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