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Decomposition methods for a spatial model for long-term energy pricing problem

Author

Listed:
  • Philippe Mahey

    (Université Clermont)

  • Jonas Koko

    (Université Clermont)

  • Arnaud Lenoir

    (EDF Lab)

Abstract

We consider an energy production network with zones of production and transfer links. Each zone representing an energy market (a country, part of a country or a set of countries) has to satisfy the local demand using its hydro and thermal units and possibly importing and exporting using links connecting the zones. Assuming that we have the appropriate tools to solve a single zonal problem (approximate dynamic programming, dual dynamic programming, etc.), the proposed algorithm allows us to coordinate the productions of all zones. We propose two reformulations of the dynamic model which lead to different decomposition strategies. Both algorithms are adaptations of known monotone operator splitting methods, namely the alternating direction method of multipliers and the proximal decomposition algorithm which have been proved to be useful to solve convex separable optimization problems. Both algorithms present similar performance in theory but our numerical experimentation on real-size dynamic models have shown that proximal decomposition is better suited to the coordination of the zonal subproblems, becoming a natural choice to solve the dynamic optimization of the European electricity market.

Suggested Citation

  • Philippe Mahey & Jonas Koko & Arnaud Lenoir, 2017. "Decomposition methods for a spatial model for long-term energy pricing problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 137-153, February.
    • Handle: RePEc:spr:mathme:v:85:y:2017:i:1:d:10.1007_s00186-017-0573-5
    DOI: 10.1007/s00186-017-0573-5
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    References listed on IDEAS

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    1. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
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    3. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
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