Research On Vulnerability And Controllability Of Power Grids Based On Complex Network Theory

With the realization of large-scale interconnection of smart grids,today's power system has become a huge high-dimensional,multi-level nonlinear dynamic system,which is closely related to national production and life,its reliability,vulnerability,controllability and safety is becoming more and more important and has received widespread attention from scholars all over the world.When analyzing large-scale power networks,because of the complexity of the environment,the unpredictable state of the system operation,and the randomness of faults,the analysis of its dynamic characteristics and operating conditions is very difficult.Based on the traditional reductionism method,it is impossible to perfectly construct a large-scale interconnection grid model and it is also difficult to analyze the overall dynamic and macro characteristics of the system.Complex network theory uses mathematics and statistics to analyze the overall dynamic characteristics of the network,focusing on how the interaction between sub-networks in large networks affects the overall nonlinear dynamics,so that the analysis of problems based on complex networks has been widely used in various disciplines.As a nonlinear large-scale dynamic system,the power system is a typical complex network.For the vulnerability analysis,the previous methods are based on the differential equations theory.However,in the smart grid situation,the power system structure has changed a lot,and the traditional analysis methods have been unable to do so.In addition,the control problems of real complex systems can be abstracted into controllability problems,and few studies have been carried out for the controllability of power networks.Based on the above background and problems,considering the limitations of the traditional reductionism method,this dissertation seeks to analyze the modeling,vulnerability and controllability of the power network from the structural aspect based on complex networks,and also to verify the latest complex network theory,and lay the foundation for future structural analysis and trend analysis.The main research work of this dissertation is as follows:(1)Aiming at the problem of power network modeling,this thesis proposes a new evolving model based on geographical location clustering,considering that the local world evolving model of power networks can not fully reflect the characteristics of real world power networks,and the geographical location of new nodes in the evolution of power grid can greatly influence the network topology connection and comprehensive performance.The proposed model takes into account the geography locations and the degree of nodes,and the growth process is in line with the characteristics of the power network.Compared with the characteristics of real-world networks,the results show that the model can simulate the distribution of China's power grids when the number of nodes is small.When the number of nodes exceeds 800,this model can simulate the USA western power grid's degree distribution.And the average distances and clustering coefficients of the proposed model are close to that of the real world network.These properties confirm the validity and rationality of our model.(2)Aiming at the problem of vulnerability analysis based on the centrality of power grids,a variety of classic centrality indicators are investigated.This thesis presents a new centrality,called overall information centrality.It not only considers the information of each node itself,but also considers the mutual information between each node and its neighbors.Based on the IEEE power grids and the domestic power networks,we do the simulation test and compare the proposed centrality with the classic centralities in terms of the effectiveness of attacking the power grid structure.Simulation tests showed that the overall information centrality is superior to other centralities,especially for networks with smaller average degree values.(3)Aiming at the problem of vulnerability analysis based on the centrality of power grids,we continue to examine various betweenness based centralities.Aiming at the defect of traditional betweenness metric and Newman's first order betweenness centrality,this thesis uses the distributed second-order centrality proposed by Kermarrec et al.Based on the IEEE power grids and the domestic power networks,we do the simulation test and compare the second-order centrality with the classic centralities in terms of the effectiveness of attacking the power grid structure.Simulation tests showed that the second-order centrality based schemes are better than other centrality based schemes,especially for diaassortive or near neutral real-world power grids.(4)The controllability of the power system is studied by using the controllability theory in the field of complex networks developed in recent years.Currently,the research object of complex network controllability theory is mainly biased towards a network model with randomness,and there are few reports on real deterministic power network analysis.Considering the certainty and unique degree distribution characteristics of power network,this dissertation studies the controllability of power grid from the perspective of undirected network by using the strict controllability theory,first calculates the controllability of the actual power grid at home and abroad.Then,the law of controllability and the influence of the structural characteristics(betwwennness,degree distribution,degree heterogeneity,etc.)of the network on the controllability are found,and several unique and important conclusions are obtained as follows: most of the driver nodes of the power grid are nodes with low degree values of 1 or 2;the power grid is more difficult to control than the WS network and the CM network,and it is easier to control than the BA network.The controllability of the power network depends mainly on the degree distribution and degree heterogeneity.It is the most difficult to control the spatially heterogeneous power network.The driving nodes of the power network tend to be the low degree nodes and avoid the Hub nodes,but the neighboring nodes of the driver nodes tend to be the Hub nodes.The driving nodes tend to be low betweenness nodes and avoid high betweenness nodes.(5)The application of the vulnerability and controllability of the power network in the actual power grid analysis and processing is researched.Aiming at the vulnerability of a power grid,a circuit isolation method based on circuit vulnerability is proposed.Firstly,the link is selected as the object of vulnerability assessment.The integrated state vulnerability,link betweenness and node second-order centrality establish indicators to identify link vulnerability and construct a vulnerable link set.Secondly,the link isolation algorithm is used to isolate a link in a vulnerable link set to prevent the accident from spreading over a large area.Taking the IEEE118 system as an example for simulation experiments,the results show that this method not only isolates the faults when dealing with the cascading accidents caused by fragile lines,but also ensures the power balance of each part,which is effective and feasible.Aiming at the controllability of power grid,this dissertation proposes a vulnerability analysis method for power grid nodes based on the controllability derived control capability,that is,attack testing based on the control ability of nodes.Through the analysis and research on the actual US Power Grid network,it is found that the control capacity ascending order based attacking method is more effective than other attacking methods,indicating that the node with smaller control capacity is more important to the network,and greater damage will be imposed on the network if it is attacked.