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Real-time state estimation and forecasting is critical for efficientoperation of power grids. In this paper, a physics-informed Gaussian processregression (PhI-GPR) method is presented and used for probabilistic forecastingand estimating the phase angle, angular speed, and wind mechanical power of athree-generator power grid system using sparse measurements. In standarddata-driven Gaussian process regression (GPR), parameterized models for theprior statistics are fit by maximizing the marginal likelihood of observeddata, whereas in PhI-GPR, we compute the prior statistics by solving stochasticequations governing power grid dynamics. The short-term forecast of a powergrid system dominated by wind generation is complicated by the stochasticnature of the wind and the resulting uncertain mechanical wind power. Here, weassume that the power-grid dynamic is governed by the swing equations, and wetreat the unknown terms in the swing equations (specifically, the mechanicalwind power) as random processes, which turns these equations into stochasticdifferential equations. We solve these equations for the mean and variance ofthe power grid system using the Monte Carlo simulations method. We demonstratethat the proposed PhI-GPR method can accurately forecast and estimate bothobserved and unobserved states, including the mean behavior and associateduncertainty. For observed states, we show that PhI-GPR provides a forecastcomparable to the standard data-driven GPR, with both forecasts beingsignificantly more accurate than the autoregressive integrated moving average(ARIMA) forecast. We also show that the ARIMA forecast is much more sensitiveto observation frequency and measurement errors than the PhI-GPR forecast.

Physics-Informed Gaussian Process Regression for Probabilistic States Estimation and Forecasting in Power Grids