复杂配电网健康诊断及隐藏故障识别
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摘要
随着用电负荷的快速增长、供电可靠性要求的提高,使得以城市、负荷集中区域为代表的配电网规模逐渐增大、拓扑结构越来越复杂；加之陆续有分布式能源的接入、电动汽车充电站的应用,配电网的运行复杂性也大大增加。因此,传统的针对已发生故障进行处置的配电网故障诊断技术已经不能适应复杂配电网安全、可靠、经济运行的需要。所以,对复杂配电网的健康诊断进行研究讨论是非常有必要的。
将复杂配电网当作一个生命体来研究,介绍了复杂配电网系统健康诊断和评估的概念,在将复杂配电网运行健康状况与人的健康状态相类比的基础上,使用健康指标体系描述复杂配电网的功能和性能表征。
从主、次作用因子,内、外影响因素等方面对指标进行筛选,同时明确各项指标的健康标准,建立一套衡量复杂配电网健康状况的定量参考系,通过与参考系的比较,找出系统自身差距和变化态势,对己造成或可能发生的病症异常,及早给出响应动作建议,保障其处于稳定健康状态。对某地10kV配电网进行实例分析,从小时间尺度上系统的健康评估和大时间尺度上的健康趋势预测两个方面对该诊断方法的适用性和正确性进行验证。
隐藏故障的研究是近年来电网故障研究的新热点,若互感器存在隐藏故障,将对电网故障时继电保护等设备的正常工作造成直接影响。现有研究多针对继电保护、断路器等设备进行,甚少涉及对互感器隐藏故障的在线识别。对互感器可能存在的隐藏故障类型进行分析总结,使用潮流追踪技术和解析冗余方法建立各支路功率和电流之间的关系式,通过验证其残差向量是否满足约束条件来对该互感器的隐藏故障进行识别。通过对一个5节点配电网网络的算例分析,验证了该方法对互感器存在的隐藏故障等异常具有较好的识别能力。
给出了一种对复杂配电网进行健康诊断的思路,有助于调度人员及时掌握系统健康状况与趋势,实现在时间、空间和内容上对以往故障诊断的拓展。同时,对互感器隐藏故障的识别进行探索性研究,旨在对现有的隐藏故障研究进行补充和完善。
With the rapid growth in electricity loads and the improvement of power supply reliability, the scale of the distribution grid represented by cities and load concentrated regions is getting bigger and bigger, and its topology is more and more complex. Its operational complexity is greatly increased because of the access of distributed energy and the application of the electric car charging station at the same time. Such, the traditional fault diagnosis technology aimed at occurred fault of distribution network cannot meet the demand of safe, reliable and economic operation. Therefore, it is quite necessary to discuss the real-time health diagnosis of complex distribution grid (CDG).
Regarding CDG as a living body, introduce in the concept of CDG health diagnosis and use health index system to describe its functionality and performance conditions by means of the analogy of CDG health status and human health state.
Screen index by considering primary-secondary effect as well as internal and external influence factors. Determine the health standard of each index and establish a quantitative reference frame to measure its health state. Find its gap and changing trend by compared with the reference frame, and then give response action suggestions to the abnormality occurred or likely to occur to guarantee that it is in a stable health state. Verify the applicability and accuracy of the diagnostic structure by analyzing certain real lOkV distribution network including health assessment of the system in small time scales and health trend prediction in large time scales.
The study of hidden failure is a new focus of power system fault diagnosis in recent years. The hidden failure of CT/PT has a direct impact on the normal work of equipments such as relay protection etc. Few studies have been done on the research of transformer hidden failure in contrast with the study of relay protection and breaker etc. The main manifestations of transformer hidden failure is analyzed and summarized in this paper. Establish the relationship between every branch power and its current using power flow tracing technology and Analytical Redundancy Relation (ARR), and recognition its hidden failure by verifying whether the residual vector satisfy the constraint condition or not. The analysis result of a5nodes distribution network shows that this method is capable to recognize the hidden failure and other abnormality.
This paper finally gives a method of CDG health diagnosis which is helpful for dispatchers to master the health state and operation trend of the system, and achieve the expansion of the previous fault diagnosis in content, time and space. Meanwhile, study on the recognition of the hidden failure of CT/PT, which could be a supplementary to the research.
