# REDEMPTORIS MATER

Jun 22nd, 2015
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University of Georgia
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NETWORK ADMITTANCE AND IMPEDANCE MATRICESAs we have seen in Chapter 1 that a power system network can be converted into an equivalent impedance diagram. This diagram forms the basis of power flow (or load flow) studies and short circuit analysis. In this chapter we shall discuss the formation of bus admittance matrix (also known as Ybus matrix) and bus impedance matrix (also known as Zbus matrix). These two matrices are related byZbus1bus(3.1)We shall discuss the formation of the Ybus matrix first. This will be followed by the discussion of the formation of the Zbus matrix.3.1 FORMATION OF BUS ADMITTANCE MATRIXConsider the voltage source VS with a source (series) impedance of ZS as shown in Fig. 3.1 (a). Using Nortons theorem this circuit can be replaced by a current source IS with a parallel admittance of YS as shown in Fig. 3.1 (b). The relations between the original system and the Norton equivalent areI VSZ S1 and YS Z S(3.2)We shall use this Nortons theorem for the formulation of the Ybus matrix.Fig. 3.1 (a) Voltage source with a source impedance and (b) its Norton equivalent circuit.For the time being we shall assume the short line approximation for the formulation of the bus admittance matrix. We shall thereafter relax this assumption and use the - representation of the network for power flow studies. Consider the 4-bus power system shown in Fig. 3.2. This cont

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