Kettemann Stefan
Department of Physics and Earth Science, Jacobs University, Campus Ring 1, 28759 Bremen, Germany and Division of Advanced Materials Science Pohang University of Science and Technology (POSTECH) San 31, Hyoja-dong, Nam-gu, Pohang 790-784, South Korea.
Phys Rev E. 2016 Dec;94(6-1):062311. doi: 10.1103/PhysRevE.94.062311. Epub 2016 Dec 21.
In order to study how local disturbances affect the ac grid stability, we start from nonlinear power balance equations and map them to complex linear wave equations. Having obtained stationary solutions with phases φ_{i} at generator and consumer nodes i, we next study the dynamics of deviations. Starting with an initially localized perturbation, it is found to spread in a periodic grid diffusively throughout the grid. We find the parametric dependence of diffusion constant D. We apply the same solution strategy to general grid topologies and analyze their stability against local perturbations. The perturbation remains either localized or becomes delocalized, depending on grid topology, power capacity, and distribution of consumers and generator power P_{i}. Delocalization is found to increase the lifetime of perturbations and thereby their influence on grid stability, whereas localization results in an exponentially fast decay of perturbations at all grid sites. These results may therefore lead to new strategies to control the stability of electricity grids.
为了研究局部扰动如何影响交流电网的稳定性，我们从非线性功率平衡方程入手，并将其映射到复线性波动方程。在发电机节点和用电节点(i)处获得了具有相位(\varphi_{i})的稳态解后，我们接下来研究偏差的动态变化。从最初的局部扰动开始，发现它会以周期性网格扩散的方式在整个电网中传播。我们找到了扩散常数(D)的参数依赖性。我们将相同的求解策略应用于一般的电网拓扑结构，并分析它们对局部扰动的稳定性。扰动要么保持局部化，要么变得非局部化，这取决于电网拓扑结构、功率容量以及用电设备和发电机功率(P_{i})的分布。发现非局部化会增加扰动的寿命，从而增强它们对电网稳定性的影响，而局部化则导致所有电网节点处的扰动呈指数快速衰减。因此，这些结果可能会带来控制电网稳定性的新策略。
