Stochastic Mean Field Game for Strategic Bidding of Consumers in Congested Distribution Networks (2403.11836v1)
Abstract: The rapid increase of photovoltaic cells, batteries, and Electric Vehicles (EVs) in electric grids can result in congested distribution networks. An alternative to enhancing network capacity is a redispatch market, allowing Distribution System Operators (DSOs) to alleviate congested networks by asking energy consumers to change their consumption schedules. However, energy consumers can anticipate the redispatch market outcomes and strategically adjust their bids in the day-ahead market. This behaviour, known as increase-decrease gaming, can result in the exacerbation of congestion and enable energy consumers to gain windfall profits from the DSO. In this paper, we consider a two-stage problem consisting of the day-ahead market (first stage) and redispatch market (second stage). Then, we model the increase-decrease game for large populations of energy consumers in power networks using a stochastic mean field game approach. The agents (energy consumers) maximize their individual welfare in the day-ahead market with anticipation of the redispatch market. We show that all the agent strategies are ordered along their utilities and there exists a unique Nash equilibrium for this game.
- X. Jin, Q. Wu, and H. Jia, “Local flexibility markets: Literature review on concepts, models and clearing methods,” Appl. Energy, vol. 261. Elsevier Ltd, p. 114387, Mar. 2020.
- J. Radecke, J. Hefele, and L. Hirth, “Markets for Local Flexibility in Distribution Networks,” Kiel, Hamburg, 2019.
- S. Minniti, N. Haque, P. Nguyen, and G. Pemen, “Local Markets for Flexibility Trading: Key Stages and Enablers,” Energies, vol. 11, no. 11, p. 3074, Nov. 2018.
- S. Huang, Q. Wu, Z. Liu, and A. H. Nielsen, “Review of congestion management methods for distribution networks with high penetration of distributed energy resources,” in IEEE PES Innovative Smart Grid Technologies Conference Europe, Istanbul, Turkey, Oct. 2014.
- Bundesnetzagentur, “Flexibility in the electricity system,” 2017.
- Clean Energy Group, “ConnectedSolutions An Assessment for Massachusettes.”
- S. Bjarghov, H. Farahmand, and G. Doorman, “Capacity subscription grid tariff efficiency and the impact of uncertainty on the subscribed level,” Energy Policy, vol. 165, p. 112972, Jun. 2022.
- N. Govaerts, K. Bruninx, H. Le Cadre, L. Meeus, and E. Delarue, “Forward-looking distribution network charges considering lumpy investments,” J. Regul. Econ., vol. 59, no. 3, pp. 280-302, Jun. 2021.
- A. Scheidler, M. Kraiczy, L. Thurner, and M. Braun, “Automated Grid Planning for Distribution Grids with Increasing PV Penetration,” 6th Int. Workshop on Integration of Solar Power into Power Systems, Vienna, Austria, Nov. 2016.
- R. Hennig, S. H. Tindemans, and L. De Vries, “Market Failures in Local Flexibility Market Proposals for Distribution Network Congestion Management,” in Proc. 18th Conf. Eur. Energy Market (EEM), Ljubljana, Slovenia, Sep. 2022.
- L. Hirth and I. Schlecht, “Market-Based Redispatch in Zonal Electricity Markets: Inc-Dec Gaming as a Consequence of Inconsistent Power Market Design (not Market Power),” ZBW - Leibniz Information Centre for Economics, Kiel, Hamburg, 2019.
- M. Sarfati, M. R. Hesamzadeh, and P. Holmberg, “Increase-Decrease Game under Imperfect Competition in Two-stage Zonal Power Markets - Part I: Concept Analysis,” JSTOR, 2018.
- J. Sun, N. Gu, and C. Wu, “Strategic Bidding in Extended Locational Marginal Price Scheme,” IEEE Control Syst. Lett., vol. 5., no. 1 2021.
- A. M. Systad and J. L. Eilertsen, “An analysis of mitigating measures for inc-dec gaming in market-based redispatch,” NTNU, Jun. 2022.
- M. Kohansal, A. Sadeghi-Mobarakeh, S. D. Manshadi, and H. Mohsenian-Rad, “Strategic Convergence Bidding in Nodal Electricity Markets: Optimal Bid Selection and Market Implications,” in IEEE Trans. Power Syst., vol. 36, no. 2, pp. 891-901, Mar. 2021.
- Q. Liu, X. Fang, C. Bai, and X. Fang, “Modeling and Analysis of Generator’s Strategic Bidding Under Marginal Pricing and Pay-as-bid Pricing Methods,” in 2022 5th International Conference on Energy, Electrical and Power Engineering (CEEPE), Chongqing, China, Jun. 2022.
- N. Groot, G. Zaccour, and B. De Schutter, “Hierarchical game theory for system-optimal control: Applications of reverse stackelberg games in regulating marketing channels and traffic routing,” IEEE Control Syst. Mag., vol. 37, no. 2, pp. 129-152, Apr. 2017.
- M. A. Tajeddini, H. Kebriaei, and L. Glielmo, “Decentralized Hierarchical Planning of PEVs Based on Mean-Field Reverse Stackelberg Game,” IEEE Trans. Autom. Sci. Eng., vol. 17, no. 4, pp. 2014-2024, Oct. 2020.
- J. Fattahi, D. Wright, and H. Schriemer, “An energy internet DERMS platform using a multi-level Stackelberg game,” Sustainable Cities and Society, vol. 60, Sep. 2020.
- J.-M. Lasry and P.-L. Lions, “Mean field games,” in Jpn. J. Mathemat., vol. 2, pp. 229-260, 2007.
- Y. Achdou, F. Camilli, and I. Capuzzo Dolcetta, “Mean Field Games: Numerical Methods for the Planning Problem,” in SIAM J. Control Opt., vol. 50, no. 1, pp. 77-109, 2012.
- S. Grammatico, F. Parise, M. Colombino, and J. Lygeros, “Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control,” IEEE Trans. Autom. Control, vol. 61, no. 11, pp. 3315-3329, 2016.
- F. Parise, M. Colombino, S. Grammatico, and J. Lygeros, “Mean field constrained charging policy for large populations of Plug-in Electric Vehicles,” in Proc. 53rd IEEE Conf. Decis. Control (CDC), pp. 5101-5106, Los Angeles, CA, USA, Dec. 2014.
- Z. Ma, D. S. Callaway, and I. A. Hiskens, “Decentralized Charging Control of Large Populations of Plug-in Electric Vehicles,” IEEE Trans. Control Syst. Technol., vol. 21, no. 1, pp. 67-78, 2013.
- W.H. Yang, “On generalized Hölder inequality,” Nonlinear Analysis, Theory, Methods & Applications, vol. 16, no. 5, pp. 489-498, 1991.