Comparison of two mathematical programming models for the solution of a convex portfolio-based European day-ahead electricity market

In this paper two mathematical programming models are presented and compared for the solution of the European electricity day-ahead market with adjustable block orders. The concept of “adjustable” products is initially introduced, as products that can be partially cleared; thus, they do not bear the inherent indivisibilities of the classical block orders that are tradable in the European markets. Also, the clearing conditions of these adjustable products are analytically described. Due to their flexibility, the market clearing can adjust their clearing status accordingly, in order to match supply offers with demand bids avoiding non-convexities in the problem solution surface. This leads to the elimination of paradoxically accepted and rejected block orders. These adjustable products are modeled within the context of the European electricity day-ahead market problem, which is formulated as two different mathematical programming models: a Mixed Complementarity Problem (MCP) and a Linear Programming model (LP). The two models are evaluated in terms of computational efficiency using the pan-European zonal power system, by considering an increasing number of adjustable products per product type. The MCP model can formulate more adjustable product types, by efficiently formulating respective non-linear mixed pricing rules, but it is computationally demanding; on the other hand, the LP model is computational efficient, but it is not flexible enough to handle an extended variety of adjustable supply/demand block orders.