Kernel Regression Method for Stochastic Real-time State Estimation in Power Grid

The paper presents a physics-informed Gaussian/kernel process regression method for real-time state estimation and forecasting of the phase angle, angular speed, and mechanical wind power in a three-generator power grid system using sparse measurements. The method treats unknown terms in the swing equations, such as mechanical wind power, as random processes, which transforms these equations into stochastic differential equations. The proposed method accurately forecasts and estimates both observed and unobserved states, providing a forecast comparable to the standard data-driven GP/kernel for observed states. The method also demonstrates improved accuracy with increased observation frequency and reduced measurement errors.