14 Single- Phase A.C. Motors I

Size: px

Start display at page:

Download "14 Single- Phase A.C. Motors I"

Theresa Craig
5 years ago
Views:

1 Lectures 14-15, Page 1 14 Single- Phase A.C. Motors I There exists a very large market for single-phase, fractional horsepower motors (up to about 1 kw) particularly for domestic use. Like many large volume markets, the cost per unit is very low The single Phase Induction Motor The single-phase induction motor is a popular choice for applications requiring essentially constant speed operation, e.g. refrigerator compressors, water pumps, etc. Their popularity is due to a large extent to the fact that these motors are extremely robust, reliable and cheap to manufacture Basic Concepts Consider a single phase, concentrated winding with N turns, as shown in Fig The airgap mmf waveform for this winding is a square wave with a peak-to-peak amplitude of NI. Fig The Fourier expansion of this m.m.f. Waveform F is F(θ) = (14.1) To simplify the analysis we will only consider the fundamental component: 2NI F(θ) = cos (14.2) The machine is connected to a single phase supply and the current in the

2 Lectures 14-15, Page 2 windings is I(t) = (14.3) Substituting equation 14.3 into equation 14.2 gives 2N I F(θ,t) = cos(t) cos (14.4) and applying the trigonometric identity for the product of cosines N I F(θ,t) = cos(t +) + N I cos(t ) (14.5) Equation 14.5 shows that the mmf field is equivalent to two constant amplitude waves, counter-rotating at synchronous speeds of + ω S. The graphical vector representation is Fig The behaviour of a single-phase induction motor can be explained in terms of the superposition of these two rotating mmf waves in an otherwise ordinary induction motor: The forward rotating stator mmf induces currents in the rotor. In the usual way for an induction motor, the rotor currents rotate at the at the synchronous frequency ω S with respect to the stator and at the forward slip frequency s f ω with respect to the rotor. The rotor currents form an mmf (ampere-turns) that is superimposed on the stator forward rotating mmf wave in the airgap (linear!). The resultant of the forward stator mmf and the forward rotor mmf produce a

3 Lectures 14-15, Page 3 forward airgap flux that induces an emf E f in the stator windings, as usual. Similarly, the backward rotating stator mmf vector gives rise to rotor currents at the backward slip frequency with respect to the rotor. The resultant of the backward stator mmf and the backward rotor mmf produces a backward airgap flux that induces an emf E b in the stator windings. Clearly with the rotor running in the forwards direction, the power factor of the rotor to the backwards rotating mmf is extremely poor, so little torque is produced by that set of backwards rotating vectors. The important features are: No starting torque. Fig 14.1 If the rotor rotates (or is made to rotate) in one direction or the other it will generate an accelerating torque that tends to keep it spinning in that direction. The torque at synchronous speed is a braking torque (from the mmf in the other direction). So the running speed at no load will less than the synchronous speed.

4 Lectures 14-15, Page Equivalent circuit model The two mmf components and reactions to them gives rise to the equivalent circuit of which shows that the sum of the two component stator emf's is approximately equal to the terminal voltage (R 1 should be considered as the machine is small). The resultant mmf that produces each emf is represented by a stator current flowing in the magnetising reactance (Xm) and a rotor current flowing in the referred rotor circuit X 2 and R 2 /s as for the conventional three phase IM. The forwards slip is as usual. The backwards slip is s s r f = s, s b = s r s = 2 - s Hence, the rotor components are as shown in Fig R 1 JX 1 Fig The torque for the forward and backward rotating waves can be found in the usual way, noting that the circuit analysis is more complicated:

5 Lectures 14-15, Page 5 Tf = (14.5) Tb = (14.6) T = (14.7) where Z f and Z b are the impedances of the forward and backward branches, respectively. 8 Other than the emfs adding (because they are at the same frequency), the derivation is the same as for the three phase induction motor. The speed at which the motor generates no torque, s O can be determined by equating the torques produced by the forward and backward fields. Using equations 14.6 and 14.7, this amounts to from which it can be shown that R s O = 1, (14.9) X 2 +X m The first solution signifies that there is no torque at starting, while the two other solutions represent the forward and backward speeds at which the motor runs at no load. We can see from equation that if R 2 > ( X 2 +X m ), then there is no real solution for the running speed. The physical consequence of this is that the motor will not run even if given a start.

