Howavailability Changed in a Competitive Market

Characteristic multipliers (CM) of the Mathieu equation are the equivalent of eigenvalues of a linearized nonlinear differential equation. Oscillations will be stable when the real part of CMs is less than unity. The characteristic of an oscillation will change if the real part of CMs have magnitude greater than unity. In this letter, the investigation is directed to the effect of changes in CM on the stability of power systems. The significant role of nonlinearity is demonstrated by finding CM for the nontrivial single-machine system. The nonautonomous form of the Mathieu equation obtained models the effect of time dependent perturbations at the quasi-infinite bus.