Abstract — The parameters of a permanent split-capacitor single-phase induction motor can be estimated by conducting the DC test, blocked rotor test and no-load test which later can be used to facilitate the prediction of motor torque-speed characteristics. To improve further its performance, an exact motor model is simulated and investigated in 2D finite element analysis under influence of different capacitor values, winding turn ratio and impedance ratio. A prototype is built and tested. Experimental results are compared with those obtained in 2D finite element analysis.

I. INTRODUCTION

Due to its simplicity in construction and easy availability of single-phase power supply in almost every household, single-phase induction motors (SPIM) have been used for a long time for trivial and repetitive chores. They are also often used in light-duty industrial applications where three-phase supply is not readily available. They are robust, almost free of maintenance, relatively cheap and have reasonable efficiency and operating torque [1]. Compared with a three-phase induction motor, SPIM is simpler in construction but it is more complicated to be analyzed and modelled through an equivalent circuit [2]. SPIM is not self-starting machine since its torque due to single-phase winding alone would only cause the motor to vibrate instead of rotating.

In order to create a starting torque for SPIM, a phase-shifted magnetic field has to be generated. This is normally accomplished by having main and auxiliary windings in quadrature to ensure that the auxiliary winding current from the main supply is phase shifted [3]. There are several types of SPIM which use the concept of main and auxiliary windings to start the motors such as split-phase, capacitor-start, capacitor-run and capacitor-start capacitor-run. A rotating magnetic field can be produced if two-phase symmetrical ac voltages excite the main and auxiliary windings that are wound 90° elect. apart around the stator air gap. However, in reality, a common single-phase source feeds both windings. Therefore, a capacitor is normally connected in series with the auxiliary winding to generate leading phase current in order for the SPIM to self-start by producing sufficiently high starting torque.

II. DOUBLE REVOLVING FIELD THEORY When the rotor is at standstill and the stator winding is

connected to single-phase ac supply, the generated pulsating

stator flux will induce current in the rotor bars, hence producing rotor pulsating flux acting along the same axis as the stator flux. According to Lenz’s law, these two fluxes will oppose each other. Therefore, no starting torque is developed as the angle between these fluxes is zero. Double revolving field theory states that stator magnetic field can be decomposed into two rotating magnetic fields, each of equal magnitude but rotating in opposite directions. Forward field rotates in the direction of mechanical movement, whereas backward field rotates in the opposite direction [4-5].

As stated in [6], torque is only developed when the motor is in running condition, which can be done by spinning the motor manually or using auxiliary circuit. Let the mmf along rotor angular position for sinusoidally distributed stator winding be

(1) where N = the effective number of turns of the stator winding and the stator current i is given by

(2) Therefore, the MMF is given by

(3) Although rotating in different directions, the forward rotating mmf Ff (rotating in the direction of ) and the backward rotating mmf Fb (rotating in the opposite direction of ) produce a useful net torque except when the rotor is at standstill. This is because during standstill, the forward and backward torques are equal in magnitude, therefore, they cancel each other. Whereas at other speed, the unequal torque produced will keep the rotor rotating in direction of rotation. The slip with respect to forward field can be represented as

(4) The slip with respect to backward field can be represented as

(5) Again, double-revolving field theory is used to analyse the qualitative and quantitative performance of the single-phase induction motor. It is also used to obtain the equivalent circuit of single phase induction motor including the effects of forward

Performance Evaluation of Permanent Split-Capacitor Single-Phase Induction Motor for

Ceiling Fan Application D. Ishak*, T. L. Tiang, S. K. Choy

School of Electrical and Electronic Engineering, Universiti Sains Malaysia, Penang, Malaysia. *E-mail: dahaman@usm.my

field and backward field. To estimate equivalent circuit parameters, both no-load and locked-rotor tests are performed. Magnetizing reactance can be obtained using the no-load test results. Stator and rotor leakage reactance and stator referred rotor winding resistance can be computed using locked-rotor test data [7].

III. MATHEMATICAL MODELING

SPIM is equivalent to a secondary short-circuited transformer when the rotor is at standstill and the stator winding is excited with single-phase supply. Using double revolving field theory as discussed earlier, qualitative and quantitative performance of SPIM can be analysed. Due to the effect of forward and backward fields, the equivalent circuit is split into two halves.

If the SPIM is running at some speed and certain slip s in the direction of forward field, the forward field induces rotor current at frequency of sf (slip, s multiplies with the stator supply frequency, f ). The rotor mmf rotates at the slip speed with respect to the rotor but at synchronous speed with respect to the stator. Forward air gap flux that induces the voltage Ef is produced by the resultant of the forward stator mmf and the rotor mmf. The equivalent circuit of forward rotor part reflected to the stator side has impedance of as shown in Fig. 1.

