PERFORMANCE OF A 7.5 Kw INDUCTION MOTOR UNDER HARMONICALLY DISTORTED SUPPLY CONDITIONS

A. Jalilian Department of Electrical Engineering,

Iran University of Science and Technology Narmak, Tehran, 16844, Iran

Jalilianosun. iust . ac . ir, a i alilianoyahoo .com

Abstract: The behaviour of a 7.5 kW high efficiency cage induction motor fed by distorted supply has been investigated in this paper. Experimental data were collected by developing a testing facility consisting of a three phase harmonic generator, a double chamber calorimeter and a PC based data acquisition system. Motor additional losses due to the presence of harmonics were estimated using the calorimetric method. It has been shown that a distorted voltage containing low order harmonics causes more losses in the motor as compared with the high order harmonics. Accordingly, weighted THD (WTHD) has been defined to specify the limits for additional losses in a motor supplied by distorted voltages. The variation of test motor parameters with harmonic order as well as the variation of additional losses with WTHD has led to establishment of derating factor (DF) for the test induction motor. Applicability of the DF on several induction motors with different power ratings has been examined. It has been demonstrated that with a service factor of 1.15, most induction motors are capable to handle distorted voltages as definedby standards.

I. INTRODUCTION ,

The presence of time harmonic voltages in the supply of induction motors cause additional losses and hot spot temperature. The accurate measurement of induction motor additional (harmonic) losses has been a difficult task due to the limited frequency bandwidth of standard measuring equipment. Another problem is the inaccuracy involved in the measurement of motor output power.

The development of the new type of loss measurement technique, a double chamber calorimeter (DCC) [ 11, has made it possible to estimate total machine losses, including harmonic losses, accurately regardless of the supply voltage conditions. The approach is quite usel l , even when the machine is loaded, since the motor losses can be estimated directly under any desired loading conditions. Investigations on the heat loss measurement

V. J. Gosbell and B.S.P. Perera School of Electrical, Computer and Telecommunications Engineering

University of Wollongong, NSW 2522, Australia V.Gosbell@,uow.edu.au, S.Perera@,uow.edu.au

procedure using the DCC and the loaded machine mechanism has been described in [ 11.

The difficulty in providing a flexible and controllable source of harmonics has resulted in a limited access to experimental data for harmonic analysis of induction motors. However, with the aid of a testing facility including a harmonic generator [2], the DCC, and a data logging system, the effects of different time harmonics on performance of a 7.5 kW cage induction motor (see App. I) has been examined. Using the experimental data, frequency variation of motor parameters under different loading conditions has been investigated [3]. Variation of motor harmonic losses and its relation with THD as well as deriving a Derating Factor will be investigated and introduced in this paper.

11. INDUCTION MOTOR HARMONIC/CALOFUMETRIC TESTS

Using the developed testing facility, four series of tests were conducted on the test motor under different supply conditions including nominal voltage (ie 415 V, 50 Hz) as well as the harmonically distorted voltages. Two series of tests were performed at no-load, one at half load and one at full load conditions. For harmonic tests, distorted voltages containing fundamental frequency and one of the non-triplen odd harmonics under 1 kHz (ie n lckl for any integer value of k) were applied to the

test motor separately. The reason for choosing the given harmonics was that they are the most common and harmful harmonics that could be present in the mains

Each series of tests was commenced by supplying the machine by nominal voltage over a period long enough to achieve thermally steady state conditions. For a given loading condition, total machine losses under fundamental and distorted supply conditions, W,, and W, respectively, were measured using the DCC approach. For each harmonic test, the additional losses due to the presence of time harmonics in the supply of the test motor were estimated as:

supply.

0-7803-5957-7/00/$10.00 Q 2000 IEEE

355

This simple approach is quite acceptable if the losses due to the fundamental component of the applied distorted voltages remain the same and equal to Wtl in all of the consecutive harmonic tests. This assumptionis valid due to the fact that all the harmonic tests were performed while a nominal value of 41 5 V was given as the desired magnitude for the fundamental component of the waveform produced by the harmonic generator.

