Short-term hydropower production scheduling : feasibility and modeling

Abstract : In the electricity industry, and more specifically at the French utility company EDF, mathematical optimization is used to model and solve problems related to electricity production management.To name a few applications: planning for capacity investments, managing depletion risks of hydro-reservoirs, scheduling outages and refueling for nuclear plants.More specifically, hydroelectricity is a renewable, cheap, flexible but limited source of energy.Harnessing hydroelectricity is thus critical for electricity production management.We are interested in Mixed-Integer Non-Linear Programming (MINLP) optimization problems.They are optimization problems whose decision variables can be continuous or discrete and the functions to express the objective and constraints can be linear or non-linear.The non-linearities and the combinatorial aspect induced by the integer variables make these problems particularly difficult to solve.Indeed existing methods cannot always solve large MINLP problems to the optimum within limited computational timeframes.Prior to solution performance, feasibility is preliminary challenge to tackle since we want to ensure the MINLP problems to solve admit feasible solutions.When infeasibilities occur in complex models, it is useful but not trivial to analyze their causes.Also, certifying the exactness of the results compounds the difficulty of solving MINLP problems as solution methods are generally implemented in floating-point arithmetic, which may lead to approximate precision.In this thesis, we work on two optimization problems - a Mixed-Integer Linear Program (MILP) and a Non-Linear Program (NLP) - related to Short-Term Hydropower production Scheduling (STHS).Given finite resources of water in reservoirs, the purpose of STHS is to prescribe production schedules with largest payoffs that are compatible with technical specifications of the hydroelectric plants.While water volumes, water flows, and electric powers can be represented with continuous variables, commitment statuses of turbine units usually have to be formulated with binary variables.Non-linearities commonly originate from the Input/Output functions that model generated power according to water volume and water flow.We decide to focus on two distinguished problems: a MILP with linear discrete features and a NLP with non-linear continuous features.In the second chapter, we deal with feasibility issues of a real-world MILP STHS.Compared with a standard STHS problem, the model features two additional specifications:discrete operational points of the power-flow curve and mid-horizon and final strict targets for reservoir levels.Issues affecting real-world data and numerical computing, together with specific model features, make our problem harder to solve and often infeasible.Given real-world instances, we reformulate the model to make the problem feasible.We follow a step-by-step approach to exhibit and cope with one source of infeasility at a time, namely numerical errors and model infeasibilities.Computational results show the effectiveness of the approach on an original test set of 66 real-world instances that demonstrated a high occurrence of infeasibilities.The third chapter is about the transposition of the Multiplicative Weights Update algorithm to the (nonconvex) nonlinear and mixed integer nonlinear programming setting, based on a particular parametrized reformulation of the problem - denoted pointwise.We define desirable properties for deriving pointwise reformulation and provide generic guidelines to transpose the algorithm step-by-step.Unlike most metaheuristics, we show that our MWU metaheuristic still retains a relative approximation guarantee in the NLP and MINLP settings.We benchmark it computationally to solve a hard NLP STHS.We find it compares favorably to the well-known Multi-Start method, which, on the other hand, offers no approximation guarantee.
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Youcef Sahraoui. Short-term hydropower production scheduling : feasibility and modeling. Operations Research [cs.RO]. Université Paris-Saclay, 2016. English. ⟨NNT : 2016SACLX025⟩. ⟨tel-01474538⟩

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