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

该项目的目标是找到一种结构化的方法来实现智能电网的分布式优化和调节，该方法不仅考虑到网络层的特定功能属性，而且考虑到这些层之间的实际互连。重点将放在智能电网的多组件模型上。基于复杂系统理论分析智能电网面临的新挑战，本文选择了三层模型。其思想是通过博弈论和分布式优化在每个层面制定全局目标。在这个项目中，我们将开发相应的博弈论和分布式优化方法，适用于不同层次的智能电网模型。这项工作有望回答以下问题：如何正式定义智能电网不同结构级别的目标，以尽可能好地满足实际应用？什么数学工具可以考虑大规模能源系统的通信技术和信息限制，从而提供使我们能够处理最一般的基于收益的均衡学习和约束分布非凸优化问题的方法？在哪些假设下，与目前文献中提出的技术相比，该项目提出的理论方法将为智能电网运行提供一些整体改进？所提出的理论方法如何同步才能实现智能电网的稳定高效运行？本项目所解决的主要问题将通过工程和数学工具进行研究，包括博弈论、分布式优化理论、基于共识的方法、随机鞅过程（包括遍历马尔可夫链）和随机逼近方法。

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.