Decentralized optimization methods for solving social profit optimization problems in electricity market - Wang, Jianzheng (Nanyang Technological University, 2023)
Social profit optimization problem in the electricity market has become an active topic in the recent research works due to its benefit in maintaining the satisfaction of market participants and enhancing the sustainability of whole market. Generally speaking, social profit optimization usually considers the benefit of the whole market, where the objective function could be the sum of all the individual profits or a tradeoff of them. Among the various research works on this topic, the instinct of the agents can be classified into two categories: social-centric and self-centric. Social-centric agents usually aim to optimize the social profit of a community by making centralized or cooperative decisions. By contrast, self-centric agents may pursue their optimal profits selfishly and noncooperatively without caring about the benefit of others. Hence, two problems arise hereby: 1. How to make effective strategies for the social-centric agents to improve the social profit of the market? 2. How to induce the self-centric agents with some effective coordination strategies to improve the social profit of the market? To address the aforementioned problems, some distributed optimization methods are proposed in this dissertation. Specifically, two classes of problems will be discussed: cooperation- and non-cooperation-based problems. In the first scenario, some distributed optimization problems (DOPs) in the market are studied, where all the agents are social-centric and make strategies cooperatively. In the second scenario, game-theoretic methods are considered to characterize the behaviour of the agents. To optimize the social profit, a coordinator is introduced, which is responsible for making policies to influence the equilibrium of the market. The details of the dissertation are summarised as follows. 1. In Chapter 2, a social profit optimization problem in the electricity market with strategic demand response (DR) management is proposed. Specifically, two interaction mechanisms, namely Nash game and Stackelberg game, are studied. At the energy user side, individual profit optimization problems are formulated for the users. At the utility company (UC) side, Nash games among normal UCs are formulated and a governmental UC (G-UC) is introduced to influence the Nash equilibrium (NE) of the market. Finally, a multi-timescale leader-following problem is formulated and a demand function amelioration (DFA) strategy is proposed to optimize the market efficiency. 2. In Chapter 3, a social welfare optimization problem in the electricity market is considered, where all the agents jointly optimize a global composite cost function with coupling linear constraints. An asynchronous penalized proximal gradient (Asyn-PPG) algorithm is proposed by considering the asynchronous action instants of the agents and communication delays in the network. Specifically, a slot-based asynchronous network (SAN) is proposed by splitting the whole time domain into sequential time slots. An explicit convergence rate can be guaranteed based on deterministic derivations. 3. In Chapter 4, a social welfare optimization problem with coupling constraints in the electricity market is considered. The dual problem is derived by the concept of Fenchel conjugate. Then a dual proximal gradient (DPG) algorithm is proposed, where the agents only need to update dual variables and the computational complexity can be reduced if the proximal mapping of the nonsmooth part of the objective functions can be analytically derived. In addition, an asynchronous dual proximal gradient (Asyn-DPG) algorithm is proposed by considering the heterogenous step sizes and communication delays in the network. In summary, the focus of this dissertation is to develop several distributed optimization algorithms for optimizing the social profit of the electricity market, which is of great significance to the sustainability of the electricity market.