Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets
Abstract
:1. Introduction
1.1. Notation
1.2. Operator Theory
2. Peer-to-Peer Energy Markets as a Generalized Nash Equilibrium Problem
3. Market Clearing Mechanism with Improved Convergence Speed
3.1. Market Clearing Algorithms Based on the Preconditioned Proximal Point Method
Algorithm 1 PPP-based Market Clearing Mechanism |
Algorithm 2 Central update of DNO |
Step sizes: set , , , and , for all busses .
|
Algorithm 3 Local update of prosumer |
Step sizes: For each , set , , for all .
|
- a.
- (Inertial PPP variant),,, , for all, and;
- b.
- (Over-relaxed PPP variant),,,, for all, and.
3.2. Rate Improvement Evaluation
4. Equilibrium Selection as Preferred by the Network Operator
4.1. Formulation of Optimal Equilibrium Selection Problem
4.2. Optimal Equilibrium Selection Algorithm
4.3. Equilibria That Minimize Line Congestion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DNO | Distribution network operator |
HSDM | Hybrid steepest descent |
GNE | Generalized Nash equilibrium |
GNEP | Generalized Nash equilibrium problem |
IEEE | Institute of Electrical and Electronics Engineers |
KKT | Karush–Kuhn–Tucker |
PPP | Preconditioned proximal point |
VI | Variational inequality |
Appendix A. Proof of Proposition 2
References
- Sousa, T.; Soares, T.; Pinson, P.; Moret, F.; Baroche, T.; Sorin, E. Peer-to-peer and community-based markets: A comprehensive review. Renew. Sustain. Energy Rev. 2019, 104, 367–378. [Google Scholar] [CrossRef] [Green Version]
- Soto, E.A.; Bosman, L.B.; Wollega, E.; Leon-Salas, W.D. Peer-to-peer energy trading: A review of the literature. Appl. Energy 2021, 283, 116268. [Google Scholar] [CrossRef]
- Tushar, W.; Saha, T.K.; Yuen, C.; Smith, D.; Poor, H.V. Peer-to-peer trading in electricity networks: An overview. IEEE Trans. Smart Grid 2020, 11, 3185–3200. [Google Scholar] [CrossRef] [Green Version]
- Tushar, W.; Yuen, C.; Saha, T.K.; Morstyn, T.; Chapman, A.C.; Alam, M.J.E.; Hanif, S.; Poor, H.V. Peer-to-peer energy systems for connected communities: A review of recent advances and emerging challenges. Appl. Energy 2021, 282, 116131. [Google Scholar] [CrossRef]
- Tushar, W.; Yuen, C.; Mohsenian-Rad, H.; Saha, T.; Poor, H.V.; Wood, K.L. Transforming energy networks via peer-to-peer energy trading: The potential of game-theoretic approaches. IEEE Signal Process. Mag. 2018, 35, 90–111. [Google Scholar] [CrossRef] [Green Version]
- Noor, S.; Yang, W.; Guo, M.; van Dam, K.H.; Wang, X. Energy demand side management within micro-grid networks enhanced by blockchain. Appl. Energy 2018, 228, 1385–1398. [Google Scholar] [CrossRef]
- Yang, X.; Wang, G.; He, H.; Lu, J.; Zhang, Y. Automated demand response framework in ELNs: Decentralized scheduling and smart contract. IEEE Trans. Syst. Man Cybern. Syst. 2020, 50, 58–72. [Google Scholar] [CrossRef]
- Bhatti, B.A.; Broadwater, R. Energy trading in the distribution system using a non-model based game theoretic approach. Appl. Energy 2019, 253, 113532. [Google Scholar] [CrossRef]
- Wang, Z.; Liu, F.; Ma, Z.; Chen, Y.; Jia, M.; Wei, W.; Wu, Q. Distributed generalized Nash equilibrium seeking for energy sharing games in prosumers. IEEE Trans. Power Syst. 2021, 36, 3973–3986. [Google Scholar] [CrossRef]
- Belgioioso, G.; Ananduta, W.; Grammatico, S.; Ocampo-Martinez, C. Energy management and peer-to-peer trading in future smart grids: A distributed game-theoretic approach. In Proceedings of the 2020 European Control Conference (ECC), Saint Petersburg, Russia, 12–15 May 2020; pp. 1324–1329. [Google Scholar]
- Belgioioso, G.; Ananduta, W.; Grammatico, S.; Ocampo-Martinez, C. Operationally-safe peer-to-peer energy trading in distribution grids: A game-theoretic market-clearing mechanism. IEEE Trans. Smart Grid 2022. [Google Scholar] [CrossRef]
- Belgioioso, G.; Yi, P.; Grammatico, S.; Pavel, L. Distributed generalized Nash equilibrium seeking: An operator-theoretic perspective. IEEE Control Syst. Mag. 2022, 42, 87–102. [Google Scholar] [CrossRef]
- Yi, P.; Pavel, L. An operator splitting approach for distributed generalized Nash equilibria computation. Automatica 2019, 102, 111–121. [Google Scholar] [CrossRef] [Green Version]