Fig. 1. Equivalent circuit of SPIM with rotor rotating at slip s.

On the other hand, rotor circuit current at frequency of (2-s)f

is induced by the backward rotating field. The corresponding rotor mmf rotates in the air gap at synchronous speed in backward direction. A voltage Eb is produced by the resultant of the backward stator mmf and the rotor mmf. The equivalent circuit of backward rotor circuit reflected to the stator side has impedance of as shown in Fig. 1.

It can be noted that the forward flux is always greater than backward flux at slip other than s=1 (since

˃ for any s except s=1). It also implies that forward impedance Zf is always larger than the backward impedance Zb , hence, the forward voltage Ef is always bigger than the backward voltage Eb.

Traditional method to obtain single-phase induction motor parameters can be carried out using no-load test and blocked rotor test with the auxiliary winding opens. However, in our case, auxiliary winding parameters is also included when obtaining equivalent circuit for permanent split-capacitor motor, even though the rest of the procedure in obtaining main and auxiliary parameters is the same as normal single-phase induction motor. That is why the equivalent circuit for permanent-split capacitor motor is slightly different from the equivalent circuit of other single-phase induction motor such as split-phase induction motor [8,10]. The equivalent circuit considering the auxiliary winding effect is shown in Fig. 2.

It is noted that in permanent split-capacitor SPIM, the main winding flux can be resolved into main forward flux and main backward flux. The auxiliary winding flux can also be resolved into auxiliary forward flux and auxiliary backward flux. Voltages are induced in both main and auxiliary windings due to the forward and backward revolving fluxes in main and auxiliary windings.

From Fig. 2, the main winding equivalent circuit includes Efm and Ebm which are the voltages induced by its own forward flux, Øfm and backward flux, Øbm respectively. The fluxes from the auxiliary winding, Øfa and Øba also induce voltage -jEfa/a and jEba/a in the main winding, which can be represented as internal voltages, and a is the turn ratio of auxiliary winding Na to the main winding Nm. The –j in the induced voltage represents a phase lag of 90o since Øfa induces voltage in the main winding that peaks 90o later. On the other hand, a voltage of jEba/a induced in the main winding means that the voltage peaks 90o earlier. From Fig. 2, the auxiliary winding equivalent circuit includes Efa and Eba which are the voltages induced by its own forward flux Øfa and backward flux Øba respectively. The fluxes from main winding Øfm and Øbm also induce voltage jaEfm and -jaEbm in the auxiliary winding, which can be represented as internal voltages.

(a) (b)

Fig. 2. Equivalent circuits of permanent split-capacitor SPIM (a) main winding. (b) auxiliary winding.

..

+

X1R1I1

V1

0.5 Xmag

0.5 Xmag

..

0.5 X2'

0.5 X2'

0.5 R2'/s

0.5 R2'/(2-s) ..

..

+

++

..

..

+

++

Vm

X1mR1m

Rf

Xf

Rb

Xb

-jEf,aux/a

j Eb,aux/a

Va

X1mR1m

(a^2)Rf

(a^2)Xf

(a^2)Rb

(a^2)Xb

jaEfm

-jaEbm

Xc

For testing SPIM, [9] is referred. DC test, blocked rotor test

and no-load test are carried out in order to obtain motor parameters.

A. DC TEST After removing the capacitor in the auxiliary winding, dc

voltage is applied across the stator winding and the dc current is then measured. Stator winding dc resistance R1m thus can be computed. To obtain the auxiliary winding dc resistance R1a, main winding is made open and dc voltage is applied across the auxiliary winding. The dc current is then measured.

Main winding resistance (6)

Auxiliary winding resistance (7)

B. BLOCKED ROTOR TEST In blocked rotor test, the rotor is held at standstill while

exciting main winding with blocked rotor voltage VBR such that the blocked rotor line current IBR equals the rated current. The blocked rotor resistance RBR is computed as

(8) The blocked rotor impedance is given by

(9) Blocked rotor reactance is thus computed as

(10) Rotor winding resistance R2’ is then computed as

′ (11) Assuming that the stator and rotor leakages to be equal, X1 = X2’ = 0.5XBR. Therefore, R1, X1, R2’ and X2’ can be determined.

