This study considers the performance impacts of false data injection attacks on the cascading failures of a power cyber-physical system,and identifies vulnerable nodes.First,considering the monitoring and control func...This study considers the performance impacts of false data injection attacks on the cascading failures of a power cyber-physical system,and identifies vulnerable nodes.First,considering the monitoring and control functions of a cyber network and power flow characteristics of a power network,a power cyber-physical system model is established.Then,the influences of a false data attack on the decision-making and control processes of the cyber network communication processes are studied,and a cascading failure analysis process is proposed for the cyber-attack environment.In addition,a vulnerability evaluation index is defined from two perspectives,i.e.,the topology integrity and power network operation characteristics.Moreover,the effectiveness of a power flow betweenness assessment for vulnerable nodes in the cyberphysical environment is verified based on comparing the node power flow betweenness and vulnerability assessment index.Finally,an IEEE14-bus power network is selected for constructing a power cyber-physical system.Simulations show that both the uplink communication channel and downlink communication channel suffer from false data attacks,which affect the ability of the cyber network to suppress the propagation of cascading failures,and expand the scale of the cascading failures.The vulnerability evaluation index is calculated for each node,so as to verify the effectiveness of identifying vulnerable nodes based on the power flow betweenness.展开更多
This paper designs a decentralized resilient H_(∞)load frequency control(LFC)scheme for multi-area cyber-physical power systems(CPPSs).Under the network-based control framework,the sampled measurements are transmitte...This paper designs a decentralized resilient H_(∞)load frequency control(LFC)scheme for multi-area cyber-physical power systems(CPPSs).Under the network-based control framework,the sampled measurements are transmitted through the communication networks,which may be attacked by energylimited denial-of-service(DoS)attacks with a characterization of the maximum count of continuous data losses(resilience index).Each area is controlled in a decentralized mode,and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area.Then,the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances.Under this modeling,a decentralized resilient H_(∞)scheme is presented to design the state-feedback controllers with guaranteed H∞performance and resilience index based on a novel transmission interval-dependent loop functional method.When given the controllers,the proposed scheme can obtain a less conservative H_(∞)performance and resilience index that the LFC system can tolerate.The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.展开更多
Cyber-physical systems(CPS) are characterized by integrating cybernetic and physical processes. The theories and applications of CPS face the enormous challenges. The aim of this paper is to provide a latest understan...Cyber-physical systems(CPS) are characterized by integrating cybernetic and physical processes. The theories and applications of CPS face the enormous challenges. The aim of this paper is to provide a latest understanding of this emerging multi-disciplinary methodology. First, the features of CPS are described, and the research progresses are summarized from different components in CPS, such as system modeling,information acquisition, communication, control and security.Each part is also followed by the future directions. Then some typical applications are given to show the prospects of CPS.展开更多
Cyber-physical systems(CPS) are complex systems with organic integration and in-depth collaboration of computation, communications and control(3C) technology. Subject to the theory and technology of existing network s...Cyber-physical systems(CPS) are complex systems with organic integration and in-depth collaboration of computation, communications and control(3C) technology. Subject to the theory and technology of existing network systems and physical systems, the development of CPS is facing enormous challenges.This paper first introduces the concept and characteristics of CPS and analyzes the present situation of CPS researches. Then the development of CPS is discussed from perspectives of system model, information processing technology and software design.At last it analyzes the main obstacles and key researches in developing CPS.展开更多
Cyber-physical systems(CPSs) are man-made complex systems coupled with natural processes that, as a whole,should be described by distributed parameter systems(DPSs) in general forms. This paper presents three such gen...Cyber-physical systems(CPSs) are man-made complex systems coupled with natural processes that, as a whole,should be described by distributed parameter systems(DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.展开更多
