paper-with-me

Papers

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

2020-10-09 · Tong Ma, David Alonso Barajas-Solano, Ramakrishna Tipireddy, Alexandre M. Tartakovsky

Real-time state estimation and forecasting is critical for efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for probabilistic forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data, whereas in PhI-GPR, we compute the prior statistics by solving stochastic equations governing power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertain mechanical wind power. Here, we assume that the power-grid dynamic is governed by the swing equations, and we treat the unknown terms in the swing equations (specifically, the mechanical wind power) as random processes, which turns these equations into stochastic differential equations. We solve these equations for the mean and variance of the power grid system using the Monte Carlo simulations method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate both observed and unobserved states, including the mean behavior and associated uncertainty. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR, with both forecasts being significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is much more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

📄 PDF Abstract BibTeX arXiv:2010.04591

Code (0)

등록된 구현이 없습니다.

Tasks

GPRregressionState Estimation

Methods 이 논문이 사용한 방법론

Gaussian Process Gaussian Processes are non-parametric models for approximating functions. They rely upon a measure of similarity between points (the kernel function) to predict the value for…

Similar Papers 제목 키워드 기반

An interpretation of the Brownian bridge as a physics-informed prior for the Poisson equation

2025-02-28 · Alex Alberts, Ilias Bilionis

Physics-informed machine learning is one of the most commonly used methods for fusing physical knowledge in the form of partial differential equations with experimental data. The idea is to construct a loss function wher…

FormGaussian ProcessesPhysics-informed machine learningregression

Physics-informed Gaussian Process Regression in Solving Eigenvalue Problem of Linear Operators

2026-01-10 · Tianming Bai, Jiannan Yang arxiv

Applying Physics-Informed Gaussian Process Regression to the eigenvalue problem $(\mathcal{L}-λ)u = 0$ poses a fundamental challenge, where the null source term results in a trivial predictive mean and a degenerate margi…

Online tuning and light source control using a physics-informed Gaussian process Adi

2019-11-04 · A. Hanuka, J. Duris, J. Shtalenkova, D. Kennedy 외

Operating large-scale scientific facilities often requires fast tuning and robust control in a high dimensional space. In this paper we introduce a new physics-informed optimization algorithm based on Gaussian process re…

regression

Physics-Informed Gaussian Process Regression Generalizes Linear PDE Solvers

2022-12-23 · Marvin Pförtner, Ingo Steinwart, Philipp Hennig, Jonathan Wenger

Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, special…

Bayesian Inferenceregression

Deep Latent Force Models: ODE-based Process Convolutions for Bayesian Deep Learning

2023-11-24 · Thomas Baldwin-McDonald, Mauricio A. Álvarez

Modelling the behaviour of highly nonlinear dynamical systems with robust uncertainty quantification is a challenging task which typically requires approaches specifically designed to address the problem at hand. We intr…

Time SeriesUncertainty QuantificationVariational Inference