C. NO-LOAD TEST There is no eddy current induced in rotor bars and slip=0 when

motor is rotating at synchronous speed [3]. Rotating mmf produced by stator winding is also rotating at synchronous speed. The test is called as no-load test of induction motor where rotor region becomes part of the stator region and magnetic flux paths is completed through rotor region. From [9], rated voltage VNL is applied during no-load test, and current INL and power PNL are measured at no-load. For s = 0, the rotor resistance of forward branch is assumed to be infinite as the term 0.5

approaches infinity. This makes rotor branch becomes open-circuit, leaving only Zf = j0.5Xmag. At standstill where s=1, PBL = IBL

2 (R1m+R2’) (12) ZBL = VBL/IBL (13) ZBL

2 = (R1m + R2’)2 + (X1m+X2’)2 (14) In normal case, X1m is usually assumed to be equal to X2’. At no-load, slip s=0, PNL = INL

2(RNL) (15) ZNL = VNL/INL (16) = [RNL

2 + (0.5Xmag + X1m + 0.5X2’)2 ]1/2 (17)

Consequently, Xmag can be determined. Therefore, it is obvious that from dc test, blocked rotor test and no-load test, R1m, R1a, R2’, X1m, X2’, Xmag can be computed. The auxiliary stator leakage reactance is obtained from the equation: X1a = a2X1m (18) Also, Zc = (19) To simplify the calculations of obtaining SPIM parameters, Zf = Rf + jXf

= (20)

Zb = Rb + jXb

= (21)

Applying Kirchoff’s Voltage Law on Fig. 2, Vm = (Z1m + Zf + Zb) Im – jEfa/a + jEba/a (22) Va = jaEfm – jaEbm + (Zc + Z1a + a2 Zf + a2 Zb) Ia (23) Since in SPIM, only one power supply is applied to the motor, we know that Vm = Va = 240 0° V. The input current,

Is = Im + Ia. (24) It is also noticed that Efa = Iaa2Zf (25)

Eba = Iaa2Zb (26) Efm = ImZf (27) Ebm = ImZb (28)

Therefore the equations (22) and (23) can be simplified as below: Vm = (Z1m + Zf + Zb) Im – ja (Zf – Zb) Ia (29) Va = ja (Zf – Zb) Im + (Zc + Z1a + a2 Zf + a2 Zb) Ia (30) Solving these two equations simultaneously, Im and Ia are obtained. The air gap power due to forward and backward flux can be expressed as below:

Pgf – Pgb = (|Im|2 + |a Ia|2) (Rf – Rb) + 2a|Im||Ia|(Rf + Rb)sin (Ɵa – Ɵm) (31)

Since P = Tω, the operating torque for the SPIM is expressed as below:

T =

T = Ɵ Ɵ (32)

By running the motor at different speed, or in other word

different slip, s, different torque can be obtained and from here, torque-speed characteristic of the SPIM can be plotted.

IV. FINITE ELEMENT ANALYSIS

In order to obtain high accuracy of parameters estimation, 2D finite element method (FEM) is used to build motor models. This is because FEM includes the consideration of the real representation of the complex machine geometry, correct spatial distribution of stator winding, actual representation of winding

distribution on the stator slots, magnetic saturation and non-linear behaviours of the iron materials. These considerations provide accurate calculation of electromagnetic fields and estimation of machine parameters.

A 18-pole permanent split-capacitor SPIM model is built using Opera2D, a 2D finite element software from Cobham Technical Services. The rotor consists of 65 bars. The outer layer of the stator slots is for main windings whereas the inner layer of the stator slots is for the auxiliary windings, as shown in Fig. 3. This motor has external rotor structure which is rotating while the inner stator core is stationary.

Fig. 3. 2D FE model for 18-pole permanent split-capacitor SPIM with external

rotor.

Fig. 4. Magnetic field distribution across motor area during no-load test.

To carry out blocked rotor test and no-load test on the motor

model in 2D FEM, the auxiliary circuit is made open by setting the resistance in the auxiliary circuit to a very high value so that no current can pass through the auxiliary winding, as if it is open-circuited. Circuit editor is used to couple the single-phase ac voltage source and also to connect the appropriate slot conductors into series connected main windings and auxiliary winding respectively. During blocked rotor test, command input (comi) file is written to set the speed for both stator and rotor to be zero, whereas for no-load test, comi file is written to set the stator to be stationary and the external rotor is rotated at synchronous speed of 333rpm. For both tests, power supply 240 Vrms is used. Rotating machine analysis is conducted on the motor model for both tests and data such as input voltage, input current, main current, auxiliary current and average power for the tests are computed. Having obtained these data, the motor parameters as discussed in previous section can be estimated.

Consequently, torque-speed profile of permanent split-capacitor SPIM can be plotted. Fig. 4 shows the magnetic field distribution across motor area during no-load test.

