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THREE-PHASE INDUCTION MOTOR
March 2007

A
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2
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Rotor Currents

4
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Torque and Power Characteristics

6
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Determination of Motor Constants

8
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Introduction

Bibliography

EXPERIMENT
1
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Speed and Direction of Rotation

3
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No Load Test

5
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Equipment List

Locked Rotor Test

REPORT

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Rather than the equivalent circuit of Fig
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9
to yield the result shown in Fig
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Based on past experience, the following
simplifying assumptions can be made for this model:

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X0 >> X1 , │R0 + jX0│ >> │R2 + jX2│, and X1 ≈ X2
...

For the rotor locked, s = 1 so that the following equations can be written from the equivalent circuit of
Figure 13 assuming │R0 + jX0│ >> │R2 + jX2│:
Z11 = (R1 + R2) + j(X1 + X2),
│Z11│ = V1/I1 , and
PPH = (R1 + R2)I12
These equations can be solved for R2, X1 , and X2 as follows:
R2 = (PPH/I12) − R1
and (by assumption)
X1 = X2 = ½ │Z11│2 − (R1 + R2)2
...

From the data obtained from the no-load test, we can determine the values for the series circuit
elements R0 and X0
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First the measured I1 and the measured phase power PPH are used to calculate
PC + PFW = PPH − I12R1 ,
2
where I1 R1 is the copper loss in this no-load case, PC [W] is the per-phase core loss and PFW [W] is
the per-phase friction-and-windage
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This will be explored further on the next page
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Figure 14

For no load, s = 0 so that the following equations can be written from the equivalent circuit of Figure
13:
ZIN = (R1 + R0) + j(X1 + X0)
│ZIN│ = V1/I1
...

Thus:

R0 = [PPH − PFW]/I12 - R1
X0 = │ZIN│2 − (R1 + R0)2 − X1
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8
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S
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ed
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(2) T
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Reynolds and T
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1339-1343, Sept
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(3) P
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Alger and R
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Arnold, "The History of Induction Motors in America", Proceedings of
IEEE, (64), pgs
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1976
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EXPERIMENT
1
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75 HP, 3-phase induction motor
One dynamometer with torque controller
One Phase Sequence Indicator
One single-phase wattmeter plus miscellaneous apparatus as needed
2
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You should also
make a DC measurement of stator winding line-to-line resistance using a DMM
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Speed and Direction of Rotation
The motor is mounted in a test rig that allows one to control the torque
applied to the motor shaft and to measure both rpm and torque
...
Observe that, by counting the output of the detector, you will get
a frequency, φ [Hz] , that is twice the actual rotational frequency of the motor
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To observe the rpm sensor in operation, proceed as follows
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Power up the motor normally and determine
the no-load * rpm when the motor, as viewed from the front, is rotating clockwise
(CW); repeat with the motor spinning counter clockwise (CCW)
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A successful salesman for General Electric's motor division once
remarked to one of your instructors that, when asked by a customer how a motor

*

The “no-load” condition is that which obtains when the controller knob is fully counter-clockwise
...
This attitude is typical
of a technologically mature discipline: one really can afford to treat the device as
if it were a black box
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To this end, it will be assumed that the motor is a balanced
three phase wye connected load and that you will therefore need to measure
only one line-neutral voltage, only one line current, and only one phase power to
characterize Pin completely
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Take note that Vrms is the phase voltage Vline-neutral = Vline-line/

3
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m in order to obtain power in watts
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Starting Current
Wire up the motor for CW motion so that starting current can be measured
accurately using the oscilloscope #
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5
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Precisely 1 h after the scheduled start of the lab, you must be prepared to
measure Vrms and φ(Vrms), Irms(Vrms), Pphase(Vrms)
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Line-to-line voltage will be varied from 30 to 210 V in steps of 30 V
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Locked Rotor Test
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With the motor de-energized, lock the rotor with the wooden
clamp-on fixture provided
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Note that Vrms will initially be low,
#

Remember that you are working with polyphase power
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&
Just how this is done is up to you
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It just can’t be done swiftly unless you design your
measurement in advance
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Measure Vrms
and φ(Vrms), Irms(Vrms), Pphase(Vrms)
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7
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Speed Curves
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The dynamometer is a
device that allows placing a variable load on the motor
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This control
current is feedback regulated by the output from the rpm sensor, but only if you
run the necessary coax: should you omit this coax, your data will be subtly
degraded
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This energy is dissipated
primarily as heat, and the dynamometer temperature will therefore rise
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Note that the torque exerted upon the motor by the dynamometer is
indicated by the appropriate scale on the dynamometer circumference
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These can slam the dynamometer against its limit stops
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Complete the experiment as follows
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Continue this until you reach rated current
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However, if it does stall, quickly reduce the
dynamometer current to restart the motor
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But, in the entire history of the course, no one has ever been able to detect one
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C
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Plot graphs similar to those described in Figure 14 and find the power
lost due to friction and windage
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Assume that X1 is equal to X2
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Is your calculated
value close to the observed value? Comment
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13 and Section 7 with care to answer this question successfully
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All of these
parameters are to be computed at 120 Vrms, line-line and six separate graphs are to
be made using the same motor speed scale
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(d)

Using your equivalent circuit, compute the motor horsepower at

rated line-to-line voltage of 208V and rated speed
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75 Hp given as the rated output on the motor nameplate
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75 Hp a
conservative value for this motor?

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