Transients in Power Systems
Transients in Power Systems ECE 524
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This 8 page Class Notes was uploaded by Fredy Okuneva on Thursday October 22, 2015. The Class Notes belongs to ECE 524 at University of Idaho taught by Brian Johnson in Fall. Since its upload, it has received 23 views. For similar materials see /class/227723/ece-524-university-of-idaho in ELECTRICAL AND COMPUTER ENGINEERING at University of Idaho.
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Date Created: 10/22/15
OZ 39OU NOISSEIS SIAELLSAS HEMOd NI SiNElISNVEIJ 1729 333 m Univensityofldaho v I W m who rMsuwquot Lioquot Q 510quot 539 Zea 02333325 i m Universityofldaho 3 Session 39 Page 38 Q Spring 2008 eOdA a ECE524 Transients in Power Systems Which can be re arranged as quot835 Tel llZ llY HTeiEmAEm 11 83 l lquot1Y Hz39Tirmum 12 Notice that both Z Y and Y HZ have the same eigenvalues The theorem predicting this result is explained in many graduate level linear systems texts The matrix A is a diagonal matrix of eigenvalues resulting in m uncoupled equations where m is the number of modes Both voltage and current will have the same modes of propagation as is demonstrated by having the same eigenvalues The transformation matrix T6 is not unique Any matrix of the form DHTE is also a modal matrix Where D dill where l is the identity matrix In addition T6 and T are related as would be expected since they lead to the same eigenvalues We know that A Tel 1W 3 Tel 13 Then we can take the transpose A llTel1Z39llY llTellt 14 We know A At since A is diagonal We can simplify this expression to be recall that Y andZ l are symmetric A C L llY llz39llT l 1 15 So Tir1 is also a modal matrix for Y HZ which also has a modal matrix T de ned by A Til 1iYlizlii l 16 We can therefore conclude that Tellel D 17 where D elm and 1 could possibly equal one We can now diagonalize equations 3 and 4 as well ils m m Universityofldaho on 0m a 5 an an Q13 m ahm at qu d39lquot n 34 Gsmniobm mzc 2
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