# hw10 - = rm r br P N P w 2 sin 2 Express the mutual...

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EE321 Spring 2010 Homework 10 Problem 1 – Electrical and mechanical rotor speed The electrical frequency applied to an synchronous machine (an AC machine in which the rotor travels at the same speed of the MMF) is 60 Hz. The mechanical rotor speed is 900 RPM. How many poles does the machine have? What is the electrical rotor speed in rad/s? Problem 2 – Rotating MMF Using the configuration we studied in class (a two pole version of which is in 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 3 – 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

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Unformatted text preview: = 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 μ and electrical rotor position r θ . Problem 4 – Back EMF A PMSM has a radius of 0.1 m and a length of 0.05 m. The conductor density of the a-phase of a PMSM is given by ) 4 sin( 200 sm as n = With no stator current, the B-field due to the PM on this machine may be expressed ) 4 sin( rm B = The mechanical rotor position is given by t rm 100 = θ Compute the voltage across the a-phase at t=0.1 s. Problem 5 – QD Transformation Starting with abcs T abcs cs cs bs bs as as i v i v i v P i v = + + = Show that ( 29 s s r ds r ds r qs r qs i v i v i v P 2 2 3 + + =...
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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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hw10 - = rm r br P N P w 2 sin 2 Express the mutual...

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