A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

Shinde, Priyanka; Aravena, Ignacio

doi:10.1016/j.ejor.2025.06.002

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

Journal Article · Mon Jun 30 00:00:00 EDT 2025 · European Journal of Operational Research

DOI:https://doi.org/10.1016/j.ejor.2025.06.002· OSTI ID:3004154

Shinde, Priyanka ^[1]; Aravena, Ignacio ^[2]

KTH Royal Inst. of Technology, Stockholm (Sweden)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 3004154

Report Number(s):: LLNL--JRNL-867722

Journal Information:: European Journal of Operational Research, Journal Name: European Journal of Operational Research Journal Issue: 3 Vol. 328; ISSN 0377-2217

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (48)

Applications of Bilevel Optimization in Energy and Electricity Markets Wogrin, Sonja; Pineda, Salvador; Tejada-Arango, Diego A. Bilevel Optimization https://doi.org/10.1007/978-3-030-52119-6_5	book	January 2020
Multi-stage stochastic optimization applied to energy planning Pereira, M. V. F.; Pinto, L. M. V. G. Mathematical Programming, Vol. 52, Issue 1-3 https://doi.org/10.1007/BF01582895	journal	May 1991
Optimal bidding functions for renewable energies in sequential electricity markets Finnah, Benedikt OR Spectrum, Vol. 44, Issue 1 https://doi.org/10.1007/s00291-021-00646-9	journal	July 2021
Day-ahead market bidding for a Nordic hydropower producer: taking the Elbas market into account Faria, Eduardo; Fleten, Stein-Erik Computational Management Science, Vol. 8, Issue 1-2 https://doi.org/10.1007/s10287-009-0108-5	journal	September 2009
Randomized Progressive Hedging methods for multi-stage stochastic programming Bareilles, Gilles; Laguel, Yassine; Grishchenko, Dmitry Annals of Operations Research, Vol. 295, Issue 2 https://doi.org/10.1007/s10479-020-03811-5	journal	September 2020
A deep reinforcement learning framework for continuous intraday market bidding Boukas, Ioannis; Ernst, Damien; Théate, Thibaut Machine Learning, Vol. 110, Issue 9 https://doi.org/10.1007/s10994-021-06020-8	journal	July 2021
Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme Lara, Cristiana L.; Siirola, John D.; Grossmann, Ignacio E. Optimization and Engineering, Vol. 21, Issue 4 https://doi.org/10.1007/s11081-019-09471-0	journal	October 2019
An optimal trading problem in intraday electricity markets Aïd, René; Gruet, Pierre; Pham, Huyên Mathematics and Financial Economics, Vol. 10, Issue 1 https://doi.org/10.1007/s11579-015-0150-8	journal	July 2015
Sampling strategies and stopping criteria for stochastic dual dynamic programming: a case study in long-term hydrothermal scheduling Homem-de-Mello, Tito; de Matos, Vitor L.; Finardi, Erlon C. Energy Systems, Vol. 2, Issue 1 https://doi.org/10.1007/s12667-011-0024-y	journal	January 2011
Portfolio size’s effects on gains from coordinated bidding in electricity markets Kongelf, Håkon; Overrein, Kristoffer; Klæboe, Gro Energy Systems, Vol. 10, Issue 3 https://doi.org/10.1007/s12667-018-0294-8	journal	June 2018
Bilevel programming for price-based electricity auctions: a revenue-constrained case Fernández-Blanco, Ricardo; Arroyo, JoséM.; Alguacil, Natalia EURO Journal on Computational Optimization, Vol. 3, Issue 3 https://doi.org/10.1007/s13675-015-0037-8	journal	September 2015
Integrated European intra-day electricity market: Rules, modeling and analysis Le, Hong Lam; Ilea, Valentin; Bovo, Cristian Applied Energy, Vol. 238 https://doi.org/10.1016/j.apenergy.2018.12.073	journal	March 2019
A Multi-agent Model for Cross-border Trading in the Continuous Intraday Electricity Market Shinde, Priyanka; Gamberi, Giulia; Amelin, Mikael Energy Reports, Vol. 9 https://doi.org/10.1016/j.egyr.2023.05.070	journal	December 2023
Bidding in sequential electricity markets: The Nordic case Boomsma, Trine Krogh; Juul, Nina; Fleten, Stein-Erik European Journal of Operational Research, Vol. 238, Issue 3 https://doi.org/10.1016/j.ejor.2014.04.027	journal	November 2014
Generation flexibility in ramp rates: Strategic behavior and lessons for electricity market design Moiseeva, Ekaterina; Wogrin, Sonja; Hesamzadeh, Mohammad Reza European Journal of Operational Research, Vol. 261, Issue 2 https://doi.org/10.1016/j.ejor.2017.02.028	journal	September 2017
Modeling time-dependent randomness in stochastic dual dynamic programming Löhndorf, Nils; Shapiro, Alexander European Journal of Operational Research, Vol. 273, Issue 2 https://doi.org/10.1016/j.ejor.2018.08.001	journal	March 2019