6 Lectures 14-15, Page Windings A single-phase motor has only one main winding which may consist of a single concentrated winding wound on a bobbin which forms part of the stator core, as in the dishwasher pump motor. Or it may be a distributed winding with a number of concentric coils as shown in Fig Fig 14.5 Sometimes more effort is made to give a pure sinusoidal mmf. This is to make the motor as quiet as possible, noting it is in a domestic environment. This is true of diswasher motors, as dishwashers are usually located in the kitchen and run after dinner! Starting We have already seen that a pure single-phase motor cannot start without some assistance. It is normally inconvenient to do this by mechanical means. Instead, single-phase machines are often wound with a second winding, called a starter winding, to provide a unidirectional torque at standstill. This winding is physically displaced from the main winding by some angle α. The current in the starter winding is also temporally displaced from the main winding by an angle ø. This gives the motor a taste of a conventional rotating field which is enough to start it in the desired direction.

7 Lectures 14-15, Page 7 Fig 14.6 Equ for the main winding: F M (θ, t ) = 2N I M cos(t) cos And for the starter winding: F S (θ, t ) = 2N I S cos(t ) cos( ) Where φ is the current displacement and α is the angular displacement. These add by superposition to give new forward and backward rotating waves of obviously different magnitude, therefore there is a dominant forward or backward rotating field that will start the motor in the dominant direction. Intuitively, we want a 90 O phase in the current and a 90 O displacement of the windings (for two pole, p=1, machines). Then we have an ideal two phase motor which will have no backwards rotating field. Various electronic converters are being suggested for such motors, although it seems a little odd to use this technology, as a three phase converter only has one extra output connection!

8 Lectures 14-15, Page 8 15 Single-Phase A.C. Motors II 15.1 Starting Single Phase Induction Motors Split-Phase Motor The starter winding is wound onto the stator at 90 electrical degrees to the main winding. Both windings are fed directly from the same single-phase supply. The time displacement that is required between the main and starter currents is produced by making the impedance of the starter winding different to the impedance of the main winding by giving it a high resistance. This is usually accomplished by fabricating the starter winding coils from wire with a cross-sectional area of conductor of about one quarter that of the main winding coils. Fig The higher resistance of the starter winding results in a difference of around 30º in phase angle between the currents in each winding. Combined with the spatial phase shift of 90º between the windings results in a starting torque which is typically % of the full load torque. Once the motor is in motion the starter winding can be disconnected from the supply. Fig. 15.2

9 Lectures 14-15, Page Capacitor-Start Motor The phase difference between the current in the main and starter windings can be increased to nearer 90 by inserting a capacitor in series with the starter winding. As for the split-phase motor, the capacitor and starter windings are switched out at some speed so the winding can be rated for intermittent use. Fig Because the current phase angle has been increased to approximately 90, the starting torque produced by these motors is much higher than that of a split-phase motor of equal rating. Typically, the starting torque can be as high as 300% of the rated torque, so they are more suitable for driving high inertia loads such as compressors, loaded conveyors and reciprocating pumps. These motors can usually be found with ratings in the range W Permanent Split Capacitor (PSC) Motor A small value of capacitance can be shown to improve the running performance, by reducing the slip on load (by reducing the effect of the backwards field). Fig. 15.4

10 Lectures 14-15, Page 10 The permanently connected capacitor improves the input power factor which is normally very poor for ordinary single-phase machines. Clearly the reduced value of capacitance results in a lower starting torque than the equivalent capacitor-start motor (typically 80% of full-load torque) so that these motors find favour in applications where a low starting torque is acceptable, such as fan drives and pumps (range approximately W. e.g. dishwashers). The auxiliary (starter) winding and capacitor now have to be continuously rated and the main and auxiliary windings are normally identical Capacitor-Start Capacitor-Run (CSCR) Motor The capacitor-start capacitor-run motor, combines the benefits of the PSC motor and capacitor-start motor, to produce a motor which has a high starting torque and improved running performance. However, these motors are inherently more expensive than the other motors discussed as they require: two capacitors; some kind of switch and a continuously rated auxiliary winding. Fig These motors are capable of developing up to 300% of full-load torque at standstill and have increased efficiency and a higher power factor while running. Consequently they are manufactured in larger sizes, 100 W to 4 kw. It must be remembered however that the running value of capacitance is chosen for a particular load so that for optimal running conditions, different capacitors are required for different load values.

