基于数值特性聚类的日前光伏出力预测误差分布模型
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摘要
光伏出力预测误差难以避免且不容忽视,预测误差分布的准确描述有利于电力系统的优化调度和稳定运行。基于此,分析预测误差分布与其影响因素之间的相关性,提出一种基于数值特性聚类的日前光伏出力预测误差概率模型。利用模糊C均值聚类法对预测误差的整体水平进行分类,再依据预测出力的数值特性进行分区处理,并建立了适用于估计误差分布的通用型高斯混合模型。该分析方法综合考虑了气象因素和预测出力数值特性对预测误差的影响,可以较为准确地估计不同时刻的预测误差,给出预测误差分布的置信区间,且不受预测算法和光伏电站地理信息的限制。基于比利时和中国西北地区光伏系统历史数据的分析结果表明,所提误差模型可描述光伏出力预测误差分布偏态性和峰度多样性,效果优于其他分布模型,能够用于描述不同情况下的日前光伏出力预测误差分布。
The forecasting error of photovoltaic(PV) output is difficult to avoid and cannot be ignored. The accurate description of the forecasting error distribution is beneficial to the optimal dispatch and stable operation of the power system. The correlation between the forecasting error distribution and influencing factors is analyzed, and a probabilistic model of the PV output forecasting error based on numerical characteristic clustering is proposed. The whole level of forecasting errors will be classified through the fuzzy C-means clustering and the classification on the output forecasting will be conducted according to its numerical characteristics. A general Gauss mixed model available to estimate error distribution is established. Considering the influences of meteorological factors and numerical characteristics on forecasting errors, the model could estimate forecasting errors at different times and produce the confidence interval of error distribution. At the same time, the proposed model is free from the influences brought by different forecasting algorithms and the geographic information of PV power station. Based on the historical data of PV systems in Belgium and Northwest China, analysis results show that the skewness, multi-peak and kurtosis diversity of PV power forecasting error distribution can be described by the proposed model more accurately compared with other distribution models, which can be used to describe the forecasting error distribution of day-ahead PV power in different situations.
The forecasting error of photovoltaic(PV) output is difficult to avoid and cannot be ignored. The accurate description of the forecasting error distribution is beneficial to the optimal dispatch and stable operation of the power system. The correlation between the forecasting error distribution and influencing factors is analyzed, and a probabilistic model of the PV output forecasting error based on numerical characteristic clustering is proposed. The whole level of forecasting errors will be classified through the fuzzy C-means clustering and the classification on the output forecasting will be conducted according to its numerical characteristics. A general Gauss mixed model available to estimate error distribution is established. Considering the influences of meteorological factors and numerical characteristics on forecasting errors, the model could estimate forecasting errors at different times and produce the confidence interval of error distribution. At the same time, the proposed model is free from the influences brought by different forecasting algorithms and the geographic information of PV power station. Based on the historical data of PV systems in Belgium and Northwest China, analysis results show that the skewness, multi-peak and kurtosis diversity of PV power forecasting error distribution can be described by the proposed model more accurately compared with other distribution models, which can be used to describe the forecasting error distribution of day-ahead PV power in different situations.
引文
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[21] 赵唯嘉,张宁,康重庆,等.光伏发电出力的条件预测误差概率分布估计方法[J].电力系统自动化,2015,39(16):8-15.ZHAO Weijia,ZHANG Ning,KANG Chongqing,et al.A method of probabilistic distribution estimation of conditional forecast error for photovoltaic power generation[J].Automation of Electric Power Systems,2015,39(16):8-15.
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[24] 吴问足,乔颖,鲁宗相,等.风电功率概率预测方法及展望[J].电力系统自动化,2017,41(18):167-175.DOI:10.7500/AEPS20160914002.WU Wenzu,QIAO Ying,LU Zongxiang,et al.Methods and prospects for probabilistic forecasting of wind power[J].Automation of Electric Power Systems,2017,41(18):167-175.DOI:10.7500/AEPS20160914002.
