Research On Structural Complexity And Vulnerability Of Power Grids Based On Complex Network Theory

Power grid is one of the most complex artificial systems in the world. Frequent large scale blackouts expose the potential problems of current analysis methods based on the reduction theory. Thus, it is a new focus to apply complexity science to study the complexity of power grids and the mechanisms of blackouts.Power grids can be conceptually described as networks, where nodes represent the buses in power grids and where the edges connecting them represent transmission lines. Complex network theory can be used to study the structural complexity and vulnerability of power grids. But in the current research, the models applied in power grids based on complex networks are very simple and abstract. These models ignore the electrical characteristics of power grids, so the conclusions are different from practical situations. It was assumed that electric power was transmitted through the shortest or the most effective paths. The existing studies do not consider the influence of load levels in power grids. The indexes evaluating the performances of power grids after failures or attacks are based on graph theory, and can not fully reflect the changes of electrical states. In this paper, complex network theory will be combined with electrical characteristics to make the conclusions close to practical situations of power grids. The main research works and results are as follows:The structural complexity of power grids is studied based on complex networks. The electrical betweenness of nodes and lines is defined, and the calculation method is proposed. Compared with the existing betweenness index, the model proposed in this paper no longer assumes that electric power is transmitted through the shortest or the most effective paths and can consider the influence of the capacity and distributions of generators and load. It can also handle the power grids containing HVDC and FACTS. The simulation results of the IEEE-118 bus system and the 500kV grid of Central China Power Gird show that the electrical betweenness distributions of nodes and lines follow the powe-law. The power grids possess a highly heterogeneous distribution of electrical betweenness. It means that there are a few nodes and lines with high electrical betweenness which have to transmit extremely high power in the network. The heterogeneity is the root of the structural vulnerability of power grids.The structural vulnerability of power grids is studied based on the static analysis method. An index called loss of load is introduced to measure the power supply ability of power grids after failures or attacks. The simulations results show that high voltage power transmission grids are robust against random attacks, but the power supply ability and the network connectivity will suffer significantly if the nodes and lines with high electrical betweenness are removed continuously. It not only shows that it is reasonable to measure the vulnerability from the power supply ability and the network connectivity, but also verify that the heterogeneity can be reflected by electrical betweenness. Then, the cause and importance of the nodes and lines with high electrical betweenness are analyzed. The electrical betweenness of the long-distance transmission lines and their end-points will be higher due to the small-world characteristics of power grids. The electrical betweenness of the nodes with a large amount of generated and consumed power will be higher due to the uneven capability distribution of generators and load. The nodes and lines with high electrical betweenness play important roles in maintaining the power supply ability and the network connectivity of power grids.The cascading failure and its critical characteristic are studied. A node cascading failure model based on complex networks is proposed. In the proposed model, the node electrical betweenness is used to define the load carried by the nodes, and the tolerance parameter can reflect the relationship between the maximal power transfer capability and the current load level. The probability method is applied to select and remove the overloaded nodes. The simulation results reveal that there is a critical state in the behavior of cascading failures of power grids. When the load level increases to a certain critical value, the random attacks will cause serious cascading failures. Finally, the calculation method of critical tolerance parameters is proposed.The identification method of key nodes and lines to prevent large scale blackouts is studied. The structure importance indexes and the calculation methods are proposed to identify the key nodes and lines of power grids. The static importance index can reflect the significance of nodes and lines in maintaining the power supply ability and the network connectivity of power grids. The dynamic importance index can reflect the probability of nodes and lines to cause the cascading failures. It will reduce the risk of large scale blackouts by protecting those key nodes and lines.