Potential malicious cyber-attacks to power systems which are connected to a wide range of stakeholders from the top to tail will impose significant societal risks and challenges.The timely detection and defense are of...Potential malicious cyber-attacks to power systems which are connected to a wide range of stakeholders from the top to tail will impose significant societal risks and challenges.The timely detection and defense are of crucial importance for safe and reliable operation of cyber-physical power systems(CPPSs).This paper presents a comprehensive review of some of the latest attack detection and defense strategies.Firstly,the vulnerabilities brought by some new information and communication technologies(ICTs)are analyzed,and their impacts on the security of CPPSs are discussed.Various malicious cyber-attacks on cyber and physical layers are then analyzed within CPPSs framework,and their features and negative impacts are discussed.Secondly,two current mainstream attack detection methods including state estimation based and machine learning based methods are analyzed,and their benefits and drawbacks are discussed.Moreover,two current mainstream attack defense methods including active defense and passive defense methods are comprehensively discussed.Finally,the trends and challenges in attack detection and defense strategies in CPPSs are provided.展开更多
CPS1(Control Performance Standard 1)标准在应用于负荷规模悬殊控制区域中,存在适用性问题,故有必要对CPS1标准进行分析以便改进。通过对CPS1标准频率调节责任分配本质内涵的剖析,和负荷波动幅度与负荷规模之间关系的探究,指出CPS1标...CPS1(Control Performance Standard 1)标准在应用于负荷规模悬殊控制区域中,存在适用性问题,故有必要对CPS1标准进行分析以便改进。通过对CPS1标准频率调节责任分配本质内涵的剖析,和负荷波动幅度与负荷规模之间关系的探究,指出CPS1标准是依据系统的负荷规模分配频率调节责任。由于负荷波动的平滑效应,负荷规模较大控制区域的负荷随机波动与负荷规模(与发电规模相当)的比值较小,因此,在实际运行中大区域获得较好的评价结果是一个必然现象。在明确了这两种模式下(分别按照系统负荷规模和波动幅度分配频率调节责任)评价标准适用条件的基础上,提出了适用于我国电网运行现状标准的改进方法,即:无需进行B系数分配原则的改动,直接对标准中的B系数进行相关修正即可解决其适应性问题。仿真算例结果分析表明,按照原有标准进行评价,大区域将获得较好的评价结果,而所提出CPS1标准调整方法可有效解决该问题。展开更多
Cyber-physical electrical energy systems(CPEES)combine computation,communication and control technologies with physical power system,and realize the efficient fusion of power,information and control.This paper summari...Cyber-physical electrical energy systems(CPEES)combine computation,communication and control technologies with physical power system,and realize the efficient fusion of power,information and control.This paper summarizes and analyzes related critical scientific problems and technologies,which are needed to be addressed with the development of CPEES.Firstly,since the co-simulation is an effective method to investigate infrastructure interdependencies,the co-simulation platform establishment of CPEES and its evaluation is overviewed.Then,a critical problem of CPEES is the interaction between energy and information flow,especially the influence of failures happening in information communication technology(ICT)on power system.In order to figure it out,the interaction is analyzed and the current analysis methods are summarized.For the solution of power system control and protection in information network environment,this paper outlines different control principles and illustrates the concept of distributed coordination control.Moreover,mass data processing and cluster analysis,architecture of communication network,information transmission technology and security of CPEES are summarized and analyzed.By solving the above problems and technologies,the development of CPEES will be significantly promoted.展开更多
AADL (architecture analysis and design language) concentrates on the modeling and analysis of application system architectures.It is quite popular for its simple syntax,powerful functionality and extensibility and has...AADL (architecture analysis and design language) concentrates on the modeling and analysis of application system architectures.It is quite popular for its simple syntax,powerful functionality and extensibility and has been widely applied in embedded systems for its advantage.However,it is not enough for AADL to model cyber-physical systems (CPS) mainly because it cannot be used to model the continuous dynamic behaviors.This paper proposes an approach to construct a new sublanguage of AADL called AADL+,to facilitate the modeling of not only the discrete and continuous behavior of CPS,but also interaction between cyber components and physical components.The syntax and semantics of the sublanguage are provided to describe the behaviors of the systems.What's more,we develop a plug-in to OSATE (open-source AADL tool environment) for the modeling of CPS.And the plug-in supports syntax checking and simulation of the system model through linking with modelica.Finally,the AADL+ annex is successfully applied to model a lunar rover control system.展开更多
