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On Cutting Plane Algorithms and Dynamic Programming for Hydroelectricity Generation

In: Handbook of Risk Management in Energy Production and Trading

Author

Listed:
  • Andy Philpott

    (University of Auckland)

  • Anes Dallagi

    (EDF R&D)

  • Emmanuel Gallet

    (EDF R&D)

Abstract

We consider dynamic programming (DP) approximations to hydro-electric reservoir scheduling problems. The first class of approximate DP methods uses decomposition and multi-modeling heuristics to produce policies that can be expressed as the sum of one-dimensional Bellman functions. This heuristic allows us to take into account non-convexities (appearing in models with head effect) by solving a MIP at each time stage. The second class of methods uses cutting planes and sampling. It is able to provide multidimensional policies. We show that the cutting plane methods will produce better policies than the first DP approximation on two convex problem formulations of different types. Modifying the cutting plane method to approximate the effect of reservoir head level on generation also yields better results on problems including these effects. The results are illustrated using tests on two river valley systems.

Suggested Citation

  • Andy Philpott & Anes Dallagi & Emmanuel Gallet, 2013. "On Cutting Plane Algorithms and Dynamic Programming for Hydroelectricity Generation," International Series in Operations Research & Management Science, in: Raimund M. Kovacevic & Georg Ch. Pflug & Maria Teresa Vespucci (ed.), Handbook of Risk Management in Energy Production and Trading, edition 127, chapter 0, pages 105-127, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-9035-7_5
    DOI: 10.1007/978-1-4614-9035-7_5
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