Inria Sophia Antipolis Méditerranée Research Centre, 06902 Valbonne, France.
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany.
Phys Rev E. 2019 Dec;100(6-1):062306. doi: 10.1103/PhysRevE.100.062306.
We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal natural frequency distribution representing the generators and the loads. The Kuramoto model describes the dynamics of the ac voltage phase and allows for a comprehensive understanding of fundamental network properties capturing the essential dynamical features of a power grid on coarse scales. We identify critical nodes through solitary frequency deviations and Lyapunov vectors corresponding to unstable Lyapunov exponents. To cure dangerous deviations from synchronization we propose time-delayed feedback control, which is an efficient control concept in nonlinear dynamic systems. Different control strategies are tested and compared with respect to the minimum number of controlled nodes required to achieve synchronization and Lyapunov stability. As a proof of principle, this fast-acting control method is demonstrated for different networks (the German and the Italian power transmission grid), operating points, configurations, and models. In particular, an extended version of the Kuramoto model with inertia is considered that includes the voltage dynamics, thus taking into account the interplay of amplitude and phase typical of the electrodynamical behavior of a machine.
我们研究了具有惯性的 Kuramoto 相振荡器模型内的电网同步和稳定性，该模型具有双模态自然频率分布，代表发电机和负载。Kuramoto 模型描述了交流电压相位的动态，允许全面了解基本的网络特性，捕捉电网在粗尺度上的基本动态特征。我们通过单独的频率偏差和对应于不稳定李雅普诺夫指数的李雅普诺夫向量来识别关键节点。为了治愈同步的危险偏差，我们提出了时滞反馈控制，这是非线性动力系统中的一种有效控制概念。针对实现同步和李雅普诺夫稳定性所需的最小控制节点数量，测试并比较了不同的控制策略。作为原理验证，该快速作用的控制方法已针对不同的网络（德国和意大利输电网）、运行点、配置和模型进行了演示。特别是，考虑了具有惯性的 Kuramoto 模型的扩展版本，其中包括电压动态，从而考虑了机器的电磁行为的幅度和相位相互作用的典型情况。
