The various constant of the equivalent circuit of the induction motor can be determined as detailed below:

###
Determination of G_{o} and B_{o} and hence R_{o} and X_{o}:

To find out G

_{o}and B_{o}the induction motor is made to run at synchronous speed by using another machine. The additional machine helps to supply the friction and Windage losses, under this conditions, the slip s=0 and the current drawn by the induction motor is I_{o}only since s=0, the term R_{L}=R_{2}{(1/s)-1)} becomes the load resistance R_{L}=0. In this test the wattmeter reading, say
W=3G

_{o}V_{2},
where,

V is the supply voltage.

Therefore, G

_{o}= W/3V^{2}
Also, No load current I

_{0}= V.Y_{o}
Therefore Y

_{o}=I_{o}/V
B

_{o}= √ (Y_{o}2 – G_{o}2)Here, G

_{o}is the exciting conductor and B

_{o}is the exciting susceptance. Knowing these values R

_{o}and X

_{o}can be determined. These quantities are required for drawing the equivalent circuit.

Normally it is not possible to run the induction motor at synchronous speed. If it coupled with another motor and whose speed can be varied up to the synchronous speed of the induction motor to run without any mechanical load on it. The speed is assumed to be synchronous speed. With this assumption the G

_{o}and B_{o}can determined as detailed below.### No Load Test

The connection diagram for no load test on three phase induction motor is shown above. The wattmeter, ammeter and voltmeter, readings are taken. The total power input is given by the two wattmeters W

_{1}and W_{2}.
Let the total input power = W

_{0}watts
No load input current = I

_{0}amps
Voltage applied = V

_{o}volts
At no load, the input power is supplied to meet out the losses.

The various losses are,

1. Stator winding loss 3I

_{o}^{2}R_{1}
2. Core loss 3G

_{o}V^{2}
3. Friction and Windage losses.

The core loss, friction Windage losses totally are called fixed losses.

Since the total power input is known, and is equal to W

_{o}and
W

_{o}= √3V_{L}I_{0}CosΦ_{0}
From this relation

CosΦ

_{o}= W / √3V_{L}I_{0}
Where V

_{L}= Line Voltage
I

_{0}= Input current at no load
W

_{0}= Input power at no load
From this test,

_{Io}, W_{o}, CosΦ_{o}are observed and determined.### Locked Rotor Test

This test is also called as Locked Rotor test or short circuit test. Connection diagram of blocked rotor test on three phase induction motor is shown in the figure.

Under this test, the rotor is locked (not allowed to rotate or allowed to rotate at very slow speed). In case of slip ring induction motor, the rotor windings are short circuited at the slip rings. A reduced voltage, nearly 15% of normal voltage is applied to the stator winding. The voltage is so adjusted to allow full load current to the stator windings.

The power input, the current voltage applied is measured using the meters connected in the circuit. They are, V

_{s}the short circuit voltage, I

_{S}, short circuit current with the voltage V

_{s}, and W

_{s}total power taken by the motor on short circuit.

From the measured values the followings are calculated:

#### 1. Short circuit current with respect to the normal supply voltage of the stator.

That is I

_{SN}, = I_{s }x (V/V_{s})
Where

I

_{SN}= Short circuit current w.r.t normal voltage
V

_{s}= Reduced voltage applied during the short circuit
I

_{s}= Short circuit current with voltage applied during short circuit
V = Normal supply voltage to stator winding

#### 2. Power factor blocked rotor test

It is determined as, W

_{s}= √3V_{s}I_{s}CosΦ_{s}
Therefore CosΦ

_{s}= W_{s}/ √3V_{s}I_{s}_{}

Where W

_{s}= Total power drawn by the motor on short circuit
V = Voltage applied on short circuit

I

_{s}= Current on short circuit#### 3. Resistance and Leakage reactance values

On blocked rotor test, the motor input is supplied against the stator copper losses, rotor copper losses and core losses. Since, under this test the voltage is very low the core loss is very small and it may be neglected.

Therefore Total Copper loss = W

_{s}
W

_{s}= 3I^{2}_{s}R_{01}
Thus, R

_{01}= W_{s}/ 3I^{2}_{s }----> 1
Knowing the values of V

_{s}and I_{s}, Z_{o1}is calculated as
Z

_{o1}= V_{s}/I_{s }-----> 2
Z

_{01}=**√**(Z^{2}_{01}– R^{2}_{01)}_{}

Using the equation 1 and 2

In order to find out X

_{1}and X_{2}, it is normally assumed X_{1}= X_{2}’
Therefore, X

_{1}= X_{2}’ = X_{01}/2
To determine the value of R1 and R2’

In case of squirrel cage type rotor, R1 is found out by conducting suitable test on the stator windings. Then subtracting R

_{1}from R_{01}the value R_{2}’ is obtained.In case of wound rotor, R

_{1}and R

_{2}’ are determined by knowing the ratio of resistances of stator and rotor windings.

In the above stated expression,

R

_{01}= Motor winding of stator and rotor as per phase referred to stator
Z

_{o1}= motor impedance per phase referred to stator
X

_{01}= Motor leakage reactance per phase referred to stator
R

_{1}= Stator resistance per phase
R

_{2}’ = Rotor resistance per phase referred to stator
X

_{1}= Stator reactance per phase
X

_{2}’ = Rotor reactance per phase referred to statorFrom the test data’s obtained on no load test and blocked rotor test of the three phase induction motor are used to determine the above mentioned constants. These constants are used for developing the equivalent circuit of three phase induction motor and for construction of circle diagram.

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