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

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

2. Name Enrollment No.
Abhishek Chokshi 140120109005
Himal Desai 140120109008
Harsh Dedakia 140120109012
Guided By – Prof. Yogesh Sir

3. 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.

4. • 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
𝐸 𝑅𝑂 = 𝑠𝐸 𝑅𝑂
Where,
ER0 = largest value of the rotor’s induced voltage
obtained at s = 1(blocked rotor)

5. • This is same for the frequency i.e,
𝑓𝑟 = 𝑠𝑓𝑒
• So, as the frequency of the induced voltage in the rotor
changes, the reactance of the rotor circuit also changes,
𝑋𝑟 = 𝜔 𝑟 𝐿 𝑟 = 2𝜋𝑓𝑟 𝐿 𝑟
= 2𝜋𝑠𝑓𝑒 𝐿 𝑟
= 𝑠𝑋𝑟𝑜
 Where,
Xr0 = rotor reactance at the supply frequency
(at blocked rotor)

6. • Then, we can draw the rotor equivalent circuit as follows
Where
ER = induced voltage in the rotor
RR = rotor resistance

7. • Now we can calculate the rotor current as
𝐼 𝑅 =
𝐸 𝑅
𝑅 𝑅+𝑗𝑋 𝑅
=
𝑠𝐸 𝑅𝑂
𝑅 𝑅+𝑗𝑠𝑋 𝑅𝑂
• Dividing both the numerator and denominator by s so
nothing changes we get
𝐼 𝑅 =
𝐸 𝑅𝑂
𝑅 𝑅
𝑆
+𝑗𝑋 𝑅𝑂
Where
ER0 = induced voltage at blocked rotor condition (s = 1)
XR0 = rotor reactance at blocked rotor condition (s = 1)

8. • 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

9. Where,
𝑋′
2 =
𝑋 𝑅𝑂
𝐾2 , Reflected rotor reactance
𝑅′
2 =
𝑅 𝑅
𝐾2 , reflected rotor resistance
𝐼′
2 = 𝐾𝐼 𝑅 , reflected rotor current
𝐸1 =
𝐸 𝑅𝑂
𝐾
𝐾 =
𝐸2
𝐸1

10. Approximate Equivalent Circuit
• Similar to the transformer equivalent circuit can be
modified by shifting the exciting circuit (𝑅0 𝑎𝑛𝑑 𝑋0)
purely across the supply, to the left of 𝑅1 𝑎𝑛𝑑 𝑋1.
• Due to this we are neglecting the drop across
𝑅1 𝑎𝑛𝑑 𝑋1due to 𝐼0, which is very small.
• Hence the circuit is called approximation equivalent
circuit.

11. • Now the resistance 𝑅1 𝑎𝑛𝑑 𝑅′
2while the reactance
𝑋1 𝑎𝑛𝑑 𝑋′
2 can be combined. So we get,
𝑅1𝑒 = 𝑅1 + 𝑅′
2 = 𝑅1 +
𝑅2
𝐾2
and
𝑋1𝑒 = 𝑋1 + 𝑋′
2 = 𝑋1 +
𝑋2
𝐾2
while
𝐼1 = 𝐼0 + 𝐼′
2
and
𝐼0 = 𝐼𝑐 + 𝐼 𝑚

12. On Load Phasor Diagram of Induction Motor

13. 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.

14. • 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……..

15. • 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 equals
Pin = Pstator+Pcore+PF+W
= 3I1
2R1+Protor
Where,
Protor = Pcore+PF+W

16. • The 𝐼0 𝑎𝑛𝑑 cos ∅0 parameters of equivalent circuit can
be obtained as,
𝐼 𝐶 = 𝐼0 cos ∅0
𝐼 𝑚 = 𝐼0 sin ∅0
𝑅0 =
𝑉∅
𝐼 𝐶
𝑋0 =
𝑉∅
𝐼 𝑚
And
𝑊0 = 3𝑉∅ 𝐼0 cos ∅0
cos ∅0 =
𝑊0
3𝑉∅ 𝐼0

17. Equivalent circuit with phasor diagram

18. 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.

19. • 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,

20. • The blocked rotor power factor can be found as,
𝑃𝐹 = cos ∅ =
𝑃𝑖𝑛
3𝑉1 𝐼1
• The magnitude of total impedance is,
𝑍𝑖𝑛 =
𝑉∅
𝐼
Now,
𝑅 𝑒𝑞 =
𝑃𝑖𝑛
3𝐼2
𝑅 𝑒𝑞 = 𝑅1 + 𝑅2
𝑅2 = 𝑅 𝑒𝑞 − 𝑅1
And,
𝑋 𝑒𝑞 = 𝑍2
𝑒𝑞 − 𝑅2
𝑒𝑞

21. Equivalent circuit with phasor diagram

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