Strict linear prices in non-convex European day-ahead electricity markets

TL;DR

This paper addresses the challenge of computing strict linear prices in non-convex European day-ahead electricity markets, proposing algorithms to solve a complex mathematical program with equilibrium constraints.

Contribution

It introduces an exact algorithm and a heuristic for efficiently solving large-scale MPECs in non-convex electricity markets, applicable to various combinatorial auctions.

Findings

The algorithms decompose the MPEC into a MIQP master problem and LP subproblems.

Both algorithms effectively compute prices ensuring no participant incurs a loss.

The methods are applicable to a broad class of combinatorial auctions based on mixed integer programming.

Abstract

The European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous hourly bid curves and combinatorial bids with associated quantities given the prices. The goal of our auction is to maximize the economic surplus of all participants subject to quantity constraints and price constraints. The price constraints ensure that no one incurs a loss. Only traders who submitted a combinatorial bid might miss a not-realized profit. The resulting problem is a large scale mathematical program with equilibrium constraints (MPEC) and binary variables that cannot be solved efficiently by standard solvers. We present an exact algorithm and a fast heuristic for this type of problem. Both algorithms decompose the MPEC into a master problem (a MIQP) and pricing subproblems (LPs). The modeling technique and the algorithms are applicable to a wide variety of combinatorial auctions that are based on mixed integer programs.