基于SMP状态空间等值的智能变电站保护系统短期可靠性评估
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摘要
电气设备短期可靠性为电力系统风险评估提供数据支持,状态空间法中传统转移频率守恒等值算法基于稳态指标定义,不适用于短期可靠性评估,故需进行改进.本文研究等值条件,首次证明满足等值条件的系统等值后仍为马尔可夫过程,暂态状态概率可由矩阵相乘得到.不满足等值条件的系统,提出用半马尔可夫过程描述.确立等值前后转移率及分布函数的关系,推导半马尔可夫核矩阵与等值后转移率、分布函数的关系,以矩阵描述形式求得暂态状态概率和灵敏度指标.运用所提算法对一智能变电站保护系统进行短期可靠性评估,结果表明传统算法低估系统可用率,暂态灵敏度的峰值和出现时间也存在误差.初始状态影响系统暂态可用率以及暂态灵敏度的收敛速度.
The risk assessment of power systems is supported by the short-term reliability of electrical equipments.Due to its steady definition,the traditional frequency equilibrium in state space method is not suitable for short-term reliability assessment,which should be improved.In this paper,the equivalent condition is studied.It is proved that for the systems satisfying the equivalent condition,the instantaneous state probabilities are multiplied by matrices.Otherwise,an equivalent algorithm is newly proposed.The equivalent systems are described by the semi-Markov process.The relationships of the transition rates and distribution functions before and after equivalence are found.The kernel elements are derived from them.The instantaneous state probabilities and sensitivities are derived by matrix form from the kernel matrix.An example of short-term reliability assessment for smart substation protection system is presented.Numerical results show that the traditional method underestimates the availability.Errors also occur in the peak value and time of the instantaneous sensitivity.The state probabilities and convergence rate of sensitivities are significantly influenced by the initial state.
The risk assessment of power systems is supported by the short-term reliability of electrical equipments.Due to its steady definition,the traditional frequency equilibrium in state space method is not suitable for short-term reliability assessment,which should be improved.In this paper,the equivalent condition is studied.It is proved that for the systems satisfying the equivalent condition,the instantaneous state probabilities are multiplied by matrices.Otherwise,an equivalent algorithm is newly proposed.The equivalent systems are described by the semi-Markov process.The relationships of the transition rates and distribution functions before and after equivalence are found.The kernel elements are derived from them.The instantaneous state probabilities and sensitivities are derived by matrix form from the kernel matrix.An example of short-term reliability assessment for smart substation protection system is presented.Numerical results show that the traditional method underestimates the availability.Errors also occur in the peak value and time of the instantaneous sensitivity.The state probabilities and convergence rate of sensitivities are significantly influenced by the initial state.
引文
[1]孙羽,王秀丽,王建学,等.电力系统短期可靠性评估综述[J].电力系统保护与控制,2011,39(8):143-154.Sun Y,Wang X L,Wang J X,et al.An overview of the short-term reliability evaluation of power system[J].Power System Protection and Control,2011,39(8):143-154.
[2]李生虎,王京景,刘正楷.基于瞬时状态概率的保护系统短期可靠性评估[J].中国电机工程学报,2009,29(25):50-55.Li S H,Wang J J,Liu Z K.Short term reliability evaluation for protection system based on instantaneous state probability[J].Proceedings of the CSEE,2009,29(25):50-55.
[3]Billinton R,Allan R N.Reliability evaluation of power systems[M].2nd ed.New York:Plenum Press,1996:83-114.
[4]郑涛,王方,金乃正.双重化继电保护系统确定最佳检修周期新方法[J].电力系统自动化,2010,34(10):67-70.Zheng T,Wang F,Jin N Z.A novel algorithm of determining the optimal routine test interval of the dualredundant relay protection system[J].Automation of Electric Power Systems,2010,34(10):67-70.
