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lecture14 - inversion of the bus admittance matrix is a n3...

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Power Systems I The Bus Impedance Matrix Definition Direct formation of the matrix inversion of the bus admittance matrix is a n 3 effort for small and medium size networks, direct building of the matrix is less effort for large size networks, sparse matrix programming with gaussian elimination technique is preferred 1 = bus bus Y Z
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Power Systems I bus node = graph vertex line branch = edge Forming the Bus Impedance Matrix Graph theory techniques helps explain the building process 0 1 2 3 1 2 3 4 5 co-tree 0 1 2 3 1 2 3 4 5 selected tree j0.2 j0.4 j 0.4 j0.4 j0.8 1 2 3 extending tree branch loop closing branch
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Power Systems I Partial Network m bus Z 1 2 i j 0 Reference bus bus bus I Z V = Forming the Bus Impedance Matrix Basic construction of the network and the matrix
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Power Systems I Partial Network m bus Z 1 2 p m 0 Reference Partial Network m bus Z 1 2 p m 0 Reference q q q qp p q I z V V + = q q q I z V 0 0 + = Adding a Line
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Power Systems I Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ + = = = = = = = = = = Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ q m p pq pp pm pp p p mp mm mp m m pp pm pp p p p m p p m p q m p I I I I I z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z V V V V V 2 1 2 1 2 1 2 1 2 2 2 22 21 1 1 1 21 11 2 1 Adding a Line to an Existing Line
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Power Systems I Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ ΢ਯ Σਿ Ρਟ = = = = = = = = = = Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Υ੟ Φ੯ Τ੏ ΢ਯ ΢ਯ
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