- Bianchi, M.; Belgioioso, G.; Grammatico, S. Fast generalized Nash equilibrium seeking under partial-decision information. Automatica 2022, 136, 110080. [Google Scholar] [CrossRef]
- Belgioioso, G.; Grammatico, S. Semi-decentralized generalized Nash equilibrium seeking in monotone aggregative games. IEEE Trans. Autom. Control. 2021. [Google Scholar] [CrossRef]
- Gadjov, D.; Pavel, L. Single-timescale distributed GNE seeking for aggregative games over networks via forward–backward operator splitting. IEEE Trans. Autom. Control 2021, 66, 3259–3266. [Google Scholar] [CrossRef]
- Benenati, E.; Ananduta, W.; Grammatico, S. Optimal selection and tracking of generalized Nash equilibria in monotone games. arXiv 2022, arXiv:2203.07765. [Google Scholar]
- Benenati, E.; Ananduta, W.; Grammatico, S. On the optimal selection of generalized Nash equilibria in linearly-coupled aggregative games. In Proceedings of the 61st Conference on Decision and Control, Cancún, Mexico, 6–9 December 2022. to appear. [Google Scholar]
- Sorin, E.; Bobo, L.; Pinson, P. Consensus-based approach to peer-to-peer electricity markets With product differentiation. IEEE Trans. Power Syst. 2019, 34, 994–1004. [Google Scholar] [CrossRef] [Green Version]
- Atzeni, I.; Ordóñez, L.G.; Scutari, G.; Palomar, D.P.; Fonollosa, J.R. Demand-side management via distributed energy generation and storage optimization. IEEE Trans. Smart Grid 2013, 4, 866–876. [Google Scholar] [CrossRef]
- Le Cadre, H.; Jacquot, P.; Wan, C.; Alasseur, C. Peer-to-peer electricity market analysis: From variational to generalized Nash equilibrium. Eur. J. Oper. Res. 2020, 282, 753–771. [Google Scholar] [CrossRef] [Green Version]
- Baroche, T.; Moret, F.; Pinson, P. Prosumer markets: A unified formulation. In Proceedings of the 2019 IEEE Milan PowerTech, Milan, Italy, 23–27 June 2019; pp. 1–6. [Google Scholar]
- Facchinei, F.; Pang, J.S. 12 Nash equilibria: The variational approach. In Convex Optimization in Signal Processing and Communications; Palomar, D.P., Eldar, Y.C., Eds.; Cambridge University Press: Cambridge, UK, 2010; pp. 443–491. [Google Scholar]
- Bauschke, H.H.; Combettes, P.L. Convex Analysis and Monotone Operator Theory in Hilbert Spaces; Springer: Berlin/Heidelberg, Germany, 2011. [Google Scholar]
- Polyak, B.T. Some methods of speeding up the convergence of iteration methods. USSR Comput. Math. Math. Phys. 1964, 4, 1–17. [Google Scholar] [CrossRef]
- Nesterov, Y. Introductory Lectures on Convex Optimization: A Basic Course; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2004; Volume 87. [Google Scholar]
- Ghadimi, E.; Feyzmahdavian, H.R.; Johansson, M. Global convergence of the heavy-ball method for convex optimization. In Proceedings of the 2015 European control conference (ECC), Linz, Austria, 15–17 July 2015; pp. 310–315. [Google Scholar]
- Yamada, I.; Ogura, N. Hybrid steepest descent method for variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings. Numer. Funct. Anal. Optim. 2005, 25, 619–655. [Google Scholar] [CrossRef]
- Ogura, N.; Yamada, I. Nonstrictly convex minimization over the bounded fixed point set of a nonexpansive mapping. Numer. Funct. Anal. Optim. 2003, 24, 129–135. [Google Scholar] [CrossRef]
- Auslender, A.; Teboulle, M. Lagrangian duality and related multiplier methods for variational inequality problems. SIAM J. Optim. 2000, 10, 1097–1115. [Google Scholar] [CrossRef]
Test Case | (Normalized) of Algorithm 1 | ||
---|---|---|---|
Baseline | For Equilibrium Selection | On Modified Game | |
37-bus | |||
123-bus |
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Ananduta, W.; Grammatico, S. Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets. Games 2022, 13, 66. https://doi.org/10.3390/g13050066
Ananduta W, Grammatico S. Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets. Games. 2022; 13(5):66. https://doi.org/10.3390/g13050066
Chicago/Turabian StyleAnanduta, Wicak, and Sergio Grammatico. 2022. "Equilibrium Seeking and Optimal Selection Algorithms in Peer-to-Peer Energy Markets" Games 13, no. 5: 66. https://doi.org/10.3390/g13050066