Optimal bidding of a virtual power plant on the Spanish day-ahead and intraday market for electricity Wozabal, David; Rameseder, Gunther European Journal of Operational Research, Vol. 280, Issue 2 https://doi.org/10.1016/j.ejor.2019.07.022	journal	January 2020
Multistage stochastic demand-side management for price-making major consumers of electricity in a co-optimized energy and reserve market Habibian, Mahbubeh; Downward, Anthony; Zakeri, Golbon European Journal of Operational Research, Vol. 280, Issue 2 https://doi.org/10.1016/j.ejor.2019.07.037	journal	January 2020
Strategic offering of a flexible producer in day-ahead and intraday power markets Rintamäki, Tuomas; Siddiqui, Afzal S.; Salo, Ahti European Journal of Operational Research, Vol. 284, Issue 3 https://doi.org/10.1016/j.ejor.2020.01.044	journal	August 2020
Gas storage valuation in incomplete markets Löhndorf, Nils; Wozabal, David European Journal of Operational Research, Vol. 288, Issue 1 https://doi.org/10.1016/j.ejor.2020.05.044	journal	January 2021
A complementarity model for electric power transmission-distribution coordination under uncertainty Hermann, Alexander; Jensen, Tue Vissing; Østergaard, Jacob European Journal of Operational Research, Vol. 299, Issue 1 https://doi.org/10.1016/j.ejor.2021.08.018	journal	May 2022
Integrated day-ahead and intraday self-schedule bidding for energy storage systems using approximate dynamic programming Finnah, Benedikt; Gönsch, Jochen; Ziel, Florian European Journal of Operational Research, Vol. 301, Issue 2 https://doi.org/10.1016/j.ejor.2021.11.010	journal	September 2022
Energy storage operation and electricity market design: On the market power of monopolistic storage operators Bjørndal, Endre; Bjørndal, Mette Helene; Coniglio, Stefano European Journal of Operational Research, Vol. 307, Issue 2 https://doi.org/10.1016/j.ejor.2022.09.012	journal	June 2023
Stochastic optimization of trading strategies in sequential electricity markets Kraft, Emil; Russo, Marianna; Keles, Dogan European Journal of Operational Research, Vol. 308, Issue 1 https://doi.org/10.1016/j.ejor.2022.10.040	journal	July 2023
Can the European intraday market be designed as a congestion management tool? Alangi, Somayeh Rahimi; Bjørndal, Endre; Bjørndal, Mette Energy Economics, Vol. 113 https://doi.org/10.1016/j.eneco.2022.106171	journal	September 2022
Optimal scheduling of industrial combined heat and power plants under time-sensitive electricity prices Mitra, Sumit; Sun, Lige; Grossmann, Ignacio E. Energy, Vol. 54 https://doi.org/10.1016/j.energy.2013.02.030	journal	June 2013
Applying different decomposition schemes using the progressive hedging algorithm to the operation planning problem of a hydrothermal system Gonçalves, Raphael E. C.; Finardi, Erlon Cristian; Silva, Edson Luiz da Electric Power Systems Research, Vol. 83, Issue 1 https://doi.org/10.1016/j.epsr.2011.09.006	journal	February 2012
Risk-averse stochastic dual dynamic programming approach for the operation of a hydro-dominated power system in the presence of wind uncertainty Morillo, José L.; Zéphyr, Luckny; Pérez, Juan F. International Journal of Electrical Power & Energy Systems, Vol. 115 https://doi.org/10.1016/j.ijepes.2019.105469	journal	February 2020
Optimizing trading decisions of wind power plants with hybrid energy storage systems using backwards approximate dynamic programming Finnah, Benedikt; Gönsch, Jochen International Journal of Production Economics, Vol. 238 https://doi.org/10.1016/j.ijpe.2021.108155	journal	August 2021
Internal hydro- and wind portfolio optimisation in real-time market operations Riddervold, Hans Ole; Aasgård, Ellen Krohn; Haukaas, Lisa Renewable Energy, Vol. 173 https://doi.org/10.1016/j.renene.2021.04.001	journal	August 2021
Stochastic Optimization of a Multireservoir Hydroelectric System: A Decomposition Approach Pereira, M. V. F.; Pinto, L. M. V. G. Water Resources Research, Vol. 21, Issue 6 https://doi.org/10.1029/WR021i006p00779	journal	June 1985
Multi‐stage stochastic long‐term planning of grid‐connected hydrogen‐based energy system based on improved SDDIP Cao, Binrui; Wu, Xiong; Liu, Bingwen IET Generation, Transmission & Distribution, Vol. 17, Issue 13 https://doi.org/10.1049/gtd2.12863	journal	June 2023
Applying High Performance Computing to Transmission-Constrained Stochastic Unit Commitment for Renewable Energy Integration Papavasiliou, Anthony; Oren, Shmuel S.; Rountree, Barry IEEE Transactions on Power Systems, Vol. 30, Issue 3 https://doi.org/10.1109/TPWRS.2014.2341354	journal	May 2015
