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Model Predictive Control for Aggregative Games


P. Pienroj

Semester Thesis, SS17

Plug-in electric vehicles (PEVs) have been forecasted to increase in the next decade. As of today, the electrical market penetration from PEVs is still small. In some countries, the PEVs are simultaneously charged during o_-peak of the electricity demand for economics reason [1], or in other words, they are simultaneously charge during the night when the demand is lower. However, as the number of PEVs grows, the electricity market penetration will also grow. This may lead to an issue such as the stability of the grid as shown in [1] and [2]. The effects of uncontrolled charging of PEVs can be a major threat to grid utilities [3]. [4] formulated the problem of PEV charging as a non-cooperative game, where there are set of players choosing their own charging strategy to minimize their own cost function which depends on other players' strategies. This can be seen as an aggregative game [5], in which each agent is not subject to a one-to-one interaction with others but inuenced only by the average strategy. [4] and [6] also focuses on decentralized algorithm where each agent only announces his charging plan to the central coordinator, whose role is to measure and broadcast aggregate information. The proposed control law used in [4] and [6] is an open loop control where each agent applies his own strategy that is agreed before the game. In practice, this can lead to a relatively large cost if some players do not do as agreed. For example, some agents join the game later than what agreed in the beginning. Open-loop control does not introduce feedback to the system. With open-loop control scheme, late agents can not satisfy some of their constraints since they only charge as agreed in the beginning of the night. For example, late agents may not satisfy the amount of charging that he needs for the next day. This study aims at filling the gap, by using tools from the model predictive control (MPC). In MPC [4], at every instant of time, the current status of the system is measured and the controller readjusts consequently. A similar problem can be posed in game theory, where players adapt to the current status by optimizing their future cost starting from the current state. The challenges arising include the definition of an equilibrium for the game [6] over the shifting or receding horizon. In order to make the strategies more robust, the equilibrium could be defined in terms of the feedback laws of each agent. MPC is a control scheme which is known to be robust to error and uncertainty [3]. Moreover, different from open loop laws, MPC can guarantee that the late players can satisfy their constraints. This is because when implementing MPC, at every sampling time step, each agent solves his own optimization problem again subject to the current situation. We will focus on a detailed discussion of MPC again in Section 4. We study the PEVs charging game after MPC is implemented instead of open loop control laws. We explore the scenario when after an agreement before the game, some players do not do as what agreed at the beginning of the night. We especially focus on the final cost of energy in such situation comparing to the situation when every agent does as agreed. The analytical studies and numerical simulations are performed on the electricity bill of each day in different situations when MPC is implemented to the game.

Supervisors: Basilio Gentile, Dario Paccagnan, John Lygeros


Type of Publication:

(13)Semester/Bachelor Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2017:IFA_5648
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