# hw13 - Show in detail that ms s s T sr s r L K L K =-1 '...

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EE321 Spring 2010 Homework 13 Problem 1 – Rotating MMF Using the configuration we studied in class (Figure 5.2-1 in text), the stator currents of a 4 pole machine are given by ) 200 cos( 50 ) 200 sin( 50 t i t i bs as - = = The speed of the machine is 500 rpm in the CW direction. What is the physical speed and direction of the stator MMF as viewed from the rotor. Problem 2 – Phase Inductance Suppose the winding function of a-phase of the stator is given by = sm s as P N P w φ 2 cos 2 and the winding function of the b-phase of the rotor is given by = rm r br P N P w 2 sin 2 Express the mutual inductance between the a-phase stator and b-phase rotor windings in terms of s N , r N , P , the rotor radius r , the rotor length L , the airgap g , the permeability of free space 0 μ and electrical rotor position r θ . Problem 3 – QD Transformation
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Unformatted text preview: Show in detail that ms s s T sr s r L K L K =-1 ' where ' sr L is given by (5.3-48) and ms L is given by (5.5-23). Problem 4 – Steady-State Operation Consider a 2-phase machine with the following parameters: Ω = m r s 5 . 72 , 32 . 1 ' = = lr ls L L mH, 1 . 20 = m L mH, Ω = m r r 3 . 41 ' , and 4 = P . The load torque varies with the speed cubed, and is such that 50 Hp is required to spin the load at 1800 rpm. A balanced 2-phase voltage source with of 3 / 460 V rms amplitude and 60 Hz frequency is applied to the machine. Taking the a-phase voltage to be of zero reference, find the rotor speed, the phasor representation of the a-phase current, the input power, the output power, and the efficiency....
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## This note was uploaded on 04/08/2012 for the course ECE 321 taught by Professor Staff during the Spring '08 term at Purdue.

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