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[27] 耿博,高贞彦,白恒远,等.结合相似日GA-BP神经网络的光伏发电预测[J].电力系统及其自动化学报,2017,29(6):118-123.GENG Bo,GAN Zhenyan,BAI Hengyuan,et al.PV generation forecasting combined with similar days and GA-BP neural network[J].Proceedings of the CSU-EPSA,2017,29(10):118-123.
[28] 诸克军,苏顺华,黎金玲.模糊C-均值中的最优聚类与最佳聚类数[J].系统工程理论与实践,2005,25(3):52-61.ZHU Kejun,SU Shunhua,LI Jinling.Optimal number of clusters and the best partition in fuzzy C-mean[J].System Engineering Theory and Practice,2005,25(3):52-61.
[29] 刘燕华,李伟花,刘冲,等.短期风电功率预测误差的混合偏态分布模型[J].中国电机工程学报,2015,35(10):2375-2382.LIU Yanhua,LI Weihua,LIU Chong,et al.Mixed skew distribution model of short-term wind power prediction error[J].Proceedings of the CSEE,2015,35(10):2375-2382.
[30] GNEITING Y,BALABDAOUI F,RAFTERY A E.Probabilistic forecasts,calibration and sharpness[J].Journal of the Royal Statistical Society:Series B (Statistical Methodology),2007,69(2):243-268.
[31] 颜伟,李丹,朱继忠,等.月前日负荷曲线的概率预测和随机场景模拟[J].电力系统自动化,2017,41(17):155-162.DOI:10.7500/AEPS20160908017.YAN Wei,LI Dan,ZHU Jizhong,et al.Probabilistic forecasting and stochastic scenario simulation of month-ahead daily load curve[J].Automation of Electric Power Systems,2017,41(17):155-162.DOI:10.7500/AEPS20160908017.
[2] ZAMO M,MESTRE O,ARBOGAST P,et al.A benchmark of statistical regression methods for short-term forecasting of photovoltaic electricity production:Part Ⅰ deterministic forecast of hourly production[J].Solar Energy,2014,105:792-803.
[3] BACHER P,MADSEN H,NIELSEN H A.Online short-term solar power forecasting[J].Solar Energy,2009,83(10):1772-1783.
[4] ZHONG Zhifeng,YANG Chenxi,CAO Wenyang,et al.Short-term photovoltaic power generation forecasting based on multivariable grey theory model with parameter optimization[J].Mathematical Problems in Engineering,2017(7):1-9.
[5] TANG P,CHEN D,HOU Y.Entropy method combined with extreme learning machine method for the short-term photovoltaic power generation forecasting[J].Chaos Solitons & Fractals,2016,89(Supplement 1):243-248.
[6] 王昕,黄柯,郑益慧,等.基于PNN/PCA/SS-SVR的光伏发电功率短期预测方法[J].电力系统自动化,2016,40(17):156-162.WANG Xin,HUANG Ke,ZHENG Yihui,et al.Short-term forecasting method of photovoltaic output power based on PNN/PCA/SS-SVR[J].Automation of Electric Power Systems,2016,40(17):156-162.
[7] 董雷,周文萍,张沛,等.基于动态贝叶斯网络的光伏发电短期概率预测[J].中国电机工程学报,2013,33(增刊1):38-45.DONG Lei,ZHOU Wenping,ZHANG Pei,et al.Short-term photovoltaic output forecast based on dynamic Bayesian network theory[J].Proceedings of the CSEE,2013,33(Supplement 1):38-45.
[8] BAE K Y,JANG H S,SUNG D K.Hourly solar irradiance prediction based on support vector machine and its error analysis[J].IEEE Transactions on Power Systems,2017,32(2):935-945.
[9] 赵书强,王明雨,胡永强,等.基于不确定理论的光伏出力预测研究[J].电工技术学报,2015,30(16):213-220.ZHAO Shuqiang,WANG Mingyu,HU Yongqiang,et al.Research on the prediction of PV output based on uncertainty theory[J].Transactions of China Electrotechnical Society,2015,30(16):213-220.
