Abstract
This paper is concerned with 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. We propose an L-shaped algorithm to solve the problem.
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References
D. Anderson, Models for determining least-cost investments in electricity supply. Bell J. Econom. Management Sci.,3 (1972), 267–301.
J.R. Birge, Decomposition and partitioning methods for multistage stochastic linear programs. Oper. Res.,33 (1985), 989–1007.
J.R. Birge, Stochastic programming computation and applications. INFORMS J. Comput.,9 (1997), 111–133.
J.R. Birge and F. Louveaux, Introduction to Stochastic Programming. Springer-Verlag, 1997.
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. Math. Programming,75 (1996), 327–352.
W.D. Dapkus and T.R. Bowe, Planning for new electric generation technologies — a stochastic dynamic programming approach —. IEEE Trans. Power Appar. Syst.,PAS-103 (1984), 1447–1453.
J.K. Delson and S.M. Shahidehpour, Linear programming applications to power system economics, planning and operations. IEEE Trans. Power Syst.,7 (1992), 1155–1163.
R. Fourer, D.M. Gay and B.W. Kernighan, AMPL: A Modeling Langage for Mathematical Programming. Scientific Press, 1993.
K. Frauendorfer, H. Glavitsch and R. Bacher, Optimization in Planning and Operation of Electric Power Systems. Springer-Verlag, 1993.
B.G. Gorenstin, N.M. Campodonico, J.P. Costa and M.V.F. Pereira, Power system expansion planning under uncertainty. IEEE Trans. Power Syst.,8 (1993), 129–136.
M. Kleinpeter, Energy Planning and Policy. John Wiley & Sons, 1995.
F.V. Louveaux, A solution method for multistage stochastic programs with recourse, with application to an energy investment problem. Oper. Res.,28 (1980), 889–902.
F.V. Louveaux, Multistage stochastic programs with block-separable recourse. Math. Programming Stud.,28 (1986), 48–62.
F.H. Murphy, S. Sen and A.L. Soyster, Electric utility capacity expansion planning with uncertain load forecasts. HE Trans.,14 (1982), 52–59.
T. Shiina, Numerical solution technique for joint chance constrained programming problem — an application to electric power capacity expansion —. J. Oper. Res. Soc. Japan,42 (1999), 128–140.
T. Shiina, L-shaped decomposition method for multi-stage stochastic concentrator location problem. J. Oper. Res. Soc. Japan,43 (2000), 317–332.
T. Shiina, Stochastic programming model for the design of computer network (in Japanese). Trans. Japan Soc. Indust. Appl. Math.,10 (2000), 37–50.
R. Van Slyke and R.J.-B. Wets, L-shaped linear programs with applications to optimal control and stochastic linear programs. SIAM J. Appl. Math.,17 (1969), 638–663.
A.J. Wood and B.J. Wollenberg, Power Generation, Operation and Control. John Wiley & Sons, 1996.
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Shiina, T., Birge, J.R. Multistage stochastic programming model for electric power capacity expansion problem. Japan J. Indust. Appl. Math. 20, 379–397 (2003). https://doi.org/10.1007/BF03167428
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DOI: https://doi.org/10.1007/BF03167428