# Distributionally Robust Optimal Power Flow with Contextual Information

arXiv: https://arxiv.org/abs/2109.07896 · HTML: https://mlsanity.com/paper/2109.07896/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 45 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Distributionally Robust Optimization: A Review](https://mlsanity.com/paper/1908.05659/) (2019)
- [Distributionally robust stochastic programs with side information based on trimmings -- Extended version](https://mlsanity.com/paper/2009.10592/) (2020)
- [Dynamic optimization with side information](https://mlsanity.com/paper/1907.07307/) (2019)
- [Wasserstein Distributionally Robust Look-Ahead Economic Dispatch](https://mlsanity.com/paper/2003.04874/) (2020)
- [Security Constrained Optimal Power Flow with Distributionally Robust Chance Constraints](https://mlsanity.com/paper/1508.06061/) (2015)
- [Distributionally Robust Chance-Constrained Approximate AC-OPF with Wasserstein Metric](https://mlsanity.com/paper/1706.05538/) (2017)
- [Data-based Distributionally Robust Stochastic Optimal Power Flow, Part I: Methodologies](https://mlsanity.com/paper/1804.06388/) (2018)
- [A Robust Approach to Chance Constrained Optimal Power Flow with Renewable Generation](https://mlsanity.com/paper/1504.06011/) (2015)
- [DC Optimal Power Flow with Joint Chance Constraints](https://mlsanity.com/paper/1911.12439/) (2019)
- [Data-Driven Distributionally Robust Optimal Power Flow for Distribution Systems](https://mlsanity.com/paper/1803.04912/) (2018)
- [Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes](https://mlsanity.com/paper/1809.07254/) (2018)
- [Iterative Decomposition of Joint Chance Constraints in OPF](https://mlsanity.com/paper/2010.11746/) (2020)

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

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)

## Abstract (arXiv)

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.