将复杂配电网当作一个生命体来研究,介绍了复杂配电网系统健康诊断和评估的概念,在将复杂配电网运行健康状况与人的健康状态相类比的基础上,使用健康指标体系描述复杂配电网的功能和性能表征。
从主、次作用因子,内、外影响因素等方面对指标进行筛选,同时明确各项指标的健康标准,建立一套衡量复杂配电网健康状况的定量参考系,通过与参考系的比较,找出系统自身差距和变化态势,对己造成或可能发生的病症异常,及早给出响应动作建议,保障其处于稳定健康状态。对某地10kV配电网进行实例分析,从小时间尺度上系统的健康评估和大时间尺度上的健康趋势预测两个方面对该诊断方法的适用性和正确性进行验证。
隐藏故障的研究是近年来电网故障研究的新热点,若互感器存在隐藏故障,将对电网故障时继电保护等设备的正常工作造成直接影响。现有研究多针对继电保护、断路器等设备进行,甚少涉及对互感器隐藏故障的在线识别。对互感器可能存在的隐藏故障类型进行分析总结,使用潮流追踪技术和解析冗余方法建立各支路功率和电流之间的关系式,通过验证其残差向量是否满足约束条件来对该互感器的隐藏故障进行识别。通过对一个5节点配电网网络的算例分析,验证了该方法对互感器存在的隐藏故障等异常具有较好的识别能力。
给出了一种对复杂配电网进行健康诊断的思路,有助于调度人员及时掌握系统健康状况与趋势,实现在时间、空间和内容上对以往故障诊断的拓展。同时,对互感器隐藏故障的识别进行探索性研究,旨在对现有的隐藏故障研究进行补充和完善。
With the rapid growth in electricity loads and the improvement of power supply reliability, the scale of the distribution grid represented by cities and load concentrated regions is getting bigger and bigger, and its topology is more and more complex. Its operational complexity is greatly increased because of the access of distributed energy and the application of the electric car charging station at the same time. Such, the traditional fault diagnosis technology aimed at occurred fault of distribution network cannot meet the demand of safe, reliable and economic operation. Therefore, it is quite necessary to discuss the real-time health diagnosis of complex distribution grid (CDG).
Regarding CDG as a living body, introduce in the concept of CDG health diagnosis and use health index system to describe its functionality and performance conditions by means of the analogy of CDG health status and human health state.
Screen index by considering primary-secondary effect as well as internal and external influence factors. Determine the health standard of each index and establish a quantitative reference frame to measure its health state. Find its gap and changing trend by compared with the reference frame, and then give response action suggestions to the abnormality occurred or likely to occur to guarantee that it is in a stable health state. Verify the applicability and accuracy of the diagnostic structure by analyzing certain real lOkV distribution network including health assessment of the system in small time scales and health trend prediction in large time scales.
The study of hidden failure is a new focus of power system fault diagnosis in recent years. The hidden failure of CT/PT has a direct impact on the normal work of equipments such as relay protection etc. Few studies have been done on the research of transformer hidden failure in contrast with the study of relay protection and breaker etc. The main manifestations of transformer hidden failure is analyzed and summarized in this paper. Establish the relationship between every branch power and its current using power flow tracing technology and Analytical Redundancy Relation (ARR), and recognition its hidden failure by verifying whether the residual vector satisfy the constraint condition or not. The analysis result of a5nodes distribution network shows that this method is capable to recognize the hidden failure and other abnormality.
This paper finally gives a method of CDG health diagnosis which is helpful for dispatchers to master the health state and operation trend of the system, and achieve the expansion of the previous fault diagnosis in content, time and space. Meanwhile, study on the recognition of the hidden failure of CT/PT, which could be a supplementary to the research.
引文
[1]李志伟.城市配电网规划设计介绍[J].电工电气.2011,7：62-64.
[2]卢永,甘德强,John N JIANG.美国智能电网和分布式发电重点方向的调研分析[J].电力系统自动化.2010,34(9)：12-16.
[3]胡小正,王鹏.2009年全国城市用户供电可靠性现状分析[J].供用电.2010,27(5)：15-18.
[4]高占宝,梁旭,李行善.复杂系统综合健康管理[J].测控技术.2005,24(8)：1-5.
[5]高金吉.装备系统故障自愈原理研究[J].中国工程科学.2005,7(5)：43-48.
[6]张晓阳.孙宇.基于生物免疫机制的复杂系统健康监测与评估[J].系统仿真学报.2005,17(5)：1212-1215.
[7]Roger L. King, Samuel H. Russ. Aric B. Lambert, Donna S. Reese. An Artificial Immune System Model for Intelligent Agents[J].Future Generation Computer Systems.2001. 17(4):335-343.
