Game Theoretical Framework for Distributed Dynamic Control in Smart Grids



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In the emerging smart grids, production increasingly relies on a greater number of decentralized generation sites based on renewable energy sources. The variable nature of the new renewable energy sources will require a certain form of distributed energy storage, such as batteries, flywheels, compressed air and so on to help maintain supply security. Moreover, integration of demand response programs in conjunction with distrusted generation makes an economic and environmental advantage by altering end-users’ normal consumption patterns in response to changes in the electricity price. These new techniques change the way we consume and produce energy also enable the possibility to reduce the greenhouse effect and improve grid stability by optimizing energy streams. In order to accommodate these technologies, solid mathematical tools are essential to ensure robust operation of heterogeneous and distributed nature of smart grids. In this context, game theory could constitute a robust framework that can address relevant and timely open problems in the emerging smart grid networks. In this dissertation, three dynamic game-theoretical approaches are proposed for distributed control of generation and storage units and demand response applications in smart grid networks. We first study the competitive interactions between an autonomous pumpedstorage hydropower plant and a thermal power plant in order to optimize power generation and storage. Each type of power plant individually tries to maximize its own profit by adjusting its strategy: both types of plants can sell their power to the market; or alternatively, the thermal-power plant can sell its power at a fixed price to the pumped-storage hydropower plant by storing the energy in the reservoir. A stochastic differential game is formulated to characterize this competition. The solutions are derived using the stochastic Hamilton-Jacobi-Bellman equations. Based on the effect of real-time pricing on users’ daily demand profile, the simulation results demonstrate the properties of the proposed game and show how we can optimize consumers’ electricity cost in presence of time-varying prices. Second, we focus on controllable load types in energy-smart buildings that are associated with dynamic systems. In this regard, we propose a new demand response model based on a two-level differential game framework. At the beginning of each demand response interval, the price is decided by the upper level (aggregator, utility, or market) given the total demand of lower level users. Given the price from the upper level, the electricity usage of air conditioning unit and the battery storage charging/discharging schedules are controlled for each player (buildings that are equipped with automated load control systems and local renewable generators), in order to minimize the user’s total electricity cost. The optimal user strategies are derived, and we also show that the proposed game can converge to a feedback Nash equilibrium. Finally, the problem of distributed control of the heating, ventilation and air conditioning (HVAC) system for multiple zones in an energy-smart building is addressed. This analysis is based on the idea of satisfaction equilibrium, where the players are exclusively interested in the satisfaction of their individual constraints instead of individual performance optimization. This configuration enables a HVAC unit as a player to make stochastically stable decisions with limited information from the rest of players. To achieve satisfaction equilibrium, a learning dynamics based on trialand- error learning is proposed. In particular, it is shown that this algorithm reaches stochastically stable states that are equilibria and maximizers of the global welfare of the corresponding game.



Smart Buildings, Energy efficiency, Distributed Control, Game theory