However, there was still a possibility of alteration in the fundamental losses from time to time due to the various reasons such as variation of motor operating conditions and harmonic generator output voltage fluctuations. Therefore, it was decided to perform at least two tests under nominal conditions one at the beginning and one at the end of each series of harmonic tests. The esfimated losses using these two tests were then averaged and considered as W,, to be used in Equation (1). Experimental results conf i ied that the discrepancies are often less than the resolution of the loss measurement and therefore can be disregarded. The values ofW,, under different loading conditions and additional (harmonic) losses related to each test, W , are given in Table 1.

The motor line-to-line voltages and line currents were also captured using the voltage and current measurement circuits and the data logging system withappropriate sampling rates. For each test, the pu values for harmonic voltages and currents were calculated using spectrum analysis as shown in Table 1. Considering the measurement error and the inaccuracy of the actual sampling frequency and the leakage effect, the calculated harmonic voltages and currents are subject to a maximum uncertainty of 2% of the measured values. The corresponding absolute error could be as highas 0.001 pu in the case that a harmonic component is

no-load test 1 Wtl = 370 W I no-load test 2

Wtl = 385 W

I - I -

calculated to be 0.05 pu (ie 5% of the fundamental component). This figure is small enough to be neglected.

HI. ANALYSIS OF THE EXPERIMENTAL DATA

A comparison between the test results indicates that, for a given pu voltage distortion due to a particular harmonic order, the additional losses in the motor increase with load. For instance, additional losses due to the presence of about 16% of the 5th harmonic voltage at full load is about 40% higher than that in half load and more than twice as in no-load. In terms of harmonic currents, no significant difference is observed between the cases of similar voltage distortion, ie no-load test 2, half load and full load results. Frequency variation of the test motor parameters (total resistance, total leakage reactance, and total leakage inductance) has already been investigated by the authors [3]. Further data analysis is given in the following sections.

A. Variation of Harmonic Losses with THD

According to the experimental data, it can be seen that, with almost the same voltage distortion level, harmonic losses due to the lower order harmonics are higher than losses due to the higher order harmonics. Usingdata analysis, total pu harmonic losses ofthe test motor can be expressed as:

which suggests that total harmonic losses are almost . . inversely proportional to the harmonic order n. Therefore, for a constant Vn, low order harmonics cause more pronounced harmonic losses in induction motors. This conf i i s that the THD cannot be considered as the most appropriate criteria in applying supply distortion to

I full load test Wtl = 1015 W I half load test

Wtl = 500 w

0.131 0.094 35 0.142 0.106 40

Table 1 : Motor harmonic losses and pu harmonic voltages and currents under different load and supply conditions

356

estimate induction motor harmonic losses. However, using Equation (2), a more appropriate figure, a weighted THD (WTHD), can be defined as:

w n 1 7 i D = J p (3)

which gives a larger weighting to the lower order harmonics. The quantity WX2 varies for machines with different power ratings and can be used to specify the motor harmonic limits. The larger the machine the lower the R/X ratio is and hence the higher WTHD that can be specified.

Test motor

7.5kW,

B. Specijjing Derating for Induction Motors

Equations (2) and (3) can be utilised to specify a derating factor for induction motors when supplied by distorted waveforms. The derating factor should be determined so that the machine heating does not exceed the allowable limit while harmonics are present. In other words, the extra losses produced due to the presence of harmonics should be compensated by reducing the rated load according to a suitable derating factor.

Based on the analysis presented in Appendix Il total fundamental losses, W,,, can be approxeated by:

Motor A Motor B Motor C 3.7 kW, 300 kW, 1.645 MW, 460 v 415 v 11 k v

where W,,, represents that part of the losses which is independent of load and Wload is the load dependent part of the losses which can be expressed as:

yoad = (1 + 2 Im@J 1; R (5)

where Im is the magnetising current, I2 is the rotor current representing the load, R is the pu total machine resistance (ie R = R1 + R2 + R11) and QO is the phase angle between the input voltage and 12 at full load. It is shown in Appendix I1 that Qo can be approximated by:

where so is the full load slip.

