0. Polyphase Induction Machines
PowerPoint Slides
to accompany
Electric Machinery
Sixth Edition
A.E. Fitzgerald
Charles Kingsley, Jr.
Stephen D. Umans
Chapter 6
Polyphase Induction Machines

1. 6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
Two types of motor:
Squirrel-Cage
Wound Rotor

2. 6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
How does an induction motor work?
Apply AC three-phase current to stator winding to produce rotating magnetic field.
Rotating magnetic field induces voltages in rotor windings resulting with rotor currents.
Then, rotor currents will create rotor magnetic field.
Constant speed stator magnetic field will drag rotor magnetic field.
ns: Synchronous speed (the speed of stator rotating field in rpm).
n : Rotor speed (rpm). ns n
SLIP: It is defined as the difference between synchronous speed and the rotor speed divided by synchronous speed.

3. 6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
The speed of rotor magnetic field with respect to rotor is
The relative motion of stator flux and the rotor conductors induces voltages of frequency (fr is called slip frequency)
The rotor speed
Mechanical angular velocity

4. 6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
Breakdown torque
Typical induction-motor torque-speed curve for constant-voltage, constant-frequency operation.
6-4

5. 6.2 CURRENTS AND FLUXES IN POLYPHASE INDUCTION MACHINE
Developed rotor winding of an induction motor with its flux-density and mmf waves in their relative positions for (a) zero and (b) nonzero rotor leakage reactance.

6. 6.2 CURRENTS AND FLUXES IN POLYPHASE INDUCTION MACHINE
Reactions of a squirrel-cage rotor in a two-pole field.
Figure 6.6

7. 6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Stator equivalent circuit for a polyphase induction motor.
Counter emf generated by the resultant air-gap flux

8. 6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Rotor equivalent circuit for a polyphase induction motor at slip frequency.

9. 6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Single-phase equivalent circuit for a polyphase induction motor.
Models the combined effect of rotor resistance and shaft load

10. 6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Alternative form of equivalent circuit.
Electromechanical power is equal to the power delivered to this resistance

11. 6.4 ANALYSIS OF THE EQUIVALENT CIRCUIT
Pmech is not the net power but it includes the losses such as friction, windage.
Output power and torque from the shaft is

12. 6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
(a) General linear network and (b) its equivalent at terminals ab by Thevenin’s theorem.

13. 6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
Equivalent circuits with the core-loss resistance Rc neglected.

14. 6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
Induction-motor equivalent circuits simplified by Thevenin’s theorem.

15. Induction-machine torque-slip curve showing braking, motor, and generator regions.
Figure 6.14

16. The End of This Chapter

17. Computed torque, power, and current curves for the 7
Computed torque, power, and current curves for the 7.5-kW motor in Examples 6.2 and 6.3.
Figure 6.15

18. Induction-motor torque-slip curves showing effect of changing rotor-circuit resistance.
Figure 6.16

19. Electromechanical torque vs
Electromechanical torque vs. speed for the wound-rotor induction motor of Example 6.4 for various values of the rotor resistance R2.
Figure 6.17

20. Deep rotor bar and slot-leakage flux.
Figure 6.18

21. Skin effect in a copper rotor bar 2.5 cm deep.
Figure 6.19

22. Double-squirrel-cage rotor bars and slot-leakage flux.
Figure 6.20

23. Typical torque-speed curves for 1800-r/min general-purpose induction motors.
Figure 6.21

24. Connections of a one-step starting autotransformer.
Figure 6.22

25. Interconnected induction and synchronous machines (Problems 6. 7 and 6
Figure 6.23

26. Induction-motor equivalent circuits simplified by Thevenin’s theorem.
Figure 6.13