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The present report is a public deliverable (Deliverable D3.2) of the MAGNITUDE H2020 funded European project.The objective of this deliverable is to identify, elaborate and evaluate future market schemes for multi-energy systems. Currently, electricity, gas and heat are traded in separated markets with very different trading principles (e.g., trade types, pricing methods) and different temporal specifications (i.e., temporal resolution, clearing horizon, gate closure times). As an example, the majority of gas is traded on a long term yearly basis, whereas more and more electricity is traded on a more short term hourly basis typically a day in advance or even closer to real time. Organised heat markets are currently non-existent and, in most situations, a fixed heat price applies. This report proposes possible multi-carrier market schemes which can better reflect the interaction and interdependencies between the different energy carriers, which eventually can lead to higher overall social welfare. The report specifically focuses on the design of day-ahead (DA) multi-carrier energy markets as this is seen as the first step

In Europe, orders are submitted to power exchanges integrated under the Price Coupling of Region project, to sell or buy substantially large amounts of electricity for the next day. The orders involved render the underlying microeconomic optimization problem “non-convex”, departing from more classical assumptions in microeconomic theory. Uniform prices are computed, in the sense that every market participant in a given location and hour of the day will pay or receive the same electricity price and no other side payments are considered. This is done at the expense of having some bids "paradoxically rejected" at the computed market prices, as some bids may propose a price which is "good enough" but are yet rejected. It is also at the expense of welfare optimality, as most of the time, no welfare optimal solution can be supported by uniform prices such that no financial losses are incurred. The present thesis proposes mixed integer programming models and algorithms for such non-convex uniform price auctions. In particular, a new bidding product is proposed which generalizes both block orders used in the Central Western Europe Region or Northern countries, and, mutatis mutandis, complex orders with a minimum income condition used in Spain and Portugal. (ECGE - Sciences économiques et de gestion) -- UCL, 2017

We examine the problem of clearing day-ahead electricity market auctions where each bidder, whether a producer or consumer, can specify a minimum profit or maximum payment condition constraining the acceptance of a set of bid curves spanning multiple time periods in locations connected through a transmission network with linear constraints. Such types of conditions are for example considered in the Spanish and Portuguese day-ahead markets. This helps describing the recovery of start-up costs of a power plant, or analogously for a large consumer, utility reduced by a constant term. A new market model is proposed with a corresponding MILP formulation for uniform locational price day-ahead auctions, handling bids with a minimum profit or maximum payment condition in a uniform and computationally-efficient way. An exact decomposition procedure with sparse strengthened Benders cuts derived from the MILP formulation is also proposed. The MILP formulation and the decomposition procedure are similar to computationally-efficient approaches previ- ously proposed to handle so-called block bids according to European market rules, though the clearing conditions could appear different at first sight. Both solving approaches are also valid to deal with both kinds of bids simultaneously, as block bids with a minimum acceptance ratio, generalizing fully indivisible block bids, are but a special case of the MP bids introduced here. We argue in favour of the MP bids by comparing them to previous models for minimum profit conditions proposed in the academic literature, and to the model for minimum income conditions used by the Spanish power exchange OMIE.

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.

A new formulation of the optimization problem implementing European market rules for non- convex day-ahead electricity markets is presented, that avoids the use of complementarity constraints to express market equilibrium conditions, and also avoids the introduction of auxiliary binary variables to linearise these constraints. Instead, we rely on strong duality theory for linear or convex quadratic optimization problems to recover equilibrium constraints imposed by most of European power exchanges facing indivisible orders. When only so-called stepwise preference curves are considered to describe continuous bids, the new formulation allows to take full advantage of state-of-the-art solvers, and in most cases, an optimal solution together with market clearing prices can be computed for large-scale instances without any further algorithmic work. The new formulation also suggests a very competitive Benders-like decomposition procedure, which helps to handle the case of interpolated preference curves that yield quadratic primal and dual objective functions, and consequently a dense quadratic constraint. This procedure essentially consists in strengthening classical Benders cuts locally. Computational experiments on real data kindly provided by main European power exchanges (Apx-Endex, Belpex and Epex spot) show that in the linear case, both approaches are very efficient, while for quadratic instances, only the decomposition procedure is tractable and shows very good results. Finally, when most orders are block orders, and instances are combinatorially very hard, the new MILP approach is substantially more efficient.