On the existence of energy function for power systems with transmission losses

In this paper we show that any energy (Lyapunov) function to analyze the stability of equilibrium points of systems with transmission losses would, in general, not be a continuous (with respect to transmission losses) deformation of the standard energy function used for a lossless system. This result implies that stability analysis using Lyapunov functions for systems with losses would require Lyapunov functions that are substantially different from the energy function used for lossless systems.