复杂电力系统脆弱性评估方法研究
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摘要
电力系统的安全稳定运行关系到国计民生与国家安全，近年来国内外频繁发生的大停电事故引起了人们的广泛关注。随着电力系统容量和规模的逐步扩大，为了增强电力系统的鲁棒性，不断通过高度结构化、最优的设计来实现电网现代化，电力系统变得越来越复杂，而复杂的系统在具有鲁棒性的同时，又增加了其脆弱性，“鲁棒性造就了复杂性，复杂性造就了脆弱性，脆弱性威胁了安全性”。研究表明大规模停电事故往往是由故障连锁反应引起，事故扩大发展阶段则与电力系统中的脆弱环节有着紧密的联系。电力系统脆弱性，是电网安全性概念的拓展，它是从全局角度来评估电力系统安全稳定性的新思路。研究电力系统脆弱性的目的在于，弥补已有大电网安全性研究的不足，深入探讨脆弱性对大电网安全性的影响，为部署电力系统防御策略建立稳固的基础。
针对电力系统脆弱性评估的需求，对复杂电力网络脆弱性评估方法相关问题进行了研究，包括复杂电力系统固有脆弱环节辨识、系统整体脆弱性评估。本文的具体工作如下：
基于复杂网络理论，选取输电线路阻抗值作为线路权重，建立了电网加权拓扑模型，分析了电力系统具有的复杂网络特性。首先，将复杂网络特征参数用于电网脆弱性评估，提出电力系统结构脆弱性评估方法。并将所提方法应用于长沙地区电网，分析了长沙地区电网整体及局部结构特征和脆弱性，时域仿真结果表明系统固有脆弱环节发生故障会极大地威胁到整个电网的安全稳定运行。其次，提出将静态及动态分析法与电网运行状态指标相结合的脆弱性分析方法，长沙地区电网和IEEE-118节点系统算例研究表明，对薄弱环节的攻击会给电力系统带来严重的影响。
针对大规模互联电网连锁故障的复杂传播机理，在电网加权拓扑模型基础上，定义了综合考虑节点和边差异性的加权网络拓扑结构熵的概念。连锁故障过程中结构熵的变化能有效地反映故障传播的速度。为准确描述连锁故障过程中电网结构脆弱性变化趋势，利用遗传算法迭代计算相同规模下系统结构熵指标的最大值与最小值，将连锁故障过程中结构熵值归一化从而消除电网规模对结构熵指标的影响，得到标准化结构熵值。通过分析故障前后电网标准化结构熵值的变化辨识电网结构中的脆弱因素：“异构”线路。对IEEE-118节点系统和华北电网仿真实验说明通过主动移除“异构”线路能改善电网结构脆弱性，增强网络抵抗连锁故障的能力。
分析了电力网潮流分布机理，针对经典复杂网络模型不能很好地结合决定网络潮流分布定律的问题，提取蕴含于电网特征参数中的物理信息，根据叠加原理计算得出电网节点间电气距离，基于电气距离提出了网络节点电气耦合连接度的概念。建立了基于节点电气耦合连接度的电力系统复杂网络特性辨识模型。与已有复杂电网模型相比，该模型更符合电力系统实际。通过对IEEE标准示例系统的计算，揭示了电网内在的异质结构特性。并将电气耦合连接度指标应用于电力网关键节点识别，对IEEE-39节点系统和湖南某地区电网进行了分析计算，时域仿真结果表明所提指标比拓扑度指标更为合理有效。
采用影响模型对电力网节点之间相互作用进行描述，结合马尔科夫链模拟电力系统状态演化过程，建立了一种概括电网关键特征的简单电力系统动态模型。根据二进制影响模型下，系统由初始时刻节点故障引发“崩溃”事故概率等于系统影响矩阵对应于特征值1的左特征向量相应位置元素值的原理，提出一种考虑状态演化过程的电网脆弱性评估方法。利用基于节点度值和边介数指标的评估模型分析比较了几种典型拓扑结构网络的脆弱性，结果表明无标度电网较随机网络和小世界网络表现出更高的脆弱性。考虑决定电网节点之间相互作用大小的主要因素：节点“能量”和节点之间等效电气距离，建立了更符合电网实际的系统状态演化模型。将其应用于EPRI-36系统和广东省电网脆弱性分析，与已有基于网络凝聚度的节点关键性指标和节点介数的比较表明所提方法考虑了系统状态演化过程，比已有模型更为合理有效，有利于从系统层面指导电网的在线安全分析。
提出考虑发电机调速及负荷电压、频率特性的动态潮流连锁故障模式搜索方法，并将其应用于电力系统连锁故障机理分析。根据故障状态下雅克比矩阵对角元素值的变化，推导出系统电压稳定评估指标和系统处于电压崩溃临界点时的电压临界值。随着负载率的增大，系统电压稳定指标会逐渐下降，但临界值始终维持在0.5左右。将所提评估指标应用于电网关键线路辨识，对IEEE-39节点系统的仿真表明：所提线路关键性指标比传输功率和权重介数指标更为全面。PSASP时域仿真结果验证了所提方法的有效性。
The safe and stable operation of power system is crucial for national economy aswell as people’s livelihood and national security, but the blackouts occurringfrequently in recent years have attracted extensive attention. In order to enhance therobustness of power system, we must modernize the power grid through highlystructured and optimal design because of the capacity and scale of power systemexpanding gradually. As the power system becomes increasing complex, the complexsystem which is always considered as robust one is getting more and more vulnerable,which means robustness creates complexity while complexity creates vulnerability,causing threats on the security of power system that is brought by vulnerability. Muchresearch has been observed that blackouts are often triggered by