Rohden Martin, Sorge Andreas, Witthaut Dirk, Timme Marc
Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany.
Chaos. 2014 Mar;24(1):013123. doi: 10.1063/1.4865895.
Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. In particular, power generation in the resulting grid will be far more decentralized, with a distinctly different topology. Here, we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random, and small-world topologies and focusing on the influence of decentralization. We model the consumers and sources of the power grid as second order oscillators. First, we analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage), and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular, star-like networks and regular grid motifs. For larger networks, we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in exhibiting a stable state for lower transmission line capacities. Decentralization may thus be beneficial for power grids, regardless of the details of their resulting topology. Regular grids show a specific sharper transition not found for random or small-world grids.
在当前电网中用可再生能源取代传统电源会极大地改变其结构和功能。特别是，由此产生的电网中的发电将更加分散，具有明显不同的拓扑结构。在此，我们分析电网拓扑对自发同步的影响，考虑规则、随机和小世界拓扑，并着重于分散化的影响。我们将电网的用户和电源建模为二阶振荡器。首先，我们分析最简单的非平凡（两节点）网络的全局动态，该网络呈现同步（正常运行）状态、极限环（停电）以及两者共存的情况。其次，我们估计小型网络 motif（特别是星型网络和规则网格 motif）集体动态的稳定性阈值。对于更大的网络，我们通过数值研究分散化场景，发现分散化本身可能有助于电网在较低输电线路容量下呈现稳定状态。因此，无论其最终拓扑的细节如何，分散化对电网可能是有益的。规则网格显示出一种特定的更尖锐的转变，而随机或小世界网格则没有这种情况。
