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 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.

Automated summary

This study presents a method for linearizing bilinear terms in bilevel optimization problems, specifically when the terms involve both primal and dual variables. Such terms are frequently found in energy market optimization models. Previous works have addressed linearization for specific problems, but this study demonstrates the general case and the conditions for linearization in bilevel problems with integer or continuous variables. An open source Julia module is provided to facilitate intuitive programming for researchers working on bilevel programs.