The spectral graph theory is introduced to establish the effective resistance matrix of power system network topology from the mathematical point of view, and the index of nodal coupling degree is put forward based on the effective resistance matrix. By analyzing the cumulative probability distribution of node coupling degree, the scale-free characteristic of power system is verified. Then the index is applied to identification of the key nodes in actual power system. The index not only satisfies the Kirchhoff's law, but also can show the quantitative relationship between nodal phase angle and nodal power, meanwhile, its physical meaning is more consistent with actual power system. In addition, the capacity survivability index, load survivability index, line survivability index and synthetical survivability index are adopted to describe the effects of failure of the nodes on power system. Finally, the simulation verification of IEEE-39 bus system is done, which shows that the index of nodal coupling degree has a certain recognition to the nodes in the key position of the system topology, so it can provide guidance for the safe and stable operation of actual power system.%引入图谱理论从数学角度建立了电力系统网络拓扑图的有效电阻矩阵,并基于有效电阻矩阵提出了节点耦合关键度指标.通过对节点耦合关键度累积概率分布进行分析,验证了电力系统的无标度特性,进而将节点耦合关键度用于电力系统关键节点的识别.该指标不仅满足基尔霍夫定律,也能表明节点相角与节点功率的定量关系,其物理意义更加符合实际电力系统.另外,通过容量生存率、负荷生存率、线路生存率和综合生存率4个指标来描述节点发生全失故障对电力系统造成的影响.最后,对IEEE-39节点算例的仿真验证表明,基于有效电阻矩阵得到的节点耦合关键度指标对处于系统拓扑结构中关键位置的节点有一定识别作用,能为电力系统的安全稳定运行提供指导.
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