基于形态距离的日负荷数据自适应稳健聚类算法
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摘要
为克服传统划分式聚类算法的聚类数k值难以确定以及聚类结果稳定性较差的问题,提出一种基于日负荷曲线形态距离的自适应稳健聚类方法。利用差分算法和分位数对原始日负荷曲线进行特征提取,将其转化为描述负荷曲线形态特征的离散类属性数据,用曲线形态差异度量替代对负荷数据的欧氏距离度量,避免数据标幺化可能带来的信息缺失;进一步引入特征属性加权和隶属度惩罚,根据样本形态特征,提出基于动态层次Fuzzy U-K-modes的自适应聚类算法,通过多阶段聚类和构建聚类系谱,自适应地确定聚类中心和k值,在不过多损失效率的前提下,使聚类结果的稳定性大幅提升;最后以某地区4869个用户的日负荷数据为研究对象,验证了所提算法的有效性。
Based on the definition of morphological distance, a self-adaptive clustering algorithm was introduced to accurately group a large amount of daily load profiles according to the shape similarity. Firstly, the morphological characteristic of each load curve was computed by using difference algorithm and quantile. In clustering procedure, the conventional Euclidean distance was replaced by the extracted morphological characteristics. By doing so, the information loss of data preprocessing caused by simple normalization can be avoided. Additionally, the moving hierarchical fuzzy U-K-modes based on attribute weighting and membership penalty was introduced to determine the number of clustering centers adaptively by multi-stage clustering and clustering genealogy on the premise of efficiency and stability. Finally, the presented algorithm was applied in clustering analysis of 4869 daily users load data. The results of case study demonstrate the effectiveness of the method.
Based on the definition of morphological distance, a self-adaptive clustering algorithm was introduced to accurately group a large amount of daily load profiles according to the shape similarity. Firstly, the morphological characteristic of each load curve was computed by using difference algorithm and quantile. In clustering procedure, the conventional Euclidean distance was replaced by the extracted morphological characteristics. By doing so, the information loss of data preprocessing caused by simple normalization can be avoided. Additionally, the moving hierarchical fuzzy U-K-modes based on attribute weighting and membership penalty was introduced to determine the number of clustering centers adaptively by multi-stage clustering and clustering genealogy on the premise of efficiency and stability. Finally, the presented algorithm was applied in clustering analysis of 4869 daily users load data. The results of case study demonstrate the effectiveness of the method.
引文
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[26]朱林,王士同,邓超红.改进模糊划分的FCM聚类算法的一般化研究[J].计算机研究与发展,2009,46(5):814-822.Zhu Lin,Wang Shitong,Deng Chaohong.Research on generalized fuzzy C-means clustering algorithm with improved fuzzy partitions[J].Journal of Computer Research and Development,2009,46(5):814-822(in Chinese).
[2]Mai Weijie,Chung C Y.Economic MPC of aggregating commercial buildings for providing flexible power reserve[J].IEEE Transactions on Power Systems,2015,30(5):2685-2694.
[3]Asad Z,Chaudhry M A R.A two-way street:green big data processing for a greener smart grid[J].IEEE Systems Journal,2017,11(2):784-795.
[4]Izadkhast S,Garcia-Gonzalez P,Frías P.An aggregate model of plug-in electric vehicles for primary frequency control[J].IEEE Transactions on Power Systems,2015,30(3):1475-1482.
[5]蒋雯倩,李欣然,钱军.改进FCM算法及其在电力负荷坏数据处理的应用[J].电力系统及其自动化学报,2011,23(5):1-5.Jiang Wenqian,Li Xinran,Qian Jun.Application of improved FCM algorithm in outlier processing of power load[J].Proceedings of the CSU-EPSA,2011,23(5):1-5(in Chinese).
[6]Conejo A J,Morales J M,Baringo L.Real-time demand response model[J].IEEE Transactions on Smart Grid,2010,1(3):236-242.
[7]Chicco G.Overview and performance assessment of the clustering methods for electrical load pattern grouping[J].Energy,2012,42(1):68-80.
[8]李培强,李欣然,陈辉华,等.基于模糊聚类的电力负荷特性的分类与综合[J].中国电机工程学报,2005,25(24):73-78.Li Peiqiang,Li Xinran,Chen Huihua,et al.The characteristics classification and synthesis of power load based on fuzzy clustering[J].Proceedings of the CSEE,2005,25(24):73-78(in Chinese).
[9]Liu Yi,Yuen C,Huang Shisheng,et al.Peak-to-average ratio constrained demand-side management with consumer’s preference in residential smart grid[J].IEEEJournal of Selected Topics in Signal Processing,2014,8(6):1084-1097.
[10]Petr P.Data mining[J].Tools and Techniques,1994,29(1):47.