cascading failures,enlarging by the vulnerabilities of power system. Vulnerability of power grid isextending concept of security contributing to evaluate the security and stability ofpower system from global perspective. Research on vulnerability of power system ismaking up for its security study, but also it worth to be realized deeply as well tobuild stronger foundation for strategic power infrastructure defense system.
This paper is focused on the practical requirements of power systemvulnerability assessment, and then in-depth researches have been carried out bymethods of complex power grid vulnerability assessment, including identification ofvulnerabilities of power system and power system vulnerability assessment. The mainstructure and the research content of this paper are summarized as follows:
Firstly, the weighted power grid was established based on complex networktheory by choosing impedance of transmission lines as the weighted parameter, andthen the structural vulnerability assessment method for power grid was presented.With regional network of Changsha as example, complex network feature parameterswere applied to vulnerability assessment of power grid. The vulnerabilities andstructural characteristics of Changsha regional network had been analyzed andreviewed. The time-domain simulation results show that vulnerable component outagewould lead to catastrophic failure in power system. What’s more, the structuralvulnerability assessment of Changsha regional network and IEEE118-bus system,which based on static and dynamic analysis method, was also combining with running state of power grid. Simulation results indicated that intentional attack on vulnerableelements could lead to serious problems such as cascading failure.
Secondly, To figure out how large-scale blackouts take place, animpedance-based topological model and cascading failure model for weighted powergrid was proposed. Considering differences of both node and edge to define a newnetwork structure entropy which was used to describe the faults evolutionquantitatively and unbalanced distribution edges in power network structure. Thestructure entropy had important influence on the spread of cascading failures. Thestandard structure entropy was proposed by GA(genetic algorithm)in order to easeinfluence of varying size of power grid during cascade. The change of standardstructure entropy during cascading failure was a way to capture “heterogeneity” ofpower grid. Simulation results of IEEE118-bus system and North-China powersystem indicated that intentional removal of some edges according to their standardstructure entropy could decrease heterogeneity of the grid structure and migratecascading failure.