[10] MARQUEZ R,COIMBRA C F M.Forecasting of global and direct solar irradiance using stochastic learning methods,ground experiments and the NWS database[J].Solar Energy,2011,85(5):746-756.
[11] 殷加玞,赵冬梅.考虑源荷双侧预测误差的实时发电计划闭环控制模型[J].电力系统自动化,2018,42(6):98-105.DOI:10.7500/AEPS20170604004.YIN Jiafu,ZHAO Dongmei.Closed-loop control model for real-time generation scheduling considering source-side and load-side prediction error[J].Automation of Electric Power Systems,2018,42(6):98-105.DOI:10.7500/AEPS 20170604004.
[12] 赵波,薛美东,陈荣柱,等.高可再生能源渗透率下考虑预测误差的微电网经济调度模型[J].电力系统自动化,2014,38(7):1-8.ZHAO Bo,XUE Meidong,CHEN Rongzhu,et al.An economic dispatch model for microgrid with high renewable energy resource penetration considering forecast errors[J].Automation of Electric Power Systems,2014,38(7):1-8.
[13] 胡永强,刘晨亮,赵书强,等.基于模糊相关机会规划的储能优化控制[J].电力系统自动化,2014,38(6):20-25.HU Yongqiang,LIU Chenliang,ZHAO Shuqiang,et al.Optimal control of energy storage based on fuzzy correlated-chance programming[J].Automation of Electric Power Systems,2014,38(6):20-25.
[14] 叶瑞丽,郭志忠,刘瑞叶,等.基于风电功率预测误差分析的风电场储能容量优化方法[J].电力系统自动化,2014,38(16):28-34.YE Ruili,GUO Zhizhong,LIU Ruiye,et al.An estimation method for wind power forecast errors based on numerical feature extraction[J].Automation of Electric Power Systems,2014,38(16):28-34.
[15] 林少伯,韩民晓,赵国鹏,等.基于随机预测误差的分布式光伏配网储能系统容量配置方法[J].中国电机工程学报,2013,33(4):25-33.LIN Shaobo,HAN Minxiao,ZHAO Guopeng,et al.Capacity allocation of energy storage in distributed photovoltaic power system based on stochastic prediction error[J].Proceedings of the CSEE,2013,33(4):25-33.
[16] 包江民,刘德伟,耿天翔,等.考虑风功率预测误差相关性的旋转备用容量优化[J].可再生能源,2015,33(12):1845-1852.BAO Jiangmin,LIU Dewei,GENG Tianxiang,et al.Spining reserve capacity optimization considering correlations of wind power forecast errors[J].Renewable Energy Resources,2015,33(12):1845-1852.
[17] LORENZ E,HURKA J,HEINEMANN D,et al.Irradiance forecasting for the power prediction of grid-connected photovoltaic systems[J].IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing,2009,2(1):2-10.
[18] 丁明,楚明娟,潘浩,等.交直流混合微电网运行优化建模与不确定性分析[J].电力系统自动化,2017,41(5):1-7.DOI:10.7500/AEPS20160531012.DING Ming,CHU Mingjuan,PAN Hao,et al.Operation optimization modeling and uncertainty analysis for hybrid AC/DC microgrids[J].Automation of Electric Power Systems,2017,41(5):1-7.DOI:10.7500/AEPS20160531012.
[19] 姜欣,陈红坤,熊虎,等.基于预测误差不确定性的规模化间歇式电源机组组合研究[J].电网技术,2014,38(9):2455-2460.JIANG Xin,CHEN Hongkun,XIONG Hu,et al.A prediction error uncertainty based day-ahead unit commitment of large-scale intermittent power generation[J].Power System Technology,2014,38(9):2455-2460.
