Conditions for existence of equilibrium points of systems with constant power loads

Abstract

In this paper we investigate the sine qua non condition of existence of equilibria for electrical systems with external sources furnishing constant power to the loads, which is a scenario encountered in modern applications. Two general cases are considered, when the system is (i) linear time–invariant or (ii) nonlinear, with dynamic behavior described by a port–Hamiltonian model with constant dissipation and switching interconnection matrix. The latter class includes the practically important case of power converters. For both cases necessary and suf¿cient conditions for existence of equilibria are given, which impose that the power dissipated in steady–state should exceed the extracted constant power. The equilibrium is ensured if and only if the inequality is satis¿ed.