Lecture 25 :
Analysis of Power Swings in a Multi – Machine System
Given that we now have the requisite background to analyze power swings on a transmission line in a two area system, for analysis of power swings in a multimachine system, it makes sense to develop a two machine equivalent at the ends of the transmission line. This is the approach, we will be following in this lecture. In other words, we will develop a 2 port Thevenin's equivalent of the system at the terminal nodes (i and j) of the transmission line (see fig 25.1).
Vth1 and Vth2 are the equivalent Thevenin's sources behind the terminals i and j.
ZTR is the transfer impedance between the nodes i and j. The transmission line, is then connected as a load across the terminal nodes i and j. Now to compute parameters of the Thevenin's equivalent across A – B, we will first disconnect line A – B from the network and form the Zbus matrix.
The admittance matrix formulation for the power system is given by,
(1)
Ybus corresponds to positive sequence admittance matrix used in short circuit analysis. The transmission line under investigation is kept disconnected while forming the Ybus. Assuming Ybus to be invertible, we get the following equivalent Zbus model,
(2)
and
,
Remark: If there is shunt impedance to ground, then Ybus will be invertible. This usually holds true for Ybus of short circuit analysis because the corresponding shunt impedances are the machine positive sequence impedances.
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