[8]燕文明.三峡库区生态系统健康诊断及水资源管理研究[D].河海大学硕士学位论文.2007.
[9]Green A J. The Future Direction and Development of Engine Health Monitoring (EHM) Within the United States Air Force.Report of the Air Force Research Lab Wright-Patterson AFB OH.1998,1-25.
[10]殷苏东.陈旭华.基于状态的维修研究现状与发展趋势[J].科学技术与工程.2008,8(5)：1530-1534.
[11]孟详萍,徐雪芳.电网脆弱性预警指标对比分析及应用[J].黑龙江电力.2010,32(4)：247-251.
[12]牛东晓,刘达,邢棉.应对灾害电网危机管理[M].中国电力出版社.2010.
[13]周双喜,王庆红.关注电力战略防御系统[J].中国电力.2003,36(1)：32-37.
[14]陈明.控制系统可靠性设计[M].西北工业大学.2006.
[15]Roerner M J, Kacprzynski G J.Advanced Diagnostics and Prognostics for Gas Turbine Engine Risk Assessment[C].Proceedings of the IEEE Aerospace Conference.2000,Vol.6:345-353.
[16]Nickerson B, Lally R. Development of a Smart Wireless Networkable Sensor for Aircraft Engine Health Management[C].Proceedings of the IEEE Aerospace Conference.2001, Vol.7:32-38.
[17]张宝珍,曾天翔.先进的故障预测与状态管理技术[J].测控技术.2003,22(11)：4-6.
[18]Ming Dong, David He. Hidden Semi-Markov Model-based Methodology for Multi-Sensor Equipment Health Diagnosis and Prognosis[J].European Journal of Operational Research.2007,178: 858-878.
[19]M. Polycarpou, G. Ellinas, E. Kyriakides, C. Panayiotou. Intelligent Health Monitoring of Critical Infrastructure Systems[J].Complexity in Engineering.2010:18-20.
[20]许丽佳.电子系统的故障预测与健康管理技术研究[D].电子科技大学博士学位论文.2009.
[21]李玉芬.电气量与油气量结合的变压器状态监测与健康诊断研究[D].河海大学硕士学位论文.2005.
[22]蔡晶晶.真空断路器健康诊断系统的研究[D].河海大学硕土学位论文.2007.
[23]鞠平.左英飞等.电力系统健康诊断[J].电力自动化设备.2004.24(6)：22-25.
[24]孙宏斌.胡江溢.刘映尚,张伯明.吴文传.调度控制中心功能的发展——电网实时安全预警系统[J].电力系统自动化.2004.28(15)：1-6.
[25]Peng Ge, Qian Guo, Haina Zhou, Xinran Li.Wide Area Power Grid Health State Diagnosis and Early Warning System Based on Fault Power Flow Fingerprint Identification and MAS Technology[C].Proceedings of DRPT2008.2008.6-9April.
[26]Mirrasoul J. Mousavi, Karen L. Butler-Purry. Detecting Incipient Faults via Numerical Modeling and Statistical Change Detection[J].IEEE TRANSACTION ON POWER DELIVERY.2010,25(3):1275-1283.
[27]Tarlochan S. Sidhu, Zhihan Xu. Detection of Incipient Faults in Distribution Underground Cables[J].IEEE TRANSACTION ON POWER DELIVERY.2010,25(3):1363-1371.
[28]蔡伟贤.继电保护隐藏故障风险分析及电网扰动记录方法研究[D].重庆大学硕士毕业论文.2008.
[29]S Tamronglak. Analysis of Power System Disturbances Due to Relay Hidden Failures[D].1994.
[30]A G Phadke, JS Thorp. Expose Hidden Failures to Prevent Cascading Outages in Power Systems [J].IEEE Computer Applications in Power.1996,9(3):20-23.
[31]J De La Ree, DC Elizondo. A Methodology to Assess the Impact of Hidden Failures in Protection Schemes[A].2004:1782-1783.
[32]Q Qiu. Risk Assessment of Power System Catastrophic Failures and Hidden Failure Monitoring & Control System [D].2003.
[33]ELIZONDO D C, DE LAREE J. Analysis of Hidden Failures of Protection Schemes in Large Interconnected Power Systems.Proceedings of IEEE Power Engineering Society General Meeting[C].2004.1:107-114.
