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Unformatted text preview: ted by a very high resistive
branch representing the rotor circuit. The reactance of this parallel
combination is almost the same as X m . Therefore the total
reactance X NL , measured at no load at the stator terminals, is
essentially X 1 + X m . The equivalent circuit at no load is shown in
Fig.4.11a. (a) Noload equivalent circuit (b) Blockedrotor equivalent circuit. (c) Blockedrotor equivalent circuit for improved value for R2 .
Fig.4.11
The primary phase voltage can be obtained from the following
equation: 240 Chapter Four V1 = VLL
V / Phase
3 (4.30) Then the noload impedance can be obtained as following: Z NL = V1
I1 (4.31) The noload resistance is: RNL = PNL
3I12 (4.32) The noload reactance is:
2
2
X NL = Z NL − RNL (4.33) In the IEEE recommended equivalent circuit we assume that X 1 + X m = X NL (4.35) Then from no load test we only get the value of X 1 + X m
Lockedrotor test Under rated line voltage, when the rotor of an
induction motor is locked, the stator current I P is almost six times
its rated value. Furthermore, the slip s is equal to one. This means
that R2 / s is equal to R2 , where R2 is the resistance of the rotor
reflected into the stator. Because I p is much greater than the
exciting current I o , we can neglect the magnetizing branch. This
leaves us with the circuit of Fig.4.8 (without magnetizing branch), 241 ThreePhase Induction Machine composed of the leakage reactance X, the stator resistance R1 , and
the reflected rotor resistance R2 / s . Their values can be
determined by measuring the voltage, current, and power under
lockedrotor conditions, as follows:
a. Apply reduced 3phase voltage to the stator and gradually
increase it from zero until the stator current is about equal to its
rated value. Sometimes it is recommended to use lower
frequency than the rated to avoid the errors due to skin effect in
the rotor circuit.
b. Take readings of VLL BL (linetoline), I1 BL , and the total 3phase power PBL (Fig.4.12).
So, for the blockedrotor test the slip is 1. In the equivalent
circuit of Fig.4.9, the magnetizing reactance X m is shunted by the ′
′
′
′
lowimpedance branch R2 + jX 2 . Because X m >> R2 + jX 2 ,
the impedance X m can be neglected and the equivalent circuit for
the blockedrotor test reduces to the form shown in Fig.4.11b.
From the blockedrotor test, the blockedrotor resistance is: RBL = PBL
3I12 (4.36) BL The blockedrotor impedance at frequency of blocked rotor test
is: 242 Chapter Four Z BL fBL = V1 BL (4.37) I1 BL The blockedrotor reactance at frequency of blocked rotor test is: X BL fBL = (Z 2
BL fBL 2
− RBL ) (4.38) Its value at rated frequency is: X BL = X BL *
fBL Rated Frequency
(4.39)
Frequency at blocked rotor test ′
X BL ≅ X 1 + X 2 (4.40) ′
assume, X 1 = X 2 (at rated frequency)
′
then X 1 and X 2 can be obtained.
From no load test we know that X 1 + X m = X NL and X 1 are
known then the magnetizing reactance is : X m = X NL − X 1 (4.41) ′
Comments: The rotor equivalent resistance R2 plays an
important role in the performance of the induction machine. So, an ′
accurate determination of R2 is recommended by the IEEE as
follows:
The blocked resistance RBL is the sum of R1 and an equivalent ′
′
resistance, say R, which is the resistance of R2 + jX 2 in parallel
with X m as shown in Fig.4.11c; therefore, ThreePhase Induction Machine
2
Xm
R= 2
R′
22
′
′
R2 + ( X 2 + X m ) 243
(4.42) ′
′
If X 2 + X m >> R2 , as is usually the case,
2 X′ + Xm ′
R
R2 = 2
Xm (4.43) 2 Xm or R ≅ X ′ + X R2
′
2
m (4.44) Now R = RBL − R1 . So, we can use this value of R to determine ′
R2 from equation (4.43)
More elaborate tests are conducted on large machines, but the
abovementioned procedure gives results that are adequate in most
cases. Fig.4.12 A lockedrotor test permits the calculation of the total
leakage reactance x and the total resistance (R1 + R2 ). From these
results we can determine the equivalent circuit of the induction
motor. 244 Chapter Four
Example 4.2 A noload test conducted on a 30 hp, 835 r/min,
440 V, 3phase, 60 Hz squirrelcage induction motor yielded the
following results:
Noload voltage (linetoline): 440 V
Noload current: 14 A
Noload power: 1470 W
Resistance measured between two terminals: 0.5 Ω
The lockedrotor test, conducted at reduced voltage, gave the
following results:
Lockedrotor voltage (linetoline): 163 V
Lockedrotor power: 7200 W
Lockedrotor current: 60 A
Determine the equivalent circuit of the motor.
Solution:
Assuming the stator windings are connected in wye, the
resistance per phase is: R1 = 0.5 / 2 = 0.25 Ω
From the noload test:
The primary phase voltage can be obtained from the following
equation: V1 = VLL 440
=
= 254V / Phase
3
3 ThreePhase Induction Machine 245 Then, the noload impedance can be obtained as following: Z NL = V1 254
=
= 18.143 Ω
I1 14 The noload resistance is: RNL = PNL 1470
=
= 2.5 Ω
3I12 3 *14 2 The noload reactance is:
2
2
X NL = Z NL − RNL = 1...
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This document was uploaded on 03/12/2014 for the course ENGINEERIN electrical at University of Manchester.
 Spring '14

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