[5]薛安成,罗麟,景琦,等.继电保护装置的多因素时变Markov模型及其检修策略分析[J].电力系统自动化,2015,39(7):124-129.Xue A C,Luo L,Jing Q,et al.Research on the maintenance strategies of protective relay based on time-varying markov model including multi-factors[J].Automation of Electric Power Systems,2015,39(7):124-129.
[6]Li S,Ma Y,Hua Y,et al.Reliability equivalence and sensitivity analysis to UHVDC systems based on matrix description of F&D method[J].IEEE IVans on Power Delivery,2015(99):1-8.
[7]周忠宝,马超群,周经伦,等.基于动态贝叶斯网络的动态故障树分析[J].系统工程理论与实践,2008,28(2):35-42.Zhou Z B,Ma C Q,Zhou J L,et al.Dynamic fault tree analysis based on dynamic Bayesian networks[J].Systems Engineering—Theory&Practice,2008,28(2):35-42.
[8]董学军,武小悦,陈英武,等.基于Markov链互模拟的航天器发射任务可靠度模型[J].系统工程理论与实践,2012,32(10):2323-2331.Dong X J,Wu X Y,Chen Y W,et al.Mission reliability model of spacecraft launch based on bisimulation of continuous-time Markov processes[J].Systems Engineering—Theory&Practice,2012,32(10):2323-2331.
[9]张沛超,胡炎,侯伟宏.IEC61850全数字化保护系统的分层马尔科夫模型[J].电力自动化设备,2010,30(2):28-32.Zhang P C,Hu Y,Hou W H.Layered Markov model of IEC61850-compliant protection system[J].Electric Power Automation Equipment,2010,30(2):28-32.
[10]何旭,姜宪国,张沛超,等.考虑检修策略的智能变电站保护系统可用性分析[J].电网技术,2015,39(4):1121-1126.He X,Jiang X G,Zhang P C,et al.Availability analysis of smart substation protection system considering maintenance strategies[J].Power System Technology,2015,39(4):1121-1126.
[11]Buzacott J A.Markov approach to finding failure times of repairable systems[J].IEEE Trans on Reliability,1970,19(4):128-134.
[12]Singh C,Billinton R.Frequency and duration concepts in system reliability evaluation[J].IEEE Trans on Reliability,1975,24(1):31-36.
[13]Kemeny J G,Snell J L.Finite Markov chainsfM].2nd ed.New York:Springer-Verlag,1976:123-132.
[14]Papazoglou I A,Gyftopoulos E P.Markov processes for reliability analyses of large systems[J].IEEE Trans on Reliability,1977,26(3):232-237.
[15]Li S,Dai C,Zhu Y.Short-term reliability equivalence algorithm for flexible transmission equipment[J].International Journal of Electrical Power&Energy Systems,2012,43(1):427-432.
[16]李生虎,华玉婷,陈鹏,等.UHVDC系统故障树分析误差及灵敏度分析[J].电网技术,2015,39(5):1233-1239.Li S H,Hua Y T,Chen P,et al.FTA error analysis and probabilistic sensitivities of UHVDC systems[J].Power System Technology,2015,39(5):1233-1239.
[17]Singh C,Billinton R.A frequency and duration approach to short term reliability evaluation[J].IEEE Trans on Power Apparatus and Systems,1973,92(6):2073-2083.
[18]郭永基.可靠性工程原理[M].北京:清华大学出版社,施普林格出版社,2002:137-142.Guo Y J.Principle of reliability engineering(M).Beijing:Tsinghua University Press,Springer,2002:137-142.
[19]曹晋华,程侃.可靠性数学引论(修订版)[M].2版.北京:高等教育出版社,2012:250-301.Cao J H,Cheng K.Introduction to reliability mathematic theories(revised)[M).2nd ed.Beijing:Higher Education Press,2012:250-301.
[20]Cao Y,Sun H,Trivedi K S,et al.System availability with non-exponentially distributed outages(J).IEEE Trans on Reliability,2002,51(2):193-198.
