Transient stabilization of multimachine power systems with nontrivial transfer conductances

In this paper we provide a solution to the long-standing problem of transient stahilizalion of multimachine power systems with non-negligible transfer conductances. More specifically, we consider the full 3n-dimensional model of the n-generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. Our derivations underscore the deleterious effects of resistive elements which, as is well-known, hamper the assignment of simple "gradient" energy functions and compel us lo include non-standard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system dial play the role of multipliers in classical passivity theory.