Gandhinagar Institute Of Technology

Subject – AC Machines (2140906)Branch – Electrical Topic – (1) No-load & blocked rotor test (2) Equivalent circuit, Phasor diagram

Name Enrollment No. Abhishek Chokshi 140120109005 Himal Desai 140120109008Harsh Dedakia 140120109012

Guided By – Prof. Yogesh Sir

Equivalent Circuit of Induction Motor• The induction motor is similar to the transformer with the

exception that its secondary windings are free to rotate

• As we noticed in the transformer, it is easier if we can combine these two circuits in one circuit but there are some difficulties in induction motor due to slip.

• When the rotor is blocked (or locked), i.e. s =1, the largest voltage and rotor frequency are induced in the rotor,

• On the other side, if the rotor rotates at synchronous speed, i.e. s = 0, the induced voltage and frequency in the rotor will be equal to zero,

• Now, if in the running condition

Where, ER0 = largest value of the rotor’s induced voltage obtained at s = 1(blocked rotor)

• This is same for the frequency i.e,

• So, as the frequency of the induced voltage in the rotor changes, the reactance of the rotor circuit also changes,

Where, Xr0 = rotor reactance at the supply frequency

(at blocked rotor)

• Then, we can draw the rotor equivalent circuit as follows

Where ER = induced voltage in the rotor RR = rotor resistance

• Now we can calculate the rotor current as • Dividing both the numerator and denominator by s so

nothing changes we get Where ER0 = induced voltage at blocked rotor condition (s = 1) XR0 = rotor reactance at blocked rotor condition (s = 1)

• Now we can have the rotor equivalent circuit

• Now as we managed to solve the induced voltage and different frequency problems, we can combine the stator and rotor circuits in one equivalent circuit

Where, , Reflected rotor reactance , reflected rotor resistance , reflected rotor current

Approximate Equivalent Circuit

• Similar to the transformer equivalent circuit can be modified by shifting the exciting circuit () purely across the supply, to the left of

• Due to this we are neglecting the drop across due to , which is very small.

• Hence the circuit is called approximation equivalent circuit.

• Now the resistance while the reactance can be combined. So we get,

and

while

and

On Load Phasor Diagram of Induction Motor

No Load Test

• The test is conducted by rotating the motor without load.• The test is performed at rated frequency and with

balanced poly-phase voltages applied to the stator terminals

• The only load on the motor is the friction and windage losses, so all Pconv is consumed by mechanical losses

• As the motor is on no load, the power factor is very low which is less than 0.5.

• The motor speed on no load is almost equal to its synchronous speed hence for practical purpose, the slip can be assumed to be zero.

• The equivalent circuit reduce to……..

• Combining Rc and RF+W we get,

• At the no-load conditions, the input power measured by meters must equal the losses in the motor.

• The input power equalsPin = Pstator+Pcore+PF+W = 3I1

2R1+Protor Where,

Protor = Pcore+PF+W

• The parameters of equivalent circuit can be obtained as,

And

Equivalent circuit with phasor diagram

Blocked Rotor Test

• In this test, the rotor is locked or blocked so that it cannot move, a voltage is applied to the motor, and the resulting voltage, current and power are measured.

• Now, as the rotor is blocked, the slip s = 1 hence the magnetizing reactance is much higher than the rotor impedance and hence it can be neglected.

• Hence the equivalent circuit reduce to,

• The blocked rotor power factor can be found as,

• The magnitude of total impedance is,

Now,

And,

Equivalent circuit with phasor diagram

References• www.wikipedia.org• https://iitg.vlab.co.in/• https://coep.vlab.co.in/• https://www.youtube.com/watch?v=dtzn63hlBrU• Technical Publication

THANK-YOU