基于灰色-三参数威布尔分布模型的继电保护装置可靠性参数估计
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摘要
由于小样本问题的存在使得继电保护装置可靠性评估受到限制,提出一种基于三参数威布尔分布的灰色估计法。首先针对继电保护装置故障数据投运初期可靠性高的特点,引入了相对于二参数威布尔分布有明显改善的三参数威布尔分布作为继电保护装置可靠性的分布模型,门限参数的引入可以更直观的判断继电保护装置进入损耗期的时间点;其次为解决失效样本少的问题,通过结合灰色模型与三参数威布尔分布模型,得到一种针对小样本灰色–三参数威布尔分布模型,并对继电保护装置可靠寿命进行参数估计;最后通过实例计算与其他方法进行对比,证明了新方法对小样本继电保护装置进行可靠性参数估计时在保证高精度的同时计算速度更快。
As reliability of protective relays is limited due to existence of small sample problem, a gray estimation method based on three-parameter Weibull distribution is proposed.Firstly, for the characteristics of high reliability at initial stage of failure data of protective relays, a three-parameter Weibull distribution with respect to two-parameter Weibull distribution is introduced as a distribution model for reliable life of protective relays. Introduction of threshold parameter can more intuitively determine the time point of the protective relay entering loss period. Secondly, in order to solve the problem of insufficient failure samples, a parameter estimation of the three-parameter Weibull distribution for small sample is obtained by combining gray model with the three-parameter Weibull distribution model, and the reliable life of the protective relay is estimated. Finally, example calculation is compared with other methods, proving that the new method can calculate reliability of the small-sample protective relay faster while ensuring accuracy.
As reliability of protective relays is limited due to existence of small sample problem, a gray estimation method based on three-parameter Weibull distribution is proposed.Firstly, for the characteristics of high reliability at initial stage of failure data of protective relays, a three-parameter Weibull distribution with respect to two-parameter Weibull distribution is introduced as a distribution model for reliable life of protective relays. Introduction of threshold parameter can more intuitively determine the time point of the protective relay entering loss period. Secondly, in order to solve the problem of insufficient failure samples, a parameter estimation of the three-parameter Weibull distribution for small sample is obtained by combining gray model with the three-parameter Weibull distribution model, and the reliable life of the protective relay is estimated. Finally, example calculation is compared with other methods, proving that the new method can calculate reliability of the small-sample protective relay faster while ensuring accuracy.
引文
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[15]朱晓翠.基于灰色理论的数控机床可靠性及维修性分析技术[D].长春:吉林大学,2013.
[2]徐岩,白静,戴志辉.一种基于威布尔分布的继电保护装置可靠性分析的新方法[J].华北电力大学学报:自然科学版,2012,39(4):15-19.Xu Yan,Bai Jing,Dai Zhihui.A new method for protective relay reliability analysis based on Weibull distribution[J].Journal of North China Electric Power University,2012,39(4):15-19(in Chinese).
[3]张恒喜,郭基联,朱家元.小样本多元数据分析方法及应用[M].西安:西北工业大学出版社,2002:22-23.
[4]韩冬,马进,贺仁睦.基于Bootstrap的实测负荷模型参数优选[J].电工技术学报,2012,27(8):141-146.Han Dong,Ma Jin,He Renmu.Parameter optimization ofmeasurement-based load model based on bootstrap[J].Transactions of China Electrotechnical Society,2012,27(8):141-146(in Chinese).
[5]段晓军,王正明.小子样下的Bootstrap方法[J].弹道学报,2003,15(3):1-5.Duan Xiaojun,Wang Zhengming.The bootstrap method based on small sample[J].Journal of Ballistic,2003,15(3):1-5(in Chinese).
[6]何旭,姜宪国,张沛超,等.基于SVM的小样本条件下继电保护可靠性参数估计[J].电网技术,2015,39(5):1432-1437.He Xu,Jiang Xianguo,Zhang Peichao,et al.SVM based parameter estimation of relay protection reliability with small sampl[J].Power System Technology,2015,39(5):1432-1437(in Chinese).
[7]戴志辉,李芷筠,焦彦军,等.基于BP神经网络的小样本失效数据下继电保护可靠性评估[J].电力自动化设备,2014,34(11):129-134.Dai Zhihui,Li Zhijun,Jiao Yanjun,et al.Reliability assessment based on BP neural network for relay protection system with a few failure data samples[J].Electric Power Automation Equipment,2014,34(11):129-134(in Chinese).
[8]王成山,谢莹华.基于双层同构贝叶斯网络模型的配电网可靠性评估[J].电网技术,2005,29(7):41-46.Wang Chengshan,Xie Yinghua.A new bayesian network model for distribution system reliability evaluation based on dual isomorphic bayesian network model[J].Power System Technology,2005,29(7):41-46(in Chinese).
[9]李芷筠,戴志辉,焦彦军.小样本失效数据下保护可靠性的贝叶斯-蒙特卡罗评估方法[J].电力系统及其自动化学报,2016,28(5):9-14.Li Zhijun,Dai Zhihui,Jiao Yanjun.Bayes monte-carlo reliability assessment method of protection systems with small failure samples[J].Proceedings of the CSU-EPSA,2016,28(5):9-14(in Chinese).
[10]郑锐.三参数威布尔分布参数估计及在可靠性分析中的应用[J].振动与冲击,2015(5):78-81.Zheng Rui.Parameter estimation of three-parameter Weibull distribution and its application in reliability analysis[J].Journal of Vibration and Shock.2015(5):78-81(in Chinese).
[11]严晓东,马翔,郑荣跃,等.三参数威布尔分布参数估计方法比较[J].宁波大学学报(理工版),2005,18(3):301-305.Yan Xiandong,Ma Xiang,Zheng Rongyue,et al.Comparison of the parameters estimation methods for 3-parameters Weibull distribution[J].Journal of NNGBO University(NSEE),2005,18(3):301-305(in Chinese).
[12]薛安成,罗麟,景琦,等.基于三参数Weibull分布的继电保护装置老化失效率估算[J].电力系统保护与控制,2014,42(24):72-78.Xue Ancheng,Luo Lin,Jing Qi,et al.Research on aging failure rate estimation of protective relay based on three-parameter Weibull distribution[J].Power System Protection and Control,2014,42(24):72-78(in Chinese).
[13]张小奇,白昕,万筱钟,等.灰色模型在西北电网风电发电量预测中的应用[J].电网与清洁能源,2011,27(4):66-70.Zhang Xiaoqi,Bai Xin,Wan Xiaozhong,et al.A gray model for wind power generation forecast in northwest power grid[J].Power System and Clean Energy,2011,27(4):66-70(in Chinese).
[14]王大鹏.灰色预测模型及中长期电力负荷预测应用研究[D].武汉:华中科技大学,2013.
[15]朱晓翠.基于灰色理论的数控机床可靠性及维修性分析技术[D].长春:吉林大学,2013.