Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization

Emiliano Dall-Anese, Yi Guo, Kyri Baker, Zechun Hu, Tyler Summers

Research output: Contribution to conferencePaper

12 Scopus Citations


We propose a data-driven method to solve a stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The objective is to determine power schedules 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 scheduled power output adjustments 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 assume the distributions are only observable through a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real data-generating distribution, we formulate a distributionally robust optimization OPF problem to search for power schedules and reserve policies that are robust to sampling errors inherent in the dataset. A multi-stage closed-loop control strategy based on model predictive control (MPC) is also discussed. A simpIe numerical example illustrates inherent tradeoffs between operational cost and risk of constraint violation, and we show how our proposed method offers a data-driven framework to balance these objectives.
Original languageAmerican English
Number of pages7
StatePublished - 2018
Event2018 Annual American Control Conference (ACC) - Milwaukee, Wisconsin
Duration: 27 Jun 201829 Jun 2018


Conference2018 Annual American Control Conference (ACC)
CityMilwaukee, Wisconsin

NREL Publication Number

  • NREL/CP-5D00-72489


  • cost function
  • probability distribution
  • robustness
  • schedules
  • stochastic processes
  • training


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