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On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management

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  • Tamás Kis

    (EPIC Center of Excellence in Production Informatics and Control, Institute for Computer Science and Control (SZTAKI), Eötvös Loránd Research Network (ELKH), Kende u. 13-17, 1111 Budapest, Hungary)

  • András Kovács

    (EPIC Center of Excellence in Production Informatics and Control, Institute for Computer Science and Control (SZTAKI), Eötvös Loránd Research Network (ELKH), Kende u. 13-17, 1111 Budapest, Hungary)

  • Csaba Mészáros

    (EPIC Center of Excellence in Production Informatics and Control, Institute for Computer Science and Control (SZTAKI), Eötvös Loránd Research Network (ELKH), Kende u. 13-17, 1111 Budapest, Hungary)

Abstract

This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in the field. That is, the overwhelming majority of existing research deals with the so-called optimistic variant of the problem where, in case of multiple optimal consumption schedules for a consumer (follower), the consumer chooses an optimal schedule that is the most favorable for the electricity retailer (leader). However, this assumption is usually illegitimate in practice; as a result, consumers may easily deviate from their expected behavior during realization, and the retailer suffers significant losses. One way out is to solve the pessimistic variant instead, where the retailer prepares for the least favorable optimal responses from the consumers. The main contribution of the paper is an exact procedure for solving the pessimistic variant of the problem. First, key properties of optimal solutions are formally proven and efficiently solvable special cases are identified. Then, a detailed investigation of the optimistic and pessimistic variants of the problem is presented. It is demonstrated that the set of optimal consumption schedules typically contains various responses that are equal for the follower, but bring radically different profits for the leader. The main procedure for solving the pessimistic variant reduces the problem to solving the optimistic variant with slightly perturbed problem data. A numerical case study shows that the optimistic solution may perform poorly in practice, while the pessimistic solution gives very close to the highest profit that can be achieved theoretically. To the best of the authors’ knowledge, this paper is the first to propose an exact solution approach for the pessimistic variant of the problem.

Suggested Citation

  • Tamás Kis & András Kovács & Csaba Mészáros, 2021. "On Optimistic and Pessimistic Bilevel Optimization Models for Demand Response Management," Energies, MDPI, vol. 14(8), pages 1-22, April.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:8:p:2095-:d:533008
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    References listed on IDEAS

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    1. Jalali, Mehdi & Zare, Kazem & Seyedi, Heresh, 2017. "Strategic decision-making of distribution network operator with multi-microgrids considering demand response program," Energy, Elsevier, vol. 141(C), pages 1059-1071.
    2. de Souza Dutra, Michael David & Alguacil, Natalia, 2020. "Optimal residential users coordination via demand response: An exact distributed framework," Applied Energy, Elsevier, vol. 279(C).
    3. Yu, Mengmeng & Hong, Seung Ho, 2016. "Supply–demand balancing for power management in smart grid: A Stackelberg game approach," Applied Energy, Elsevier, vol. 164(C), pages 702-710.
    4. Qi Zhang & Shaohua Zhang & Xian Wang & Xue Li & Lei Wu, 2020. "Conditional-Robust-Profit-Based Optimization Model for Electricity Retailers with Shiftable Demand," Energies, MDPI, vol. 13(6), pages 1-19, March.
    5. Jerome Bracken & James T. McGill, 1973. "Mathematical Programs with Optimization Problems in the Constraints," Operations Research, INFORMS, vol. 21(1), pages 37-44, February.
    6. Ah-Yun Yoon & Hyun-Koo Kang & Seung-II Moon, 2020. "Optimal Price Based Demand Response of HVAC Systems in Commercial Buildings Considering Peak Load Reduction," Energies, MDPI, vol. 13(4), pages 1-20, February.
    7. Bo Zeng, 2020. "A Practical Scheme to Compute the Pessimistic Bilevel Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1128-1142, October.
    8. Wei, F. & Jing, Z.X. & Wu, Peter Z. & Wu, Q.H., 2017. "A Stackelberg game approach for multiple energies trading in integrated energy systems," Applied Energy, Elsevier, vol. 200(C), pages 315-329.
    9. Yelena Vardanyan & Henrik Madsen, 2019. "Stochastic Bilevel Program for Optimal Coordinated Energy Trading of an EV Aggregator," Energies, MDPI, vol. 12(20), pages 1-18, October.
    10. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    11. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2000. "A Bilevel Model and Solution Algorithm for a Freight Tariff-Setting Problem," Transportation Science, INFORMS, vol. 34(3), pages 289-302, August.
    12. Zugno, Marco & Morales, Juan Miguel & Pinson, Pierre & Madsen, Henrik, 2013. "A bilevel model for electricity retailers' participation in a demand response market environment," Energy Economics, Elsevier, vol. 36(C), pages 182-197.
    13. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    14. Xueying Song & Hongyu Lin & Gejirifu De & Hanfang Li & Xiaoxu Fu & Zhongfu Tan, 2020. "An Energy Optimal Dispatching Model of an Integrated Energy System Based on Uncertain Bilevel Programming," Energies, MDPI, vol. 13(2), pages 1-24, January.
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    3. Samy Faddel & Guanyu Tian & Qun Zhou, 2021. "Decentralized Management of Commercial HVAC Systems," Energies, MDPI, vol. 14(11), pages 1-18, May.

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