Properties of the Frequency–Amplitude Curve

The frequency-amplitude (F-A) curve has been proposed to characterize the electromechanical oscillation frequency of a single-machine-infinite-bus (SMIB) system considering nonlinearity of the swing equation. For a multi-machine system, the F-A curve regarding one oscillation mode is a projection of the system trajectory between the stable equilibrium point and the stability boundary onto the F-A plane. This letter provides rigorous proofs of six general properties of the F-A curve.