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Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power System

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  • Benjamin F. Hobbs

    (Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, Maryland 21218)

  • Yuandong Ji

    (Operations Simulation Associates, Ringgold, Georgia 30376)

Abstract

A bounding-based method is developed for estimating the expected operation cost of a multiarea electric power system in which transmission capacity limits interarea flows. Costs include the expense of power generation and losses suffered by consumers because of supply shortfalls, averaged over random generator outage states and varying demand levels. The calculation of this expectation, termed the distribution problem , is a large-scale stochastic programming problem. Rather than solving this problem directly, lower and upper bounds to the expected cost are created using two more easily solved models. The lower bound is from a deterministic model based on the expected value of the uncertain inputs. The upper bound results from a linear program with recourse whose structure permits relatively quick solution by Benders decomposition. The Benders subproblems use probabilistic production costing, which can be viewed as a stochastic greedy algorithm, to consider random outages and demands. These bounds are iteratively tightened by partitioning realizations of the random variables into subsets based on the status of larger generators and a cluster analysis of demands. Computational examples are described and application issues addressed.

Suggested Citation

  • Benjamin F. Hobbs & Yuandong Ji, 1999. "Stochastic Programming-Based Bounding of Expected Production Costs for Multiarea Electric Power System," Operations Research, INFORMS, vol. 47(6), pages 836-848, December.
  • Handle: RePEc:inm:oropre:v:47:y:1999:i:6:p:836-848
    DOI: 10.1287/opre.47.6.836
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    References listed on IDEAS

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    Cited by:

    1. Munoz, F.D. & Hobbs, B.F. & Watson, J.-P., 2016. "New bounding and decomposition approaches for MILP investment problems: Multi-area transmission and generation planning under policy constraints," European Journal of Operational Research, Elsevier, vol. 248(3), pages 888-898.
    2. Märkle-Huß, Joscha & Feuerriegel, Stefan & Neumann, Dirk, 2020. "Cost minimization of large-scale infrastructure for electricity generation and transmission," Omega, Elsevier, vol. 96(C).
    3. Francisco Munoz & Jean-Paul Watson, 2015. "A scalable solution framework for stochastic transmission and generation planning problems," Computational Management Science, Springer, vol. 12(4), pages 491-518, October.
    4. De Jonghe, C. & Hobbs, B. F. & Belmans, R., 2011. "Integrating short-term demand response into long-term investment planning," Cambridge Working Papers in Economics 1132, Faculty of Economics, University of Cambridge.

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