An optimization scheme for locating power system equilibria ranked by a scalar Lyapunov function

A constrained optimization algorithm for implementing a geometric approach to ranking UEPs (unstable equilibrium points) is proposed. The formulation seeks to minimize a Euclidean norm of the vector field along a constraint manifold defined by a constant contour of the Lyapunov function. When the norm is driven to zero on the manifold, one has located an equilibrium point having the given value of energy. A scheme for modifying the constraint contour is proposed, and a limit on the number of local minima in a neighborhood of the operating point is demonstrated.<>