Stochastic Programming Model for Power Generation

Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1084786

References:

[1] J. R. Birge, Decomposition and partitioning methods for multistage stochastic linear programs. Operations Research, 33(1985) 989-1007.
[2] J. R. Birge, Stochastic programming computation and applications. INFORMS Journal on Computing, 9(1997) 111-133.
[3] J. R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer-Verlag, 1997.
[4] J. R. Birge, C. J. Donohue, D. F. Holmes and O. G. Svintsitski, A parallel implementation of the nested decomposition algorithm for multistage stochastic linear programs. Mathematical Programming, 75(1996) 327- 352.
[5] R. Fourer, D. M. Gay and B. W. Kernighan, AMPL: A Modeling Langage for Mathematical Programming. Scientific Press, 1993.
[6] F. V. Louveaux, A solution method for multistage stochastic programs with recourse, with application to an energy investment problem. Operations Research, 28(1980) 889-902.
[7] F. V. Louveaux, Multistage stochastic programs with block-separable recourse. Mathematical Programming Study, 28(1986) 48-62.
[8] T. Shiina, L-shaped decomposition method for multi-stage stochastic concentrator location problem. Journal of the Operations Research Society of Japan, 43(2000) 317-332.
[9] T. Shiina, Stochastic programming model for the design of computer network (in Japanese). Transactions of the Japan Society for Industrial and Applied Mathematics, 10(2000) 37-50.
[10] R. Van Slyke and R. J.-B. Wets, L-shaped linear programs with applications to optimal control and stochastic linear programs. SIAM Journal on Applied Mathematics, 17(1969) 638-663.