[21]汪隆君,王钢,李博.基于半马尔可夫过程的继电保护可靠性建模[J].电力系统自动化,2010,34(18):6-10.Wang L J,Wang G,Li B.Reliability modeling of a protection system based on the semi-Markov process(J).Automation of Electric Power Systems,2010,34(18):6-10.
[22]宁辽逸,吴文传,张伯明.运行风险评估中的变压器时变停运模型(二)基于延迟半马尔可夫过程的变压器时变停运模型[J].电力系统自动化,2010,34(16):24-28.Ning L Y,Wu W C,Zhang B M.Time-varying transformer outage model for operational risk assessment part two time-varying transformer outage model based on delayed semi-Markov process(J).Automation of Electric Power Systems,2010,34(16):24-28.
[23]Pievatolo A,Tironi E,Valade I.Semi-Markov processes for power system reliability assessment with application to uninterruptible power supply[J].IEEE Trans on Power Systems,2004,19(3):1326-1333.
[24]Tomasevicz C L,Asgarpoor S.Preventive maintenance using continuous-time semi-Markov processes[C]//Power Symposium,Carbondale IL:NAPS 2006,38th North American,2006:3-8.
[25]张沛超,高翔.全数字化保护系统的可靠性及元件重要度分析[J].中国电机工程学报,2008,28(1):77-82.Zhang P C,Gao X.Analysis of reliability and component importance for all-digital protective systems[J].Proceedings of the CSEE,2008,28(1):77-82.
[2]李生虎,王京景,刘正楷.基于瞬时状态概率的保护系统短期可靠性评估[J].中国电机工程学报,2009,29(25):50-55.Li S H,Wang J J,Liu Z K.Short term reliability evaluation for protection system based on instantaneous state probability[J].Proceedings of the CSEE,2009,29(25):50-55.
[3]Billinton R,Allan R N.Reliability evaluation of power systems[M].2nd ed.New York:Plenum Press,1996:83-114.
[4]郑涛,王方,金乃正.双重化继电保护系统确定最佳检修周期新方法[J].电力系统自动化,2010,34(10):67-70.Zheng T,Wang F,Jin N Z.A novel algorithm of determining the optimal routine test interval of the dualredundant relay protection system[J].Automation of Electric Power Systems,2010,34(10):67-70.
[5]薛安成,罗麟,景琦,等.继电保护装置的多因素时变Markov模型及其检修策略分析[J].电力系统自动化,2015,39(7):124-129.Xue A C,Luo L,Jing Q,et al.Research on the maintenance strategies of protective relay based on time-varying markov model including multi-factors[J].Automation of Electric Power Systems,2015,39(7):124-129.
[6]Li S,Ma Y,Hua Y,et al.Reliability equivalence and sensitivity analysis to UHVDC systems based on matrix description of F&D method[J].IEEE IVans on Power Delivery,2015(99):1-8.
[7]周忠宝,马超群,周经伦,等.基于动态贝叶斯网络的动态故障树分析[J].系统工程理论与实践,2008,28(2):35-42.Zhou Z B,Ma C Q,Zhou J L,et al.Dynamic fault tree analysis based on dynamic Bayesian networks[J].Systems Engineering—Theory&Practice,2008,28(2):35-42.
[8]董学军,武小悦,陈英武,等.基于Markov链互模拟的航天器发射任务可靠度模型[J].系统工程理论与实践,2012,32(10):2323-2331.Dong X J,Wu X Y,Chen Y W,et al.Mission reliability model of spacecraft launch based on bisimulation of continuous-time Markov processes[J].Systems Engineering—Theory&Practice,2012,32(10):2323-2331.
[9]张沛超,胡炎,侯伟宏.IEC61850全数字化保护系统的分层马尔科夫模型[J].电力自动化设备,2010,30(2):28-32.Zhang P C,Hu Y,Hou W H.Layered Markov model of IEC61850-compliant protection system[J].Electric Power Automation Equipment,2010,30(2):28-32.
