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

TL;DR

This paper introduces a new primal-dual MIP framework for non-convex day-ahead electricity auctions, enabling exact solutions and economic analysis of complex market objectives in the PCR market.

Contribution

It presents a novel linearization of non-convex conditions, MILP formulations for economic objectives, and demonstrates efficiency on large-scale instances.

Findings

Exact linearization of non-convex minimum income condition

MILP formulations for volume maximization and opportunity costs

Efficient solution of large-scale market clearing instances

Abstract

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. We also recover directly a previously noted property of an alternative market model. 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.