[34]霍超,张沛超,廖晓辉.考虑隐性故障的继电保护重要度分析方法[J].华东电力.2008,36(003)：62-66.
[35]熊小伏,蔡伟贤,周家启等.继电保护隐藏故障造成输电线路连锁跳闸的概率模型[J].电力系统自动化.2008,32(14)：6-10.
[36]孙鑫,熊小伏,杨洋.基于故障录波信息的输电线路继电保护内部故障在线检测方法[J].电力系统保护与控制.2010.38(3)：6-10.
[37]张文斌.汽轮发电机组状态趋势预测及故障诊断方法研究[D].浙江大学博十学位论文.2009.
[38]余晓丹,贾宏杰,陈建华.电力系统连锁故障预测初探[J].电网技术.2008,30(13)：20-25.
[39]沈力,滕乐天,徐宛容.用于衡量资产管理实效的综合评价指标体系[J].华东电力.2010,38(3)：432-435.
[40]肖安南.浅析中压城市配电网的规划及建设[J].华东电力.2011,28(2)：61-64.
[41]韩柳,庄博,王智冬,张琳.电网利用效率指标研究[J].华东电力.2011.39(6)：850-854.
[42]SINHA A K, HAZARIKA D. A Comparative Study of Voltage Stability Indices in a Power System [J]. International Journal of Electrical Power & Energy Systems.2000.22(8):589-596.
[43]张建设,张尧,武志刚等.广东电网区域负荷裕度分析[J].电网技术.2006,30(6)：30-34.
[44]栗秋华.基于人工免疫的电力系统电压稳定性预警模型研究[D].重庆大学硕士学位论文.2007.
[45]王守相,王成山编.现代配电系统分析[M].北京：高等教育出版社.2007.
[46]刘永泰,果果.城市电网安全性模糊评估[J].昆明大学学报.2007,18(4)：68-71.
[47]翁嘉明,刘东,何维国等.基于层次分析法的配电网运行方式多目标优化[J].电力系统自动化.2012,36(4)：56-61.
[48]郝祥琪,党志良,杨世雷.层次分析法在建筑热水供应系统评价中的应用[J].西南给排水.2008,30(2)：28-31.
[49]朱建军.层次分析法的若干问题研究及应用[D].东北大学博士学位论文.2005.
[50]栗秋华,周林.张凤等.基于模糊理论和层次分析法的电力系统电压态势预警等级综合评估[J].电网技术.2008.32(4)：40-45.
[51]刘宝柱,朱涛,于继来.电力系统电压态势预警等级的多级模糊综合评判[J].电网技术.2005,29(24)：31-36.
[52]韩水,苑舜,张近珠编.国外典型电网事故分析[M].北京：中国电力出版社.2005.
[53]李存锋.城市配电网自动化研究之我见[J].中国新技术新产品.2011,18(2)：188-189.
[54]吴涛,周有庆,曹志辉,彭红海.新型电子式互感器及其误差分析[J].电网技术.2010,34(4)：209-213.
[55]Branislav D, Eddy S. Calibration System for Electronic Instrument Transformers with Digital Output[J].IEEE Transactions on Instrumentation and Measurement.2005,54(2):479-482.
[56]王秋生,樊久铭,徐敏强等.基于解析冗余关系的动态系统故障检测和隔离[J].哈尔滨工业大学学报.2007.39(6)：924-927.
[57]张佳洁.基于解析冗余关系的HXD2型机车法维莱制动机测试系统的研制[D].中南大学硕士毕业论文.2011.
[58]R. Billinton. R. N.Allan. Reliability Evaluation of Engineering Systems[M].Plenum Press.1992.
[59]IEEE Task Force,"IEEE reliability test system".IEEE Transaction Power App. System.1979,98(6):2047-2054.
[60]吴晓蓉,谢开贵,周家启.基于电流实部与虚部双向追踪的输电设备利用份额模型及应用[J].中国电机工程学报.2006,26(10)：12-17.
[61]幸荣霞,姚爱明,谢开等.大电网可靠性影响分析的潮流跟踪方法[J].电网技术.2006,30(10)：54-58.
[2]卢永,甘德强,John N JIANG.美国智能电网和分布式发电重点方向的调研分析[J].电力系统自动化.2010,34(9)：12-16.
[3]胡小正,王鹏.2009年全国城市用户供电可靠性现状分析[J].供用电.2010,27(5)：15-18.
[4]高占宝,梁旭,李行善.复杂系统综合健康管理[J].测控技术.2005,24(8)：1-5.