[10]何旭,姜宪国,张沛超,等.考虑检修策略的智能变电站保护系统可用性分析[J].电网技术,2015,39(4):1121-1126.He X,Jiang X G,Zhang P C,et al.Availability analysis of smart substation protection system considering maintenance strategies[J].Power System Technology,2015,39(4):1121-1126.
[11]Buzacott J A.Markov approach to finding failure times of repairable systems[J].IEEE Trans on Reliability,1970,19(4):128-134.
[12]Singh C,Billinton R.Frequency and duration concepts in system reliability evaluation[J].IEEE Trans on Reliability,1975,24(1):31-36.
[13]Kemeny J G,Snell J L.Finite Markov chainsfM].2nd ed.New York:Springer-Verlag,1976:123-132.
[14]Papazoglou I A,Gyftopoulos E P.Markov processes for reliability analyses of large systems[J].IEEE Trans on Reliability,1977,26(3):232-237.
[15]Li S,Dai C,Zhu Y.Short-term reliability equivalence algorithm for flexible transmission equipment[J].International Journal of Electrical Power&Energy Systems,2012,43(1):427-432.
[16]李生虎,华玉婷,陈鹏,等.UHVDC系统故障树分析误差及灵敏度分析[J].电网技术,2015,39(5):1233-1239.Li S H,Hua Y T,Chen P,et al.FTA error analysis and probabilistic sensitivities of UHVDC systems[J].Power System Technology,2015,39(5):1233-1239.
[17]Singh C,Billinton R.A frequency and duration approach to short term reliability evaluation[J].IEEE Trans on Power Apparatus and Systems,1973,92(6):2073-2083.
[18]郭永基.可靠性工程原理[M].北京:清华大学出版社,施普林格出版社,2002:137-142.Guo Y J.Principle of reliability engineering(M).Beijing:Tsinghua University Press,Springer,2002:137-142.
[19]曹晋华,程侃.可靠性数学引论(修订版)[M].2版.北京:高等教育出版社,2012:250-301.Cao J H,Cheng K.Introduction to reliability mathematic theories(revised)[M).2nd ed.Beijing:Higher Education Press,2012:250-301.
[20]Cao Y,Sun H,Trivedi K S,et al.System availability with non-exponentially distributed outages(J).IEEE Trans on Reliability,2002,51(2):193-198.
[21]汪隆君,王钢,李博.基于半马尔可夫过程的继电保护可靠性建模[J].电力系统自动化,2010,34(18):6-10.Wang L J,Wang G,Li B.Reliability modeling of a protection system based on the semi-Markov process(J).Automation of Electric Power Systems,2010,34(18):6-10.
[22]宁辽逸,吴文传,张伯明.运行风险评估中的变压器时变停运模型(二)基于延迟半马尔可夫过程的变压器时变停运模型[J].电力系统自动化,2010,34(16):24-28.Ning L Y,Wu W C,Zhang B M.Time-varying transformer outage model for operational risk assessment part two time-varying transformer outage model based on delayed semi-Markov process(J).Automation of Electric Power Systems,2010,34(16):24-28.
[23]Pievatolo A,Tironi E,Valade I.Semi-Markov processes for power system reliability assessment with application to uninterruptible power supply[J].IEEE Trans on Power Systems,2004,19(3):1326-1333.
[24]Tomasevicz C L,Asgarpoor S.Preventive maintenance using continuous-time semi-Markov processes[C]//Power Symposium,Carbondale IL:NAPS 2006,38th North American,2006:3-8.
[25]张沛超,高翔.全数字化保护系统的可靠性及元件重要度分析[J].中国电机工程学报,2008,28(1):77-82.Zhang P C,Gao X.Analysis of reliability and component importance for all-digital protective systems[J].Proceedings of the CSEE,2008,28(1):77-82.