Motor Parameters

INDUCTION MOTOR* PARAMETERS EXTRACTION Sinisa Jurkovic

INTRODUCTION The parameters of equivalent circuit of Induction Machines are crucial when considering advanced control techniques (i.e. Vector Control). Accidentally these are also uncertain parameters when the machine is released from production. The most common ways, to manually determine induction motor parameters, are to test motor under no-load and locked rotor conditions. FIRST NO-LOAD TEST The no-load test, like the open circuit test on a transformer, gives information about exciting current and rotational losses. The test is performed by applying balanced rated voltage on the stator windings at the rated frequency. The small power provided to the machine is due to core losses, friction and winding loses. Machine will rotate at almost a synchronous speed, which makes slip nearly zero. This test is represented with an equivalent circuit in Figure 1.

Figure 1. Equivalent Circuit for No-Load Test Values measured during this test are current and it’s angle with respect to know voltage. From this we can calculate total power supplied to the machine. Measured values are shown in Table 1. N o L o a d M o to r T e s t

LOCKED ROTOR TEST The locked rotor test, like short circuit test on a transformer, provides the information about leakage impedances and rotor resistance. Rotor is at the stand still, while low voltage is applied to stator windings to circulate rated current. Measure the voltage and power to the phase. Since there is no rotation slip, s=1 which gives us following equivalent circuit.

Figure 2. Equivalent Circuit for Locked Rotor Test Note that Rr is much less than Rc so that part of the circuit is ignored. Values measured during the locked rotor test are shown in Table 2.

L o c k e d R o to r T e s t

208 V

I0

1 .5 A

I0 m a x

1 .7 A

fs

60 Hz

P

49 W

Table 1. Values measured during no-load test. Assuming that Rc is much bigger than Rs and Xlr we can calculate Rc and Lm from the equivalent circuit. The formulas and complete calculations are shown below.

49 P ph 3 cos( φ 0) = = = 0.09 V ph I 0 121.4 • 1.5 φ 0 = 84.8 ° Im = I 0 sin( φ 0) = 1.5 sin(84.8 °) = 1.485 A Ic = I 0 cos( φ 0) = 1.5 cos(84.8 °) = 0.135 A V ph 121.4 = = 0.23 H 2 πf sIm 2 π • 60 • 1.485 V ph 121.4 Rc = = = 900 Ω Ic 0.135 Lm =

90 V

I r a te d

6 .1 A

Im e a su re d

6 .1 A

fs

60 Hz

P

724 W

Table 2. Values Measured during Locked Rotor Test Assuming known Rs and values in the Table 2, we can calculate Lls, Llr and Rr, ss shown below.

cos( φ sc ) = V ll

V

P ph 724 / 3 = = 0 . 44 V ph I sc 90 • 6 . 1

φ sc = 64 ° V ph 90 = = 14 . 8 Ω I sc 6 .1 R r = Z sc cos( φ sc ) − R s = 14 . 8 • 0 . 44 − 2 . 3 = 4 . 2 Ω X eq = Z sc sin( φ sc ) = 14 . 8 • sin( 64 ° ) = 13 . 3 Ω X eq = X ls + X lr

Z sc =

X ls = X lr = 6 . 7 Ω L ls = L lr = 17 . 5 mH EXPERIMENT REMARKS The parameters extracted from the Induction Machine are reasonable when compared with similar examples, however they do raise the question of how confident can one be in them? To answer this question another set of tests is performed on the same machine. NO-LOAD TEST Performing a no-load test under same conditions, but this time a rotor is rotated at the synchronous speed with DC machine and rated voltage and frequency is applied. This test should yield more accurate results, since the slip is now exactly zero (i.e. rotating at the synchronous speed).Following the exact same formulas to calculate the parameters we obtain results shown below.

First No-Load Test

Parameter

Second No-Load Test

Percent Error **

Im [A]

1.485

1.345

10.409

Ic [A]

0.135

0.113

19.469

Rc {Ohms]

900.000

2010.000

55.224

Lm [H]

0.230

0.323

28.793

pf

0.090

0.084

7.143

Table 3. No-Load Tests Comparisson RESULTS VALIDATION For the validation of the results we calculate the torque under rated conditions and compare it with torque specifications provided by the manufacturer of the machine. Rated torque is 11.2 Nm as provided by the machine manufacturer. Given the rated voltage of 208 V line-to-line and rated speed of 1725 RPM using the following formula we can calculate the torque under rated conditions. Note that this is 2 pole machine.

T =3

p Vs 1 ( )^ 2 ωr Rr 2 ωs

where ωr is the frequency of the currents induced in the rotor, and ωs is the frequency of stator voltage. This calculation yields a torque of 11.2 Nm. Alternatively torque can be calculated from the equivalent circuit in Figure 3. using the following formula.

T =3

p Pg ( ) 2 ωs

Pg is power in the air gap of the machine. As the circuit indicates part of this power is converted to mechanical energy, while the other part represents the losses in the rotor resistance.

Figure 3. Induction Machine Equivalent Circuit Solving the circuit at rated conditions we obtain the following: Pg = 678W which gives us the torque of T=10.6 Nm. This gives us a error 10% between the manufacturer’s specified rated torque and calculate torque based on the parameters extracted. This error is minimal and acceptable which validates the accuracy of test results. CONCLUSION We assume that the second test provided us with more accurate results; therefore the percent error is expressed with respect to those results. The percent error between the two tests is reasonable for each parameter with the exception of core equivalent resistance Rc. It is however still safe to say that we can be fairly confident in the results of either test (looking from the control point of view) since the Rc does not play a role in implementing a control for the machine. Rc is more important when it comes to estimating the efficiency of the machine, in which case results of the second case would be more credible.

In addition to this a second locked rotor test was performed, where we used lower frequency (15 Hz)*** to circulate the rated current. This test returned results that were almost identical to the results of the first test, so comparison of the two is omitted. NOTES * 2HP 4 Pole Induction Machine, 1725 RPM, 208/230V-460V, 6.2/5.8A-2.9A. ** The error is calculated with respect to second no-load test. *** Lower frequency is used to circulate the rated current. IEEE recommends a frequency of ¼ of the rated when performing the locked rotor test. [2]. This method will generally yield more accurate results in case of larger machines (20 HP and up), while for the smaller machines using the rated frequency is satisfactory. REFERENCES [1]. R. Krishnan, Electric Motor Drives Modeling, Analysis, and Control, Prentice Hall 2001 [2]. P. C. Sen, Principles of Electric Machines & Power Electronics, Wiley 1999 [3]. W. Leonhard, Control of Electrical Drives, Springer 2001 [4]. E.G. Strangas, Notes for an Introductory Course On Electrical Machines and Drive, MSU