Linear Clearing Prices in Non-Convex European Day-Ahead Electricity Markets

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 transmission constraints and the existence of linear prices. In general strict linear prices do not exist in non-convex markets. Therefore we enforce the existence of linear prices where no one incurs a loss and only combinatorial bids might see a not realized gain. The resulting optimization problem is an MPEC that can not be solved efficiently by a standard solver. We present an exact algorithm and a fast heuristic for this type of problem. Both algorithms decompose the MPEC into a master MIP and price subproblems (LPs). The modeling technique and the algorithms are applicable to all MIP based combinatorial auctions. 1