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Numerical Computation of Critical Parameter Values for Fault Recovery in Power Systems

For a given power system disturbance, it is useful to determine the critical parameter values that cause the resulting trajectory to lie exactly on the boundary (in state space) of the region of attraction of the operating point. These critical parameter values form the boundary, in parameter space, between sets of parameter values for which the system recovers to its original stable operating point, and sets of parameter values for which it does not. The paper presents an algorithm for numerically computing critical parameter values and their associated boundaries in parameter space by exploiting the presence of a controlling unstable equilibrium point (CUEP) on the boundary of the operating point's region of attraction. The key idea is to vary a parameter value in such a way as to maximize the time spent by the trajectory in a ball centred at the CUEP. This will drive parameter values to their critical values. The algorithm is demonstrated on a test case where it is used to find the critical amount of inertia in the network such that the system is marginally able to recover from a particular fault. It is also used to numerically trace a curve of critical parameter values given by varying the moments of inertia for a pair of generators.