Cyber-physical systems (CPSs) are new emerging systems that seamlessly integrate physical systems, communication systems and computation systems. Their wide use has been witnessed in the past decades in many crossdi...Cyber-physical systems (CPSs) are new emerging systems that seamlessly integrate physical systems, communication systems and computation systems. Their wide use has been witnessed in the past decades in many crossdiscipline fields such as smart energy systems, industrial process control, aerospace and automobile engineering, health-care and assisted living, to just name a few. For many of these systems, secure operations are of key con- cerns. In particular, for some safety-critical applications, security is of paramount importance. Diverse motivations and strong incentives exist everywhere and at any time for launching malicious attacks on the CPSs, for example, economic reasons (e.g., by reducing or even not paying electricity charge) and terrorism the purpose of which is apparent.展开更多
Cyber-physical systems(CPSs) are integrations of networks, computation and physical processes, where embedded computing devices continually sense, monitor, and control the physical processes through networks. Networke...Cyber-physical systems(CPSs) are integrations of networks, computation and physical processes, where embedded computing devices continually sense, monitor, and control the physical processes through networks. Networked industrial processes combining internet, real-time computer control systems and industrial processes together are typical CPSs. With the increasingly frequent cyber-attack, security issues have gradually become key problems for CPSs. In this paper, a cyber-physical system security protection approach for networked industrial processes, i.e., industrial CPSs, is proposed. In this approach, attacks are handled layer by layer from general information technology(IT) security protection, to active protection, then to intrusion tolerance and physical security protection. The intrusion tolerance implemented in real-time control systems is the most critical layer because the real time control system directly affects the physical layer. This novel intrusion tolerance scheme with a closed loop defense framework takes into account the special requirements of industrial CPSs. To illustrate the effectiveness of the CPS security protection approach, a networked water level control system is described as a case study in the architecture analysis and design language(AADL) environment. Simulation results show that 3 types of injected attacks can be quickly defended by using the proposed protection approach.展开更多
The utilization levels of the transmission network can be enhanced by the use of automated protection schemes that rapidly respond to disturbances. However,such corrective systems may suffer from malfunctions that hav...The utilization levels of the transmission network can be enhanced by the use of automated protection schemes that rapidly respond to disturbances. However,such corrective systems may suffer from malfunctions that have the potential to exacerbate the impact of the disturbance. This paper addresses the challenge of jointly optimizing the dispatch of generators and protection settings in this context. This requires a holistic assessment of the cyber(protection logic) and physical(network) systems,considering the failures in each part and their interplay.Special protection schemes are used as a prototypical example of such a system. An iterative optimization method is proposed that relies on power system response simulations in order to perform detailed impact assessments and compare candidate solutions. The candidate solutions are generated on the basis of a security-constrained dispatch that also secures the system against a set of cyber failure modes. A case study is developed for a generation rejection scheme on the IEEE reliability testsystem(RTS): candidate solutions are produced based on a mixed integer linear programming optimisation model, and loss-of-load costs are computed using a basic cascading outage algorithm. It is shown that the partial security approach is able to identify solutions that provide a good balance of operational costs and loss-of-load risks, both in a fixed dispatch and variable dispatch context.展开更多
正常运行时互联电网交流联络线上存在随机功率波动的现象。基于实际2大区互联电网的历史数据,分析了联络线功率偏差、频率偏差以及2大区电网区域控制偏差(area control error,ACE)的统计特性,结果显示:联络线功率偏差表现出良好的正态...正常运行时互联电网交流联络线上存在随机功率波动的现象。基于实际2大区互联电网的历史数据,分析了联络线功率偏差、频率偏差以及2大区电网区域控制偏差(area control error,ACE)的统计特性,结果显示:联络线功率偏差表现出良好的正态分布特性;系统频率偏差和正态分布存在较大差别,原因是电网的频率控制使得频率偏差大于0.03 Hz的概率减小;各控制区的ACE基本服从正态分布。文章认为联络线功率偏差由两端电网的ACE引起,可以通过两端电网ACE的均方根值和相关系数计算出联络线功率偏差的均方根值,从而得到对联络线功率偏差大小分布的估计。对目前采用的T标准进行了分析,得出结论:为实现联络线功率控制的目标,两端电网责任度阈值之和为2即可,不一定要求两端电网责任度的阈值都是1;两端电网责任度阈值的分配还需要综合考虑各种因素进行详细研究,以得到公平合理的方案。展开更多
基金the National Natural Science Foundation of China(61873057)the Education Department of Jilin Province(JJKH20200118KJ).
