lecture14

lecture14 - Power Systems I The Bus Impedance Matrix l...

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Unformatted text preview: Power Systems I The Bus Impedance Matrix l Definition l Direct formation of the matrix u inversion of the bus admittance matrix is a n 3 effort u for small and medium size networks, direct building of the matrix is less effort u for large size networks, sparse matrix programming with gaussian elimination technique is preferred 1- = bus bus Y Z Power Systems I bus node = graph vertexline branch = edge Forming the Bus Impedance Matrix l Graph theory techniques helps explain the building process 1 2 3 1 2 3 4 5 co-tree 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 Power Systems I Partial Network m bus Z 1 2 i j Reference bus bus bus I Z V = Forming the Bus Impedance Matrix l Basic construction of the network and the matrix Power Systems I Partial Network m bus Z 1 2 p m Reference Partial Network m bus Z 1 2 p m Reference q q q qp p q I z V V + = q q q I z V + = Adding a Line Power Systems I + = = = = = = = = = = 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 M M L L L L M M O M O M M L L M M O M O M M L L L L M M 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 Power Systems I...
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lecture14 - Power Systems I The Bus Impedance Matrix l...

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