Three Phase Induction Motor Performance under Unbalanced Voltage Conditions

Transcription

1 Three Phase Induction Motor Performance under Unbalanced Voltage Conditions A Jalilian, IUST 1. Introduction Three phase induction motors are normally designed to operate under balanced supply voltage conditions. Australian Standards [AS86] specifies that a polyphase voltage system is virtually balanced if the negative sequence does not exceed 1% of positive sequence component of the system voltage over a long period. IEEE Std 112 [IEEE91] allows 0.5% voltage unbalance when performing standard tests on polyphase induction motors. Some manufacturers suggest an allowable deviation (mostly ±5%) from the nameplate voltage, however, little or no information is available on the manufacturer's data on the level of allowable unbalance. Voltage unbalance, in turn, affects the performance of induction motors as well as other power system loads and equipment. This report deals with a review of three phase induction motor performance under unbalanced voltage conditions. Two common definitions of the voltage unbalance are given and their method of calculations are presented. Experimental tests are conducted on a 7.5 kw high efficiency induction motor supplied by nominal balanced and unbalanced supply voltages under different loading conditions. Experimental results are utilised to investigate the effect of unbalanced supply on motor losses as well as on motor output power. 2. Voltage Unbalance in Power System There are two commonly used definitions for voltage unbalance. The simple approach is the NEMA definition [Lin72] which gives a numerical description for voltage unbalance, VU, as: V VU = max V av (1) where Vav is the average value of three phase voltages and Vmax is the maximum voltage deviation from Vav. Most standards organisations such as IEEE [IEEE93], IEC [IEC90] and Australian Standards [AS86] also recognise the given definition as a way to express the voltage unbalance in a system of

2 Induction Motor Performance under Unbalanced Voltage Conditions 1 voltages. However, the given simple definition is only an approximation of the negative sequence component present in a system of unbalanced voltages. Example 1: If the line to neutral voltages of a system are: Van = 240 V Vbn = 230 V and Vcn = 250 V, then Vav = 240 V and VU = 10/240 = (4.2%). The second definition is based on the theory of symmetrical components in three phase systems where a set of 3-phase unbalanced voltages can be specified as three balanced symmetrical components namely; positive, negative and zero sequence components. The positive sequence components have the same sequence as the main system having a 120 degree phase shift. The negative sequence components, however, have a sequence opposite to the sequence of the main system. The zero sequence components have no phase shift and are ineffective in 3-wire 3-phase systems. As a standard definition, the voltage unbalance, known as the Voltage Unbalance Factor (VUF), is defined as the ratio of the negative sequence component to the positive sequence component [IEEE93] [IEC90] as: VUF V V = 2 1 (2) where V1 and V2 are the positive and negative sequence components respectively. Both V1 and V2 can be calculated using the magnitude and phase shift of the 3-phase voltages. This definition is more complicated than that defined by NEMA definition, Equation (1). Assuming 120 degree phase shift for the unbalanced voltages given in example 1, the positive and negative sequence values and the VUF are: V1= V V2 = 11.6 V VUF = V2/V1 = (4.8%)

3 Induction Motor Performance under Unbalanced Voltage Conditions 2 It can be seen that the positive sequence voltage is almost the same as the average value of the three phase voltages (ie V1=Vav) but the VU and the VUF defined by Equations (1) and (2) differ by more than 10%. Example 2: Van=245 V, Vbn=237 V and Vcn=238 V According to NEMA definition: Vav=240 V and VU=5/240=0.021 (2.1%). Using symmetrical components: V1=240.0 V, V2=5.1 V and VUF=V2/V1=0.021 (2.1%). It can be seen that the two figures (VU and VUF) are almost the same for the given unbalanced supply. According to a graphical presentation given in [Cum85] the two definitions are almost equivalent for unbalanced voltages of less than 4% defined according to NEMA definition. Increased losses and relatively large unbalanced currents are two of the main effects of voltage unbalance in relation to induction motors [And54] [Wil54] [Gaf59] [AS86] [IEC90]. Depending on the level of voltage unbalance the machine temperature tends to exceed the specified limits causing motor overheating. The severity of the voltage unbalance has been emphasised in early issues of NEMA publications where it has been reported that a 3.5% voltage unbalance can cause about 25% increase in machine temperature rise [Lin72]. The current imbalance may introduce difficulties in motor overcurrent protection and results in nonuniform distribution of heating in the stator windings. Reduced torque and full load speed and increased noise and vibration are also other unwanted effects of voltage unbalance present in the supply of induction motors [Wol75] [[AS86]. 3. Equivalent Circuits In order to analyse the induction motor performance under unbalanced voltage supply conditions two equivalent circuits corresponding to positive and negative sequence components can be developed [Wil54]. The positive sequence equivalent circuit is the same as the conventional equivalent circuit as shown in Figure 1 (a). The negative sequence component of the supply voltage produces

