Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning and Operations

Nicholas Laws, Grani Hanasusanto

Research output: Contribution to journalArticlepeer-review

4 Scopus Citations

Abstract

This work presents a method for linearizing bilinear terms in the upper level of bilevel optimization problems when the bilinear terms are products of the primal and dual variables of the lower level. Bilinear terms of this form often appear in energy market optimization models where the dual variable represents the market price of energy and the primal variable represents a generator dispatch decision. Prior works have linearized such bilinear terms for specific problems. This work is the first to demonstrate how to linearize these terms in the most general case and the conditions required to perform the linearization for bilevel problems with integer or continuous variable in the upper level. The method is provided in an open source Julia module that allows researchers to write their bilevel programs in an intuitive fashion.
Original languageAmerican English
Pages (from-to)668-680
Number of pages13
JournalIEEE Transactions on Power Systems
Volume38
Issue number1
DOIs
StatePublished - 2023

NREL Publication Number

  • NREL/JA-7A40-80820

Keywords

  • duality
  • optimization methods
  • power system economics
  • power system planning

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