基于复杂系统理论的电网故障时空分布特性及结构脆弱性研究

发布时间：2018-06-20 02:30

本文选题：电网故障 + 连锁故障　；参考：《华南理工大学》2014年博士论文

【摘要】：随着电网规模不断扩大和区域联网，电网发生连锁故障的风险不断增加。大量的故障统计数据表明，尽管电网发生连锁故障的概率较小，但其一旦发生，其后果是极其严重的。因此，认识电网连锁故障并揭示其形成机理具有重要的现实意义和理论价值。本文应用复杂系统理论分析电网故障的时空分布特性和电网结构的分形特性，试图从新的角度认识电网的自组织临界性，从而更细致地描述电网的脆弱性以及电网连锁故障的发生机理。本文重点在以下几个方面开展了较为深入的研究：第一，发现电网故障在时间上具有强长程相关性，空间上具有幂律分布特性。经统计分析某省级电网12年零8个月的实际故障数据，得出电网故障时间间隔序列具有无标度特性；采用R/S和SWV模型计算Hurst指数，得到的Hurst指数均为0.86以上，说明电网故障序列具有强长程相关性，存在异常扩散；将故障序列按故障发生位置所属的设备分为五个子序列，各子序列仍然具有无标度性和长程相关性。通过对该省级电网故障的发生地点进行统计，，得到电网故障的地点与其出现的频次呈幂律分布。第二，发现电网拓扑结构具有相似性。通过对五个电网分别构建无权和加权网络模型，实证分析了电网的中心性和层次性，得到五个电网都具有小世界特性，并寻找到电网拓扑结构中的关键节点；发现无权电网具有异配性，度分布为指数分布，而加权电网具有同配性，点权分布有幂律尾现象。此外，详细讨论了在电网中起重要传输作用的三节点和四节点模体，得出由500kV和220kV线路构成的子图是电网模体的主要结构形式。这些结构子图也是电网的关键组元，并起着主要的传输作用。由于高电压等级的节点互连成为电网的模体，使得加权电网总体上表现为同配性质。第三，发现电网拓扑结构的特征值谱具有多重分形特征。基于IEEE118节点系统和某省级电网系统，构建了以导纳为边权的加权拓扑模型，得到相应拓扑结构的邻接矩阵和拉普拉斯矩阵。采用MF-DFA方法对电网两类矩阵的特征值谱进行分析，发现这两类矩阵的特征值谱都表现出典型的多重分形特征，说明了电网结构在生长和演化过程中具有某种程度上的统计相似性，而且是一种内在的固有特性。虽然不同电网系统特征值谱的多重分形特性之间有些差异，但基于拉普拉斯矩阵特征值谱的多重分形特性在不同电网系统间的差异明显减少，表明拉普拉斯矩阵特征值谱体现了更一般的网络结构特征。第四，提出分析电网线路故障传播的阈值模型。基于该阈值模型定量地分析了电网线路故障引起连锁故障的临界阈值，并发现线路的临界阈值越大，该线路对电网系统的脆弱性影响程度就越大。此阈值模型为电网寻找关键线路提供了新方法。通过两个不同规模的算例实证分析，证明了此方法的正确性和有效性。
[Abstract]:With the expansion of power grid scale and regional interconnection, the risk of cascading faults is increasing. A large number of fault statistics show that, although the probability of cascading faults in power network is small, once they occur, the consequences are extremely serious. Therefore, it is of great practical significance and theoretical value to understand the cascading faults and reveal the formation mechanism of them. In this paper, the space-time distribution characteristics of power network faults and the fractal characteristics of power network structure are analyzed by using the complex system theory, and the self-organized criticality of the power network is analyzed from a new angle. Thus, the vulnerability of power grid and the occurrence mechanism of cascading faults are described in more detail. This paper focuses on the following aspects: first, it is found that the power grid faults have strong long-term correlation in time and power law distribution in space. Based on the statistical analysis of the actual fault data of a provincial power network for 12 years and 8 months, it is concluded that the fault interval series has scale-free characteristics, and the Hurst exponents are calculated by using the R / S and SWV models, and the Hurst exponents are all above 0.86. The fault sequence is divided into five sub-sequences according to the fault location, and each sub-sequence still has scale-free and long-range correlation. Based on the statistics of the fault location of the provincial power grid, the power law distribution between the fault location and the frequency is obtained. Secondly, it is found that the topology of the power system is similar. Through the establishment of weighted and weighted network models for five power grids, this paper empirically analyzes the centrality and hierarchy of power grid, and obtains that all five power grids have small-world characteristics, and find out the key nodes in the network topology. It is found that the power grid has the heterogeneity, the degree distribution is exponential distribution, and the weighted power grid has the same distribution, and the point weight distribution has the phenomenon of power law tail. In addition, the three-node and four-node motifs which play an important role in transmission in the power network are discussed in detail. It is concluded that the sub-graph composed of 500kV and 220kV transmission lines is the main structural form of the motifs. These structural subgraphs are also key components of the grid and play a major role in transmission. Because of the interconnection of nodes of high voltage level into the mode of power grid, the weighted power grid is identical in nature. Thirdly, it is found that the eigenvalue spectrum of power network topology has multifractal features. Based on the IEEE 118 bus system and a provincial power network system, a weighted topological model with admittance as the edge weight is constructed, and the adjacent matrix and Laplace matrix of the corresponding topology structure are obtained. The MF-DFA method is used to analyze the eigenvalue spectrum of two kinds of matrices in power network. It is found that the eigenvalue spectrum of these two kinds of matrices shows typical multifractal characteristics. It is shown that the network structure has some degree of statistical similarity in the process of growth and evolution, and it is an inherent characteristic. Although there are some differences between multifractal characteristics of eigenvalue spectrum in different power systems, the multifractal characteristics based on Laplace matrix eigenvalue spectrum are significantly reduced among different power systems. It is shown that the eigenvalue spectrum of Laplace matrix embodies more general characteristics of network structure. Fourth, a threshold model for power line fault propagation is proposed. Based on the threshold model, the critical threshold of cascading fault caused by power line fault is quantitatively analyzed, and it is found that the greater the critical threshold of line, the greater the influence of the line on the vulnerability of power system. This threshold model provides a new method for power grid to find key lines. The validity and validity of this method are proved by two examples of different scales.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM711

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