Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning and Operations
Linearizing Bilinear Products of Shadow Prices and Dispatch Variables in Bilevel Problems for Optimal Power System Planning and Operations
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DOI：
10.1109/tpwrs.2022.3156475
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发表时间：
2023-01
影响因子：
6.6
通讯作者：
Nicholas D. Laws;G. A. Hanasusanto
中科院分区：
文献类型：
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作者：
Nicholas D. Laws;G. A. Hanasusanto
这项工作提出了一种在双层优化问题的上层中对双线性项进行线性化的方法，当双线性项是下层原始变量和对偶变量的乘积时。这种形式的双线性项经常出现在能源市场优化模型中，其中对偶变量代表能源的市场价格，原始变量代表发电机调度决策。先前的工作已经针对特定问题对这类双线性项进行了线性化。这项工作首次展示了如何在最一般的情况下对这些项进行线性化，以及对上层具有整数或连续变量的双层问题进行线性化所需的条件。该方法在一个开源的Julia模块中提供，这使得研究人员能够以一种直观的方式编写他们的双层程序。
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.