4 Induction Motor Performance under Unbalanced Voltage Conditions 3 an air gap flux which rotates at the synchronous speed but opposite to the direction of the rotor motion. Therefore, under normal operating conditions (ie low slip where s 0), the frequency of the rotor current due to the induced emf produced by the negative sequence component is almost twice that of the supply frequency, ie (2-s) f1. As a result of skin effect, both rotor resistance and leakage reactance will be different from the low slip values, X2 and R2. The new parameters X' 2 and R' 2 illustrated in a modified equivalent circuit of Figure 1 (b) represent the corresponding rotor parameters at frequency (2-s)f1. In general, R1, X1 and Xm remain the same in both circuits. For motors with double cage rotors and/or deep bar rotors, R' 2 >> R2 and X' 2 < X2 mainly due to rotor skin effect. As an example, in a 10 hp induction motor having a double cage rotor, R' 2 3R2 and X' X2 as reported in [Wil54]. For the same motor a single cage rotor has been designed where R' 2 R2 and X' 2 X2 [Wil54]. R X X R X X' V 1 X m R s 2 V 2 X m R' 2 2-s (a) (b) Figure 1: Equivalent circuits to determine positive (a) and negative (b) sequence impedances of an induction motor Nowadays, most induction motors are designed with double cage and/or deep bar rotors in order to utilise the high starting torque characteristics. Therefore, it is most likely that the rotor parameters under frequencies higher than the low slip value (nominally a small fraction of the supply frequency) are significantly higher than the nominal rotor parameters. A comparison of the equivalent circuits of Figure 1 (a) and (b) indicates that the rotor circuit corresponding to the negative sequence component has a relatively smaller impedance compared to the positive sequence equivalent circuit. The reason is obviously the term R' 2 / (2-s) in the rotor circuit of Figure 1 (b) as compared with the term R2 /s in Figure 1 (a). The overall negative sequence impedance, Z2, is about 10% to 20% of the positive sequence impedance, Z1 [And54] [Wil54] [Lin72] [Ber63]. Therefore, a small negative sequence voltage in the supply can cause rather a large negative sequence current in the motor and hence a relatively large unbalanced current. For instance, for 5% negative sequence voltage (VUF = 5%) present in the supply of a motor having

5 Induction Motor Performance under Unbalanced Voltage Conditions 4 Z2 = 15% Z1, the Unbalanced Current Factor (UCF=I2/I1) is calculated to be 33% as: I2 = V2/Z2 = 0.05 V1/0.15 Z1 = 0.33 I1. In addition to increased losses and reduced torque, such unbalance in the current might activate thermal relays used to protect the motor [And54]. 4. Unbalanced Voltage Tests on an Induction Motor In order to experimentally investigate the effects of unbalanced voltages on the performance of induction motors, a 3-phase high efficiency cage induction motor with specifications shown in Table 1 was selected for testing purposes. Power rating Nominal voltage/frequency Connection Full load current Full load speed 7.5 kw 415 V, 50 Hz 14.5 A 1440 rpm Full load efficiency 0.88 Full load power factor 0.82 Table 1: Specifications of the test induction motor 4.1 Experimental setup and test procedure A three phase variac was employed to supply the test motor under balanced and unbalanced voltage conditions. The unbalanced voltage was produced by connecting the mains supply to different taps available on the variac windings. The line-to-line voltages, three line currents and motor input power level were measured continuously using a 3-phase digital AC meter and calibrated voltmeters/ammeters. Since one of the objectives of the tests was to estimate the motor losses under different supply/load conditions, the double chamber calorimeter (DCC) [JalI97] was employed for the direct measurement of motor losses. The loaded machine tests were conducted using previously developed experimental setup as shown in Figure 2 [JalII97]. A DC generator supplying a

