短期风电功率动态云模型不确定性预测方法
|
摘要
高比例风电并网场景下,电力系统优化运行势必对风电功率预测精度及其不确定性分析结果的可靠性提出更高要求。现有的不确定性预测研究中大多为整体性的误差分析与建模,难以满足模型在各个时刻和各类天气下的适应性。因此,提出了动态云模型的短期风电功率不确定性预测方法。首先,建立各个预测功率区间段内的单点预测误差云模型,利用云模型数字特征(期望、熵、超熵)生成云滴分布图,以此量化预测不确定性态势。然后,计算给定置信水平下的云滴分位点,以及与之相对应的预测功率可能发生波动的置信范围,即风电功率预测不确定性分析结果。根据实时条件更新云模型,可以提高各个运行时刻点不确定性预测结果的可靠性。以中国北方某风电场运行数据为例进行验证,结果表明与传统的分位数回归方法相比,所提方法可靠性有所提升,能够为电力系统调度决策、备用安排等提供更为可靠的指导信息。
Power system with high penetration of wind power requires much better performance for the accuracy of wind power forecasting(WPF)and reliability of its uncertainty analysis.Most of studies on the WPF uncertainty analysis mainly focus on the static error analysis and modelling for the overall span,and this will limit the model performance and adaptabilities at various time slots and weather conditions.Therefore,a time-switching cloud model is presented for the short-term WPF uncertainty analysis.First,the cloud models of the deterministic forecasting deviation for each selected predictive power range are established in a real-time updating manner.Then,the distribution of cloud drops can be generated according to three mathematical characteristics of the cloud,i.e.expectation,entropy and ultra-entropy.In this way,the uncertainty conditions of given predictive power ranges can be quantified.Moreover,by calculating the quantile of generated cloud drops,the uncertainty forecasting results can be achieved and expressed as the possible power range at given confidence level.The model performance at each time slot could be improved by updating the cloud model according to the current conditions.To take a Chinese wind farm as an example,the results show that the proposed method achieves more reliable uncertain intervals compared with the traditional quantile regression model and it can provide more reliable information for the dispatch and reserve of the power system.
Power system with high penetration of wind power requires much better performance for the accuracy of wind power forecasting(WPF)and reliability of its uncertainty analysis.Most of studies on the WPF uncertainty analysis mainly focus on the static error analysis and modelling for the overall span,and this will limit the model performance and adaptabilities at various time slots and weather conditions.Therefore,a time-switching cloud model is presented for the short-term WPF uncertainty analysis.First,the cloud models of the deterministic forecasting deviation for each selected predictive power range are established in a real-time updating manner.Then,the distribution of cloud drops can be generated according to three mathematical characteristics of the cloud,i.e.expectation,entropy and ultra-entropy.In this way,the uncertainty conditions of given predictive power ranges can be quantified.Moreover,by calculating the quantile of generated cloud drops,the uncertainty forecasting results can be achieved and expressed as the possible power range at given confidence level.The model performance at each time slot could be improved by updating the cloud model according to the current conditions.To take a Chinese wind farm as an example,the results show that the proposed method achieves more reliable uncertain intervals compared with the traditional quantile regression model and it can provide more reliable information for the dispatch and reserve of the power system.
引文
[1]薛禹胜,雷兴,薛峰,等.关于风电不确定性对电力系统影响的评述[J].中国电机工程学报,2014,34(29):5029-5040.XUE Yusheng,LEI Xing,XUE Feng,et al.A review on impacts of wind power uncertainties on power systems[J].Proceedings of the CSEE,2014,34(29):5029-5040.
[2]鲁宗相,闵勇.基于功率预测的波动性能源发电的多时空尺度调度技术[J].电力科学与技术学报,2012,27(3):28-33.LU Zongxiang,MIN Yong.Multiple time and spatial scale dispatching techniques of volatile energy generation based on power prediction[J].Journal of Electric Power Science and Technology,2012,27(3):28-33.
