A constraint generation scheme to probabilistic linear problems with an application to power system expansion planning |
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Authors: | Cristina M A Leopoldino Mário V F Pereira Leontina M V Pinto Celso C Ribeiro |
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Institution: | (1) Department of Electrical Engineering, Catholic University of Rio de Janeiro, P.O. Box 38063, 22452 Rio de Janeiro, Brazil;(2) Power Systems Research, Inc., Rua Alberto de Campos 250, 22471 Rio de Janeiro, Brazil;(3) Department of Computer Science, Catholic University of Rio de Janeiro, Rua Marquês de São Vicente 225, 22453 Rio de Janeiro, Brazil |
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Abstract: | In this paper, we first describe a constraint generation scheme for probabilistic mixed integer programming problems. Next, we present a decomposition approach to the peak capacity expansion planning of interconnected hydrothermal generating systems, with bounds on the transmission capacity between the regions. The objective is to minimize investments in generating units and interconnection links, subject to constraints on supply reliability. The problem is formulated as a stochastic integer program. The constraint generation scheme, which is similar to Benders decomposition, is applied in the solution of the peak capacity expansion problem. The master problem in this decomposition scheme is an integer program, solved by implicit enumeration. The operating subproblem corresponds to a stochastic network flow problem, and is solved by a maximum flow algorithm and Monte Carlo simulation. The approach is illustrated through a case study involving the expansion of the system of the Brazilian Southeastern region. |
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Keywords: | Peak expansion hydrothermal systems reliability constraint generation Benders decomposition cutting planes Monte Carlo simulation |
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