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

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

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.

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

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

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.

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

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

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

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

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

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

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.

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

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

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

The End of This Chapter

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

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

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

Deep rotor bar and slot-leakage flux. Figure 6.18

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

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

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

Connections of a one-step starting autotransformer. Figure 6.22

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

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