mws_ele_sle_txt_ludecomp_examples

mws_ele_sle_txt_ludecomp_examples - 04.07.1 Chapter 04.07...

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Unformatted text preview: 04.07.1 Chapter 04.07 LU Decomposition More Examples Electrical Engineering Example 1 Three-phase loads are common in AC systems. When the system is balanced the analysis can be simplified to a single equivalent circuit model. However, when it is unbalanced the only practical solution involves the solution of simultaneous linear equations. In one model the following equations need to be solved. = 9 . 103 00 . 60 9 . 103 00 . 60 000 . 120 8080 . 6040 . 0100 . 0080 . 0100 . 0080 . 6040 . 8080 . 0080 . 0100 . 0080 . 0100 . 0100 . 0080 . 7787 . 5205 . 0100 . 0080 . 0080 . 0100 . 5205 . 7787 . 0080 . 0100 . 0100 . 0080 . 0100 . 0080 . 7460 . 4516 . 0080 . 0100 . 0080 . 0100 . 4516 . 7460 . ci cr bi br ai ar I I I I I I Find the values of ar I , ai I , br I , bi I , cr I , and ci I using LU decomposition. Solution [ ] [ ][ ] = = 66 56 55 46 45 44 36 35 34 33 26 25 24 23 22 16 15 14 13 12 11 65 64 63 62 61 54 53 52 51 43 42 41 32 31 21 1 1 1 1 1 1 u u u u u u u u u u u u u u u u u u u u u U L A The [ ] U matrix is the same as the one found at the end of the forward elimination steps of the nave Gauss elimination method. Forward Elimination of Unknowns Since there are six equations, there will be five steps of forward elimination of unknowns. First step Divide Row 1 by 0.7460 and multiply it by 0.4516, that is, multiply Row 1 by 60536 . 7460 . 4516 . = . ( ) [ ] [ ] 643 . 72 0048429 . 0060536 . 0048429 . 0060536 . 27338 . 4516 . 60536 . 1 Row = Subtract the result from Row 2 to get 04.07.2 Chapter 04.07 = 9 . 103 00 . 60 9 . 103 00 . 60 643 . 72 120 8080 . 6040 . 0100 . 0080 . 0100 . 0080 . 6040 . 8080 . 0080 . 0100 . 0080 . 0100 . 0100 . 0080 . 7787 . 5205 . 0100 . 0080 . 0080 . 0100 . 5205 . 7787 . 0080 . 0100 . 014843 . 0019464 . 014843 . 0019464 . 0194 . 1 0080 . 0100 . 0080 . 0100 . 4516 . 7460 . ci cr bi br ai ar I I I I I I Divide Row 1 by 0.7460 and multiply it by 0.0100, that is, multiply Row 1 by 013405 . 7460 . 0100 . = ....
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_ele_sle_txt_ludecomp_examples - 04.07.1 Chapter 04.07...

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