T SREEJITH KAILAS Edited By Sarath S Nair MODELLING AND ANALYSIS OF A TWO PHASE INDUCTION MACHINE WITH NON-ORTHOGONAL STATOR WINDINGS

Introduction Starting torque is produced by designing the stator windings to be electrically different. Unsymmetrical 2-phase IM is designed to operate from a single- phase source Stationary reference frame is used in order to obtain voltage equations with constant coefficients. Rating of two phase induction machine is usually low.

2Pole,Unsymmetrical 2-phase induction machine θrθr

V QS,V DS =QS and DS-axis stator voltages Rm,Xm and Ra,Xsa-QS and DS-axis resistance and leakage inductance Rotor voltages are set to zero(because of squirrel-cage rotors) Voltage and flux equations 4 V DS =R a *i DS +(P/ ω b * ψ DS ) ……(2) V QS =R m *i QS + (P/ ω b * ψ QS ) ……(1) 0=(R r *i QR )-1/k* ( ω r / ω b )* ψ DR +(P/ ω b )* ψ QR …….(3) 0=(K ^2 *Rr*i DR )-k* ( ω r / ω b )* ψ QR +(P/ ω b )* ψ DR.....(4)

5

Te,Tl =electromagnetic instantaneous torque and load torque J= inertia constant of motor P= number of poles Torque Equation 7

8 Equivalent circuit 88

Advantages Robustness in its operation Low cost Highly reliable Disadvantage Inability to produce a smoothly rotating internal flux Needs two capacitors

Applications Mostly used in single phase applications such as Refrigerators Washing machines Furnace fans Air conditioners

References Krause, P.C., Wasynczuk, O., Sudhoff, S.D.,Analysis of Electric Machinery, IEEE Press, Walls, T.A., Sudhoff, S.D., Analysis of a single-phase induction machine with a shifted auxiliary winding, IEEE, Trans. on Energy Conversion, dec.1996, p phase induction motor.html

Conclusion The mathematical model for a two-phase unsymmetrical induction machine was developed and its equivalent circuit is drawn

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