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We study the equilibrium-independent (EI) passivity of a nonlinear powersystem composed of two-axis generator models. The model of our interestconsists of a feedback inter-connection of linear and nonlinear subsystems,called mechanical and electromagnetic subsystems. We mathematically prove thefollowing three facts by analyzing the nonlinear electromagnetic subsystem.First, a lossless transmission network is necessary for the EI passivity of theelectromagnetic subsystem. Second, the convexity of a strain energy functioncharacterizes the largest set of equilibria over which the electromagneticsubsystem is EI passive. Finally, we prove that the strain energy function forthe network of the two-axis generator models is convex if and only if its fluxlinkage dynamics is stable, and the strain energy function for the network ofthe classical generator models derived by singular perturbation approximationof the flux linkage dynamics is convex. Numerical simulation of the IEEE 9-buspower system model demonstrates the practical implications of the variousmathematical results. In particular, we validate that the convex domain of thestrain energy function over which the electromagnetic subsystem is EI passiveis almost identical to the set of all stable equilibria. This result is alsogeneralized to lossy power systems based on our finding that the convexity ofthe strain energy function is equivalent to the positive semidefiniteness of asynchronizing torque coefficient matrix.

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