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

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, uniformprice 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.An extensive literature now exists on non-convex day-ahead electricity markets or electricity pools, dealing in particular with market equilibrium issues in the presence of indivisibilities, see e.g. [3,4,5,11,10,13,14,15] and references therein. Research on the topic has been fostered by the ongoing liberalization and integration of electricity markets around the world during the past two decades. As electricity cannot be efficiently stored, non-convexities of production sets cannot be neglected, and bids introducing non-convexities in the mathematical formulation of the market clearing problem have been proposed for many years by most of power exchanges or electricity pools, allowing participants to reflect more accurately their operational constraints and cost structure.It is now well known that due to these non-convexities, a market equilibrium with uniform prices may fail to exist (a single price per market area and time slot, no transfer payments, no losses incurred, and no excess demand nor excess supply for the given uniform market prices). To deal with this issue, almost all ideas proposed revolve around reaching back, or getting close to a convex situation where strong duality holds and shadow prices exist. For example, a now classic proposition in [11] is to fix integer variables to optimal values for a welfare maximizing primal program whose constraints describe physically feasible dispatches of electricity, and compute multipart equilibrium prices using dual variables of these fixing constra...

Revisiting minimum profit conditions in uniform price day-ahead electricity auctions

“…Sketch of the proof. This is a straightforward adaptation of Theorem 1 in [11]. Essentially: (I) any feasible point of UMFS defines a corresponding partition C a ∪ C r of accepted and rejected MP bids, and conditions (58)-(60) ensure that (29)-(30) are satisfied whatever the corresponding partition is.…”

“…However, following [11], we can provide a MILP formulation without any auxiliary variables, exactly describing those admissible partitions C a , C r , together with a corresponding solution to…”

Efficient Formulation of Minimum Income Condition Orders on the All-European Power Exchange

“…The transparency and overall performance of this approach is remarkable but its direct European application is prevented by specific properties of the market environment (most importantly, by the presence of self-scheduling generators). However, a conceptually similar framework is available [7], and it is capable of clearing not only hourly and block bids but also complex orders with associated MICs.…”

Analysis and evaluation of pricing mechanisms in markets with non-convexities with reference to electricity markets

“…This major difference renders methods that are based on compensation payments inapplicable [30]. Madani and Van Vyve [31] 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. This work also extends the results of O'Neill et al [32], who propose a multi-part, discriminatory pricing mechanism in power exchange markets, such as in the Amsterdam Power Exchange (APX) Day-Ahead market or the Nord Pool Elspot market, that allow non-convex, "fill-or-kill" block bids by market participants.…”