A new Lyapunov function for interconnected power systems

A Lyapunov function is constructed for a general n-machine power system with nonzero transfer conductance. The theory of dissipative dynamic systems and its modifications are used. The Lyapunov function construction procedure calls for checking positive definiteness of a sparse matrix. Results are reported only for the case of nonuniform damping, which is more complex than the uniformly damped system. The procedure is iterative and is guaranteed to converge for uniform damping but may fail to converge for a very lightly nonuniformly damped system with strong interconnections. The Lyapunov function is a quadratic term plus a weighted sum of integrals, a form not reported before. This is an extension of a previously reported quadratic Lyapunov function