No Load Test and Locked Rotor Test in an Induction Motor

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

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=R₂{(1/s)-1)} becomes the load resistance R_L=0. In this test the wattmeter reading, say

where,

V is the supply voltage.

Therefore, G_o = W/3V²

Also, No load current I₀ = V.Y_o

Therefore Y_o=I_o/V

B_o = √ (Y_o2 – G_o2)

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.

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 W₁ and W₂.

Let the total input power = W₀ watts

No load input current = I₀ 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_o²R₁

2. Core loss 3G_oV²

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 I₀ CosΦ₀

From this relation

CosΦ_o = W / √3V_LI₀

Where V_L = Line Voltage

           I₀ = Input current at no load

          W₀ = Input power at no load

From this test, _Io, W_o, CosΦ_o are observed and determined.

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:

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

It is determined as, W_s= √3V_sI_sCosΦ_s

Therefore CosΦ_s = W_s / √3V_sI_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

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= 3I²_sR₀₁

Thus, R₀₁ = W_s/ 3I²_s —-> 1

Knowing the values of V_s and I_s, Z_o1 is calculated as

Z_o1 = V_s/I_s —–> 2

Z₀₁ = √ (Z²₀₁ – R²₀₁₎

Using the equation 1 and 2

In order to find out X₁ and X₂, it is normally assumed X₁ = X₂’

Therefore, X₁ = X₂’ = X₀₁/2

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 R₁ from R₀₁ the value R₂’ is obtained.

In case of wound rotor, R₁ and R₂’ are determined by knowing the ratio of resistances of stator and rotor windings.

In the above stated expression,

R₀₁ = Motor winding of stator and rotor as per phase referred to stator

Z_o1 = motor impedance per phase referred to stator

X₀₁ = Motor leakage reactance per phase referred to stator

R₁ = Stator resistance per phase

R₂’ = Rotor resistance per phase referred to stator

X₁ = Stator reactance per phase

X₂’ = Rotor reactance per phase referred to stator

From 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.

Conclusion