# Data-Driven Stochastic AC-OPF using Gaussian Processes

arXiv: https://arxiv.org/abs/2207.10781 · HTML: https://mlsanity.com/paper/2207.10781/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 21 Jul 2022.

## Builds on (most cited first, 17 of 17)

- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Cautious Model Predictive Control using Gaussian Process Regression](https://mlsanity.com/paper/1705.10702/) (2017)
- [pandapower - an Open Source Python Tool for Convenient Modeling, Analysis and Optimization of Electric Power Systems](https://mlsanity.com/paper/1709.06743/) (2017)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Gaussian Process Learning-based Probabilistic Optimal Power Flow](https://mlsanity.com/paper/2004.07757/) (2020)
- [Importance sampling approach to chance-constrained DC optimal power flow](https://mlsanity.com/paper/2111.11729/) (2021)
- [Chance Constraints for Improving the Security of AC Optimal Power Flow](https://mlsanity.com/paper/1803.08754/) (2018)
- [Stochastic AC Optimal Power Flow: A Data-Driven Approach](https://mlsanity.com/paper/1910.09144/) (2019)
- [Power Grid Reliability Estimation via Adaptive Importance Sampling](https://mlsanity.com/paper/2105.08753/) (2021)
- [A Robust Approach to Chance Constrained Optimal Power Flow with Renewable Generation](https://mlsanity.com/paper/1504.06011/) (2015)
- [Corrective Control to Handle Forecast Uncertainty: A Chance Constrained Optimal Power Flow](https://mlsanity.com/paper/1609.02194/) (2016)
- [Chance-Constrained AC Optimal Power Flow: Reformulations and Efficient Algorithms](https://mlsanity.com/paper/1706.03241/) (2017)
- [Chance-Constrained AC Optimal Power Flow -- A Polynomial Chaos Approach](https://mlsanity.com/paper/1903.11337/) (2019)
- [Chance-Constrained AC Optimal Power Flow Integrating HVDC Lines and Controllability](https://mlsanity.com/paper/1810.09218/) (2018)

## Built on by (most cited first, 2 of 2)

- [Data-Driven Chance Constrained AC-OPF using Hybrid Sparse Gaussian Processes](https://mlsanity.com/paper/2208.14814/) (2022)
- [GP CC-OPF: Gaussian Process based optimization tool for Chance-Constrained Optimal Power Flow](https://mlsanity.com/paper/2302.08454/) (2023)

## Abstract (arXiv)

In recent years, electricity generation has been responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating a significant amount of renewables into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly fluctuating and thus bring a lot of uncertainty to power grid operations and challenge existing optimization and control policies. The chance-constrained alternating current (AC) optimal power flow (OPF) framework finds the minimum cost generation dispatch maintaining the power grid operations within security limits with a prescribed probability. Unfortunately, the AC-OPF problem's chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and additional assumptions on the behavior of renewable distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach based on Gaussian process (GP) regression to close this gap. The GP approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertainty inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is illustrated over numerous IEEE test cases.