Stochastic dual dynamic programming for optimal power flow problems under uncertainty

Adriana Kiszka, David Wozabal*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

Original languageEnglish
Pages (from-to)814-836
Number of pages23
JournalEuropean Journal of Operational Research
Volume321
Issue number3
DOIs
Publication statusPublished - 16 Mar 2025

Bibliographical note

Publisher Copyright:
© 2024 The Authors

Keywords

  • Electricity storage
  • Optimal power flow
  • Semi-definite programming
  • Stochastic dual dynamic programming
  • Stochastic programming

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