CONVERSION SYSTEM

19 1 DC MACHINES Q.1 In case of an armature controlled separately excited d.c. motor drive with closed loop speed control, an inner current loop is useful because it a) limits the speed of the motor to a safe value b) helps in improving the drive energy efficiency c) limits the peak current of the motor to the permissible value d) reduces the steady state speed error [GATE-2001] Q.2 An electric motor with constant output power will have a torque speed characteristic in the form of a a) straight line through the origin b) straight line parallel to the speed axis c) circle about the origin d) rectangular hyperbola [GATE-2002] Q.3 A d.c. series motor fed from rated supply voltage is overloaded and its magnetic circuit is saturated. The torque- speed characteristic of this motor will be approximately represented by which curve of figure a) Curve A b) Curve B c) Curve C d) Curve D [GATE-2002] Q.4 A 200 V, 2000 rpm, 10 A, separately excited d.c. motor has an armature resistance of 2 Ω. Rated d.c. voltage is applied to both the armature and field winding of the motor. If the armature draws 5 A from the source, the torque developed by the motor is [GATE-2002] Q.5 The speed/torque regimes in a dc motor and the control methods suitable for the same are given respectively in List-II and List-I. List-I A. Field Control B. Armature Control List-II 1. Below base speed 2. Above base speed 3. Above base torque 4. Below base torque Codes: A B a) 1 3 b) 2 4 c) 2 3 d) 1 4 [GATE-2003] Q.6 T conduct load test on a dc shunt motor, it is coupled to a generator which is identical to the motor. The filed of the generator is also connected to the same supply source as the motor. The armature of generator is connected to a load resistance. The armature resistance is 0.02 p.u. Armature reaction and mechanical losses can be neglected. With rated voltage across the motor, the load resistance across the generator is adjusted to obtain rated armature current in both motor and 58

20 ANSWER KEY: (c) (d) (b) 4.2 (b) (c) (a) (b) (a) (c) (a) (b) (d) (b) (a) (d) (d) (a) (a) (b) (b) (b) (a) (d) EXPLANATIONS Q.1 (c) Closed loop system limits the peak value. Q.2 (d) 2πN P.T constant 60 xy C (Rectangle Hyperbola) Q.3 (b) At saturation, linear characteristics are observed. Q.4 (4.299) 5 T Nm 10 Q.5 (b) Field Control : Field control provides constant power drive. Since the speed is inversely proportional to flux/pole ω 1 ϕ field can not be increased; it can only be weakened. So this control is suitable for speed control above base speed as torque is directly proportional to flux/pole T α for a given armature current. So this control provides torque below base torque. Armature Control: It provides constant torque drive. By keeping the field current at maximum value full load torque can be obtained at full load armature current at all speeds. This control provides speeds below base speed. b E V rated Rated power W Rated torque 8.598Nm 2π2000 Torque at 5 A, T I 2 a2 T I 1 a2 Q.6 (c) 62

21 ASSIGNMENT QUESTIONS Q.1 The brush-axis of a bipolar dc motor is rotated by 90. The effect of this rotation is rotated by 90. The effect of this rotation on th back emf Eb and the torque developed Td would be such that a) both Eb and Td are unchanged b) Eb is zero, but Td is unchanged c) Eb is unchanged, but Td is zero d) both Eb and Td are zero Q.2 A dc shunt generation builds up to a voltage of 220 V at no load while running at its rated speed. If the speed of the generator is raised by 25% keeping the circuit conditions unaltered, then the voltage to which the machine then build up will a) not change and remain at 200V b) increase to 1.25 times 200V c) increase to value lying between and 1.25 times 200 V. d) in crease to value greater then 1.25 times 200V. Q.3 A dc shunt generator having a shunt field of was generating normally at 100 rpm. The critical resistance of this machine was 80. Due to some reason, the speed of the prime-mover became such that the generate or just fail generate. a) 1000 rpm b) 800 rpm c) 625 rpm d) 500 rpm Q.4) A separately-exited dc motor has an armature resistance of 0.5. It runs off a 250 V dc supply drawing an armature current of 20 A at 1500 rpm. The torque developed for an armature current of 10 A, for the same filed current, will be a) Nm b) Nm c) 15.6 Nm d) Nm Q.5 A bipolar dc machine with interpole has a main-pole flux per pole and an interpole flux of, per pole. The yoke of the machine is divided into four quadrants by the main pole axis and the commutation axis. a) 1 i in all the four quadrants 2 b) 1 i in all the four quadrants 2 c) 1 i in 2 two diametrically opposite quadrants and 1 i in the remaining 2 two quadrants d) 1 i in 2 two adjacent quadrants and 1 i in the 2 remaining quadrants Q.6 An electromechanical energy conversion device is shown in the figure. The instantaneous values of armature induced emf, busbar voltage and armature current developed torque and angular velocity of shaft respectively e, v and i. Te, Ta and ωr represent external torque armature developed torque and angular velocity of shaft respectively. Assume that the given directions of parameters in the figure are positive. If the device is working in generating mode then 118

22 EXPLANATIONS Q. 1 (d) Q.2 (b) ZN P E 60 A E N 25N N' N 100 N'=1.25N E will increase to 1.25E Q. 3 (c) E K N Q. 4 (a) n and E v lara (for generator) N R So 1 1 N R N N rpm E= =240V 240 kn 1500 T k l a a And ka kn T(at10A)= 10 π 1500 =15.28 Nm Q. 9 (b) Q. 10 (d) Q. 11 (d) Q. 12 (c) In this case the armature reaction is partially magnetizing due to Fasinθ component Facosθ component E K N n V I R K N a a n V IaRa N Kn So speed decreases Q. 13 (a) Power = EIa = (V-IaRa)Ia = p dp =V-2I a R a =0 dia Ia = V/2 Ra E = V-(V/2 Ra)Ra = V/2 = 230/2 = 115 V Q. 14 (b) Q. 5 (c) Q. 6 (a) Q. 7 (c) Q. 8 (c) Q. 15 (a) In both case drop will remain same. Voltage regulation at 1250 rpm would be less than 10%. E K ( )N n sh se N E K ( ) n sh se When series field is short circuit then sc 0 139