[11]Li Ran,Gu Chenghong,Li Furong,et al.Development of low voltage network templates--part I:substation clustering and classification[J].IEEE Transactions on Power Systems,2015,30(6):3036-3044.
[12]Gulbinas R,Khosrowpour A,Taylor J.Segmentation and classification of commercial building occupants by energy-use efficiency and predictability[J].IEEETransactions on Smart Grid,2015,6(3):1414-1424.
[13]刘友波,刘俊勇,赵岩,等.基于多目标聚类的用电集群特征属性计算[J].电力系统自动化,2009,33(19):46-51.Liu Youbo,Liu Junyong,Zhao Yan,et al.Calculation of characteristic attributes of consumer aggregations based on multi-objective clustering[J].Automation of Electric Power Systems,2009,33(19):46-51(in Chinese).
[14]张斌,庄池杰,胡军,等.结合降维技术的电力负荷曲线集成聚类算法[J].中国电机工程学报,2015,35(15):3741-3749.Zhang Bin,Zhuang Chijie,Hu Jun,et al.Ensemble clustering algorithm combined with dimension reduction techniques for power load profiles[J].Proceedings of the CSEE,2015,35(15):3741-3749(in Chinese).
[15]黄宇腾,侯芳,周勤,等.一种面向需求侧管理的用户负荷形态组合分析方法[J].电力系统保护与控制,2013,41(13):20-25.Huang Yuteng,Hou Fang,Zhou Qin,et al.A new combinational electrical load analysis method for demand side management[J].Power System Protection and Control,2013,41(13):20-25(in Chinese).
[16]Chicco G,Ionel O M,Porumb R.Electrical load pattern grouping based on centroid model with ant colony clustering[J].IEEE Transactions on Power Systems,2013,28(2):1706-1715.
[17]张少敏,赵硕,王保义.基于云计算和量子粒子群算法的电力负荷曲线聚类算法研究[J].电力系统保护与控制,2014,42(21):93-98.Zhang Shaomin,Zhao Shuo,Wang Baoyi.Research of power load curve clustering algorithm based on cloud computing and quantum particle swarm optimization[J].Power System Protection and Control,2014,42(21):93-98(in Chinese).
[18]Panapakidis I P,Alexiadis M C,Papagiannis G K.Three-stage clustering procedure for deriving the typical load curves of the electricity consumers[C]//Proceedings of 2013 IEEE Grenoble Conference.Grenoble:IEEE,2013:1-6.
[19]李哲,慕德俊,张天凡,等.基于agent形态特征的聚类分析研究与应用[J].西北工业大学学报,2016,34(4):691-697.Li Zhe,Mu Dejun,Zhang Tianfan,et al.Clustering algorithm and its application base on agent morphology[J].Journal of Northwestern Polytechnical University,2016,34(4):691-697(in Chinese).
[20]林顺富,田二伟,符杨,等.基于信息熵分段聚合近似和谱聚类的负荷分类方法[J].中国电机工程学报,2017,37(8):2242-2252.Lin Shunfu,Tian Erwei,Fu Yang,et al.Power load classification method based on information entropy piecewise aggregate approximation and spectral clustering[J].Proceedings of the CSEE,2017,37(8):2242-2252(in Chinese).
[21]Teeraratkul T,O’Neill D,Lall S.Shape-based approach to household electric load curve clustering and prediction[J].IEEE Transactions on Smart Grid,2018,9(5):5196-5206.
[22]Choi B K,Kim D W.Bounded deviation joint path algorithms for piecewise cubic polynomial trajectories[J].IEEE Transactions on Systems,Man,and Cybernetics,1990,20(3):725-733.
[23]Ning Xianghui,Wu Chunjie.Improved design of quantile-based control charts[J].Journal of the Chinese Institute of Industrial Engineers,2011,28(7):504-511.
[24]梁吉业,白亮,曹付元.基于新的距离度量的K-Modes聚类算法[J].计算机研究与发展,2010,47(10):1749-1755.Liang Jiye,Bai Liang,Cao Fuyuan.K-modes clustering algorithm based on a new distance measure[J].Journal of Computer Research and Development,2010,47(10):1749-1755(in Chinese).
[25]于剑.论模糊C均值算法的模糊指标[J].计算机学报,2003,26(8):968-973.Yu Jian.On the Fuzziness index of the FCMalgorithms[J].Chinese Journal of Computers,2003,26(8):968-973(in Chinese).
[26]朱林,王士同,邓超红.改进模糊划分的FCM聚类算法的一般化研究[J].计算机研究与发展,2009,46(5):814-822.Zhu Lin,Wang Shitong,Deng Chaohong.Research on generalized fuzzy C-means clustering algorithm with improved fuzzy partitions[J].Journal of Computer Research and Development,2009,46(5):814-822(in Chinese).