[3]YAN Jie,LIU Yongqian,HAN Shuang,et al.Reviews on uncertainty analysis of wind power forecasting[J].Renewable&Sustainable Energy Reviews,2015,52(52):1322-1330.
[4]YAO Zhang,WANG Jianxue,WANG Xifan.Review on probabilistic forecasting of wind power generation[J].Renewable&Sustainable Energy Reviews,2014,32(5):255-270.
[5]YANG Ming,ZHU Simeng,LIU Meng,et al.One parametric approach for short-term JPDF forecast of wind generation[J].IEEE Transactions on Industry Application,2014,50(4):2837-2843.
[6]兰飞,桑川川,梁浚杰,等.基于条件Copula函数的风电功率区间预测[J].中国电机工程学报,2016,36(增刊1):79-86.LAN Fei,SANG Chuanchuan,LIANG Junjie,et al.Interval prediction for wind power based on conditional Copula function[J].Proceedings of the CSEE,2016,36(Supplement 1):79-86.
[7]杨宏,苑津莎,张铁峰.一种基于Beta分布的风电功率预测误差最小概率区间的模型和算法[J].中国电机工程学报,2015,35(9):2135-2142.YANG Hong,YUAN Jinsha,ZHANG Tiefeng.A model and algorithm for minimum probability interval of wind power forecast errors based on Beta distribution[J].Proceedings of the CSEE,2015,35(9):2135-2142.
[8]刘兴杰,谢春雨.基于贝塔分布的风电功率波动区间估计[J].电力自动化设备,2014,34(12):26-30.LIU Xingjie,XIE Chunyu.Wind power fluctuation based on Beta distribution[J].Electric Power Automation Equipment,2014,34(12):26-30.
[9]ZHANG Zhaosui,SUN Yuanzhang,GAO D W,et al.Aversatile probability distribution model for wind power forecast errors and its application in economic dispatch[J].IEEETransactions on Power Systems,2013,28(3):3114-3125.
[10]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.
[11]杨茂,董骏城.基于混合高斯分布的风电功率实时预测误差分析[J].太阳能学报,2016,37(6):1594-1602.YANG Mao,DONG Juncheng.Real-time prediction error analysis of wind power based on mixed Gaussian distribution model[J].Acta Energiae Solaris Sinica,2016,37(6):1594-1602.
[12]MEN Zhongxian,YEE E,FUE-SANG L,et al.Short-term wind speed and power forecasting using an ensemble of mixture density neural networks[J].Renewable Energy,2016,87:203-211.
[13]丁华杰,宋永华,胡泽春,等.基于风电场功率特性的日前风电预测误差概率分布研究[J].中国电机工程学报,2013,33(34):119-127.DING Huajie,SONG Yonghua,HU Zechun,et al.Probability density function of day-ahead wind power forecast errors based on power curves of wind farms[J].Proceedings of the CSEE,2013,33(34):119-127.
[14]刘芳,潘毅,刘辉,等.风电功率预测误差分段指数分布模型[J].电力系统自动化,2013,37(18):14-19.LIU Fang,PAN Yi,LIU Hui,et al.Piecewise exponential distribution model of wind power forecasting error[J].Automation of Electric Power Systems,2013,37(18):14-19.
[15]阎洁,刘永前,韩爽,等.分位数回归在风电功率预测不确定性分析中的应用[J].太阳能学报,2013,34(12):2101-2107.YAN Jie,LIU Yongqian,HAN Shuang,et al.Quantile regression in uncertainty analysis of wind power forecasting[J].Acta Energiae Solaris Sinica,2013,34(12):2101-2107.
[16]李智,韩学山,杨明,等.基于分位点回归的风电功率波动区间分析[J].电力系统自动化,2011,35(3):83-87.LI Zhi,HAN Xueshan,YANG Ming,et al.Wind power fluctuation interval analysis based on quantile regression[J].Automation of Electric Power Systems,2011,35(3):83-87.