6 Induction Motor Performance under Unbalanced Voltage Conditions 5 load bank was coupled to the test motor via a flexible universal coupling. The motor loading level was adjusted to desired values by changing the field current of the DC generator. The power supplied to the load bank was calculated by measuring its DC voltage and current. The shaft speed was also measured during each test using a digital tachometer. Test induction motor Flexible coupling Insulation material (EPS) Stuffing box Plummer block Variable DC supply + - A V Load bank A Field + - V DC Generator Universal coupling Wooden base Bakelised canvas plates Metal test bed Figure 2: Experimental setup developed to conduct loaded machine tests under different supply conditions and loss measurement using the Double Chamber Calorimeter (DCC) 4.2 Experimental results and analysis Balanced supply conditions The first series of tests was conducted on the test motor supplied by balanced supply with the average line-to-line voltages adjusted to the nominal value of 415 V using the variac. The motor loading level was adjusted to cover the light load to full load conditions in seven steps. Each step was continued long enough to achieve the thermally steady state conditions for the motor operating inside the calorimeter. The motor line-to-line voltages, line currents, total motor input power, Pin, and motor shaft speed, N, were measured continuously during each test. The corresponding averaged values along with the motor total losses, Pm estimated using the DCC approach, the calculated motor shaft power, Pshaft (=Pin-Pm) and the calculated motor slip, s, are given in Table 2. The accuracy of the current and voltage measurement is ±0.5% while the input power, Pin are measured with a maximum uncertainty of ±1%. Motor losses, Pm are subject to a maximum error of ±4%.

7 Induction Motor Performance under Unbalanced Voltage Conditions 6 Averaged line Motor input input current: power: I in (A) P in (W) Motor Losses: P m (W) Motor shaft power: P shaft = P in -P m Shaft speed: N (rpm) Calculated slip: s=(n s -N)/N s Table 2: Measured quantities corresponding to test motor supplied by balanced supply voltages at different loading levels According to the motor ratings given in Table 1 the calculated input power under rated conditions ( 3*V*I*cosφ) and the measured input power (8860 W) differ by less than 4%. The calculated motor shaft power under rated conditions (7800 W) is also different compared to the motor rated power (7500 W) by 4%. The given discrepancies can be justified by consideration of the accuracy corresponding to the measured quantities (ie motor voltage, current and input power). Using the rated motor power (7500 W) and the full load efficiency (0.88) the motor losses is calculated to be 1023 W having a discrepancy of < 4% compared with the measured value (1060 W) which is again within the accuracy limits of the loss measurements. In order to find a relationship between the motor losses and the average input current a curve of the form A+B*Iin 2 was fitted to the measured data as illustrated in Figure 3 where A=207 and B=4.0. The maximum discrepancy between the measured losses and losses estimated using the fitted curve is less than 30 W which is within the accuracy limits of the motor loss measurement using the DCC.

8 Induction Motor Performance under Unbalanced Voltage Conditions measured Motor Losses: Pm (W) fitted: *Iin^ Input current: Iin (A) Figure 3: Measured motor losses vs motor input current along with the fitted curve The variation of motor shaft power, Pshaft,with motor input current, Iin, is illustrated in Figure 4. It can be seen that at smaller values of motor current the motor shaft power increases at a higher rate as compared with that at larger currents. Also for motor input currents greater than 10 A, motor shaft power increases almost linearly as: Pshaft = (591 Iin)-698. This linear relationship can be utilised to approximate the motor loading level as a function of averaged motor input current varying between 10 A and 15 A Motor shaft power: Pshaft (W) for 10A > Iin > 15A Pshaft=(591*Iin) Input current: Iin (A) Figure 4: Variation of motor shaft power vs motor input current under balanced rated supply voltage conditions

9 Induction Motor Performance under Unbalanced Voltage Conditions Unbalanced supply conditions The second and the third series of tests were conducted under two different unbalanced voltage conditions where the average line-to-line voltages was kept constant at nominal value of 415 V. The motor loading level was adjusted to four different conditions as: 1. light load, 2. half load, 3. full load 1 where the largest line current, Imax, equals to the rated current, and, 4. full load 2 where the averaged value of the three phase currents, Iav, equals to the rated current, Irated. The measured line-to-line voltages, Vab, Vbc and Vca along with the calculated average voltage, Vav, are given in Table 3. The positive and negative sequence components of the given voltages were also calculated, including for the first series of tests (Section 4.2.1), according to the principle of symmetrical components and the sine rule. These quantities along with the voltage unbalance factor, VUF, corresponding to each case are averaged and shown in Table 3. It can be seen that in all three cases, the average voltage, Vav, and the positive sequence voltage, V1, are of the same order of magnitude. The nominally balanced supply voltage (A) contains a small amount of negative sequence component giving a VUF of less than 0.4%. The slight unbalance in the variac output voltage (under balanced mode) is mainly due to the random fluctuations in the mains voltages as well as the physical asymmetry of the variac. Supply condition V ab (V) V bc (V) V ca (V) V av (V) V 1 (V) V 2 (V) VUF Balanced voltage (A) Unbalanced voltage I (B) Unbalanced voltage II (C) % % % Table 3: Measured line-to-line voltages and the calculated average, positive/negative sequence voltages and the VUF under different supply conditions