11 Lectures 14-15, Page Shaded-Pole Motors The shaded pole motor is a special case of the split-phase motor, in which the auxiliary winding takes the form of a simple copper ring left permanently in the magnetic circuit. The stator is of a salient-pole construction similar to that used in d.c. machines and the thick copper rings embrace one side of the pole tip of each pole in the motor, Fig The detailed analysis of these motors is complex, however, a simple explanation for the effect of these shading rings can be obtained by consideration of the magnetic equivalent circuit. The flux produced by the exciting coil can be split into two components -that which links the shading ring and that which does not. Fig The flux which links the copper ring induces a current around the ring, which according to Lenz's Law, tends to oppose the flux that induced it. As a consequence, the net flux linking the ring is different in both magnitude and

12 Lectures 14-15, Page 12 time phase to the flux passing through the unshaded part of the pole. Analysis of a shorted coil: Multiply both sides by N S /R S E S = Ns d (15.1) dt = I srs N s 2 R s d dt = N sis (15.2) The result has the same form as inductance. Now we can construct the equivalent magnetic circuit using the reluctances and the primary excitation N 1 I 1 This has the effect of creating a weak second field, which is displaced spacially and in time, giving the same effect as the starter windings in the previous designs. Clearly this is cheap and effective. The motor of course rotates in the direction from the unshaded to the shaded portion of the pole. Its direction cannot be reversed. The starting torque produced by these motors is very small, typically 40-80% of rated torque, and the extra I 2 R losses in the rings make this type of motor one of the least efficient single-phase motors. On the other hand, the construction is compact, rugged and very cheap compared to other types (i.e. no capacitor, no switch, etc.), so that these motors are used in large numbers where cost is very important and where they are used with pumps and fans. They are found in overhead projectors driving the cooling fan and washing machines, driving the drain pumps. Output powers range from 0.1 W to 300 W. The open frame (skeleton) construction means that they are cooled easily so their inefficiency is not an embarrassment.

13 Lectures 14-15, Page A.C. series or Universal motor Equivalent Circuit The equivalent circuit for a series connected d.c. motor is shown in Fig Fig The field flux is now dependent on the armature current, so the torque depends on rotor (armature) current squared as long as the iron does not saturate! T = K Ia 2 (15.6) K is a constant which depends on the design of the machine. Now, I a = I cos(t ) (15.7) where φ is the phase angle between I a and the terminal voltage. Substituting into equation 15.6: T(t) = KI 2 cos 2 (t ) = 1 (15.8) 2 KI 2 [1 + cos 2(t )] This equation describes a torque that is unidirectional (i.e. never goes negative) and that pulsates at twice the supply frequency.

14 Lectures 14-15, Page 14 The series a.c. motor is also known as a universal motor because it will also run from d.c. The equivalent circuit is based on that of the series d.c. motor with the addition of the inductances of the field and armature windings, X f and X a, which are important in an a.c. system. The series resistances and inductances are usually lumped into single components, R t = R f + R a and X t = X f + X a. From consideration of the d.c. machine equations we have E = KIar (15.9) This is in phase with the current, as we would expect as it accounts for the mechanical output power. The starting torque is high as there is no back emf and the current may then be high. Then as the motor gains speed the current falls and the torque falls rapidly. On light load the speed may be very high. This makes them ideal for vacuum cleaners and washing machine drum motors! On fan loads such as hair dryers, the fan load limits the maximum speed, unless the air flow is obstructed. P.R. Palmer March 2009

10. Starting Method for Induction Motors

10. Starting Method for Induction Motors A 3-phase induction motor is theoretically self starting. The stator of an induction motor consists of 3-phase windings, which when connected to a 3-phase supply