采用自适应分段聚合近似的典型负荷曲线形态聚类算法
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摘要
对海量负荷数据进行降维聚类处理是提取负荷关键信息,深度挖掘其内在规律的前提。根据负荷曲线的形态特征,文中提出了一种基于可变时间分辨率自适应分段聚合近似方法的曲线形态聚类算法。首先,根据负荷爬坡事件及基于斜率提取的边缘点来衡量负荷曲线的形态特征及其变化趋势,采用自适应分段聚合近似算法对用户日负荷数据集进行可变时间分辨率重构,进一步采用一种基于负荷曲线形态聚类的k-shape算法进行聚类处理,该聚类算法以一种基于曲线形态相似性的距离量度方式作为相似性判据,并依据斯坦纳树优化方法进行聚类中心计算。利用模拟数据、实测数据算例分析验证了所提算法在数据降维、负荷聚类中的实用性和有效性。
The dimension reduction and classification of massive load data are the premise of critical load information extraction and deep data mining.According to the shape characteristics of load curves,this paper proposes a shape clustering algorithm of load curves based on the adaptive piecewise aggregate approximation method with variable temporal resolution.The information of the ramp events and slope-extracted edge point is collected to quantify the shape characteristics and fluctuation level of load curves.Then the users'daily load data sets with variable temporal resolution are reconstructed by the adaptive piecewise aggregate approximation algorithm.Further,the k-shape algorithm is applied in the clustering of daily load curves according to the shape characteristics of load curves.In the k-shape algorithm,the distance measurement method based on the similarity of curve shape is regard as the similarity criterion,and the cluster center is calculated based on the Steiner's sequence optimization method.The practicality and effectiveness of the proposed algorithm in data dimension reduction and load clustering are verified by simulation data and measured data.
The dimension reduction and classification of massive load data are the premise of critical load information extraction and deep data mining.According to the shape characteristics of load curves,this paper proposes a shape clustering algorithm of load curves based on the adaptive piecewise aggregate approximation method with variable temporal resolution.The information of the ramp events and slope-extracted edge point is collected to quantify the shape characteristics and fluctuation level of load curves.Then the users'daily load data sets with variable temporal resolution are reconstructed by the adaptive piecewise aggregate approximation algorithm.Further,the k-shape algorithm is applied in the clustering of daily load curves according to the shape characteristics of load curves.In the k-shape algorithm,the distance measurement method based on the similarity of curve shape is regard as the similarity criterion,and the cluster center is calculated based on the Steiner's sequence optimization method.The practicality and effectiveness of the proposed algorithm in data dimension reduction and load clustering are verified by simulation data and measured data.
引文
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[19]詹艳艳,徐荣聪,陈晓云.基于斜率提取边缘点的时间序分段线性表示方法[J].计算机科学,2006,33(11):139-143.ZHAN Yanyan,XU Rongcong,CHEN Xiaoyun.Time series piecewise linear representation based on slope extract edge point[J].Computer Science,2006,33(11):139-143.
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[2]刘思,傅旭华,叶承晋,等.考虑地域差异的配电网空间负荷聚类及一体化预测方法[J].电力系统自动化,2017,41(3):70-75.DOI:10.7500/AEPS20160507003.LIU Si,FU Xuhua,YE Chengjin,et al.Spatial load clustering and integrated forecasting method of distribution network considering regional difference[J].Automation of Electric Power Systems,2017,41(3):70-75.DOI:10.7500/AEPS20160507003.
[3]陆俊,朱炎平,彭文昊,等.计及用电行为聚类的智能小区互动化需求响应方法[J].电力系统自动化,2017,41(17):113-120.DOI:10.7500/AEPS20161206006.LU Jun,ZHU Yanping,PENG Wenhao,et al.Interactive demand response method of smart community considering clustering of electricity consumption behavior[J].Automation of Electric Power Systems,2017,41(17):113-120.DOI:10.7500/AEPS20161206006.
[4]王桂兰,周国亮,赵洪山,等.大规模用电数据流的快速聚类和异常检测技术[J].电力系统自动化,2016,40(24):27-33.DOI:10.7500/AEPS20160123002.WANG Guilan,ZHOU Guoliang,ZHAO Hongshan,et al.Fast clustering and anomaly detection technique for large-scale power data stream[J].Automation of Electric Power Systems,2016,40(24):27-33.DOI:10.7500/AEPS20160123002.
[5]YA NG H T,CHEN S C,PENG P C.Genetic k-meansalgorithm-based classification of direct load-control curves[J].IEE Proceedings-Generation Transmission and Distribution,2005,152(4):489-495.
