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

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 variab...

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Bibliographic Details
Published in:IEEE transactions on power systems 2023-01, Vol.38 (1), p.668-680
Main Authors: Laws, Nicholas D., Hanasusanto, Grani A.
Format: Article
Language:English
Subjects:
Biological system modeling
Continuity (mathematics)
Costs
Duality
Electricity supply industry
Linearization
Manganese
Mathematical models
Microgrids
optimization methods
Optimization models
power system economics
Power system planning
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Summary: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.
ISSN:0885-8950
1558-0679
DOI:10.1109/TPWRS.2022.3156475