摘要
近年来,跨区跨国的大规模电网互联已经成为全世界范围电力系统发展的大趋势。但是电网这种能将电能输送到数百、上千公里以外的能力同样使得局部故障可能迅速传播到大区域甚至整个网络。传统的分析方法在深入分析电力网连锁故障和大停电机理等系统行为方面已经显露出一定的局限性,有必要发展新的系统分析方法来研究复杂电力网的动态行为。复杂性理论和复杂网络理论就为探索互联大电网提供了一个新视角和方法。
本文在对包括随机网络、小世界网络和无标度网络等复杂网络理论进行概述的基础上,关注了连锁故障及其导致的重大停电事故。通过对我国电网大停电事故中特征变量概率分布的统计分析,阐述了大停电规模与频率之间呈现出的幂律关系和自组织临界特性。进一步使用R/S时间序列分析法,求得了大停电相关特征参量时间序列的Hurst指数,并对我国电网大停电的分形分维特性进行了分析。在对实际电网进行复杂网络拓扑建模的基础上,揭示了中外电网度分布的指数分布特性、介数的负幂律自相似特性和Zipf分形特性以及小世界特性。
首先采用静态分析法,进而在动态分析法中引入节点一线路混合动态分析模式和基于故障概率法的网络流一容量模型,通过最大连通度及平均距离与移除元件比例之间的变化关系,对网络基于随机故障的鲁棒性和基于蓄意攻击的脆弱性进行了研究。实际电网度分布的不均衡性使其对于随机故障具有很高的鲁棒性,对高介数元件的蓄意攻击具有高度的脆弱性,高介数的网络元件是电网中最脆弱且最关键的部分。进而从全网角度揭示了电网节点度数和介数之间的幂律关系,对电网连锁故障中的临界行为进行了分析,并以我国华东电网为例,对网络临界行为中耐受性参数的相变点进行了理论推导。
引入了复杂网络效能模型,提出了基于电气距离矩阵的效能评估方法,对我国华东电网和华中电网在连锁故障中的效能变化进行了仿真分析。进而引入带权重的线路介数概念,以赋权线路介数作为指标进行电网脆弱性分析,对IEEE39节点系统和华中电网的脆弱线路进行了辨识,并通过时域仿真进行了验证。
在度分布符合指数规律的电力网中,提出了基于复杂网络理论的故障传播概率指标,在理论推导的基础上得出了实际电网的故障传播概率值,提出了通过改变网络拓扑参数、优化网络结构从而降低故障传播风险,特别是连锁故障传播风险的宏观调控方案。并对节点平均度数恒定不变,即给定费用经济约束条件下的无标度网进行了分析研究。通过故障传播概率分析法和基于元件移除的网络连通性分析法,利用函数图像法和遗传算法优化求解得出了度数恒定的无标度网的结构优化方案,即在区间(2,3]的范围内减小无标度网度分布的幂指数值,既可以降低故障传播的风险,也可增强网络的连通性,从而为无标度网的设计、规划和改造提供优化目标和理论参考。
以浙江省电力通信网为例,对电力通信网物理路由网的复杂网络特性进行了分析研究。浙江省电力通信网的度分布满足指数规律,为局域世界网络,其地区子网均为无标度网络,且省网和各地区子网均为小世界网络。基于静态分析法的鲁棒性和脆弱性分析表明,电力通信物理路由网对于节点和边的随机故障和意外攻击具有极强的鲁棒性,而对于针对高度数节点的蓄意攻击和破坏却具有很高的脆弱性;在基于最短路径路由的通讯原则下,应该加大对电力通信网中高度数节点和高介数节点(线路)的保护。
With the rapid development of global economics, large-scaled interconnection of power grids has become an inevitable trend for power systems all over the world. While, the capability of power grid to transfer power over hundreds or thousands of miles also enables the propagation of local failures into global network. Traditional methods have already confronted the limitation in comprehending the mechanism of cascading failure. New solutions are instantly needed to simulate and study the dynamics of complex power system. The theory of complexity and complex network provide an original perspective of global network from the point of view of system level.
Based on the summary of complex network theory, including random network, small-world network and scale-free network, the recent blackouts throughout the world and the mechanism of cascading failures draw our attention. Through the statistics and analysis of character variables of domestic power grid accidents with load loss, the power law relationship between the blackout dimension and frequency is discovered, and the theory of Self-Organized Criticality is used to explain such phenomena. Using the method of R/S Analysis, the Hurst exponents of blackout series are respectively calculated, and the fractal characteristic is also explained. With the topology modelling of real-world power grids, the exponentail law of degree distribution, the negative power law and self-similarity of betweenness, the Zipf fractal feature and small-world effect are respectively testified.
Based on the strategies of random failure and intentional attack, both the static analysis and dynamic analysis are adopted to study the robustness and vulnerability of networks. The real-world power grids are robust to random failures and are highly vulnerable to intentional attacks on components with high betweenness due to the heterogeneous topology and degree distribution disequilibrium of power grids. The relationship between node degree and average betweenness has the feature of power law, and the phase-transition point of tolerance parameter in the critical behavior of cascading failure is derived theoretically. The computed critical value shows its consistency with the practical dynamic simulation results in east China power grid.
With the utilization of global efficiency model, a new efficiency evaluation model with electric distance matrix is proposed, and the efficiency of east and central China power grid is evaluated. Then, a new vulnerability index called weighted line betweenness is proposed to identify the critical lines in the power grid. The simulations on IEEE 39 bus system and central China power grid prove the efficiency of this new vulnerability index.
In power grid with exponentail degree distribution, the method of failure propagation probability over entire network is proposd. The macro-control scheme is proposed to adjust the topological parameters in order to optimize the network structure, which could reduce the risk of component failure propagation, especially the risk of cascading failure. And scale-free network with consistent average degree, namely under the economic constraint of fixed cost, is studied. The failure propagation probalility and connectivity analysis under static removal of components are respectively introduced. Through function graphs and the computation of GA algorithm, we can draw a conclusion that, decreasing the power exponent of scale-free network in the interval of (2,3], can not only decrease the risk of failure propagation, but also improve the tolerance and connectivity of scale-free networks. This structure optimization solution can provide an optimal and theoretical reference for engineers and designers.
The research on electric power communication physical route network shows that, Zhejiang power communication network is a local-world network and its sub-networks are all scale-free networks, and these nets entirely have the character of small-world effect. The static analysis indicates that, power communication network displays topology robustness against random node and edge failures, but is fragile to intentional attacks of high degree nodes. Under the communication principle of shortest path route, the protection of components with high degree and high betweenness is of great importance.
引文
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