# Gaussian Process Learning-based Probabilistic Optimal Power Flow

arXiv: https://arxiv.org/abs/2004.07757 · HTML: https://mlsanity.com/paper/2004.07757/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [Data-Driven Stochastic AC-OPF using Gaussian Processes](https://mlsanity.com/paper/2207.10781/) (2022)
- [Learning Power Flow with Confidence: A Probabilistic Guarantee Framework for Voltage Risk](https://mlsanity.com/paper/2308.07867/) (2023)
- [Data-Driven Chance Constrained AC-OPF using Hybrid Sparse Gaussian Processes](https://mlsanity.com/paper/2208.14814/) (2022)
- [Selecting Critical Scenarios of DER Adoption in Distribution Grids Using Bayesian Optimization](https://mlsanity.com/paper/2501.14118/) (2025)
- [Power Flow Approximations for Multiphase Distribution Networks using Gaussian Processes](https://mlsanity.com/paper/2504.21260/) (2025)
- [Risk and Anomaly Identification for Distribution Network Optimal Operation Based on Reinforcement Learning and Uncertainty Quantification](https://mlsanity.com/paper/2609.03308/) (2026)

## Abstract (arXiv)

In this letter, we present a novel Gaussian Process Learning-based Probabilistic Optimal Power Flow (GP-POPF) for solving POPF under renewable and load uncertainties of arbitrary distribution. The proposed method relies on a non-parametric Bayesian inference-based uncertainty propagation approach, called Gaussian Process (GP). We also suggest a new type of sensitivity called Subspace-wise Sensitivity, using observations on the interpretability of GP-POPF hyperparameters. The simulation results on 14-bus and 30-bus systems show that the proposed method provides reasonably accurate solutions when compared with Monte-Carlo Simulations (MCS) solutions at different levels of uncertain renewable penetration as well as load uncertainties, while requiring much less number of samples and elapsed time.