Thirdly, studying the complex network characteristics of power grids andfeatures of cascading failure progress was extremely important to anticipate blackouts.The physical laws of power flow through network were also studied. However therewere some typical complex network models which were not incorporate the physicallaws of electricity explicitly. Thus, this paper defined each distance between pairs ofnodes calculated according to superimposed principle based on the informationcontaining character of power grid network. The identification model of power gridwas built on a more comprehensible physical background than the existing models.This new model was based on the electrical coupling connectivity metric which wasdefined according to electrical distance between nodes. Numeric example of IEEE testsystems show the internal heterogeneous structural character of power grids. Then theelectrical coupling connectivity metric was applied to critical nodes identification inpower grids. With IEEE39-bus system and regional power grid of Hunan province asexample, the time domain simulation as well, all simulation results indicated theindex of this paper were more reasonable and effective than the topological degree.
The dynamic model which summarized the key features of power grid waspresented by employing influence model to describe the interaction between nodes,while the evolution of the system states was within Markov chain. A vulnerabilityassessment method was presented according to a theory that the probabilit y of power system state changed from normal to collapse equaled to the corresponding element ofleft eigenvector of the irreducible influence matrix associated with its dominanteigenvalue of1based on the binary influence model. Vulnerability was treatedanalytically and numerically for several networks with different topological structureby employing assessment model based on node degree and edge betweenness. Resultsindicated that the scale-free network was more vulnerable than the random andsmall-world network. The more realistic evolvement model was built by consideringthe energy of nodes and equivalent electrical distance between nodes which determinethe influence between corresponding nodes. Numeric examples of the EPRI-36andGuangdong power grid demonstrate the validity and simpleness of the proposedmethod compared with the node betweenness and node importance according tonetwork cohesion degree, therefore it is beneficial to online security analysis from asystem perspective.
Finally, this paper proposed a search method for power system cascading outagesbased on dynamic power flow which considered the voltage and frequencydependence of loads and generator regulation characteristics. The voltage stabilityevaluation index of power system and its critical value were derived according to thevariation of the Jakob matrix diagonal elements when the operating point of a powersystem was close to voltage collapse point. The voltage stability evaluation index ofpower system would decline gradually but its critical value was steady at around0.5when the load lever increased. The voltage stability evaluation index was applied toidentify vulnerable lines. With IEEE39-bus system as example, simulation resultswere compared with the results typical index such as transmitted power and weightedline betweenness. The results show that the proposed evaluation index was moreuseful and the time-domain simulation results also verified that the proposed methodwas reasonable and valid.
