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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Bibliographic Details
Published in:EURO journal on computational optimization Vol. 5; no. 1-2; pp. 263 - 284
Main Authors: Madani, Mehdi, Van Vyve, Mathieu
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Elsevier Ltd 01.03.2017
Springer Berlin Heidelberg
Springer Nature B.V
Elsevier
Subjects:
90-08
90C06
90C11
Algorithms
Auctions
Bids
Business and Management
Costs
Day-ahead electricity market auctions
Demand
Economic analysis
Economic theory
Economics
Electric industries
Electricity
Electricity distribution
Electricity pricing
Equilibrium prices
Integer programming
Management Science
Market coupling
Market equilibrium
Market prices
Market statistics
Markets
Mathematical analysis
Mathematical models
Mixed integer programming
Non-convexities
Operations Management
Operations Research
Operations Research/Decision Theory
Opportunity costs
Optimization
Original Paper
Power
Prices
Pricing
Shadow prices
Non-convexities
90C11
Equilibrium prices
90-08
90C06
Mixed integer programming
Day-ahead electricity market auctions
Market coupling
ISSN:2192-4406, 2192-4414
Online Access:Get full text
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Summary: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.
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ISSN:2192-4406
2192-4414
DOI:10.1007/s13675-015-0047-6