Physics-informed Machine Learning Method for Forecasting and Uncertainty Quantification of Partially Observed and Unobserved States in Power Grids

TL;DR

This paper introduces a physics-informed Gaussian Process Regression model that improves forecasting accuracy and uncertainty quantification of power grid states, especially when measurements are limited or partially observed.

Contribution

The paper develops a novel physics-informed GPR approach that incorporates power grid equations to enhance prediction accuracy over traditional data-driven methods.

Findings

Physics-informed GPR outperforms standard GPR in forecasting accuracy.

The method accurately predicts unobserved variables from limited measurements.

Forecast horizon depends on input correlation and relaxation times.

Abstract

We present a physics-informed Gaussian Process Regression (GPR) model to predict the phase angle, angular speed, and wind mechanical power from a limited number of measurements. In the traditional data-driven GPR method, the form of the Gaussian Process covariance matrix is assumed and its parameters are found from measurements. In the physics-informed GPR, we treat unknown variables (including wind speed and mechanical power) as a random process and compute the covariance matrix from the resulting stochastic power grid equations. We demonstrate that the physics-informed GPR method is significantly more accurate than the standard data-driven one for immediate forecasting of generators' angular velocity and phase angle. We also show that the physics-informed GPR provides accurate predictions of the unobserved wind mechanical power, phase angle, or angular velocity when measurements from only one of these variables are available. The immediate forecast of observed variables and predictions of unobserved variables can be used for effectively managing power grids (electricity market clearing, regulation actions) and early detection of abnormal behavior and faults. The physics-based GPR forecast time horizon depends on the combination of input (wind power, load, etc.) correlation time and characteristic (relaxation) time of the power grid and can be extended to short and medium-range times.