10 Induction Motor Performance under Unbalanced Voltage Conditions 9 For each series of tests the measured line currents, Ia, Ib and Ic, motor input power, Pin, and motor losses, Pm, are given in Table 4. The calculated average, positive/negative sequence currents, CUF (=I2/I1) and motor shaft output power, Pshaft (=Pin-Pm) are also given in Table 4. For the balanced voltage test (case A) only the rated load condition is considered where the line currents are unbalanced due to the slight imbalance in the voltage (ie VUF=0.39%). The average current, Iav, and the positive sequence current, I1, are almost the same and equal to the rated current of 14.5 A. The negative sequence current, I2, is about 0.5 A giving CUF=3.6%. With unbalanced voltages applied to the test motor (ie cases B and C), the averaged motor line currents and the positive sequence current increase with load while the negative sequence current remains almost unchanged. The CUF is much larger than the corresponding VUF indicating a small negative sequence impedance of the test motor compared with its positive sequence impedance. The CUF decreases as the motor loading level increases mainly due to the increase of the positive sequence current with load. It can be seen that the negative sequence current, I2, increases only with the VUF leading to average values of 0.5 A, 0.9 A and 3.3 A for cases A, B and C respectively. Measured Calculated Supply Case I a I b I c P in P m I av I 1 I 2 CUF P shaft = P 1 * P 2 * = condition (A) (A) (A) (W) (W) (A) (A) (A) P in -P m (W) P m -P 1 Balanced voltage (A) VUF=0.39% A % Unbalanced voltage I (B) B1 B % 12.4% VUF=1.35% B3 B % 6.5% Unbalanced voltage II (C) C1 C % 44.3% VUF=3.71% C3 C % 21.7% * P 1 and P 2 are the motor losses due to the positive and negative sequence components of the motor input currents respectively. P 1 is calculated according to the fitted curve given in Figure 3 as: P 1 = 207+4*I 1 2. Table 4: Measured and calculated quantities corresponding to test motor operating under different supply/load conditions

11 Induction Motor Performance under Unbalanced Voltage Conditions 10 A comparison between cases B3 and C3, where the largest line current is equal to the rated current (14.5 A), shows that the average current in the case C3 (VUF=3.71%) is smaller than that in case B3 (VUF=1.35%). In other words, with a larger VUF, the average motor current and hence the motor loading level should be reduced so that the largest current does not exceed the rated value. For cases A, B4 and C4 where Iav = 14.5 A, the variation of motor line currents, Ia, Ib and Ic, positive and negative sequence currents, I1 and I2, with VUF is shown in Figure 5. It can be seen that, as VUF increases, one of the line currents exceeds the rated current while the other two decrease below the rated value. While I1 decreases slightly with VUF, increase of the negative sequence current, I2, with VUF is evident from the graph. Current (A) Ic I1 Ia Ib VUF% I2 Figure 5: Measured motor line currents, and the calculated positive and negative sequence currents as a function of VUF under loaded conditions where Iav=14.5 A 4.3 Limits for the motor losses In cases B and C if the effect of motor extra heating (due to the presence of voltage unbalance) on stator and rotor resistances, R1 and R2 in Figure 1 (a), is neglected then motor losses due to the positive sequence current can be calculated. In other words, it can be assumed that the motor is only supplied by a rated balanced system of voltages drawing a balanced current with an average value equal to the positive sequence current, I1. Accordingly, motor losses due to the positive sequence current is calculated based on the fitted curve presented in Figure 3 and shown in Table 4 as P1. For each case, the difference Pm-P1 (called P2 in Table 4) can be accounted for the losses due to the negative sequence current I2. It can be seen that P2 increases significantly with VUF but,