In the presence of harmonic losses, Wn, anewvalue should be defined for I2 so that the s u m of W,and Wload due to new 12 is equal to Wload due to the rated I2 The new value for I2 then can be specified by defining a derating factor, DF, as:

lpu.

(7)

By substituting Equations (2) and (3) in Equation (7), the DF can be re-expressed as:

WTHP DF= 1- d xy1+2ImcDO) I

having a value between 0 and 1. When WTHD=O then

DF= 1, and when:

WTHD = WTHD- = X , / m (9)

then DF = 0 indicating motor should operate at no-load so that it can tolerate extra heating. It should be noted that the derived DF is valid under conditions close to full load, therefore, WTHD,, only indicates a limit for WTHD and cannot be applied practically.

Example: Typical parameters corresponding to four induction motors, including the test motor, having different power ratings [4,5] are given in Table2. In order to specify derating factors for the givenmotors three different distorted waveforms as described in Table 3 are chosen. All three waveforms have 10% THD, however, waveforms I and I11 contain 5th and 19th harmonic respectively while waveform I1 contains different order/magnitude harmonics. The calculated THD and WTHD for each waveform are also shown in Table 3.

0.22 I Sn I 0.04 I 0.039 I 0.0089 I 0.0055 I

1, (pu) 0.35 0.4 0.3 0.3

Table 2: Typical parameters for three induction motors with different power ratings

0.055 11 0.040 13 0.035 17 0.020 19 1 - 1 0.015 I 0.1

‘THD I 0.1 I 0.1 I 0.1 WTHD I 0.053 I 0.046 I 0.031

Table 3: Different distorted waveforms having the same THD but different WTHD

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The calculated values for derating factor due to the given distorted waveforms are shown in Table 4. It can be seen that derating becomes more appreciable at higher values of WTHD. The given data confirms that THD is not an appropriate criterion to specify harmonic limits for induction motors. The derating factor particularly becomes significant when smaller machines such as motor A experience distorted voltages.

Test motor Motor A

0.069 0.046

I Derating Factor (DF) I

Motor B Motor C

0.071 0.084

Waveform] WTHD ]Test motor1 Motor A I Motor B I Motor C

I I 0.053 I 0.96 I 0.91 I 0.96 I 0.97 11 III

0.046 0.97 0.93 0.97 0.98 0.031 0.99 0.97 0.99 0.99

Table 4: Derating factor due to distorted waveforms for the different machines

The operational conditions of the induction motors are always subjected to changes from the rated conditions for various reasons. The variation of the supply rms voltage, the voltage unbalance and changes in motor loading level are among them which result in extra heating in the motor [6]. In order to allow for extra heating a parameter known as service factor, SF, typically equal to 1.15 has been defined where the motor temperature rise could be 6- 10°C more than the allowable limit. For the given motors, the maximum derating factor can be specified according to the 1.15 service factor as:

1 DF-=-- Jlls - 093

This figure confirms that the given distorted waveforms (I, 11 and III), except one case, can be safely applied to all motors. Also it can be said that the yh limit given for the THD in the utility power system network [7] is a conservative value in relation to induction motors. The limits for individual harmonics (ie 4% for odd harmonics and 2% for even harmonics) are even more tight since induction motors can tolerate a higher distorted voltage. Specifying the harmonic order is also required when determining standard harmonic limits for induction motors.

Using Df- 0.93 and Equation (8),themaximum allowable value for WTHD calculated for the different induction motors are shown in Tables. Itcanbeseen that the larger machines can tolerate extra losses as compared with smaller machines.

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Engineering Conference (AUPEC 97), pp. 183-188, Sept/Oct 1997.

[4] Perera, B.S.P., Gosbell, V. J., Jalilian, A., "Determining the Harmonic Withstand Capability of Induction Machines" CIGRE International Large Rotating Machines Seminar, invited presentation, paper 6, pp. 1-22, Sydney, Sept. 1996.

