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hw7 - Using reference frame transformation and Kirchoff’s...

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ECE 610 -HW#7, Due October 28, 2011 (11:59 pm Eastern time) 1) Given the machine that was used to generate Figure 6.4-3. The machine is operating at rad/sec. A, . Plot versus and versus time (show 1 cycle on each plot). What is the being used? Determine the efficiency. 2) If the machine in 1) is operating at the same torque and speed as in 1) with , determine and the efficiency. Why is the efficiency different than that obtained in 1) if the same output torque and speed are obtained? 3) Derive 6.4-29. 4) To determine the inductances of a PMSM, a so-called standstill frequency response test is often performed. In this test, . The windings are arranged as shown in Figure 1. A sinusoidal voltage is applied and the resulting sinusoidal current is measured. ϖ r 25 = I qs r 10 = I ds r 0 = V as θ r V as φ v φ v 0 = V as ϖ r 0 = v s i s + - v as v bs v cs + - + - ~ v s i s Figure 1

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a) For the q -axis inductance,
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Unformatted text preview: . Using reference frame transformation, and Kirchoff’s laws, show that . Then show that . The input impedance of the circuit , Explain how you would use the measured to find . 5) For the 4-pole synchronous machine shown in Figure 1.4-7, first express in terms of the mechanical rotor position, in a similar form as that presented in Lecture 17. Subsequently, express in terms of the electrical rotor position . Show that when expressed in terms of the rotor position, it is the same as for a 2-pole machine. Subsequently, for the flux linkage expression , derive expressions for all components in the induc-tance matrices. 6) Problem 5.6. θ r = v ds r 2 3--v s = i ds r i s = Z in V s ˜ I s ˜-----= Z in L d L asas θ rm · L asas θ r · λ abcs L s θ r ( 29 i abcs L sr θ r ( 29 i fd + =...
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