[17]HUANG Chaoming,KUO C J,HUANG Y C.Short-term wind power forecasting and uncertainty analysis using a hybrid intelligent method[J].IET Renewable Power Generation,2017,11(5):678-687.
[18]WAN Can,ZHAO Xu,PINSON P,et al.Optimal prediction intervals of wind power generation[J].IEEE Transactions on Power Systems,2014,29(3):1166-1174.
[19]PINSON P,KARINIOTAKIS G.Conditional prediction intervals of wind power generation[J].IEEE Transactions on Power Systems,2010,25(4):1845-1856.
[20]杨楠,崔家展,周峥,等.基于模糊序优化的风功率概率模型非参数核密度估计方法[J].电网技术,2016,40(2):335-340.YANG Nan,CUI Jiazhan,ZHOU Zheng,et al.Research on non-parametric kernel density estimation for modeling of wind power probability characteristic based on fuzzy ordinal optimization[J].Power System Technology,2016,40(2):335-340.
[21]LIAO Guodong,JIE Ming,WEI Boyuan,et al.Wind power prediction errors model and algorithm based on non-parametric kernel density estimation[C]//5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies,November 26-29,2015,Changsha,China:1864-1868.
[22]孙建波,吴小珊,张步涵.基于非参数核密度估计的风电功率区间预测[J].水电能源科学,2013,31(9):233-235.SUN Jianbo,WU Xiaoshan,ZHANG Buhan.Wind power interval prediction based on non-parametric kernel density estimation[J].Water Resources and Power,2013,31(9):233-235.
[23]黄坡,朱小帆,查晓明,等.基于波动过程聚类的风电功率预测极大误差估计方法[J].电力系统保护与控制,2016,44(13):130-136.HUANG Po,ZHU Xiaofan,ZHA Xiaoming,et al.An estimation method for wind power prediction great error based on clustering fluctuation process[J].Power System Protection and Control,2016,44(13):130-136.
[24]YAN Jie,LIU Yongqian,HAN Shuang,et al.Wind power grouping forecasts and its uncertainty analysis using optimized relevance vector machine[J].Renewable&Sustainable Energy Reviews,2013,27(6):613-621.
[25]杨明,范澍,韩学山,等.基于分量稀疏贝叶斯学习的风电场输出功率概率预测方法[J].电力系统自动化,2012,36(14):125-130.YANG Ming,FAN Shu,HAN Xueshan,et al.Wind farm generation forecast based on componential sparse Bayesian learning[J].Automation of Electric Power Systems,2012,36(14):125-130.
[26]杨明,朱思萌,韩学山,等.风电场输出功率的多时段联合概率密度预测[J].电力系统自动化,2013,37(10):23-28.YANG Ming,ZHU Simeng,HAN Xueshan,et al.Joint probability density forecast for wind farm output in multi-timeinterval[J].Automation of Electric Power Systems,2013,37(10):23-28.
[27]刘永前,史洁,杨勇平,等.基于预测误差分布特性的风电场短期功率预测不确定性研究[J].太阳能学报,2012,33(12):2179-2184.LIU Yongqian,SHI Jie,YANG Yongping,et al.Uncertainty analysis of short term wind power forecasting based on error characteristics statistics[J].Acta Energiae Solaris Sinica,2012,33(12):2179-2184.
[28]ZHANG Guoyong,WU Yonggang,WONG K P,et al.An advanced approach for construction of optimal wind power prediction intervals[J].IEEE Transactions on Power Systems,2015,30(5):2706-2715.
[29]KOU Peng,LIANG Deliang,GAO Feng,et al.Probabilistic wind power forecasting with online model selection and warped Gaussian process[J].Energy Conversion and Management,2014(84):649-663.
