Local Shifted Passivity Analysis of the Single-Machine Infinite-Bus System

Abstract

This letter presents a shifted passivity analysis of the single-machine infinite-bus system in the stationary ($αβ$) reference frame. We study the attractivity of a periodic synchronous steady state with constant rotor frequency and formulate shifted passivity with respect to this motion. A port-Hamiltonian representation of the machine dynamics is used to construct a local shifted passivity condition from the error Hamiltonian and a correction term adapted to the synchronous steady state. For the infinite-bus interconnection, the resulting dissipation inequality leads to a sufficient stability condition expressed in terms of field excitation magnitude, damping, inertia, and steady-state current. This condition implies local asymptotic stability of the synchronous steady state and yields a sublevel-set estimate of its region of attraction under an additional small-inertia condition. A distinctive feature of the analysis is that it preserves the periodic structure of the rotor angle and provides a compact passivity-based stability certificate for the stationary-frame model.