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Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment

Author

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  • Kai Pan

    (Department of Logistics and Maritime Studies, Faculty of Business, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong)

  • Yongpei Guan

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

Abstract

With the increasing penetration of renewable energy into the power grid system, the volatility of real-time electricity prices increases significantly. This brings challenges for independent power producers to provide optimal bidding strategies. The traditional approaches of only attending the day-ahead market might not be profitable enough without taking advantage of real-time price volatility. In this paper, we study the optimal bidding strategies for the independent power producers utilizing self-scheduling strategies to participate in the real-time market considering real-time electricity price volatility, with the objective of maximizing the total expected profit. Considering the correlations of renewable energy generation outputs among different time periods, the correlations of real-time prices are captured in our modeling framework, in which we explore a multistage stochastic scenario tree to formulate the price uncertainties. Accordingly, the derived multistage stochastic self-scheduling unit commitment problem is transformed as a deterministic equivalent mixed-integer linear programming formulation. To overcome the curse of dimensionality, we develop strong valid inequalities for the derived stochastic unit commitment polytope to speed up the algorithms to solve the problem. In particular, we derive strong valid inequalities that can provide the convex hull descriptions for the two-period case and a special class of the three-period cases with rigorous proofs provided. Furthermore, strong valid inequalities, including facet-defining proofs, for multistage cases are proposed to further strengthen the model. Finally, numerical experiments verify the effectiveness of our derived strong valid inequalities by incorporating them in a branch-and-cut framework.

Suggested Citation

  • Kai Pan & Yongpei Guan, 2016. "Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment," Operations Research, INFORMS, vol. 64(6), pages 1482-1498, December.
    • Handle: RePEc:inm:oropre:v:64:y:2016:i:6:p:1482-1498
    DOI: 10.1287/opre.2016.1520
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    References listed on IDEAS

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    1. Santiago Cerisola & Álvaro Baíllo & José M. Fernández-López & Andrés Ramos & Ralf Gollmer, 2009. "Stochastic Power Generation Unit Commitment in Electricity Markets: A Novel Formulation and a Comparison of Solution Methods," Operations Research, INFORMS, vol. 57(1), pages 32-46, February.
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