# Data-based Distributionally Robust Stochastic Optimal Power Flow, Part I: Methodologies

arXiv: https://arxiv.org/abs/1804.06388 · HTML: https://mlsanity.com/paper/1804.06388/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2018.

## Built on by (most cited first, 4 of 4)

- [Distributionally Robust Optimal Power Flow with Contextual Information](https://mlsanity.com/paper/2109.07896/) (2021)
- [Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow](https://mlsanity.com/paper/2206.01864/) (2022)
- [Deep Reinforcement Learning for Optimal Power Flow with Renewables Using Graph Information](https://mlsanity.com/paper/2112.11461/) (2021)
- [A Unified Perspective on Conformal Prediction and Wasserstein Distributionally Robust Optimization for Uncertainty Quantification](https://mlsanity.com/paper/2608.29789/) (2026)

## Abstract (arXiv)

We propose a data-based method to solve a multi-stage stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The framework explicitly combines multi-stage feedback policies with any forecasting method and historical forecast error data. The objective is to determine power scheduling policies for controllable devices in a power network to balance operational cost and conditional value-at-risk (CVaR) of device and network constraint violations. These decisions include both nominal power schedules and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming the uncertainties across the networks follow prescribed probability distributions, we consider ambiguity sets of distributions centered around a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real unknown data-generating distribution, we formulate a multi-stage distributionally robust OPF problem to compute optimal control policies that are robust to both forecast errors and sampling errors inherent in the dataset. Two specific data-based distributionally robust stochastic OPF problems are proposed for distribution networks and transmission systems.