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.
Highlights
AND BACKGROUNDSince the restructuring of electricity markets began in the early 1980’s [1] and the introduction of locational marginal pricing into large scale power markets in the 1990’s researchers have been investigating electricity market design optimization problems
From a market participant point-ofview one of the most critical terms in a problem is the price signal from the market operator multiplied by the energy delivered (MWh) by the participant, which together represent the participant’s income
This paper presents a general algorithm for linearizing the bilinear terms of interest and determines the exact conditions under which the bilinear terms can be linearized in general bilevel problems
Summary
Since the restructuring of electricity markets began in the early 1980’s [1] and the introduction of locational marginal pricing into large scale power markets in the 1990’s researchers have been investigating electricity market design optimization problems. Ruiz et al 2009 [2] is the earliest known example to demonstrate that bilinear terms for market price and participant dispatch can be linearized Their model places the market participant in the upper level, which chooses its offer curve for energy generation, while the lower level models the electricity market given the other participants’ offer curves. The upper level minimizes operating costs from the microgrid owner’s perspective with the product of its exported power and the dual variable of the lower level, linear power flow load balance in its objective. Using the open source module other researchers can take advantage of the linearization method for any bilevel problem with bilinear products of shadow prices and dispatch variables of interest
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