一种复杂电力网络的时空演化模型

Temporal and spatial evolvement model of power grid

网络拓扑对电力网络的脆弱性和鲁棒性有重要影响,当前经典网络模型与实际电力网络有较大差异。基于电力网络本身的演化机理,对BA无标度网络模型进行扩展与改进,构造了一种复杂电力网络的时空演化模型。提出网络生长点的概念,将其定义为靠近网络中原有节点但并未被占据的位置。新节点加入时,其坐标从网络生长点中随机选择;已有节点与新节点连接的概率由该节点的度数和该节点与新节点间的物理距离共同决定。分析了该模型的统计学特性,通过美国西部电网、中国北方电网与几种典型网络模型在平均度数、聚类系数、特征路径长度和度分布曲线等方面的对比,验证了新模型能很好地反映电力网络的演化规律。

Topology of power grid has great influence on its vulnerablhty and robustness. However, me classical network models show great inconsistence with the actual power grid. By the extension and improvement of BA scale-free network model, a temporal and spatial evolvement model of complex power network is proposed based on the essential evolution mechanism of power grid. The concept of growing-points is proposed, which are defined as the positions nearby the existing nodes but not occupied. The position of a new node is selected from the growing-points randomly. The probability of an existing node connecting to the new node is calculated based on the degree of the existing node and the physical distance between them. The statistical properties of the proposed model are analytically studied. Comparisons of West American power grid and North China power grid with some typical network models in average degree, clustering coefficient, degree distribution and average path length indicate that, the new network model captures the essential features of real-world power grid.