12 Induction Motor Performance under Unbalanced Voltage Conditions 11 for a given VUF, it is almost unchanged with load as in most cases shown in Table 4. On average, P2 is about 1%, 5% and 13% of the total machine losses for cases A, B and C respectively. Motor Losses: P1 and Pm (W) measured (VUF=3.71%) measured (VUF=1.35%) estimated (VUF=0.39%) Rated loss level Positive sequence current, I1 (A) Figure 6: Estimated and measured motor losses at different supply/load conditions The variation of motor losses with I1 corresponding to balanced and unbalanced voltages is also illustrated in Figure 6 (the solid line is P1). In order to find limits for the losses in the test motor due to the given unbalanced voltages, a line representing the rated motor losses (in case A where P1=1048 W due to I1=14.5 A) is specified in Figure 6. The intersection of this line with the two curves gives two new values for the line current (14.1 A when UVF=1.35% and 13.1 A when UVF=3.71%). The motor losses due to these currents are likely to be equal to the rated losses. Using the curve given in Figure 4, the motor shaft power, Pshaft, (which represents the motor loading level) corresponding to the given currents is estimated and utilised to calculate the deviation of the motor loading level from the rated value as shown in the last column of Table 5. When VUF=1.35%, the machine should supply 98% of its rated load in order to achieve the rated motor losses. This figure reduces to 90% when a higher VUF, ie 3.71%, is present in the motor supply voltage. The average value of the line currents in both cases remain under the rated value, however, the CUF is still high. The calculated pu values of the motor loading level under different conditions are summarised in Table 5. It can be seen that the motor loading level should be reduced to 97% (in case B3) and 78% (in case C3) of its rated power in order to

13 Induction Motor Performance under Unbalanced Voltage Conditions 12 keep the maximum line current equal to the rated current (Imax=Irated). According to the data given in Table 4, motor losses has reduced the rated value by a factor of 3% in case B3 and 20% in case C3. Considering cases B4 and C4, where Iav = Irated, the motor operates above the rated loading condition as shown in Table 5. According to data given in Table 4, motor losses exceed the rated value by about 3% and 12% in cases B4 and C4 respectively. Also the maximum difference in the line currents is relatively high (1.6 A with CUF=6.5% in case B4 and 4.8 A with CUF=21.7% in case C4). Such a large unbalanced current can activate the motor protection overcurrent relays. Motor loading level (pu) VUF for for for I max = I rated I av = I rated Motor losses = Rated losses 0.39% 1.00 (case A) 1.00 (case A) 1.00 (case A) 1.35% 0.97 (case B3) 1.04 (case B4) % 0.78 (case C3) 1.02 (case C4) % % Table 5: Motor loading level under different supply conditions Considering cases A, B4 and C4 where Iav=Irated, the variation of motor losses with VUF along with a straight line fitted to the experimental data is illustrated in Figure 7. It is shown that with VUF=5% and 10% the motor total losses can increase to 1210 W and 1375 W respectively. These values are about 16% and 31% more than motor rated losses (1048 W).

14 Induction Motor Performance under Unbalanced Voltage Conditions W Motor losses (W) W Measured Fitted: *VUF% VUF% Figure 7: Motor loading level as a function of VUF at different conditions 1.4 Motor loading level (pu) Iav=Irated Losses=Rated Imax=Irated VUF% Figure 8: Motor loading level as a function of VUF for different conditions Using the fitted curves of Figures 3 and 4 the motor loading level is estimated to increase by more than 11% and 21% respectively. In order to reduce the losses to the rated level, the motor load should be reduced to 84% and 69% of the rated value respectively. These figures are approximated according to the estimated motor losses due to the given VUFs. The motor loading level should be further reduced if the condition Imax=Irated is considered. The approximate figures must be less than 70% (for VUF=5%) and 40% (for VUF=10%). In order to specify the motor loading levels under different conditions the corresponding

