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HW6Sol

HW6Sol - EEL 3216 Introduction to Power Systems Homework 6...

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EEL 3216 Introduction to Power Systems Homework # 6 SOLUTIONS 4-6. The flux density distribution over the surface of a two-pole stator of radius r and length l is given by cos( ) Mm BB t Z D ± Prove that the flux density under each pole face is 2 M rlB I Solve first specifically for a 2-pole and then for a 4-pole machine and generally for a P- pole machine SOLUTION (a) P = 2: Seen from the rotor the flux density becomes time independent cos( ) M , since the rotor spins with the mechanical angular velocity Z m . The flux penetrating an infinitesimal small area dd Al r ²² is d cos( )d M lrB DD and the total flux under each pole face is the aerial integral of this d . In a 2-pole machine one pole face (e.g. one north pole) reaches over 180 q from D = -90 q to D = 90 q (assuming the peak flux density B M at D = 0). Therefore, the total flux becomes 2 2 2 2 cos( )d sin( ) sin( ) sin( ) 2 22 MM M M rlB rlB rlB rlB S SS ID ± ± ªº
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