文摘This study considers the performance impacts of false data injection attacks on the cascading failures of a power cyber-physical system,and identifies vulnerable nodes.First,considering the monitoring and control functions of a cyber network and power flow characteristics of a power network,a power cyber-physical system model is established.Then,the influences of a false data attack on the decision-making and control processes of the cyber network communication processes are studied,and a cascading failure analysis process is proposed for the cyber-attack environment.In addition,a vulnerability evaluation index is defined from two perspectives,i.e.,the topology integrity and power network operation characteristics.Moreover,the effectiveness of a power flow betweenness assessment for vulnerable nodes in the cyberphysical environment is verified based on comparing the node power flow betweenness and vulnerability assessment index.Finally,an IEEE14-bus power network is selected for constructing a power cyber-physical system.Simulations show that both the uplink communication channel and downlink communication channel suffer from false data attacks,which affect the ability of the cyber network to suppress the propagation of cascading failures,and expand the scale of the cascading failures.The vulnerability evaluation index is calculated for each node,so as to verify the effectiveness of identifying vulnerable nodes based on the power flow betweenness.
基金supported by the National Natural Science Foundation(NNSF)of China(62003037,61873303)。
文摘This paper designs a decentralized resilient H_(∞)load frequency control(LFC)scheme for multi-area cyber-physical power systems(CPPSs).Under the network-based control framework,the sampled measurements are transmitted through the communication networks,which may be attacked by energylimited denial-of-service(DoS)attacks with a characterization of the maximum count of continuous data losses(resilience index).Each area is controlled in a decentralized mode,and the impacts on one area from other areas via their interconnections are regarded as the additional load disturbance of this area.Then,the closed-loop LFC system of each area under DoS attacks is modeled as an aperiodic sampled-data control system with external disturbances.Under this modeling,a decentralized resilient H_(∞)scheme is presented to design the state-feedback controllers with guaranteed H∞performance and resilience index based on a novel transmission interval-dependent loop functional method.When given the controllers,the proposed scheme can obtain a less conservative H_(∞)performance and resilience index that the LFC system can tolerate.The effectiveness of the proposed LFC scheme is evaluated on a one-area CPPS and two three-area CPPSs under DoS attacks.
基金supported by National Natural Science Foundation of China(61221003,61174127,61573245,61273181,61503247,61301223)Shanghai Municipal Science and Technology Commission(15QA1402300,14511107903)
文摘Cyber-physical systems(CPS) are characterized by integrating cybernetic and physical processes. The theories and applications of CPS face the enormous challenges. The aim of this paper is to provide a latest understanding of this emerging multi-disciplinary methodology. First, the features of CPS are described, and the research progresses are summarized from different components in CPS, such as system modeling,information acquisition, communication, control and security.Each part is also followed by the future directions. Then some typical applications are given to show the prospects of CPS.
基金supported by National Natural Science of China(61170262,61371177)
文摘Cyber-physical systems(CPS) are complex systems with organic integration and in-depth collaboration of computation, communications and control(3C) technology. Subject to the theory and technology of existing network systems and physical systems, the development of CPS is facing enormous challenges.This paper first introduces the concept and characteristics of CPS and analyzes the present situation of CPS researches. Then the development of CPS is discussed from perspectives of system model, information processing technology and software design.At last it analyzes the main obstacles and key researches in developing CPS.
基金supported by Chinese Universities Scientific Fund(CUSF-DHD-2014061)Natural Science Foundation of Shanghai(15ZR1400800)
文摘Cyber-physical systems(CPSs) are man-made complex systems coupled with natural processes that, as a whole,should be described by distributed parameter systems(DPSs) in general forms. This paper presents three such general models for generalized DPSs that can be used to characterize complex CPSs. These three different types of fractional operators based DPS models are: fractional Laplacian operator, fractional power of operator or fractional derivative. This research investigation is motivated by many fractional order models describing natural, physical, and anomalous phenomena, such as sub-diffusion process or super-diffusion process. The relationships among these three different operators are explored and explained. Several potential future research opportunities are then articulated followed by some conclusions and remarks.