[5] IEEE 86: Definition of Basic Per-Unit Quantities for AC Rotating Machines, 1987.

[6] Cummings, P.G., "Estimating Effect of System Harmonics on Losses and Temperature Rise of Squirrel-Cage Motors" IEEE Transactions on Industxy Applications, Vol. IA22, No. 6,pp. 1121-1126,Nov./Dec. 1986.

[7] IEEE Standard 519-1992, IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems .

APPENDIX I: CALCULATION OF TEST MOTOR PARAMETERS The test motor is a delta connected 7.5 kWcageinduction motor with line-to-line voltage of 415 V. For various tests conducted on the test motor using an autotransformer, an average no-load input power of 400 W was measured. The autotransformer was also used to conduct several locked rotor tests on the machine. Based on the no-load and locked rotor test results and the manufacturer's data sheet, the motor parameters corresponding to the single phase approximate equivalent circuit are derived as: Sbase = 3 x Vbase x Ibase = 3 x 240 x 14.5 = 10440 VA Zbase = Vbase * Ibase = 240 * 14.5 = 16.55 RI = 0.47 to 0.70 Q 0.028 to 0.042 pu depending on the operating temperature R2 = 0.72 Q at low, slips (using manufacturer's data sheet) = 0.044 pu R2=1.36Q (using locked rotor test results at 50 Hz) = 0.082 pu X=X1 + X2 = 3.05 Q (using locked rotor test results) 5 0.18 pu R, = 580 Q (using no-load test results) = 35.0 pu

where R2 and X2 are the rotor parameters referred to the stator side.

= 41 L2 (using no-load test results) = 2.5 pu

APPENDIX 11: CALCULATION OF INDUCTION MOTOR VARIABLE LOSSES

It is known that the developed torque on the motor shaft, T, can be expressed as:

T = (-4.1) S

where 12 is the rotor current referred to the stator and represents the load, R2 is the rotor resistance referred to the stator and s is the rotor slip. Accordingtoinductionmotor approximate equivalent circuit:

( A 4 v, R2

I , = R , + - + j X

where VI is the motor input voltage, R1 is the stator winding resistance and X is the total machine leakage reactance. Under

normal operating conditions where V1 small (about 0.04 for the test motor), it can be written:

lpu and s is very

(A.3)

Equation (A.l), then, can be re-written as:

which describes a linear relationship between T and 12. Using Equation (A.2), the rotor slip: s, can be calculated as:

(-4.4) T = 1 2

(A.5) R2

s = g z R I

which varies almost linearly with I2 from s = 0 at I2

(no-load condition) to s so at I2 lpu (full load conditions) where SO can be calculated as:

(-4.6) R2

SO = 4- 1-X2 -RI and hence:

(-4.7) s = SJZ

The phase angle, CP between the stator input voltage, VI, and load current, 12, can be calculated as:

which is a linear function of 12 as

with @=@d2 (A.9)

(A. 10)

The following equation can be written regarding the current:

where 11 is the stator current and 1, is the magnetising current. Under normal operating conditions CP is very small and hence sin CP = 0 (rad) = 00 12. Therefore, Equation (A.ll) is modified as:

1: = 1; + I,' + 2Z2Im sin@ (A.11)

1: = I: + 1; + 2I*Im(Z2CP0) = I; + I,' (1 + 2 (A.12)

Fundamental copper losses in the motor, Wcu, can be expressed as:

w, = I:R~ +z,2(1+21~@~)~ = wmm, + w h d (A. 13)

where R is the total machine resistance (R = R1 + R2 + Rli), Wconst is the constant part of the copper losses and wload is the load dependent part of the copper losses. Since iron losses and windage and friction losses are almost constant at nominal voltage, they can be assumed as part of Wconst Therefore, total machine losses, Wtotal, can be approximated as:

Kotal = Komt + 4 o a d (A.14)

This Equation is used to derive a derating factor for induction motors as described in Section I11 B.

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