A simplified determination of transient stability regions for Lyapunov methods

One of the major difficulties in using the Lyapunov method for on-line transient stability is the determination of the critical value of the V-function which describes the stability boundary. In one method the V
critical
is taken to be the minimum value of the V-function evaluated at (2
^n-1
-1) unstable equilibrium points (u.e.p.). In this paper it is shown that an accurate determination of these points is not necessary and using the analogy of 1-mechine-infinite bus example, (2
^n-1
-1) u.e.p.'s can be approximately obtained. Two multimachine systems (4 and 9- machine) are used as examples. The error in the stability boundary by using approximate method is shown to be acceptable. The use of Newton-Raphson method to calculate the post-fault stable equilibrium point is suggested. Also the type of mathematical model which is sufficient to represent both uniformly and non-uniformly damped multimachine systems is discussed.