[5]高金吉.装备系统故障自愈原理研究[J].中国工程科学.2005,7(5)：43-48.
[6]张晓阳.孙宇.基于生物免疫机制的复杂系统健康监测与评估[J].系统仿真学报.2005,17(5)：1212-1215.
[7]Roger L. King, Samuel H. Russ. Aric B. Lambert, Donna S. Reese. An Artificial Immune System Model for Intelligent Agents[J].Future Generation Computer Systems.2001. 17(4):335-343.
[8]燕文明.三峡库区生态系统健康诊断及水资源管理研究[D].河海大学硕士学位论文.2007.
[9]Green A J. The Future Direction and Development of Engine Health Monitoring (EHM) Within the United States Air Force.Report of the Air Force Research Lab Wright-Patterson AFB OH.1998,1-25.
[10]殷苏东.陈旭华.基于状态的维修研究现状与发展趋势[J].科学技术与工程.2008,8(5)：1530-1534.
[11]孟详萍,徐雪芳.电网脆弱性预警指标对比分析及应用[J].黑龙江电力.2010,32(4)：247-251.
[12]牛东晓,刘达,邢棉.应对灾害电网危机管理[M].中国电力出版社.2010.
[13]周双喜,王庆红.关注电力战略防御系统[J].中国电力.2003,36(1)：32-37.
[14]陈明.控制系统可靠性设计[M].西北工业大学.2006.
[15]Roerner M J, Kacprzynski G J.Advanced Diagnostics and Prognostics for Gas Turbine Engine Risk Assessment[C].Proceedings of the IEEE Aerospace Conference.2000,Vol.6:345-353.
[16]Nickerson B, Lally R. Development of a Smart Wireless Networkable Sensor for Aircraft Engine Health Management[C].Proceedings of the IEEE Aerospace Conference.2001, Vol.7:32-38.
[17]张宝珍,曾天翔.先进的故障预测与状态管理技术[J].测控技术.2003,22(11)：4-6.
[18]Ming Dong, David He. Hidden Semi-Markov Model-based Methodology for Multi-Sensor Equipment Health Diagnosis and Prognosis[J].European Journal of Operational Research.2007,178: 858-878.
[19]M. Polycarpou, G. Ellinas, E. Kyriakides, C. Panayiotou. Intelligent Health Monitoring of Critical Infrastructure Systems[J].Complexity in Engineering.2010:18-20.
[20]许丽佳.电子系统的故障预测与健康管理技术研究[D].电子科技大学博士学位论文.2009.
[21]李玉芬.电气量与油气量结合的变压器状态监测与健康诊断研究[D].河海大学硕士学位论文.2005.
[22]蔡晶晶.真空断路器健康诊断系统的研究[D].河海大学硕土学位论文.2007.
[23]鞠平.左英飞等.电力系统健康诊断[J].电力自动化设备.2004.24(6)：22-25.
[24]孙宏斌.胡江溢.刘映尚,张伯明.吴文传.调度控制中心功能的发展——电网实时安全预警系统[J].电力系统自动化.2004.28(15)：1-6.
[25]Peng Ge, Qian Guo, Haina Zhou, Xinran Li.Wide Area Power Grid Health State Diagnosis and Early Warning System Based on Fault Power Flow Fingerprint Identification and MAS Technology[C].Proceedings of DRPT2008.2008.6-9April.
[26]Mirrasoul J. Mousavi, Karen L. Butler-Purry. Detecting Incipient Faults via Numerical Modeling and Statistical Change Detection[J].IEEE TRANSACTION ON POWER DELIVERY.2010,25(3):1275-1283.
[27]Tarlochan S. Sidhu, Zhihan Xu. Detection of Incipient Faults in Distribution Underground Cables[J].IEEE TRANSACTION ON POWER DELIVERY.2010,25(3):1363-1371.
[28]蔡伟贤.继电保护隐藏故障风险分析及电网扰动记录方法研究[D].重庆大学硕士毕业论文.2008.
[29]S Tamronglak. Analysis of Power System Disturbances Due to Relay Hidden Failures[D].1994.
[30]A G Phadke, JS Thorp. Expose Hidden Failures to Prevent Cascading Outages in Power Systems [J].IEEE Computer Applications in Power.1996,9(3):20-23.
[31]J De La Ree, DC Elizondo. A Methodology to Assess the Impact of Hidden Failures in Protection Schemes[A].2004:1782-1783.
