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Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders' Decomposition

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  • Jeremy A. Bloom

    (General Public Utilities Service Corporation, Parsippany, New Jersey)

Abstract

This paper discusses application of generalized Benders' decomposition in a model for planning least-cost investments in electricity generating capacity subject to probabilistic reliability constraints. The planning problem is decomposed into a set of subproblems, each representing the operation of a set of generating plants of fixed capacity in 1 year, and a master problem, representing optimal capacity investments over the entire planning horizon. The subproblems are solved using a procedure called probabilistic simulation, which calculates the expected cost of operating the generating system, the reliability level, and dual multipliers reflecting the value of small changes in the plant capacities. The master problem is a linear program which uses these dual multipliers to approximate the nonlinear cost and reliability functions. The solution to the capacity expansion problem is found by iteratively solving the master problem and the subproblems.

Suggested Citation

  • Jeremy A. Bloom, 1983. "Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders' Decomposition," Operations Research, INFORMS, vol. 31(1), pages 84-100, February.
    • Handle: RePEc:inm:oropre:v:31:y:1983:i:1:p:84-100
    DOI: 10.1287/opre.31.1.84
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    Cited by:

    1. Sajad Aliakbari Sani & Olivier Bahn & Erick Delage & Rinel Foguen Tchuendom, 2022. "Robust Integration of Electric Vehicles Charging Load in Smart Grid’s Capacity Expansion Planning," Dynamic Games and Applications, Springer, vol. 12(3), pages 1010-1041, September.
    2. Timo Lohmann & Michael R. Bussieck & Lutz Westermann & Steffen Rebennack, 2021. "High-Performance Prototyping of Decomposition Methods in GAMS," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 34-50, January.
    3. 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.
    4. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    5. Pöstges, Arne & Weber, Christoph, 2023. "Identifying key elements for adequate simplifications of investment choices – The case of wind energy expansion," Energy Economics, Elsevier, vol. 120(C).
    6. Shen Peng & Jie Jiang, 2021. "Stochastic mathematical programs with probabilistic complementarity constraints: SAA and distributionally robust approaches," Computational Optimization and Applications, Springer, vol. 80(1), pages 153-184, September.
    7. Jikai Zou & Shabbir Ahmed & Xu Andy Sun, 2018. "Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 388-401, May.
    8. A. Marín & J. Salmerón, 2001. "A risk function for the stochastic modeling of electric capacity expansion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(8), pages 662-683, December.
    9. Benjamin Böcker & Robin Leisen & Christoph Weber, "undated". "Optimal capacity adjustments in electricity market models – an iterative approach based on operational margins and the relevant supply stack," EWL Working Papers 1806, University of Duisburg-Essen, Chair for Management Science and Energy Economics.
    10. Rong, Aiying & Lahdelma, Risto, 2007. "Efficient algorithms for combined heat and power production planning under the deregulated electricity market," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1219-1245, January.
    11. Aliakbari Sani, Sajad & Bahn, Olivier & Delage, Erick, 2022. "Affine decision rule approximation to address demand response uncertainty in smart Grids’ capacity planning," European Journal of Operational Research, Elsevier, vol. 303(1), pages 438-455.
    12. Gendreau, Michel & Nossack, Jenny & Pesch, Erwin, 2015. "Mathematical formulations for a 1-full-truckload pickup-and-delivery problem," European Journal of Operational Research, Elsevier, vol. 242(3), pages 1008-1016.
    13. 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.
    14. Ritzenhofen, Ingmar & Birge, John R. & Spinler, Stefan, 2016. "The structural impact of renewable portfolio standards and feed-in tariffs on electricity markets," European Journal of Operational Research, Elsevier, vol. 255(1), pages 224-242.
    15. 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.
    16. Rong, Aiying & Lahdelma, Risto, 2007. "An efficient envelope-based Branch and Bound algorithm for non-convex combined heat and power production planning," European Journal of Operational Research, Elsevier, vol. 183(1), pages 412-431, November.
    17. 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.
    18. Timo Lohmann & Steffen Rebennack, 2017. "Tailored Benders Decomposition for a Long-Term Power Expansion Model with Short-Term Demand Response," Management Science, INFORMS, vol. 63(6), pages 2027-2048, June.
    19. Emmanuel Ogbe & Xiang Li, 2019. "A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 75(3), pages 595-629, November.
    20. Bunn, Derek W. & Oliveira, Fernando S., 2016. "Dynamic capacity planning using strategic slack valuation," European Journal of Operational Research, Elsevier, vol. 253(1), pages 40-50.
    21. Gacitua, L. & Gallegos, P. & Henriquez-Auba, R. & Lorca, Á. & Negrete-Pincetic, M. & Olivares, D. & Valenzuela, A. & Wenzel, G., 2018. "A comprehensive review on expansion planning: Models and tools for energy policy analysis," Renewable and Sustainable Energy Reviews, Elsevier, vol. 98(C), pages 346-360.
    22. Arne Pöstges & Christoph Weber, "undated". "Identifying key elements for adequate simplifications of investment choices - The case of wind energy expansion," EWL Working Papers 2101, University of Duisburg-Essen, Chair for Management Science and Energy Economics.

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