The ongoing transition to renewable energy supply comes with a restructuring of power grids, changing their effective interaction topologies, more and more strongly decentralizing them and substantially modifying their input, output, and response characteristics. All of these changes imply that power grids become increasingly affected by collective, nonlinear dynamic phenomena, structurally and dynamically more distributed and less predictable in space and time, more heterogeneous in its building blocks, and as a consequence less centrally controllable. Here cornerstone aspects of data-driven and mathematical modeling of collective dynamical phenomena emerging in real and model power grid networks by combining theories from nonlinear dynamics, stochastic processes and statistical physics, anomalous statistics, optimization, and graph theory are reviewed. The mathematical background required for adequate modeling and analysis approaches is introduced, an overview of power system models is given, and a range of collective dynamical phenomena are focused on, including synchronization and phase locking, flow (re)routing, Braess’s paradox, geometric frustration, and spreading and localization of perturbations and cascading failures, as well as the nonequilibrium dynamics of power grids, where fluctuations play a pivotal role.

中文翻译：

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分散电网中的集体非线性动力学和自组织

向可再生能源供应的持续过渡伴随着电网的重组，改变了它们的有效交互拓扑，越来越强烈地去中心化，并大大改变了它们的输入、输出和响应特性。所有这些变化意味着电网越来越多地受到集体、非线性动态现象的影响，在结构上和动态上更加分散，在空间和时间上更难以预测，在其构建块中更加异构，因此更不集中控制。通过结合非线性动力学、随机过程和统计物理学、异常统计、优化等理论，在真实和模拟电网网络中出现的集体动力现象的数据驱动和数学建模的基石方面，和图论进行了回顾。介绍了适当的建模和分析方法所需的数学背景，概述了电力系统模型，并重点关注了一系列集体动力现象，包括同步和锁相、流动（重新）路由、Braess 悖论、几何挫折，以及扰动和级联故障的传播和定位，以及电网的非平衡动力学，其中波动起着关键作用。