基于复杂网络的电网结构健壮性及Braess悖论现象研究

应用复杂网络理论，建立电力系统的改进导纳模型，结合电网拓扑特性和电气特性对电网的级联故障进行研究。通过随机移除传输线引发电网级联故障，研究网络的节点数、平均度、发电站数量以及发电站的分布状况对系统健壮性的影响，并对小世界电网级联故障过程中的布雷斯(Braess)悖论现象进行分析。研究表明：网络的健壮性与其拓扑结构密切相关，平均度较大时，最近邻耦合网络和小世界网络健壮性曲线存在多个分叉点；在小世界结构电网中，一般平均度和节点数越大，发电站的数量越多，电网健壮性越好；发电站分散分布比发电站集中分布的电网健壮性更好。对网络容量增加导致健壮性降低的布雷斯现象进行解释。

Robustness of Power Grids Structure and Braess Paradox Phenomenon: A Complex Network Theory Study

Based on complex network theory, a modified admittance model of a power system is constructed. Cascading failures of power grids are studied with topological and electrical characteristics of power grids. Cascading failures are made by removing transmission lines randomly. Effects of the number of nodes, average degree, number of power stations and distribution of power stations on system robustness are studied. Braess paradox phenomenon in the cascading failures of small world power grids is studied. It shows that robustness of a power grid is closely related to its topological structure. As the average degree is great, there exist several bifurcation points in the robustness curve of the nearest-neighbor coupled network and the small world network. In small world structure power grids, generally, the greater the average degree and the number of nodes, the more power stations, the better robustness of the power grid. Robustness of a power grid with distributed power stations is better than that with centralized distribution. In addition, the Braess phenomenon, which leads to the decrease of robustness due to the increase of network capacity, is explained.