基金supported in part by the National Science Foundation of China(No.92067106)111 Project(No.D18003)。
文摘Potential malicious cyber-attacks to power systems which are connected to a wide range of stakeholders from the top to tail will impose significant societal risks and challenges.The timely detection and defense are of crucial importance for safe and reliable operation of cyber-physical power systems(CPPSs).This paper presents a comprehensive review of some of the latest attack detection and defense strategies.Firstly,the vulnerabilities brought by some new information and communication technologies(ICTs)are analyzed,and their impacts on the security of CPPSs are discussed.Various malicious cyber-attacks on cyber and physical layers are then analyzed within CPPSs framework,and their features and negative impacts are discussed.Secondly,two current mainstream attack detection methods including state estimation based and machine learning based methods are analyzed,and their benefits and drawbacks are discussed.Moreover,two current mainstream attack defense methods including active defense and passive defense methods are comprehensively discussed.Finally,the trends and challenges in attack detection and defense strategies in CPPSs are provided.
文摘CPS1(Control Performance Standard 1)标准在应用于负荷规模悬殊控制区域中,存在适用性问题,故有必要对CPS1标准进行分析以便改进。通过对CPS1标准频率调节责任分配本质内涵的剖析,和负荷波动幅度与负荷规模之间关系的探究,指出CPS1标准是依据系统的负荷规模分配频率调节责任。由于负荷波动的平滑效应,负荷规模较大控制区域的负荷随机波动与负荷规模(与发电规模相当)的比值较小,因此,在实际运行中大区域获得较好的评价结果是一个必然现象。在明确了这两种模式下(分别按照系统负荷规模和波动幅度分配频率调节责任)评价标准适用条件的基础上,提出了适用于我国电网运行现状标准的改进方法,即:无需进行B系数分配原则的改动,直接对标准中的B系数进行相关修正即可解决其适应性问题。仿真算例结果分析表明,按照原有标准进行评价,大区域将获得较好的评价结果,而所提出CPS1标准调整方法可有效解决该问题。
文摘随着电网信息层和物理层的不断融通发展,信息流交互频繁,电力信息物理系统(CPS)面临巨大安全挑战,针对信息层的网络攻击传播至物理层,极易导致整个电力系统的崩溃。基于电力CPS的双层耦合结构,运用传播演化理论建立了一类新型的SIA IB RA RB网络攻击传播模型,描述了网络攻击在电力网络节点中的传播行为。运用动力学分析方法分析网络攻击对电力CPS的攻击力和影响范围,提供预判网络攻击破坏力的具体算法;运用偏秩相关系数法和三维关联偏微分方法对系统参数进行敏感度分析,研究发现电力CPS的网络结构和传播概率对网络安全性至关重要,通过2个仿真模拟验证了上述理论结果的正确性。以南方电网有限公司历次典型设计和典型造价为例,梳理了电力系统网络安全防护体系实际建设费用变化趋势,建议从3个角度对安全防护体系进行精准定位建设,在降低电力CPS造价成本的同时保证系统的安全性。研究结果可为电网防御者在信息物理协同攻击威胁下制定新的防御方案提供参考。
基金supported by the national Natural Science Foundation of China(NSFC)under Grant 61233008 and 51377001by the International Science and Technology Cooperation Program of China under Grant 2015DFA70580by the State Grid Science and Technology Project of China under Grant 5216A213509X.
文摘Cyber-physical electrical energy systems(CPEES)combine computation,communication and control technologies with physical power system,and realize the efficient fusion of power,information and control.This paper summarizes and analyzes related critical scientific problems and technologies,which are needed to be addressed with the development of CPEES.Firstly,since the co-simulation is an effective method to investigate infrastructure interdependencies,the co-simulation platform establishment of CPEES and its evaluation is overviewed.Then,a critical problem of CPEES is the interaction between energy and information flow,especially the influence of failures happening in information communication technology(ICT)on power system.In order to figure it out,the interaction is analyzed and the current analysis methods are summarized.For the solution of power system control and protection in information network environment,this paper outlines different control principles and illustrates the concept of distributed coordination control.Moreover,mass data processing and cluster analysis,architecture of communication network,information transmission technology and security of CPEES are summarized and analyzed.By solving the above problems and technologies,the development of CPEES will be significantly promoted.
文摘AADL (architecture analysis and design language) concentrates on the modeling and analysis of application system architectures.It is quite popular for its simple syntax,powerful functionality and extensibility and has been widely applied in embedded systems for its advantage.However,it is not enough for AADL to model cyber-physical systems (CPS) mainly because it cannot be used to model the continuous dynamic behaviors.This paper proposes an approach to construct a new sublanguage of AADL called AADL+,to facilitate the modeling of not only the discrete and continuous behavior of CPS,but also interaction between cyber components and physical components.The syntax and semantics of the sublanguage are provided to describe the behaviors of the systems.What's more,we develop a plug-in to OSATE (open-source AADL tool environment) for the modeling of CPS.And the plug-in supports syntax checking and simulation of the system model through linking with modelica.Finally,the AADL+ annex is successfully applied to model a lunar rover control system.
