Equilibrium-Independent Passivity of Power Systems: A Link Between Classical and Two-Axis Synchronous Generator Models

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Abstract: We study equilibrium-independent passivity properties of nonlinear dynamical models of electric power systems. The model of our interest comprises of a feedback interconnection of two subsystems, one being a first-order linear ordinary differential equation and the other being a set of nonlinear differential algebraic equations (DAE). We prove the following three facts by analyzing the nonlinear DAE subsystem. First, a lossless transmission network is necessary for guaranteeing equilibrium-independent passivity of the DAE. Second, the convexity of a strain energy function characterizes the largest set of equilibria over which this DAE subsystem is equilibrium-independent passive. Finally, we prove that the strain energy function of a power system with two-axis generator models is convex if and only if its flux linkage dynamics are stable, and the strain energy function of a classical generator model derived by a singular perturbation approximation of the flux linkage dynamics is convex. These novel findings are derived by elaborating on linearization and Kron reduction properties of the power system model. Numerical simulation of the IEEE 9-bus power system model demonstrates the practical implications of the various mathematical results.

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