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Alternative models for markets with nonconvexities

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  • David Fuller, J.
  • Çelebi, Emre

Abstract

In many electricity markets, the market operator solves a social welfare maximization (SW) model to determine market prices and generation (and consumption) “dispatch” instructions to firms participating in the market. When generation costs (or consumption benefits) are described as mixed integer programs, linear prices cannot, in general, be found such that all market participants are satisfied that the operator’s dispatch instructions maximize profits, i.e., they perceive an opportunity cost. Often, “make whole” payments are made to market participants to bring negative profits up to zero, but not to adjust positive, nonoptimal profits. Make whole payments are added to “uplift” charges to customers for various non-market services provided by market participants. In previous research, “uplift” is extended to include the entire opportunity costs, and prices are adjusted to minimize the part of uplift that is due to discrete variables, while keeping the SW quantity instructions. We show that the SW instructions must be modified if the non-dispatchable demand is price sensitive; to allow for this, we define a model that minimizes total opportunity cost (MTOC), and we compare it to three other models – SW, SW with non-negative profit constraints, and a minimum complementarity (MC) model recently proposed by Gabriel et al. We show that the MC model approximates the MTOC model. Two unit commitment problems illustrate the models . In an online appendix, we also present small MTOC and MC two-commodity models for which an SW model cannot be formulated due to nonintegrability of demand.

Suggested Citation

  • David Fuller, J. & Çelebi, Emre, 2017. "Alternative models for markets with nonconvexities," European Journal of Operational Research, Elsevier, vol. 261(2), pages 436-449.
  • Handle: RePEc:eee:ejores:v:261:y:2017:i:2:p:436-449
    DOI: 10.1016/j.ejor.2017.02.032
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    References listed on IDEAS

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    1. Steven A. Gabriel & Antonio J. Conejo & J. David Fuller & Benjamin F. Hobbs & Carlos Ruiz, 2013. "Complementarity Modeling in Energy Markets," International Series in Operations Research and Management Science, Springer, edition 127, number 978-1-4419-6123-5, April.
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    Cited by:

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    2. Villalobos, Cristian & Negrete-Pincetic, Matías & Figueroa, Nicolás & Lorca, Álvaro & Olivares, Daniel, 2021. "The impact of short-term pricing on flexible generation investments in electricity markets," Energy Economics, Elsevier, vol. 98(C).
    3. Hesamzadeh, M. & Holmberg, P. & Sarfati, M., 2018. "Simulation and Evaluation of Zonal Electricity Market Designs," Cambridge Working Papers in Economics 1829, Faculty of Economics, University of Cambridge.
    4. Grimm, Veronika & Grübel, Julia & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2019. "Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1097-1108.
    5. Vadim Borokhov, 2022. "Utilizing the redundant constraints for the uplift payment elimination," Operational Research, Springer, vol. 22(2), pages 1377-1402, April.
    6. Fuller, J. David & Pirnia, Mehrdad, 2022. "Nonconvex multicommodity near equilibrium models: Energy markets perspective," Operations Research Perspectives, Elsevier, vol. 9(C).
    7. Shavandi, Hassan & Pirnia, Mehrdad & Fuller, J. David, 2019. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Applied Energy, Elsevier, vol. 240(C), pages 251-264.
    8. Dimitri J. Papageorgiou & Francisco Trespalacios & Stuart Harwood, 2021. "A Note on Solving Discretely-Constrained Nash-Cournot Games via Complementarity," Networks and Spatial Economics, Springer, vol. 21(2), pages 325-330, June.
    9. Hassan Shavandi & Mehrdad Pirnia & J. David Fuller, 2018. "Extended opportunity cost model to find near equilibrium electricity prices under non-convexities," Papers 1809.09734, arXiv.org.

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