文摘Cyber-physical systems (CPSs) are new emerging systems that seamlessly integrate physical systems, communication systems and computation systems. Their wide use has been witnessed in the past decades in many crossdiscipline fields such as smart energy systems, industrial process control, aerospace and automobile engineering, health-care and assisted living, to just name a few. For many of these systems, secure operations are of key con- cerns. In particular, for some safety-critical applications, security is of paramount importance. Diverse motivations and strong incentives exist everywhere and at any time for launching malicious attacks on the CPSs, for example, economic reasons (e.g., by reducing or even not paying electricity charge) and terrorism the purpose of which is apparent.
基金supported by Natural Science Foundation of China(Nos.61272204 and 61433006)the Fundamental Research Funds for the Central Universities,China(No.2013ZZGH006)
文摘Cyber-physical systems(CPSs) are integrations of networks, computation and physical processes, where embedded computing devices continually sense, monitor, and control the physical processes through networks. Networked industrial processes combining internet, real-time computer control systems and industrial processes together are typical CPSs. With the increasingly frequent cyber-attack, security issues have gradually become key problems for CPSs. In this paper, a cyber-physical system security protection approach for networked industrial processes, i.e., industrial CPSs, is proposed. In this approach, attacks are handled layer by layer from general information technology(IT) security protection, to active protection, then to intrusion tolerance and physical security protection. The intrusion tolerance implemented in real-time control systems is the most critical layer because the real time control system directly affects the physical layer. This novel intrusion tolerance scheme with a closed loop defense framework takes into account the special requirements of industrial CPSs. To illustrate the effectiveness of the CPS security protection approach, a networked water level control system is described as a case study in the architecture analysis and design language(AADL) environment. Simulation results show that 3 types of injected attacks can be quickly defended by using the proposed protection approach.
基金supported by the UK Engineering and Physical Sciences Research Council(EPSRC)(No.EP/K036173/1)(ACCEPT)
文摘The utilization levels of the transmission network can be enhanced by the use of automated protection schemes that rapidly respond to disturbances. However,such corrective systems may suffer from malfunctions that have the potential to exacerbate the impact of the disturbance. This paper addresses the challenge of jointly optimizing the dispatch of generators and protection settings in this context. This requires a holistic assessment of the cyber(protection logic) and physical(network) systems,considering the failures in each part and their interplay.Special protection schemes are used as a prototypical example of such a system. An iterative optimization method is proposed that relies on power system response simulations in order to perform detailed impact assessments and compare candidate solutions. The candidate solutions are generated on the basis of a security-constrained dispatch that also secures the system against a set of cyber failure modes. A case study is developed for a generation rejection scheme on the IEEE reliability testsystem(RTS): candidate solutions are produced based on a mixed integer linear programming optimisation model, and loss-of-load costs are computed using a basic cascading outage algorithm. It is shown that the partial security approach is able to identify solutions that provide a good balance of operational costs and loss-of-load risks, both in a fixed dispatch and variable dispatch context.
文摘正常运行时互联电网交流联络线上存在随机功率波动的现象。基于实际2大区互联电网的历史数据,分析了联络线功率偏差、频率偏差以及2大区电网区域控制偏差(area control error,ACE)的统计特性,结果显示:联络线功率偏差表现出良好的正态分布特性;系统频率偏差和正态分布存在较大差别,原因是电网的频率控制使得频率偏差大于0.03 Hz的概率减小;各控制区的ACE基本服从正态分布。文章认为联络线功率偏差由两端电网的ACE引起,可以通过两端电网ACE的均方根值和相关系数计算出联络线功率偏差的均方根值,从而得到对联络线功率偏差大小分布的估计。对目前采用的T标准进行了分析,得出结论:为实现联络线功率控制的目标,两端电网责任度阈值之和为2即可,不一定要求两端电网责任度的阈值都是1;两端电网责任度阈值的分配还需要综合考虑各种因素进行详细研究,以得到公平合理的方案。