针对电力系统脆弱性评估的需求，对复杂电力网络脆弱性评估方法相关问题进行了研究，包括复杂电力系统固有脆弱环节辨识、系统整体脆弱性评估。本文的具体工作如下：
基于复杂网络理论，选取输电线路阻抗值作为线路权重，建立了电网加权拓扑模型，分析了电力系统具有的复杂网络特性。首先，将复杂网络特征参数用于电网脆弱性评估，提出电力系统结构脆弱性评估方法。并将所提方法应用于长沙地区电网，分析了长沙地区电网整体及局部结构特征和脆弱性，时域仿真结果表明系统固有脆弱环节发生故障会极大地威胁到整个电网的安全稳定运行。其次，提出将静态及动态分析法与电网运行状态指标相结合的脆弱性分析方法，长沙地区电网和IEEE-118节点系统算例研究表明，对薄弱环节的攻击会给电力系统带来严重的影响。
针对大规模互联电网连锁故障的复杂传播机理，在电网加权拓扑模型基础上，定义了综合考虑节点和边差异性的加权网络拓扑结构熵的概念。连锁故障过程中结构熵的变化能有效地反映故障传播的速度。为准确描述连锁故障过程中电网结构脆弱性变化趋势，利用遗传算法迭代计算相同规模下系统结构熵指标的最大值与最小值，将连锁故障过程中结构熵值归一化从而消除电网规模对结构熵指标的影响，得到标准化结构熵值。通过分析故障前后电网标准化结构熵值的变化辨识电网结构中的脆弱因素：“异构”线路。对IEEE-118节点系统和华北电网仿真实验说明通过主动移除“异构”线路能改善电网结构脆弱性，增强网络抵抗连锁故障的能力。
分析了电力网潮流分布机理，针对经典复杂网络模型不能很好地结合决定网络潮流分布定律的问题，提取蕴含于电网特征参数中的物理信息，根据叠加原理计算得出电网节点间电气距离，基于电气距离提出了网络节点电气耦合连接度的概念。建立了基于节点电气耦合连接度的电力系统复杂网络特性辨识模型。与已有复杂电网模型相比，该模型更符合电力系统实际。通过对IEEE标准示例系统的计算，揭示了电网内在的异质结构特性。并将电气耦合连接度指标应用于电力网关键节点识别，对IEEE-39节点系统和湖南某地区电网进行了分析计算，时域仿真结果表明所提指标比拓扑度指标更为合理有效。
采用影响模型对电力网节点之间相互作用进行描述，结合马尔科夫链模拟电力系统状态演化过程，建立了一种概括电网关键特征的简单电力系统动态模型。根据二进制影响模型下，系统由初始时刻节点故障引发“崩溃”事故概率等于系统影响矩阵对应于特征值1的左特征向量相应位置元素值的原理，提出一种考虑状态演化过程的电网脆弱性评估方法。利用基于节点度值和边介数指标的评估模型分析比较了几种典型拓扑结构网络的脆弱性，结果表明无标度电网较随机网络和小世界网络表现出更高的脆弱性。考虑决定电网节点之间相互作用大小的主要因素：节点“能量”和节点之间等效电气距离，建立了更符合电网实际的系统状态演化模型。将其应用于EPRI-36系统和广东省电网脆弱性分析，与已有基于网络凝聚度的节点关键性指标和节点介数的比较表明所提方法考虑了系统状态演化过程，比已有模型更为合理有效，有利于从系统层面指导电网的在线安全分析。
提出考虑发电机调速及负荷电压、频率特性的动态潮流连锁故障模式搜索方法，并将其应用于电力系统连锁故障机理分析。根据故障状态下雅克比矩阵对角元素值的变化，推导出系统电压稳定评估指标和系统处于电压崩溃临界点时的电压临界值。随着负载率的增大，系统电压稳定指标会逐渐下降，但临界值始终维持在0.5左右。将所提评估指标应用于电网关键线路辨识，对IEEE-39节点系统的仿真表明：所提线路关键性指标比传输功率和权重介数指标更为全面。PSASP时域仿真结果验证了所提方法的有效性。
The safe and stable operation of power system is crucial for national economy aswell as people’s livelihood and national security, but the blackouts occurringfrequently in recent years have attracted extensive attention. In order to enhance therobustness of power system, we must modernize the power grid through highlystructured and optimal design because of the capacity and scale of power systemexpanding gradually. As the power system becomes increasing complex, the complexsystem which is always considered as robust one is getting more and more vulnerable,which means robustness creates complexity while complexity creates vulnerability,causing threats on the security of power system that is brought by vulnerability. Muchresearch has been observed that blackouts are often triggered by cascading failures,enlarging by the vulnerabilities of power system. Vulnerability of power grid isextending concept of security contributing to evaluate the security and stability ofpower system from global perspective. Research on vulnerability of power system ismaking up for its security study, but also it worth to be realized deeply as well tobuild stronger foundation for strategic power infrastructure defense system.
