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# hw5 - reference frame Given a balanced 3-phase current with...

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ECE 610 HW#5, Due October 13, 2011 1)Using Excel, Matlab, or a programmable calculator, etc, prove to yourself the effect of apply- ing a reference frame transformation. Specifically, assume Vas = 10*cos(100*t), Vbs = 10*cos(100*t -120), Vcs = 10*cos(100*t +120) Transform these voltages to 1) the synchronous reference frame, 2) the stationary reference frame, and 3) to a reference frame that has a velocity of 20 rad/sec. Verify the amplitude and frequency of the transformed variables, i.e., plot vqs, vds, v0s versus time. 2) Using your code from 1) show that if the voltages are unbalanced then v0s is not zero. 3) Starting with 6.2-1 and 6.2-4 derive 6.3-1 and 6.5-3 (i.e. go through the matrix manipulations of the transformation so you are confident in the approach). 4) Assume you have a capacitive system Using the transformation defined in class, transform this capacitive system to the synchronous
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Unformatted text preview: reference frame. Given a balanced 3-phase current with , C = 1 F, use reference frame theory to determine . Specifically, do not solve differential equations - solve algebraic equations. 5) Work through the matrix multiplications to verify the result of 6.3-14 when saliency is neglected. 6) Problems Chapter 3 -3.4, 3.14, 3.16, 3.18 7) A 3-phase system with , , , has the following dynamic model relating voltage to current in the stationary reference frame: . a) Express the steady-state form of the model and use it to determine , . b) Transform the dynamic model into the physical-variable model ( variables). Cpv abcs i abcs = i as 377 t ( 29 cos = V as ϖ e 1 = V qs e 2 = V ds e 2 – = v s = pi qs s i qs s + v qs s = pi ds s i ds s + v ds s = p 0.1 i s ( 29 i s + v s = I as V ds s abc...
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