[20] 陈瑶琪.基于典型天气类型计及随机预测误差的光伏发电短期预测研究[J].中国电力,2016,49(5):157-162.CHEN Yaoqi.Short-term photovoltaic power prediction based on typical climate types and stochastic prediction error[J].Electric Power,2016,49(5):157-162.
[21] 赵唯嘉,张宁,康重庆,等.光伏发电出力的条件预测误差概率分布估计方法[J].电力系统自动化,2015,39(16):8-15.ZHAO Weijia,ZHANG Ning,KANG Chongqing,et al.A method of probabilistic distribution estimation of conditional forecast error for photovoltaic power generation[J].Automation of Electric Power Systems,2015,39(16):8-15.
[22] EMBRECHTS P,LINDSKOG F,MCNEIL A.Handbook of heavy tailed distributions in finance:modeling dependence with copulas and applications to risk management[M].Amsterdam:North-Holland Publishing Company,2003.
[23] 于波,陈希镇,杜江.Copula函数的选择:方法与应用[J].数理统计与管理,2008,27(6):1027-1033.YU Bo,CHEN Xizhen,DU Jiang.A method to select the best-fit Copula and its application[J].Application of Statistics and Management,2008,27(6):1027-1033.
[24] 吴问足,乔颖,鲁宗相,等.风电功率概率预测方法及展望[J].电力系统自动化,2017,41(18):167-175.DOI:10.7500/AEPS20160914002.WU Wenzu,QIAO Ying,LU Zongxiang,et al.Methods and prospects for probabilistic forecasting of wind power[J].Automation of Electric Power Systems,2017,41(18):167-175.DOI:10.7500/AEPS20160914002.
[25] 谢中华.MATLAB统计分析与应用:40个案例分析[M].北京航空航天大学出版社,2015:243-264.XIE Zhonghua.Statistical analysis and application of MATLAB:40 case studies[M].Beijing:Beihang University Press,2015:243-264.
[26] YAN C,XIU J,LIU C,et al.A high concentrated photovoltaic output power predictive model based on fuzzy clustering and RBF neural network[C]// IEEE 3rd International Conference on Cloud Computing and Intelligence Systems (CCIS),November 27-29,2014,Shenzhen,China:384-388.
[27] 耿博,高贞彦,白恒远,等.结合相似日GA-BP神经网络的光伏发电预测[J].电力系统及其自动化学报,2017,29(6):118-123.GENG Bo,GAN Zhenyan,BAI Hengyuan,et al.PV generation forecasting combined with similar days and GA-BP neural network[J].Proceedings of the CSU-EPSA,2017,29(10):118-123.
[28] 诸克军,苏顺华,黎金玲.模糊C-均值中的最优聚类与最佳聚类数[J].系统工程理论与实践,2005,25(3):52-61.ZHU Kejun,SU Shunhua,LI Jinling.Optimal number of clusters and the best partition in fuzzy C-mean[J].System Engineering Theory and Practice,2005,25(3):52-61.
[29] 刘燕华,李伟花,刘冲,等.短期风电功率预测误差的混合偏态分布模型[J].中国电机工程学报,2015,35(10):2375-2382.LIU Yanhua,LI Weihua,LIU Chong,et al.Mixed skew distribution model of short-term wind power prediction error[J].Proceedings of the CSEE,2015,35(10):2375-2382.
[30] GNEITING Y,BALABDAOUI F,RAFTERY A E.Probabilistic forecasts,calibration and sharpness[J].Journal of the Royal Statistical Society:Series B (Statistical Methodology),2007,69(2):243-268.
[31] 颜伟,李丹,朱继忠,等.月前日负荷曲线的概率预测和随机场景模拟[J].电力系统自动化,2017,41(17):155-162.DOI:10.7500/AEPS20160908017.YAN Wei,LI Dan,ZHU Jizhong,et al.Probabilistic forecasting and stochastic scenario simulation of month-ahead daily load curve[J].Automation of Electric Power Systems,2017,41(17):155-162.DOI:10.7500/AEPS20160908017.