  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.
