A MILP-Based Approach for Hydrothermal Scheduling
This paper presents new solution approaches capable of finding optimal solutions for the Hydrothermal Scheduling Problem (HSP) in power generation planning. The problem has been proven to be NP-hard and no exact methods have been able to tackle it, for pr
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1 Introduction The Hydrothermal Scheduling Problem (HSP) is one of the challenging optimization problems in power systems that optimally determines which of the thermal and hydro units must be committed/decommitted over a planning horizon (that for shortterm planning lasts from 1 day to 2 weeks, generally split into periods of 1 hour each) and aims at minimizing the overall operation cost of thermal units while satisfying practical thermal and hydro constraints. Main decision variables are: (1) which thermal generators must be committed in each period of the planning horizon, as well as their production level; and (2) the discharge rates of each hydro generator. A wide range of optimization techniques has been researched to solve the HSP ranging from exact approaches and Lagrangian Relaxation, to very elaborate heuristics and metaheuristics. Lagrangian Relaxation and augmented Lagrangian relaxation techniques are among the most popular techniques but convergence due to nonlinearity of the problem is a major issue. Furthermore, the combinatorial nature of the problem and its multi-period characteristics prevented exact approaches from being successfully used in practice: they resulted in very inefficient algorithms that were only capable of solving small size instances of no practical interest. Metaheuristics D. F. Rahman INESC TEC (formerly INESC Porto), Porto, Portugal e-mail: [email protected] A. Viana (B) School of Engineering, Polytechnic Institute of Porto and INESC TEC (formerly INESC Porto), Porto, Portugal e-mail: [email protected] J. P. Pedroso Department of Computer Science, Faculty of Sciences, University of Porto and INESC TEC (formerly INESC Porto), Porto, Portugal e-mail: [email protected] S. Helber et al. (eds.), Operations Research Proceedings 2012, Operations Research Proceedings, DOI: 10.1007/978-3-319-00795-3_23, © Springer International Publishing Switzerland 2014
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algorithms have also been used. A survey on different optimization techniques and modeling issues is provided in [2]. Lately, improvements made on Mixed Integer Linear Programming (MILP) solvers led to increasing research on MILP techniques for the thermal problem [1, 4, 7, 8]. In [8] the authors proposed a MILP-based procedure for thermal unit commitment that is able to converge to optimality, even for large size problems. In this paper we extend the procedure proposed in [8] to solve the HSP. Furthermore, we use the concept of “Matheuristics”, an optimization technique that integrates (meta)heuristics and MILP strategies to try to speed up convergence of the base iterative method. Two matheuristic approaches are explored: one based on “Local Branching” [3] and another where a “Particle Swarm Optimization” (PSO) algorithm cooperates with the MILP solver. All the proposed approaches were tested on several benchmark instances always converging to the optimal solution. Also worth mentioning that the CPU times necessary for the matheuristics to converge to optimality were not smaller than the time
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