EEL 3216 Introduction to Power Systems Homework # 6 SOLUTIONS4-6. The flux density distribution over the surface of a two-pole stator of radius r and length l is given by cos()MmBBtZD±Prove that the flux density under each pole face is 2MrlBISolve 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 Zm. The flux penetrating an infinitesimal small areaddAlr²²is dcos( )dMlrBDDand 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 180qfrom D= -90qto D= 90q(assuming the peak flux density BMat D= 0). Therefore, the total flux becomes 2222cos( )dsin( )sin() sin()222MMMMrlBrlBrlBrlBSSSID±±ªº
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