Stochastic Optimal Control of Multi‐Machine Power Systems Driven by Fractional Gaussian Noise

ABSTRACT This paper studies the optimal control of multi‐machine power systems with the excitation of fractional Gaussian noise (FGN) and applies the theory of quasi‐generalized Hamiltonian systems. First, a multi‐machine power system model is established based on the long‐range correlation of fractional Gaussian noise, which is transformed into a quasi‐generalized Hamiltonian system model. Next, according to the fractional path integral rules and the stochastic averaging method (SAM), the stochastic multi‐machine power system is reduced in dimension. Then, based on the averaged multi‐machine power system, the dynamic programming method of stochastic optimal control is utilized to propose a control strategy that maximizes the probability of the controlled system being in the desired region. Finally, the effectiveness of the proposed control strategy is verified through numerical simulations, and the superiority of the control methods has also been compared with the Linear Quadratic Regulator (LQR).