Extended Lyapunov function for power systems with transmission losses

The main proposition of this work is the development of an extended Lyapunov function for multi-machine systems taking transfer conductance parameters in consideration. This function is obtained by applying smooth perturbations on the approximated energy-like function as proposed by Athay et al. This perturbed function is used to estimate critical clearing times (CCT) based on the extension of invariance principle. These estimates are based on a solid theoretical background and also the differences between the proposed extended Lyapunov function and the energy-like function is of the order of the smooth perturbation. Examples are given in a multimachine system case to validate the proposed extended Lyapunov function.