Determination Of Equivalent Circuit Parameters Of Three Phase Induction
Motor
It is possible to find the parameters of the equivalent circuit of the three phase induction motor
experimentally as shown in Fig.1.
I1
R1
jX1
I2
Iw
Rw
V1
jX 2′
Im
jXm
R2′
s
Fig.1: Equivalent circuit of three phase induction motor.
For this purpose, three tests should be conducted:
1- The DC Test:
The DC resistance of the stator can be measured by applying DC current to the terminals of the
winding of each phase and taking the reading of the voltage and the current (or using ohmmeter)
and determine the DC resistance as fallows:
ViDC
, where i represents the number of the winding i (i = 1, 2, 3).
I iDC
After that, the average of the readings can be calculated as:
RiDC =
R1DC + R2 DC + R3 DC
3
Then, the AC resistance is given by:
(1)
R DC =
(2)
R1 = 1.15 R DC
(3)
2- The Locked Rotor Test
When the rotor is locked (i.e. prevented from running), s is equal to 1. The secondary
impedance becomes much less than the magnetizing branch and the corresponding equivalent
circuit becomes that of Fig.2. The readings to be obtained from this test are:
a) Three phase power P3φ _ BL
b) Line voltage V L _ BL
c) Line current I BL
From these readings, the per phase values of the power PBL and phase voltage VBL can be
obtained as follows:
PBL =
V BL =
I BL
P3φ _ BL
(4)
3
V L _ BL
(5)
3
R1
jX 1
jX 2′
R2′
VBL
Fig.2: Approximate equivalent circuit for the locked rotor conditions
Then, Req , Z eq , and X eq can be obtained using the following equations:
Req =
PBL
2
I BL
(6)
Z eq =
V BL
I BL
(7)
X eq = Z eq2 − Req2
(8)
Separation of X 1 , X 2′ , R1 , and R2′ can be done as follows:
X 1 = X 2′ =
1
X eq
2
R2′ = Req − R1
(9)
(10)
3- The No Load Test
When the induction motor runs at no load, the rotor speed approaches the synchronous speed.
The slip becomes very small in this case. Accordingly, the secondary impedance becomes high
compared with the magnetizing branch. the equivalent circuit can be approximated by that of Fig.3.
The readings to be obtained from this test are:
d) Three phase power P3φ _ NL
e) Line voltage V L _ NL
f) Line current I NL
From these readings, the per phase values of the power PNL and phase voltage V NL can be
obtained as follows:
PNL =
V NL =
P3φ _ NL
(11)
3
V L _ NL
(12)
3
I NL
jX1
R1
Iw
VNL
Rw
Im
jXm
E1
Fig.3: Approximate equivalent circuit for the no load conditions
Then, Rw , and X m , can be obtained as fallows:
2
Pcore+ mechanical = PNL − I NL
R1
(13)
E1 = V NL − I NL ( R1 + jX 1 )
(14)
Note: ( I NL = I NL ∠ − θ , θ = cos −1
Rw =
Iw =
E1
2
Pcore+ mechanical
E1
Rw
2
I m = I NL
− I w2
Xm =
E1
Im
PNL
)
V NL I NL
(15)
(16)
(17)
(18)