Question

Stator winding stator axis rotor axis ܕ݁ܐܶ RU in L rotor V.RO 0 0.= initial position of the rotor at standstill (rest position) a) Schematic view of SPPMSM b) Electrical equivalent circuit of SPPMSM Description of the motor: In Fig. a, cross-section of a Single Phase Permanent Magnet Synchronous Motor (SPPMSM) is seen. A U shaped stator is wound with a stator winding consisting of two coils connected in series (you can consider a single coil with N turns). A cylindrical two pole permanent magnet rotor is used to drive the external loads. Fig. b is the electrical equivalent circuit of this motor. V, is stator winding terminal voltage and Rcu is internal resistance of the stator winding. Rfe is the resistance corresponding to core losses. L is inductance of the stator coil and 'e' is the voltage induced on the stator coil due to rotor flux. Assume that the rotor flux passing through the stator coil (sr) in terms of rotor position © (O is the angle between stator axis and rotor axis as shown in Fig. a, where O, is the initial position of the rotor) is expressed by, 0g = 0.np Coso, where Orp is peak rotor flux passing through stator coil. b) Find the expression of total flux linked by stator coil that includes both the flux due to stator current itself and rotor flux (the equation should be in terms of stator coil inductance L, peak rotor flux Ørp, and stator current (iL)). Then, find expression of magnetic stored energy. Using magnetic stored energy expression, find the equation of induced electromechanical torque (Te) on the rotor (neglect saturation, hint: note dependency of stator coil inductance on rotor position).

Answer 1

so ) Motor. Given, SpPM Sm> Single phause permanent magnet synchronous Por = Ørp Cos o where Ørppeak rotor fleur passing through stator coil. → Total flux linked by stator coil that includes both the fux due to stator current itself & rotor current is: know flux is produced by stator current ; L'inductance, N Number of turns. As we LEN iL 0= Lin stutor flux part N • Total flux is given as ise on the windings of stator is : I total Ø +øsr Ø total LiL + top caso N as : → The w 2 Magnetic stored is given energy I Li,² I Norin w - Mier le terapenst) (** ho N 2

The expression of induced electro mechanical Torque (te) isa Work done = To TO Nin (LiL +dop coso coso) 2 N T= NiLLi + 20 N Lil +øopco i's .