基于超图理论的线路脆弱性评估

基于节点和线路之间的联系，利用超图理论构建了一个适用于电网的超图模型。利用数据场理论对线路的脆弱性进行了评估。定义了线路的多属性综合指标作为衡量线路质量的指标，包括线路度乘积、电气介数和潮流转移熵；采用基于超图的最短路径求解线路的辐射半径；将熵作为判断影响因子不确定性的度量，把求解最优影响因子问题转化为求最小熵值问题，并采用简单试探性算法求解；将线路对整个网络的影响程度定义为线路影响率，并将其作为线路的脆弱性评估指标。最后，通过IEEE-39节点系统进行仿真计算。结果表明：线路影响率较高的线路在电网中为脆弱线路；若这些线路发生故障或者受到恶意攻击，会对整个电网产生较大影响。仿真结果验证了该方法的有效性和准确性。

Evaluation of Line Vulnerability Based on Hypergraph Theory

A hypernetwork model for power network based on the connection between nodes and lines is constructed by hypernetwork theory.The vulnerability of the line is evaluated using data field theory.Among them,the multi-attribute comprehensive index of the line is defined as an index to measure the quality of the line.The index includes line degree product,electrical betweenness and tide transfer entropy.The shortest path based on hypergraph is used to solve the radiation radius of lines.The entropy is used as a measure of the uncertainty of influencing factors and the problem of solving the optimal influence factor is transformed into the minimum entropy value problem,and the algorithm is solved by a simple heuristic algorithm.Finally,the impact of the line on the entire network is defined as the impact rate of the line,and is taken as the index of the vulnerability evaluation of the line.IEEE-39 node system is used to test the method.The result shows that the high influence rate of lines play key roles in the network,and the faults or malicious attacks of these lines will have a great bad impact on the whole grid.The validity and accuracy of the proposed method is verified by the simulation.