V. EXPERIMENT During the experiment, the main and auxiliary winding

resistances (R1m and R1a) are determined from the DC test. Variable dc supply is used to vary the applied voltage to the main winding while the auxiliary winding of the motor is left opened. Power supply is increased slowly until the current reaches rated current of 0.35 Arms. The voltage supplied to the main winding when current is 0.35 Arms is recorded. Subsequently, the same procedure is repeated with the power supply connected to the auxiliary winding and the main winding opened. From the DC test, resistances of main winding R1m and auxiliary winding R1a can be calculated by applying Ohm’s Law on the voltage and current recorded. As mentioned in the Section II, R1m and R1a are thus easily calculated.

When blocked rotor test is conducted, the power supply of 240Vrms is applied to the main winding of the motor while the auxiliary winding is made opened. Both the rotor and stator of the motor are kept at zero speed (standstill). The current flows through the main winding and the average power consumed by the motor are recorded. Fig. 5 shows the prototype motor under test.

Fig. 5. Prototype motor under test

When no-load test is conducted, the power supply of 240Vrms

is applied to the main winding of the motor while the auxiliary winding is left opened. The stator is at zero speed, whereas the rotor is run at synchronous speed of about 333rpm. The current flows through the main winding and the average power consumed by the motor are recorded. The parameters of the permanent split-capacitor SPIM is estimated by following the methods and equations discussed in Section II. Torque of the motor is calculated at different slips and the torque-speed profile is plotted.

VI. RESULTS AND DISCUSSIONS

Blocked-rotor and no-load tests were simulated in 2D FEM rotating machine analysis. The auxiliary circuit was open-circuited, while the main winding was excited with single-phase ac supply. Voltage, current, input average power and power factor were measured and recorded. The external rotor was at rest during blocked-rotor test, and it was spinning at

synchronous speed @333rpm for no-load test. FEM results from both tests allow the estimation of motor parameters which are as follows:

Resistance in Main winding, R1m = 300 Ω Resistance in Auxiliary Winding, R1a = 320 Ω

Rotor resistance, R2’ = 290Ω Leakage Reactance in Main winding, X1m = 170 Ω

Leakage Reactance in Auxiliary Winding, X1a = 223 Ω Rotor Leakage Reactance, X2’ = 170 Ω Magnetizing Reactance, Xmag = 711 Ω

Using the rotating machine analysis in 2D FEM, the permanent split-capacitor SPIM was operated at synchronous speed @333rpm and under load condition at 250rpm. Figs. 6 shows the applied voltage and current waveforms when the motor was rotated at synchronous speed @333rpm. The peak input current is about 0.42A and quite distorted. This may be due to the effects of slot harmonics and also unsymmetrical resultant magnetic flux in the air gap. This distortion could also be associated with the appearance noise in the motor. Meanwhile, Fig. 7 displays the output torque waveform when the permanent split-capacitor SPIM was simulated to run at load condition @250rpm. The average torque is about 1.03Nm .

Fig. 6. Voltage and current waveforms when motor is operated at

synchronous speed @333rpm.

Fig. 7. Output torque waveform during load operation at 250rpm

After having known the motor parameters from 2D FEM

modelling, we can predict the characteristics of motor torque vs speed under influence of different values of capacitor which is connected in series with the auxiliary winding, as shown in Fig. 8. It can be seen that higher value of capacitor would make the starting torque higher and the operating slip smaller at similar rated load, which is very beneficial, but at higher cost since the capacitor is larger. Smaller operating slip is desirable since the motor is operating at higher efficiency. Therefore, there is a

trade-off that motor designer has to choose when selecting the most appropriate capacitor value.

Fig. 8. FEM prediction of torque vs speed profile for 18-pole permanent

split-capacitor SPIM under influence of different capacitor values.

VII. CONCLUSION

This paper has investigated the parameters of a permanent split-capacitor single-phase induction motor by conducting the DC test, blocked rotor test and no-load test, which later can be used to estimate the motor torque-vs-speed characteristics. An exact motor model is simulated and investigated in 2D FEM under rotating machine analysis where the blocked rotor test and no-load test can be performed. The FEM results are obtained to calculate motor parameters. Motor characteristics are also computed under different capacitor values. Larger value of capacitor would make the starting torque higher and the operating slip smaller at similar rated load, which is very beneficial since the motor would accelerate faster from idling and operate at higher efficiency at rated load. But higher capacitor’s value entails more cost and bulky capacitor size to be installed inside the ceiling fan motor.

ACKNOWLEDGMENT This work was supported by Universiti Sains Malaysia under

Short-Term Grant 304/PELECT/6033011.

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