Stochastic Small Signal Stability of Power System with Random Wind

We study the small signal stochastic stability of an electric power system with variable wind energy. Random wind speed is shown to appear as a multiplicative parametric uncertainty in the linearized differential-algebraic description of the power system dynamics. Recent results on the stochastic stability of linear systems with multiplicative uncertainty allow us to characterize a critical variance of wind speed, beyond which the grid dynamics becomes mean square unstable. We illustrate the role of mean square stability and the critical variance through simulations on the IEEE 39-bus system.