No-load & blocked rotor test, Equivalent circuit, Phasor diagram
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The document discusses the equivalent circuit and testing methods for induction motors, specifically focusing on the no-load and blocked rotor tests. It explains the relationship between rotor speed, induced voltage, and reactance, offering formulas to calculate key parameters. The document also includes the combination of stator and rotor circuits in an equivalent circuit, with phasor diagrams and references for further reading.
No-load & blocked rotor test, 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