This paper is focused on the practical requirements of power systemvulnerability assessment, and then in-depth researches have been carried out bymethods of complex power grid vulnerability assessment, including identification ofvulnerabilities of power system and power system vulnerability assessment. The mainstructure and the research content of this paper are summarized as follows:
Firstly, the weighted power grid was established based on complex networktheory by choosing impedance of transmission lines as the weighted parameter, andthen the structural vulnerability assessment method for power grid was presented.With regional network of Changsha as example, complex network feature parameterswere applied to vulnerability assessment of power grid. The vulnerabilities andstructural characteristics of Changsha regional network had been analyzed andreviewed. The time-domain simulation results show that vulnerable component outagewould lead to catastrophic failure in power system. What’s more, the structuralvulnerability assessment of Changsha regional network and IEEE118-bus system,which based on static and dynamic analysis method, was also combining with running state of power grid. Simulation results indicated that intentional attack on vulnerableelements could lead to serious problems such as cascading failure.
Secondly, To figure out how large-scale blackouts take place, animpedance-based topological model and cascading failure model for weighted powergrid was proposed. Considering differences of both node and edge to define a newnetwork structure entropy which was used to describe the faults evolutionquantitatively and unbalanced distribution edges in power network structure. Thestructure entropy had important influence on the spread of cascading failures. Thestandard structure entropy was proposed by GA(genetic algorithm)in order to easeinfluence of varying size of power grid during cascade. The change of standardstructure entropy during cascading failure was a way to capture “heterogeneity” ofpower grid. Simulation results of IEEE118-bus system and North-China powersystem indicated that intentional removal of some edges according to their standardstructure entropy could decrease heterogeneity of the grid structure and migratecascading failure.
Thirdly, studying the complex network characteristics of power grids andfeatures of cascading failure progress was extremely important to anticipate blackouts.The physical laws of power flow through network were also studied. However therewere some typical complex network models which were not incorporate the physicallaws of electricity explicitly. Thus, this paper defined each distance between pairs ofnodes calculated according to superimposed principle based on the informationcontaining character of power grid network. The identification model of power gridwas built on a more comprehensible physical background than the existing models.This new model was based on the electrical coupling connectivity metric which wasdefined according to electrical distance between nodes. Numeric example of IEEE testsystems show the internal heterogeneous structural character of power grids. Then theelectrical coupling connectivity metric was applied to critical nodes identification inpower grids. With IEEE39-bus system and regional power grid of Hunan province asexample, the time domain simulation as well, all simulation results indicated theindex of this paper were more reasonable and effective than the topological degree.
The dynamic model which summarized the key features of power grid waspresented by employing influence model to describe the interaction between nodes,while the evolution of the system states was within Markov chain. A vulnerabilityassessment method was presented according to a theory that the probabilit y of power system state changed from normal to collapse equaled to the corresponding element ofleft eigenvector of the irreducible influence matrix associated with its dominanteigenvalue of1based on the binary influence model. Vulnerability was treatedanalytically and numerically for several networks with different topological structureby employing assessment model based on node degree and edge betweenness. Resultsindicated that the scale-free network was more vulnerable than the random andsmall-world network. The more realistic evolvement model was built by consideringthe energy of nodes and equivalent electrical distance between nodes which determinethe influence between corresponding nodes. Numeric examples of the EPRI-36andGuangdong power grid demonstrate the validity and simpleness of the proposedmethod compared with the node betweenness and node importance according tonetwork cohesion degree, therefore it is beneficial to online security analysis from asystem perspective.
Finally, this paper proposed a search method for power system cascading outagesbased on dynamic power flow which considered the voltage and frequencydependence of loads and generator regulation characteristics. The voltage stabilityevaluation index of power system and its critical value were derived according to thevariation of the Jakob matrix diagonal elements when the operating point of a powersystem was close to voltage collapse point. The voltage stability evaluation index ofpower system would decline gradually but its critical value was steady at around0.5when the load lever increased. The voltage stability evaluation index was applied toidentify vulnerable lines. With IEEE39-bus system as example, simulation resultswere compared with the results typical index such as transmitted power and weightedline betweenness. The results show that the proposed evaluation index was moreuseful and the time-domain simulation results also verified that the proposed methodwas reasonable and valid.
引文
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