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.
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Acknowledgements
We acknowledge the following people who have assisted significantly in this research. James Milford of the National Renewable Energy Lab (NREL) introduced us to this problem. Dr. Greg Brinkman, also of NREL, provided guidance regarding data collection and analysis. Dónal O’Sullivan of the Colorado School of Mines helped with the initial coding efforts. Ryan Bracken and Maureen McDaniel, also of the Colorado School of Mines, gathered and cleaned data. Professor Luis Tenorio of the Colorado School of Mines provided suggestions for categorizing the intervals of the heat input curves. Dr. Sven Leyffer of Argonne National Labs provided general nonlinear programming recommendations. Jennifer Van Dinter was generously supported by NREL grant number KXEA-3-33607-53.
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Van Dinter, J., Rebennack, S., Kallrath, J. et al. The unit commitment model with concave emissions costs: a hybrid Benders’ Decomposition with nonconvex master problems. Ann Oper Res 210, 361–386 (2013). https://doi.org/10.1007/s10479-012-1102-9
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DOI: https://doi.org/10.1007/s10479-012-1102-9