[30]杨锡运,关文渊,刘玉奇,等.基于粒子群优化的核极限学习机模型的风电功率区间预测方法[J].中国电机工程学报,2015,35(增刊1):146-153.YANG Xiyun,GUAN Wenyuan,LIU Yuqi,et al.Prediction intervals forecasts of wind power based on PSO-KELM[J].Proceedings of the CSEE,2015,35(Supplement 1):146-153.
[31]林优,杨明,韩学山,等.基于条件分类与证据理论的短期风电功率非参数概率预测方法[J].电网技术,2016,40(4):1113-1119.LIN You,YANG Ming,HAN Xueshan,et al.Nonparametric approach for short-term probabilistic wind generation forecasts based on conditional classification and evidence theory[J].Power System Technology,2016,40(4):1113-1119.
[32]周封,金丽斯,刘健,等.基于多状态空间混合Markov链的风电功率概率预测[J].电力系统自动化,2012,36(6):29-33.ZHOU Feng,JIN Lisi,LIU Jian,et al.Probabilistic wind power forecasting based on multi-state space and hybrid Markov chain models[J].Automation of Electric Power Systems,2012,36(6):29-33.
[33]WANG Huaizhi,LI Gangqiang,WANG Guibin,et al.Deep learning based ensemble approach for probabilistic wind power forecasting[J].Applied Energy,2017,188:56-70.
[34]WAN Can,ZHAO Xu,PINSON P,et al.Probabilistic forecasting of wind power generation using extreme learning machine[J].IEEE Transactions on Power Systems,2014,29(3):1033-1044.
[35]DA SILVA N P,ROSA L.Ensemble-based estimation of wind power forecast uncertainty[C]//2015 12th International Conference on the European Energy Market(EEM),May 19-22,2015,Lisbon,Portugal:1-5.
[36]王勃,冯双磊,刘纯.考虑预报风速与功率曲线因素的风电功率预测不确定性估计[J].电网技术,2014,39(2):463-468.WANG Bo,FENG Shuanglei,LIU Chun.Uncertainty evaluation of wind power curve and predicted wind speed[J].Power System Technology,2014,39(2):463-468.
[37]甘迪,柯德平,孙元章,等.考虑爬坡特性的短期风电功率概率预测[J].电力自动化设备,2016,36(4):145-150.GAN Di,KE Deping,SUN Yuanzhang,et al.Short-term probabilistic wind power forecast considering ramp characteristics[J].Electric Power Automation Equipment,2016,36(4):145-150.
[38]朱思萌,杨明,韩学山,等.多风电场短期输出功率的联合概率密度预测方法[J].电力系统自动化,2014,38(19):8-15.DOI:10.7500/AEPS20130507013.ZHU Simeng,YANG Ming,HAN Xueshan,et al.Joint probabilistic density forecast of short-term multiple wind farms output power[J].Automation of Electric Power Systems,2014,38(19):8-15.DOI:10.7500/AEPS20130507013.
[39]李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995(6):15-20.LI Deyi,MENG Haijun,SHI Xuemei.Membership clouds and membership cloud generators[J].Computer Research and Development,1995(6):15-20.
[40]王惠中,刘轲,杨世亮.基于云模型的电力系统负荷组合预测[J].计算机系统应用,2016,25(5):209-212.WANG Huizhong,LIU Ke,YANG Shiliang.Load forecasting of power system based on cloud model SVM[J].Computer Systems and Applications,2016,25(5):209-212.
[41]栗然,崔天宝,肖进永.基于云模型的短期电价预测[J].电网技术,2009,33(17):185-190.LI Ran,CUI Tianbao,XIAO Jinyong.Short-term electricity price forecasting based on cloud model[J].Power System Technology,2009,33(17):185-190.