15 Induction Motor Performance under Unbalanced Voltage Conditions 14 figures are shown in Table 5. For comparison and clarity a graphical presentation of data given in Table 5 is also illustrated in Figure 8. It can be seen that in the worst case of VUF=10% the motor should be significantly derated in order to allow Imax=Irated. A similar graph is given in [IEEE93] and [AS86] where a the motor should operate at 75% of its rated loading level if a voltage unbalance of 5% is present in its supply. 5. Summary and Conclusions The effect of unbalanced supply voltage on induction motor operation has been reviewed in this report. The conventional definitions for the voltage unbalance have been given. The induction motor equivalent circuit corresponding to the positive and negative sequence components of the supply voltage have been presented and the basic differences have been highlighted. It has been reported that the motor negative sequence impedance is about 10-20% of the positive sequence impedance and hence a small unbalance in voltage could cause a relatively large unbalanced current which might cause problems in motor overcurrent protection. Additional losses, extra heating, unbalanced current and reduced torque are some of the unwanted effects of the unbalanced voltages applied to induction motors. The performance of a 7.5 kw induction motor operating under different supply/load conditions has been investigated in this report. Experimental tests have been conducted on the test motor under balanced and two unbalanced voltage conditions and at different loading levels. It has been shown that the additional losses due to the unbalanced voltages are almost independent of the motor loading level. However, additional motor losses are significantly increased with the level of voltage unbalance factor. It has been shown that the motor loading level should be reduced to 97%, 78%, 70% and <40% with VUF=1.35%, 3.71%, 5% and 10% respectively in order to keep the maximum line current at the rated value. In this case the current in the other two lines are smaller than the rated value and the total machine losses are less than the rated value. The current unbalance factor, however, significantly increases with VUF. Experimental tests have also been conducted to change the motor loading level so that the motor losses meet the rated value. To achieve this condition, it has been shown that the motor loading level should be reduced to 98%, 90%, 84% and 69% corresponding to VUF=1.35%, 3.71%, 5% and 10% respectively. These figures can be considered as the derating factors for the given test motor. In the case that the motor has a 1.15 service factor, it can tolerate unbalanced voltages

16 Induction Motor Performance under Unbalanced Voltage Conditions 15 with VUF up to about 4.5% without being derated. This figure is comparable with the maximum allowable VUF of 5% presented in the literature. Note: the effect of unbalanced voltage on hot spot temperature has not been studied in this report. 6. References [And54] Anderson, A., S., Ruete, R., C., "Voltage Unbalance in Delta Secondaries Serving Single-Phase and 3-Phase Loads" AIEE Transactions, Part III-B (Power Apparatus and Systems), Vol. 73, pp , August [AS86] [Ber63] Australian Standard AS , "Rotating Electrical Machines - General Requirements, Part 31: Service and Operating Conditions", Berndt, M., M., Schmitz, N., L., "Derating of Polyphase Induction Motors Operated with Unbalanced Line Voltages" AIEE Transactions, Part III-A (Power Apparatus and Systems), pp , Feb [Cum85] Cummings, P., G., Dunki-Jacobs, J., R. and Kerr, R., H., "Protection of Induction Motors Against Unbalanced Voltage Operation" IEEE Transactions on Industry Applications, Vol. IA- 21, No. 4, pp , May/June [Gaf59] [IEC90] Gafford, B., N., Duestrhoeft, W. C., Mosher, C., C., "Heating of Induction Motors on Unbalanced Voltages" AIEE Transactions, Part III-A (Power Apparatus and Systems), Vol. 78, pp , June IEC Publication , "Electromagnetic Compatibility (EMC), Part 2: Environment, Section 1: Description of the Environment - Electromagnetic Environment for Low Frequency Conducted Disturbances and Signalling in Public Power Supply Systems" [IEEE91] IEEE Standards 112: Test Procedure for Polyphase Induction Motors and Generators, [IEEE93] IEEE Standards 141, "IEEE Recommended Practice for Electric Power Distribution for Industrial Plants (Red Book), [JalI97] [JalII97] [Lin72] [Wil54] [Wol75] Jalilian, A., Gosbell, V.J., Cooper, P., Perera, B.S.P., "Double Chamber Calorimeter: a New Approach to Measure Induction Motor Harmonic Losses" Proceedings of the IEEE International Electric Machine and Drives Conference (IEMDC'97), pp. MB1/ , Milwukee, WI, May Jalilian, A., Perera, B.S.P., Gosbell, V.J., "Loading Effects in the Estimation of Induction Motor Harmonic Losses" Accepted for presentation in the Australian Universities Power Engineering Conference (AUPEC'97), University of NSW, Sept.-Oct Linders, J., R., "Effects of Power Supply Variations on AC Motor Characteristics" IEEE Transactions on Industry Applications, Vol. IA-8, No. 4, pp , July/August Williams, J., E., "Operation of 3-Phase Induction Motors on Unbalanced Voltages" AIEE Transactions, Part III-A (Power Apparatus and Systems), Vol. 73, pp , April Woll, R., F., "Effect of Unbalanced Voltage on the Operation of Polyphase Induction Motors" IEEE Transactions on Industry Applications, Vol. IA-11, No. 1, pp , Jan./Feb