Distributed Optimization in Smart Grids - Renewal of Proposal for the second funding period of Priority Programme SPP 1984

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The goal of this project is to find a structural approach to distributed optimization and regulation in Smart Grids, which will take into account not only specific functional properties of the network levels, but also realistic interconnections between these levels. The focus will be on a multi-component model of Smart Grids. The choice of the model consisting of three levels is motivated by recently formulated challenges for the analysis of Smart Grids by means of complex system theory. The idea is to formulate global objectives at each level by means of game theory and distributed optimization. In this project we will develop the corresponding game-theoretic and distributed optimization approaches applicable to the different levels of the Smart Grid model. This work promises to answer the following questions: How should objectives at different structural levels of Smart Grids be formally defined to meet realistic applications as good as possible? What mathematical tools can take communication technologies and information restrictions of large-scale energy systems into account and, thus, provide the methods enabling us to handle the most general payoff-based equilibria learning and constrained distributed non-convex optimization problems?Under which assumptions the theoretic methods proposed in the project will provide some global improvement of the Smart Grid operation in comparison with the techniques presented in the literature so far? How should the proposed theoretic methods be synchronized to achieve a stable and efficient operation of Smart Grids?The main questions addressed in this project will be studied by means of engineering and mathematical tools including game theory, distributed optimization theory, consensus-based methods, stochastic martingale processes, including ergodic Markov chains, and stochastic approximation methods.