Contributed Session Fri.3.MA 550

Friday, 15:15 - 16:45 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

MPEC problems and market coupling


Chair: Daniel Huppmann



Friday, 15:15 - 15:40 h, Room: MA 550, Talk 1

Bertrand Cornélusse
Coupling European day-ahead electricity markets with COSMOS

Coauthors: Yves Langer, Gilles Meyer, Gilles Scouvart, Mathieu Van Vyve


Market coupling allows matching orders submitted by participants of several electricity markets while satisfying network constraints. It maximizes the economic welfare and allows a more efficient usage of market interconnection capacity. Several types of orders are available, including "block orders'' that must either be accepted in full or rejected. This problem translates into a MIQP with complicating constraints. Maximizing welfare subject to clearing (matched supply equals matched demand) and network constraints yields acceptance decisions for submitted orders. However some market rules are constraints relating acceptance decisions and market prices, and all integer solutions are consequently not acceptable. We present COSMOS, a dedicated branch-and-cut algorithm to solve this difficult problem. COSMOS runs every day for coupling day-ahead markets of Belgium, France, Germany and the Netherlands. Recent developments integrate specific requirements for the Iberian peninsula, the Italian market and the Nord Pool System. The authors would like to thank the owners of COSMOS, which are currently BelPex, APX-ENDEX and EPEX Spot, for allowing them to communicate on this work.



Friday, 15:45 - 16:10 h, Room: MA 550, Talk 2

Johannes C. Müller
Linear clearing prices in non-convex european day-ahead electricity markets

Coauthors: Alexander Martin, Sebastian Pokutta


The European power grid can be divided into several market areas where the price of electricity is determined in a day-ahead auction. Market participants can provide continuous and combinatorial orders with associated quantities given the prices. The goal of our auction is to maximize the economic surplus of all participants subject to transmission constraints and the existence of linear prices. In general strict linear prices do not exist in the presence of non-convex constraints. Therefore we enforce the existence of linear prices such that no one incurs a loss and only combinatorial orders might see a not realized gain. The resulting model is an MPEC that can not be solved efficiently by standard solvers. We present an exact algorithm and a fast heuristic for this type of problem. Both algorithms decompose the MPEC into a master MIP and price subproblems (LPs). The modeling technique and the algorithms are applicable to all MIP based combinatorial auctions.



Friday, 16:15 - 16:40 h, Room: MA 550, Talk 3

Daniel Huppmann
Approximating unit commitment using mathematical programming under equilibrium constraints

Coauthors: Jan Abrell, Wolf-Peter Schill


Modeling the electricity market and computing optimal dispatch is difficult due to many specific features of the power sector, such as unit commitment (i.e., binary decision variables), non-linear cost functions due to the varying efficiency of a power plant contingent on capacity utilization, and other engineering constraints. Models that capture these aspects grow quickly in complexity and are usually intractable in large-scale applications. Hence, researchers frequently resort to linear models. This, however, raises the question of choosing the parameters for a linear model to describe a highly non-linear interrelation as accurately as possible. We propose a mathematical program under equilibrium constraints (MPEC) to solve this problem; it minimizes the “distance” between a complex unit commitment model (mixed integer non-linear program, MINLP), and a linear mixed complementarity program (MCP) by setting the parameters of the MCP accordingly. This problem is applied to several data sets and time horizons to derive an understanding of the sensitivity of the obtained parameters. We conclude that our approach offers a feasible path to calibrate linear electricity market models.


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