A two-step approach to Wasserstein distributionally robust chance- and security-constrained dispatch

Amin Maghami*, Evrim Ursavas, Ashish Cherukuri

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
121 Downloads (Pure)

Abstract

This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the mismatch caused by contingencies and renewables are handled using reserves. We consider a distributionally robust approach to solve the chance-constrained program. We assume that samples of the uncertainty are available. Using them, we construct a set of distributions, termed ambiguity set, containing all distributions that are close to the empirical distribution under the Wasserstein metric. The chance constraint is imposed for all distributions in the ambiguity set to form the distributionally robust optimization problem. This problem is nonconvex and computationally heavy to solve exactly. We adopt a two-step approach to find an approximate solution. In the first step, we construct a polyhedral set in the space of uncertainty that contains enough mass under all distributions in the ambiguity set. This set is constructed by solving several two-dimensional distributionally robust problems. In the second step, we solve a linear robust optimization problem where the uncertain constraint is imposed for all uncertainty values lying in the polyhedral set. We demonstrate the scalability and robustness of our method using numerical experiments.

Original languageEnglish
Pages (from-to)1447-1459
Number of pages13
JournalIEEE Transactions on Power Systems
Volume39
Issue number1
Early online date6-Feb-2023
DOIs
Publication statusPublished - Jan-2024

Keywords

  • Chance-constrained optimization
  • Contingency management
  • Distributionally robust optimization
  • Economics
  • Measurement
  • Optimization
  • Optimization methods
  • Power generation dispatch
  • Power system security
  • Renewable energy sources
  • Security
  • Stochastic processes
  • Uncertainty

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