On the Solution of Revenue- and Network-Constrained Day-Ahead Market Clearing Under Marginal Pricing—Part I: An Exact Bilevel Programming Approach Fernandez-Blanco, Ricardo; Arroyo, Jose M.; Alguacil, Natalia IEEE Transactions on Power Systems, Vol. 32, Issue 1 https://doi.org/10.1109/TPWRS.2016.2551046	journal	January 2017
Multistage Stochastic Investment Planning With Multiscale Representation of Uncertainties and Decisions Liu, Yixian; Sioshansi, Ramteen; Conejo, Antonio J. IEEE Transactions on Power Systems, Vol. 33, Issue 1 https://doi.org/10.1109/TPWRS.2017.2694612	journal	January 2018
Multistage Stochastic Unit Commitment Using Stochastic Dual Dynamic Integer Programming Zou, Jikai; Ahmed, Shabbir; Sun, Xu Andy IEEE Transactions on Power Systems, Vol. 34, Issue 3 https://doi.org/10.1109/TPWRS.2018.2880996	journal	May 2019
Adaptive Trading in Continuous Intraday Electricity Markets for a Storage Unit Bertrand, Gilles; Papavasiliou, Anthony IEEE Transactions on Power Systems, Vol. 35, Issue 3 https://doi.org/10.1109/TPWRS.2019.2957246	journal	May 2020
Application of Stochastic Dual Dynamic Programming to the Real-Time Dispatch of Storage Under Renewable Supply Uncertainty Papavasiliou, Anthony; Mou, Yuting; Cambier, Leopold IEEE Transactions on Sustainable Energy, Vol. 9, Issue 2 https://doi.org/10.1109/TSTE.2017.2748463	journal	April 2018
Multistage Stochastic Programming for VPP Trading in Continuous Intraday Electricity Markets Shinde, Priyanka; Kouveliotis-Lysikatos, Iasonas; Amelin, Mikael IEEE Transactions on Sustainable Energy, Vol. 13, Issue 2 https://doi.org/10.1109/TSTE.2022.3144022	journal	April 2022
Optimal Hour-Ahead Bidding in the Real-Time Electricity Market with Battery Storage Using Approximate Dynamic Programming Jiang, Daniel R.; Powell, Warren B. INFORMS Journal on Computing, Vol. 27, Issue 3 https://doi.org/10.1287/ijoc.2015.0640	journal	August 2015
Multistage Stochastic Power Generation Scheduling Co-Optimizing Energy and Ancillary Services Huang, Jianqiu; Pan, Kai; Guan, Yongpei INFORMS Journal on Computing, Vol. 33, Issue 1 https://doi.org/10.1287/ijoc.2019.0933	journal	January 2021
Combining Polyhedral Approaches and Stochastic Dual Dynamic Integer Programming for Solving the Uncapacitated Lot-Sizing Problem Under Uncertainty Quezada, Franco; Gicquel, Céline; Kedad-Sidhoum, Safia INFORMS Journal on Computing, Vol. 34, Issue 2 https://doi.org/10.1287/ijoc.2021.1118	journal	March 2022
Integrated Stochastic Optimal Self-Scheduling for Two-Settlement Electricity Markets Pan, Kai; Guan, Yongpei INFORMS Journal on Computing, Vol. 34, Issue 3 https://doi.org/10.1287/ijoc.2021.1150	journal	May 2022
Scenarios and Policy Aggregation in Optimization Under Uncertainty Rockafellar, R. T.; Wets, Roger J. -B. Mathematics of Operations Research, Vol. 16, Issue 1 https://doi.org/10.1287/moor.16.1.119	journal	February 1991
Optimizing Trading Decisions for Hydro Storage Systems Using Approximate Dual Dynamic Programming Löhndorf, Nils; Wozabal, David; Minner, Stefan Operations Research, Vol. 61, Issue 4 https://doi.org/10.1287/opre.2013.1182	journal	August 2013
Multistage Adaptive Robust Optimization for the Unit Commitment Problem Lorca, Álvaro; Sun, X. Andy; Litvinov, Eugene Operations Research, Vol. 64, Issue 1 https://doi.org/10.1287/opre.2015.1456	journal	February 2016
Strong Formulations for Multistage Stochastic Self-Scheduling Unit Commitment Pan, Kai; Guan, Yongpei Operations Research, Vol. 64, Issue 6 https://doi.org/10.1287/opre.2016.1520	journal	December 2016
Analyzing Trade in Continuous Intra-Day Electricity Market: An Agent-Based Modeling Approach Shinde, Priyanka; Boukas, Ioannis; Radu, David Energies, Vol. 14, Issue 13 https://doi.org/10.3390/en14133860	journal	June 2021

Similar Records

Mitigation-Aware Bidding Strategies in Electricity Markets

Conference · Sun Jul 16 00:00:00 EDT 2023 · OSTI ID:1989808

A Bilevel Approach for Identifying the Worst Contingencies for Nonconvex Alternating Current Power Systems

Journal Article · Wed Feb 24 23:00:00 EST 2021 · SIAM Journal on Optimization · OSTI ID:1798035

Related Subjects

Bilevel multistage stochastic programming problem
Continuous intraday electricity market
Convex hull
Stochastic dual dynamic integer programming
Stochastic programming

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

Citation Formats

References (48)

Similar Records

Related Subjects