1. Induction Motors Equations, Performance, Electrical Equivalent Circuits

2. Induction Motor by Bullet Points Stator generates rotating, sinusoidal B-Field: This field induces current in the rotor cage loops at The stator B-Field at each rotor wire is such that Torque pushes in direction of field rotation! (That’s it!!) Rotor currents generate triangular B-field rotating in the air gap at slip speed relative to rotor, so at line rate in reference frame! Rotor field reduces field in stator and line current increases to maintain the stator winding voltage and the gap magnetic field Increased line current supplies the mechanical energy and the joule heating of the rotor.

9. Formal Transformer Analogy Mutual inductance stator to rotor is time dependent The A, B, C voltages are the line voltages The rotor voltages are Given rotor frequency, calculate currents and power, subtract rotor and winding heat to get mechanical power. Ugh!

10. Simple Per-Phase Transformer Model Know that power flow is constant at constant speed (No torque variation!) Per-phase model with constant impedance that is a function of rotor speed Use basic single-phase transformer model with turns ratio and secondary impedance dependent on rotor speed Stator field is zero-slip model

11. Electrical Equivalent Circuit of Stator Alone Applies when rotor is turning at zero slip Derive from locked rotor and zero slip conditions Accounts for wire loss and stator core loss Leakage inductance usually larger than for a simple transformer because of air gap and slot shape

12. Electrical Equivalent Circuit with Ideal Transformer S is the “slip” or

13. Electrical Equivalent Circuit Referred to the Stator Basis for calculating efficiency, start inrush, etc. Mechanical energy is loss in ; all else is heat

14. Things Left Out! Inrush current No-load mechanical drag from cooling, bearing friction, etc. Design tradeoffs with cost Still to go: single phase operation Government efficiency regulation Recently – March 2015 – applies to motors to ¼ HP