A MIP framework for non-convex uniform price day-ahead electricity auctions

It is well known that a market equilibrium with uniform prices often does not exist in non-convex day-ahead electricity auctions. We consider the case of the non-convex, uniform-price Pan-European day-ahead electricity market “PCR” (Price Coupling of Regions), with non-convexities arising from so-ca...

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Autores principales:	Mehdi Madani, Mathieu Van Vyve
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2017
Materias:	90C11 90-08 90C06 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/d861f8bc121140778b78d726b723d034
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spelling	oai:doaj.org-article:d861f8bc121140778b78d726b723d0342021-12-02T05:01:01ZA MIP framework for non-convex uniform price day-ahead electricity auctions2192-440610.1007/s13675-015-0047-6https://doaj.org/article/d861f8bc121140778b78d726b723d0342017-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2192440621000812https://doaj.org/toc/2192-4406It is well known that a market equilibrium with uniform prices often does not exist in non-convex day-ahead electricity auctions. We consider the case of the non-convex, uniform-price Pan-European day-ahead electricity market “PCR” (Price Coupling of Regions), with non-convexities arising from so-called complex and block orders. Extending previous results, we propose a new primal-dual framework for these auctions, which has applications in both economic analysis and algorithm design. The contribution here is threefold. First, from the algorithmic point of view, we give a non-trivial exact (i.e., not approximate) linearization of a non-convex ‘minimum income condition’ that must hold for complex orders arising from the Spanish market, avoiding the introduction of any auxiliary variables, and allowing us to solve market clearing instances involving most of the bidding products proposed in PCR using off-the-shelf MIP solvers. Second, from the economic analysis point of view, we give the first MILP formulations of optimization problems such as the maximization of the traded volume, or the minimization of opportunity costs of paradoxically rejected block bids. We first show on a toy example that these two objectives are distinct from maximizing welfare. Third, we provide numerical experiments on realistic large-scale instances. They illustrate the efficiency of the approach, as well as the economics trade-offs that may occur in practice.Mehdi MadaniMathieu Van VyveElsevierarticle90C1190-0890C06Applied mathematics. Quantitative methodsT57-57.97Electronic computers. Computer scienceQA75.5-76.95ENEURO Journal on Computational Optimization, Vol 5, Iss 1, Pp 263-284 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	90C11 90-08 90C06 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95
spellingShingle	90C11 90-08 90C06 Applied mathematics. Quantitative methods T57-57.97 Electronic computers. Computer science QA75.5-76.95 Mehdi Madani Mathieu Van Vyve A MIP framework for non-convex uniform price day-ahead electricity auctions
description	It is well known that a market equilibrium with uniform prices often does not exist in non-convex day-ahead electricity auctions. We consider the case of the non-convex, uniform-price Pan-European day-ahead electricity market “PCR” (Price Coupling of Regions), with non-convexities arising from so-called complex and block orders. Extending previous results, we propose a new primal-dual framework for these auctions, which has applications in both economic analysis and algorithm design. The contribution here is threefold. First, from the algorithmic point of view, we give a non-trivial exact (i.e., not approximate) linearization of a non-convex ‘minimum income condition’ that must hold for complex orders arising from the Spanish market, avoiding the introduction of any auxiliary variables, and allowing us to solve market clearing instances involving most of the bidding products proposed in PCR using off-the-shelf MIP solvers. Second, from the economic analysis point of view, we give the first MILP formulations of optimization problems such as the maximization of the traded volume, or the minimization of opportunity costs of paradoxically rejected block bids. We first show on a toy example that these two objectives are distinct from maximizing welfare. Third, we provide numerical experiments on realistic large-scale instances. They illustrate the efficiency of the approach, as well as the economics trade-offs that may occur in practice.
format	article
author	Mehdi Madani Mathieu Van Vyve
author_facet	Mehdi Madani Mathieu Van Vyve
author_sort	Mehdi Madani
title	A MIP framework for non-convex uniform price day-ahead electricity auctions
title_short	A MIP framework for non-convex uniform price day-ahead electricity auctions
title_full	A MIP framework for non-convex uniform price day-ahead electricity auctions
title_fullStr	A MIP framework for non-convex uniform price day-ahead electricity auctions
title_full_unstemmed	A MIP framework for non-convex uniform price day-ahead electricity auctions
title_sort	mip framework for non-convex uniform price day-ahead electricity auctions
publisher	Elsevier
publishDate	2017
url	https://doaj.org/article/d861f8bc121140778b78d726b723d034
work_keys_str_mv	AT mehdimadani amipframeworkfornonconvexuniformpricedayaheadelectricityauctions AT mathieuvanvyve amipframeworkfornonconvexuniformpricedayaheadelectricityauctions AT mehdimadani mipframeworkfornonconvexuniformpricedayaheadelectricityauctions AT mathieuvanvyve mipframeworkfornonconvexuniformpricedayaheadelectricityauctions
_version_	1718400857865715712

A MIP framework for non-convex uniform price day-ahead electricity auctions

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