Annals of Operations Research

, Volume 210, Issue 1, pp 361–386

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

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

DOI: 10.1007/s10479-012-1102-9

Cite this article as:
Van Dinter, J., Rebennack, S., Kallrath, J. et al. Ann Oper Res (2013) 210: 361. doi:10.1007/s10479-012-1102-9

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.

Keywords

Integer programming applications Unit commitment model Power systems Benders’ Decomposition Spinning reserves Mixed integer nonlinear programming Storage Renewables Convex underestimators 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Jennifer Van Dinter
    • 1
  • Steffen Rebennack
    • 1
  • Josef Kallrath
    • 2
  • Paul Denholm
    • 3
  • Alexandra Newman
    • 1
  1. 1.Division of Economics and BusinessColorado School of MinesGoldenUSA
  2. 2.Department of AstronomyUniversity of FloridaGainesvilleUSA
  3. 3.Energy Forecasting and Modeling GroupNational Renewable Energy Laboratory (NREL)GoldenUSA

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