Unit commitment constrained Nash equilibrium in power markets
Abstract
Equilibrium modeling for power markets usually assumes convexity of each players' optimization problem. Although the importance of accounting for fixed generation costs and start-up costs, minimum generation levels and/or minimum up-time and down-time restrictions in production scheduling is widely acknowledged, such modeling does not allow for discrete decisions. This paper considers unit commitment constrained Nash equilibria. First, we derive novel optimality conditions tailored for the mixed-integer convex programming problem of joint unit commitment and economic dispatch of a self-scheduling profit-maximizing producer. Next, we use these to formulate a Nash equilibrium as a mixed-integer complementarity problem, which facilitates the development of a procedure to obtain multiple equilibria. The approach can be adapted to both perfectly and imperfectly competitive market settings. While an equilibrium may not always exist, we give sufficient conditions under which a Cournot-Nash equilibrium can be obtained by mixed-integer convex programming under the standard assumption of an affine inverse demand curve and convex generating costs, and use this to establish existence. A case study demonstrates the feasibility of using optimisation to obtain a Cournot-Nash equilibrium for unit commitment constrained market clearing. Our results confirm that ignoring unit commitment creates significant welfare losses, although these vary substantially across equilibria.
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BibTeX
@misc{boomsma2026unit,
title = {{Unit commitment constrained Nash equilibrium in power markets}},
author = {Trine Krogh Boomsma and Mel T. Devine and Miguel F. Anjos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29404},
eprint = {2609.29404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29404},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Unit commitment constrained Nash equilibrium in power markets
AU - Trine Krogh Boomsma
AU - Mel T. Devine
AU - Miguel F. Anjos
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29404
UR - https://arxiv.org/abs/2609.29404
AB - Equilibrium modeling for power markets usually assumes convexity of each players' optimization problem. Although the importance of accounting for fixed generation costs and start-up costs, minimum generation levels and/or minimum up-time and down-time restrictions in production scheduling is widely acknowledged, such modeling does not allow for discrete decisions. This paper considers unit commitment constrained Nash equilibria. First, we derive novel optimality conditions tailored for the mixed-integer convex programming problem of joint unit commitment and economic dispatch of a self-scheduling profit-maximizing producer. Next, we use these to formulate a Nash equilibrium as a mixed-integer complementarity problem, which facilitates the development of a procedure to obtain multiple equilibria. The approach can be adapted to both perfectly and imperfectly competitive market settings. While an equilibrium may not always exist, we give sufficient conditions under which a Cournot-Nash equilibrium can be obtained by mixed-integer convex programming under the standard assumption of an affine inverse demand curve and convex generating costs, and use this to establish existence. A case study demonstrates the feasibility of using optimisation to obtain a Cournot-Nash equilibrium for unit commitment constrained market clearing. Our results confirm that ignoring unit commitment creates significant welfare losses, although these vary substantially across equilibria.
ER -