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The unit commitment model with concave emissions costs: a hybrid Benders’ Decomposition with nonconvex master problems

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  • Jennifer Dinter
  • Steffen Rebennack
  • Josef Kallrath
  • Paul Denholm
  • Alexandra Newman

Abstract

We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders’ master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs; the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders’ Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Jennifer Dinter & Steffen Rebennack & Josef Kallrath & Paul Denholm & Alexandra Newman, 2013. "The unit commitment model with concave emissions costs: a hybrid Benders’ Decomposition with nonconvex master problems," Annals of Operations Research, Springer, vol. 210(1), pages 361-386, November.
    • Handle: RePEc:spr:annopr:v:210:y:2013:i:1:p:361-386:10.1007/s10479-012-1102-9
    DOI: 10.1007/s10479-012-1102-9
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    References listed on IDEAS

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    1. Niknam, Taher & Khodaei, Amin & Fallahi, Farhad, 2009. "A new decomposition approach for the thermal unit commitment problem," Applied Energy, Elsevier, vol. 86(9), pages 1667-1674, September.
    2. Tuohy, Aidan & Meibom, Peter & Denny, Eleanor & O'Malley, Mark, 2009. "Unit commitment for systems with significant wind penetration," MPRA Paper 34849, University Library of Munich, Germany.
    3. Sioshansi, Ramteen & Denholm, Paul & Jenkin, Thomas & Weiss, Jurgen, 2009. "Estimating the value of electricity storage in PJM: Arbitrage and some welfare effects," Energy Economics, Elsevier, vol. 31(2), pages 269-277, March.
    4. Samer Takriti & Benedikt Krasenbrink & Lilian S.-Y. Wu, 2000. "Incorporating Fuel Constraints and Electricity Spot Prices into the Stochastic Unit Commitment Problem," Operations Research, INFORMS, vol. 48(2), pages 268-280, April.
    5. Ralf Gollmer & Matthias Nowak & Werner Römisch & Rüdiger Schultz, 2000. "Unit commitment in power generation – a basic model and some extensions," Annals of Operations Research, Springer, vol. 96(1), pages 167-189, November.
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    Cited by:

    1. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    2. Richard Li-Yang Chen & Neng Fan & Ali Pinar & Jean-Paul Watson, 2017. "Contingency-constrained unit commitment with post-contingency corrective recourse," Annals of Operations Research, Springer, vol. 249(1), pages 381-407, February.
    3. Linghu, Dazhi & Wu, Xilin & Lai, Kee-Hung & Ye, Fei & Kumar, Ajay & Tan, Kim Hua, 2022. "Implementation strategy and emission reduction effectiveness of carbon cap-and-trade in heterogeneous enterprises," International Journal of Production Economics, Elsevier, vol. 248(C).
    4. Scioletti, Michael S. & Goodman, Johanna K. & Kohl, Paul A. & Newman, Alexandra M., 2016. "A physics-based integer-linear battery modeling paradigm," Applied Energy, Elsevier, vol. 176(C), pages 245-257.

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