[6]张铁峰,顾明迪.电力用户负荷模式提取技术及应用综述[J].电网技术,2016,40(3):804-811.ZHANG Tiefeng,GU Mingdi.Overview of electricity customer load pattern extraction technology and its application[J].Power System Technology,2016,40(3):804-811.
[7]孔祥玉,胡启安,董旭柱,等.引入改进模糊C均值聚类的负荷数据辨识及修复方法[J].电力系统自动化,2017,41(9):90-95.DOI:10.7500/AEPS20160920002.KONG Xiangyu,HU Qian,DONG Xuzhu,et al.Load data identification and correction method with improved fuzzy C-means clustering algorithm[J].Automation of Electric Power Systems,2017,41(9):90-95.DOI:10.7500/AEPS20160920002.
[8]杨东升,孔亮,胡博,等.基于多特征序列融合的负荷辨识方法[J].电力系统自动化,2017,41(22):66-73.DOI:10.7500/AEPS20170516002.YANG Dongsheng,KONG Liang,HU Bo,et al.Load identification method based on multi-feature sequence fusion[J].Automation of Electric Power Systems,2017,41(22):66-73.DOI:10.7500/AEPS20170516002.
[9]YANG J,LESKOVEC J.Patterns of temporal variation in online media[C]//Fourth ACM International Conference on Web Search and Data Mining(WSDM),February 9-12,2011,Hong Kong,China:177-186.
[10]DING H,TRAJCEVSKI G,WANG X,et al.Querying and mining of time series data:experimental comparison of representations and distance measures[J].Proceedings of the VLDB Endowment,2008,1(2):1542-1552.
[11]CHAOVALIT P,GANGOPADHYAY A,KARABATIS G,et al.Discrete wavelet transform-based time series analysis and mining[J].ACM Computing Surveys(CSUR),2011,43(2):1-37.
[12]FINK E,GANDHI H S.Compression of time series by extracting major extrema[J].Journal of Experimental&Theoretical Artificial Intelligence,2011,23(2):255-270.
[13]牟婷婷,陆微,王兰君,等.基于主成分分析的用电模式稳定性分析[J].电力系统自动化,2017,41(19):59-65.DOI:10.7500/AEPS20161222001.MOU Tingting,LU Wei,WANG Lanjun,et al.Stability analysis of consumption mode based on principal component analysis[J].Automation of Electric Power Systems,2017,41(19):59-65.DOI:10.7500/AEPS20161222001.
[14]ESLING P,AGON C.Time-series data mining[J].ACMComputing Surveys(CSUR),2012,45(1):1-34.
[15]YANG Junjing,NING Chao,DEB C,et al.k-shape clustering algorithm for building energy usage patterns analysis and forecasting model accuracy improvement[J].Energy and Buildings,2017,146:27-37.
[16]BATISTA G E,KEOGH E J,TATAW O M.An efficient complexity-invariant distance for time series[J].Data Mining and Knowledge Discovery,2013,28(3):634-669.
[17]李海林.时间序列数据挖掘中的特征表示与相似性度量方法研究[D].大连:大连理工大学,2012.LI Hailin.Research on feature representation and similarity measure methods in time series data mining[D].Dalian:Dalian University of Technology,2012.
[18]欧阳庭辉,查晓明,秦亮,等.风电功率爬坡事件预测时间窗选取建模[J].中国电机工程学报,2015,35(13):3204-3210.OUYANG Tinghui,ZHA Xiaoming,QIN Liang,et al.Modeling on selection of the time window for ramp events prediction[J].Proceedings of the CSEE,2015,35(13):3204-3210.
[19]詹艳艳,徐荣聪,陈晓云.基于斜率提取边缘点的时间序分段线性表示方法[J].计算机科学,2006,33(11):139-143.ZHAN Yanyan,XU Rongcong,CHEN Xiaoyun.Time series piecewise linear representation based on slope extract edge point[J].Computer Science,2006,33(11):139-143.
[20]SILHOUETTES P.A graphical aid to the interpretation and validation of cluster-analysis[J].Journal of Computational and Applied Mathematics,1987,20(1):53-65.
[21]THORNDIK R L.Who belongs in the family?[J].Psychometrika,1953,18(4):267-276.
[22]WANG X,MUEEN A,DING H,et al.Experimental comparison of representation methods and distance measures for time series data[J].Data Mining and Knowledge Discovery,2013,26(2):275-309.