[42]刘树洁,赖旭,邹金,等.基于云模型理论的短期风速预测方法[J].武汉大学学报(工学版),2017,50(1):69-74.LIU Shujie,LAI Xu,ZOU Jin,et al.Cloud model based short-term wind speed prediction method[J].Engineering Journal of Wuhan University,2017,50(1):69-74.
[43]凌武能,杭乃善,李如琦.基于云支持向量机模型的短期风电功率预测[J].电力自动化设备,2013,33(7):34-38.LING Wuneng,HANG Naishan,LI Ruqi.Short-term wind power forecasting based on cloud SVM model[J].Electric Power Automation Equipment,2013,33(7):34-38.
[44]阎洁,许成志,刘永前,等.基于风速云模型相似日的短期风电功率预测方法[J].电力系统自动化,2018,42(6):53-59.DOI:10.7500/AEPS20170605001.YAN Jie,XU Chengzhi,LIU Yongqian,et al.Short-term wind power prediction based on daily similar wind speed cloud model[J].Automation of Electric Power Systems,2018,42(6):53-59.DOI:10.7500/AEPS20170605001.
[45]MADSEN H,PINSON P,KARINIOTAKIS G,et al.Standardizing the performance evaluation of short term wind power prediction models[J].Wind Engineering,2005,29(6):475-489.
[46]PINSON P,NIELSEN H A,MLLER J K,et al.Nonparametric probabilistic forecasts of wind power:required properties and evaluation[J].Wind Energy,2010,10(6):497-516.
[2]鲁宗相,闵勇.基于功率预测的波动性能源发电的多时空尺度调度技术[J].电力科学与技术学报,2012,27(3):28-33.LU Zongxiang,MIN Yong.Multiple time and spatial scale dispatching techniques of volatile energy generation based on power prediction[J].Journal of Electric Power Science and Technology,2012,27(3):28-33.
[3]YAN Jie,LIU Yongqian,HAN Shuang,et al.Reviews on uncertainty analysis of wind power forecasting[J].Renewable&Sustainable Energy Reviews,2015,52(52):1322-1330.
[4]YAO Zhang,WANG Jianxue,WANG Xifan.Review on probabilistic forecasting of wind power generation[J].Renewable&Sustainable Energy Reviews,2014,32(5):255-270.
[5]YANG Ming,ZHU Simeng,LIU Meng,et al.One parametric approach for short-term JPDF forecast of wind generation[J].IEEE Transactions on Industry Application,2014,50(4):2837-2843.
[6]兰飞,桑川川,梁浚杰,等.基于条件Copula函数的风电功率区间预测[J].中国电机工程学报,2016,36(增刊1):79-86.LAN Fei,SANG Chuanchuan,LIANG Junjie,et al.Interval prediction for wind power based on conditional Copula function[J].Proceedings of the CSEE,2016,36(Supplement 1):79-86.
[7]杨宏,苑津莎,张铁峰.一种基于Beta分布的风电功率预测误差最小概率区间的模型和算法[J].中国电机工程学报,2015,35(9):2135-2142.YANG Hong,YUAN Jinsha,ZHANG Tiefeng.A model and algorithm for minimum probability interval of wind power forecast errors based on Beta distribution[J].Proceedings of the CSEE,2015,35(9):2135-2142.
[8]刘兴杰,谢春雨.基于贝塔分布的风电功率波动区间估计[J].电力自动化设备,2014,34(12):26-30.LIU Xingjie,XIE Chunyu.Wind power fluctuation based on Beta distribution[J].Electric Power Automation Equipment,2014,34(12):26-30.
[9]ZHANG Zhaosui,SUN Yuanzhang,GAO D W,et al.Aversatile probability distribution model for wind power forecast errors and its application in economic dispatch[J].IEEETransactions on Power Systems,2013,28(3):3114-3125.
[10]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.
[11]杨茂,董骏城.基于混合高斯分布的风电功率实时预测误差分析[J].太阳能学报,2016,37(6):1594-1602.YANG Mao,DONG Juncheng.Real-time prediction error analysis of wind power based on mixed Gaussian distribution model[J].Acta Energiae Solaris Sinica,2016,37(6):1594-1602.