[32]Q Qiu. Risk Assessment of Power System Catastrophic Failures and Hidden Failure Monitoring & Control System [D].2003.
[33]ELIZONDO D C, DE LAREE J. Analysis of Hidden Failures of Protection Schemes in Large Interconnected Power Systems.Proceedings of IEEE Power Engineering Society General Meeting[C].2004.1:107-114.
[34]霍超,张沛超,廖晓辉.考虑隐性故障的继电保护重要度分析方法[J].华东电力.2008,36(003)：62-66.
[35]熊小伏,蔡伟贤,周家启等.继电保护隐藏故障造成输电线路连锁跳闸的概率模型[J].电力系统自动化.2008,32(14)：6-10.
[36]孙鑫,熊小伏,杨洋.基于故障录波信息的输电线路继电保护内部故障在线检测方法[J].电力系统保护与控制.2010.38(3)：6-10.
[37]张文斌.汽轮发电机组状态趋势预测及故障诊断方法研究[D].浙江大学博十学位论文.2009.
[38]余晓丹,贾宏杰,陈建华.电力系统连锁故障预测初探[J].电网技术.2008,30(13)：20-25.
[39]沈力,滕乐天,徐宛容.用于衡量资产管理实效的综合评价指标体系[J].华东电力.2010,38(3)：432-435.
[40]肖安南.浅析中压城市配电网的规划及建设[J].华东电力.2011,28(2)：61-64.
[41]韩柳,庄博,王智冬,张琳.电网利用效率指标研究[J].华东电力.2011.39(6)：850-854.
[42]SINHA A K, HAZARIKA D. A Comparative Study of Voltage Stability Indices in a Power System [J]. International Journal of Electrical Power & Energy Systems.2000.22(8):589-596.
[43]张建设,张尧,武志刚等.广东电网区域负荷裕度分析[J].电网技术.2006,30(6)：30-34.
[44]栗秋华.基于人工免疫的电力系统电压稳定性预警模型研究[D].重庆大学硕士学位论文.2007.
[45]王守相,王成山编.现代配电系统分析[M].北京：高等教育出版社.2007.
[46]刘永泰,果果.城市电网安全性模糊评估[J].昆明大学学报.2007,18(4)：68-71.
[47]翁嘉明,刘东,何维国等.基于层次分析法的配电网运行方式多目标优化[J].电力系统自动化.2012,36(4)：56-61.
[48]郝祥琪,党志良,杨世雷.层次分析法在建筑热水供应系统评价中的应用[J].西南给排水.2008,30(2)：28-31.
[49]朱建军.层次分析法的若干问题研究及应用[D].东北大学博士学位论文.2005.
[50]栗秋华,周林.张凤等.基于模糊理论和层次分析法的电力系统电压态势预警等级综合评估[J].电网技术.2008.32(4)：40-45.
[51]刘宝柱,朱涛,于继来.电力系统电压态势预警等级的多级模糊综合评判[J].电网技术.2005,29(24)：31-36.
[52]韩水,苑舜,张近珠编.国外典型电网事故分析[M].北京：中国电力出版社.2005.
[53]李存锋.城市配电网自动化研究之我见[J].中国新技术新产品.2011,18(2)：188-189.
[54]吴涛,周有庆,曹志辉,彭红海.新型电子式互感器及其误差分析[J].电网技术.2010,34(4)：209-213.
[55]Branislav D, Eddy S. Calibration System for Electronic Instrument Transformers with Digital Output[J].IEEE Transactions on Instrumentation and Measurement.2005,54(2):479-482.
[56]王秋生,樊久铭,徐敏强等.基于解析冗余关系的动态系统故障检测和隔离[J].哈尔滨工业大学学报.2007.39(6)：924-927.
[57]张佳洁.基于解析冗余关系的HXD2型机车法维莱制动机测试系统的研制[D].中南大学硕士毕业论文.2011.
[58]R. Billinton. R. N.Allan. Reliability Evaluation of Engineering Systems[M].Plenum Press.1992.
[59]IEEE Task Force,"IEEE reliability test system".IEEE Transaction Power App. System.1979,98(6):2047-2054.
[60]吴晓蓉,谢开贵,周家启.基于电流实部与虚部双向追踪的输电设备利用份额模型及应用[J].中国电机工程学报.2006,26(10)：12-17.
[61]幸荣霞,姚爱明,谢开等.大电网可靠性影响分析的潮流跟踪方法[J].电网技术.2006,30(10)：54-58.