A Necessary and Sufficient Condition for Equilibrium-Independent Passivity of Power Systems With Two-Axis Generators

We study the equilibrium-independent (EI) passivity of a nonlinear electrical power system composed of two-axis synchronous generator models. The model of our interest consists of a feedback interconnection of electromechanical linear and electromagnetic nonlinear subsystems. We mathematically prove the following two results by analyzing the nonlinear subsystem. First, a lossless transmission network is necessary for EI passivity of the electromagnetic subsystem. Second, the convexity of a strain energy function characterizes the largest set of equilibria over which the electromagnetic subsystem is EI passive. Numerical simulation of the IEEE 9-bus power system model demonstrates the practical implications of our mathematical results. In particular, we show that the convex domain of the strain energy function over which the electromagnetic subsystem is EI passive is identical to the set of all stable equilibria.