[12]MEN Zhongxian,YEE E,FUE-SANG L,et al.Short-term wind speed and power forecasting using an ensemble of mixture density neural networks[J].Renewable Energy,2016,87:203-211.
[13]丁华杰,宋永华,胡泽春,等.基于风电场功率特性的日前风电预测误差概率分布研究[J].中国电机工程学报,2013,33(34):119-127.DING Huajie,SONG Yonghua,HU Zechun,et al.Probability density function of day-ahead wind power forecast errors based on power curves of wind farms[J].Proceedings of the CSEE,2013,33(34):119-127.
[14]刘芳,潘毅,刘辉,等.风电功率预测误差分段指数分布模型[J].电力系统自动化,2013,37(18):14-19.LIU Fang,PAN Yi,LIU Hui,et al.Piecewise exponential distribution model of wind power forecasting error[J].Automation of Electric Power Systems,2013,37(18):14-19.
[15]阎洁,刘永前,韩爽,等.分位数回归在风电功率预测不确定性分析中的应用[J].太阳能学报,2013,34(12):2101-2107.YAN Jie,LIU Yongqian,HAN Shuang,et al.Quantile regression in uncertainty analysis of wind power forecasting[J].Acta Energiae Solaris Sinica,2013,34(12):2101-2107.
[16]李智,韩学山,杨明,等.基于分位点回归的风电功率波动区间分析[J].电力系统自动化,2011,35(3):83-87.LI Zhi,HAN Xueshan,YANG Ming,et al.Wind power fluctuation interval analysis based on quantile regression[J].Automation of Electric Power Systems,2011,35(3):83-87.
[17]HUANG Chaoming,KUO C J,HUANG Y C.Short-term wind power forecasting and uncertainty analysis using a hybrid intelligent method[J].IET Renewable Power Generation,2017,11(5):678-687.
[18]WAN Can,ZHAO Xu,PINSON P,et al.Optimal prediction intervals of wind power generation[J].IEEE Transactions on Power Systems,2014,29(3):1166-1174.
[19]PINSON P,KARINIOTAKIS G.Conditional prediction intervals of wind power generation[J].IEEE Transactions on Power Systems,2010,25(4):1845-1856.
[20]杨楠,崔家展,周峥,等.基于模糊序优化的风功率概率模型非参数核密度估计方法[J].电网技术,2016,40(2):335-340.YANG Nan,CUI Jiazhan,ZHOU Zheng,et al.Research on non-parametric kernel density estimation for modeling of wind power probability characteristic based on fuzzy ordinal optimization[J].Power System Technology,2016,40(2):335-340.
[21]LIAO Guodong,JIE Ming,WEI Boyuan,et al.Wind power prediction errors model and algorithm based on non-parametric kernel density estimation[C]//5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies,November 26-29,2015,Changsha,China:1864-1868.
[22]孙建波,吴小珊,张步涵.基于非参数核密度估计的风电功率区间预测[J].水电能源科学,2013,31(9):233-235.SUN Jianbo,WU Xiaoshan,ZHANG Buhan.Wind power interval prediction based on non-parametric kernel density estimation[J].Water Resources and Power,2013,31(9):233-235.
[23]黄坡,朱小帆,查晓明,等.基于波动过程聚类的风电功率预测极大误差估计方法[J].电力系统保护与控制,2016,44(13):130-136.HUANG Po,ZHU Xiaofan,ZHA Xiaoming,et al.An estimation method for wind power prediction great error based on clustering fluctuation process[J].Power System Protection and Control,2016,44(13):130-136.
[24]YAN Jie,LIU Yongqian,HAN Shuang,et al.Wind power grouping forecasts and its uncertainty analysis using optimized relevance vector machine[J].Renewable&Sustainable Energy Reviews,2013,27(6):613-621.
