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lecture3

# lecture3 - The Bus Admittance Matrix l The matrix equation...

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Power Systems I The Bus Admittance Matrix l The matrix equation for relating the nodal voltages to the currents that flow into and out of a network using the admittance values of circuit branches l Used to form the network model of an interconnected power system u Nodes represent substation bus bars u Branches represent transmission lines and transformers u Injected currents are the flows from generator and loads node bus inj V Y I = Network I k V k

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Power Systems I The Bus Admittance Matrix l Constructing the Bus Admittance Matrix (or the Y bus matrix) u form the nodal solution based upon Kirchhoff’s current law u impedances are converted to admittances ij ij ij ij x j r z y + = = 1 1 ( 29 ( 29 ( 29 n k kn k k k k k k inj k V V y V V y V V y V y I - + + - + - + = - K 2 2 1 1 0
Power Systems I Matrix Formation Example j 1.0 j 0.8 j 0.4 j 0.2 j 0.2 j 0.08 4 3 1 2 Impedance Diagram generator 1 z = j 1.0 line 12 z = j 0.4 line 13 z = j 0.2 line 23 z = j 0.2 line 34 z = j 0.08 4 3 1 2 Network Diagram generator 2 z = j 0.8 V 2 V 1

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Power Systems I Matrix Formation Example y 10 = - j 1.0 y 20 = - j 1.25 y 12 = - j 2.5 y 13 = - j 5 y 23 = - j 5 y 34 = - j 12.5 1 2 Admittance Diagram I 2 I 1 4 3 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 (
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