Mechanism Design for Demand Management in Energy Communities
Abstract
:1. Introduction
1.1. Contributions
- (a)
- We design a baseline, “centralized” mechanism for an environment with concave utilities and convex constraints. A “centralized” mechanism allows for messages from all users to be communicated to the planner [6,8,9]. To avoid excessive communication cost brought about by direct mechanisms (due to messages being entire utility functions), the mechanisms proposed in this paper are indirect, non-VCG type [10,11,12], with messages being real vectors with finite (and small) dimensionality. Unlike related previous works [13,14,15,16], a simple form of allocation function is adopted, namely, allocation equals demand. The mechanism possesses the properties of full implementation, budget balance, and individual rationality [6,8,9]. Although we develop the mechanism for demand management in energy communities, the underlying ideas can be easily adapted to other problems and more general environments. Specifically, environments with non-monotonic utilities, external fixed unit prices, and the requirement of peak shaving are tractable with the proposed mechanism.
- (b)
- Inspired by the vast literature on distributed non-strategic optimization [17,18,19,20,21], as well as our recent work on distributed mechanism design (DMD) [22,23], we modify the baseline mechanism and design a “distributed” version of it. A distributed mechanism can be deployed in environments with communication constraints, where users’ messages cannot be communicated to the central planner; consequently the allocation and tax/subsidy functions for each user should only depend on messages from direct neighbors. The focus of our methodology is to show how a centralized mechanism can be modified into a decentralized one in a systematic way by means of introducing extra message components that act as proxies of the messages not available to a user due to communication constraints. An added benefit of this systematic design is that the new mechanism preserves all of the desirable properties of the centralized mechanism.
- (c)
- Since mechanism design (centralized or distributed) deals with equilibrium properties, one relevant question is how equilibrium is reached when agents enter the mechanism. Our final contribution in this paper is to provide “learning” algorithms [24,25,26,27,28] that address this question for both cases of the proposed centralized and decentralized mechanisms. The algorithm is based on the projected gradient descent method in optimization theory ([29] Chapter 7). Learning proceeds through price adjustments and demand announcements according to the prices. During this process, users do not need to reveal their entire utility functions. Convergence of the message profile toward one NE is conclusively proven, and since the mechanism is designed to fully implement the optimal allocation in NE, this implies that the allocation corresponding to the limiting message profile is the social welfare maximizing solution.
1.2. Related Literature
2. Model and Preliminaries
2.1. Demand Management in Energy Communities
- Primal Feasibility:
- Dual Feasibility:
- Complementary Slackness:
- Stationarity:
2.2. Mechanism Design Preliminaries
3. The Baseline “Centralized” Mechanism
4. Distributed Mechanism
4.1. Message Exchange Network
4.2. The Message Space
4.3. The Allocation and Tax Functions
4.4. Properties
5. Learning Algorithm
5.1. A Learning Algorithm for the Centralized Mechanism
- 1.
- , ,
- 2.
- , .
- , ,
- , and
Algorithm 1: Learning algorithm for the centralized mechanism. |
5.2. A Learning Algorithm for the Distributed Mechanism
Algorithm 2: Maintenance algorithm for proxy . |
Algorithm 3: Maintenance algorithm for proxy . |
Algorithm 4: Learning algorithm for user i in the distributed mechanism. |
6. A Concrete Example
6.1. The Demand Management Optimization Problem
6.2. The Centralized Mechanism
6.3. The Distributed Mechanism
6.4. The Learning Algorithm
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Equivalence of Centralized Optimization Problem (2) and Original Problem (3a)–(3c)
Appendix B. Proof of Lemma 2
Appendix C. Proof of Lemma 3
Appendix D. Proof of Theorem 2
Appendix E. Proof of Theorem 3
Appendix F. Proof of Theorem 4
Appendix G. Proof of Lemma 5
Appendix H. Convergence of the Learning Algorithm for Centralized Mechanism
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Wei, X.; Anastasopoulos, A. Mechanism Design for Demand Management in Energy Communities. Games 2021, 12, 61. https://doi.org/10.3390/g12030061
Wei X, Anastasopoulos A. Mechanism Design for Demand Management in Energy Communities. Games. 2021; 12(3):61. https://doi.org/10.3390/g12030061
Chicago/Turabian StyleWei, Xupeng, and Achilleas Anastasopoulos. 2021. "Mechanism Design for Demand Management in Energy Communities" Games 12, no. 3: 61. https://doi.org/10.3390/g12030061
APA StyleWei, X., & Anastasopoulos, A. (2021). Mechanism Design for Demand Management in Energy Communities. Games, 12(3), 61. https://doi.org/10.3390/g12030061