Electromechanical Dynamics (Part 1).0042

# Electromechanical Dynamics (Part 1).0042 - The preceding...

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Because this is a quasi-static magnetic field system, there is a perfectly conducting path between the two terminals of each terminal pair, as illus- trated in Fig. 2.1.1. Thus the voltage for any terminal pair is determined by using the contour for that terminal pair with (2.1.6). Then the flux linkage for any terminal pair (say the kth) is given by (2.1.8): k = B - n da, (2.1.15) where S, is the surface enclosed by the contour used with (2.1.6) to evaluate voltage v, at the kth terminal pair. The voltage vk is then given by (2.1.7) as d4 vk - -d (2.1.16) dt The fields in this more general situation are again described by (1.1.20) to (1.1.22) and (1.1.4). Consequently, the generalization of (2.1.10) is Lk = A 1 k(il 1, . .. iN; x 1 , 2 . .. XM), (2.1.17) k= 1,2,. .., N. We can now write the generalization of (2.1.11) by using (2.1.17) in (2.1.16) to obtain N a8 di. + a8, dxj v, =1 1- -, (2.1.18) J=1 aij dt i=l ax, dt k=1,2,. ..,N. Once again the terms in the first summation are referred to as transformer voltages and the terms in the second summation are referred to as speed voltages.
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Unformatted text preview: The preceding development has indicated the formalism by which we obtain lumped-parameter descriptions of quasi-static magnetic field systems. We have treated ideal lossless systems. In real systems losses are primarily resistive losses in wires and losses in magnetic materials.* Even though they may be quite important in system design and operation (efficiency, thermal limitations, etc.), they usually have little effect on the electromechanical interactions. Consequently, the effects of losses are accounted for by electrical resistances external to the lossless electromechanical coupling system. * Losses in magnetic materials result from hysteresis and eddy currents. For a discussion of these effects and their mathematical models see Electrical Engineering Staff, M.I.T., Magnetic Circuits and Transformers, Technology Press and Wiley, New York, 1943, Chapters 5, 6, and 13. Eddy currents are discussed in Chapter 7 of this book. 2.1.1 Circuit Theory A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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## This note was uploaded on 02/10/2012 for the course MECE 4371 taught by Professor Liu during the Fall '11 term at University of Houston.

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