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.
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Notes
- 1.
A deterministic optimization is operated on the short-term (within a day) using a more accurate model in order to provide the actual feasible releases to be performed.
- 2.
It could be the biggest one or the most valuable one from the operator’s point of view.
- 3.
These restrictions are not in favor of the MORGANE heuristics. In fact the heuristics are able to take into account stochasticity and time dependency on the prices, end non-convexity constraints.
- 4.
For confidentiality purposes, the units of measurement are omitted.
- 5.
This has a different network topology, and so it provides a useful comparison of the effect of river-chain topology on the policies from the two methodologies. As before, DOASA was run for 100 iterations, giving 100 cuts at each stage.
- 6.
An experiment with 200 cuts gave a smaller upper bound of 716.700 and an estimated value of 716.467 with a standard error of 0.833.
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Philpott, A., Dallagi, A., Gallet, E. (2013). On Cutting Plane Algorithms and Dynamic Programming for Hydroelectricity Generation. In: Kovacevic, R., Pflug, G., Vespucci, M. (eds) Handbook of Risk Management in Energy Production and Trading. International Series in Operations Research & Management Science, vol 199. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-9035-7_5
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DOI: https://doi.org/10.1007/978-1-4614-9035-7_5
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