[25]杨明,范澍,韩学山,等.基于分量稀疏贝叶斯学习的风电场输出功率概率预测方法[J].电力系统自动化,2012,36(14):125-130.YANG Ming,FAN Shu,HAN Xueshan,et al.Wind farm generation forecast based on componential sparse Bayesian learning[J].Automation of Electric Power Systems,2012,36(14):125-130.
[26]杨明,朱思萌,韩学山,等.风电场输出功率的多时段联合概率密度预测[J].电力系统自动化,2013,37(10):23-28.YANG Ming,ZHU Simeng,HAN Xueshan,et al.Joint probability density forecast for wind farm output in multi-timeinterval[J].Automation of Electric Power Systems,2013,37(10):23-28.
[27]刘永前,史洁,杨勇平,等.基于预测误差分布特性的风电场短期功率预测不确定性研究[J].太阳能学报,2012,33(12):2179-2184.LIU Yongqian,SHI Jie,YANG Yongping,et al.Uncertainty analysis of short term wind power forecasting based on error characteristics statistics[J].Acta Energiae Solaris Sinica,2012,33(12):2179-2184.
[28]ZHANG Guoyong,WU Yonggang,WONG K P,et al.An advanced approach for construction of optimal wind power prediction intervals[J].IEEE Transactions on Power Systems,2015,30(5):2706-2715.
[29]KOU Peng,LIANG Deliang,GAO Feng,et al.Probabilistic wind power forecasting with online model selection and warped Gaussian process[J].Energy Conversion and Management,2014(84):649-663.
[30]杨锡运,关文渊,刘玉奇,等.基于粒子群优化的核极限学习机模型的风电功率区间预测方法[J].中国电机工程学报,2015,35(增刊1):146-153.YANG Xiyun,GUAN Wenyuan,LIU Yuqi,et al.Prediction intervals forecasts of wind power based on PSO-KELM[J].Proceedings of the CSEE,2015,35(Supplement 1):146-153.
[31]林优,杨明,韩学山,等.基于条件分类与证据理论的短期风电功率非参数概率预测方法[J].电网技术,2016,40(4):1113-1119.LIN You,YANG Ming,HAN Xueshan,et al.Nonparametric approach for short-term probabilistic wind generation forecasts based on conditional classification and evidence theory[J].Power System Technology,2016,40(4):1113-1119.
[32]周封,金丽斯,刘健,等.基于多状态空间混合Markov链的风电功率概率预测[J].电力系统自动化,2012,36(6):29-33.ZHOU Feng,JIN Lisi,LIU Jian,et al.Probabilistic wind power forecasting based on multi-state space and hybrid Markov chain models[J].Automation of Electric Power Systems,2012,36(6):29-33.
[33]WANG Huaizhi,LI Gangqiang,WANG Guibin,et al.Deep learning based ensemble approach for probabilistic wind power forecasting[J].Applied Energy,2017,188:56-70.
[34]WAN Can,ZHAO Xu,PINSON P,et al.Probabilistic forecasting of wind power generation using extreme learning machine[J].IEEE Transactions on Power Systems,2014,29(3):1033-1044.
[35]DA SILVA N P,ROSA L.Ensemble-based estimation of wind power forecast uncertainty[C]//2015 12th International Conference on the European Energy Market(EEM),May 19-22,2015,Lisbon,Portugal:1-5.
[36]王勃,冯双磊,刘纯.考虑预报风速与功率曲线因素的风电功率预测不确定性估计[J].电网技术,2014,39(2):463-468.WANG Bo,FENG Shuanglei,LIU Chun.Uncertainty evaluation of wind power curve and predicted wind speed[J].Power System Technology,2014,39(2):463-468.
[37]甘迪,柯德平,孙元章,等.考虑爬坡特性的短期风电功率概率预测[J].电力自动化设备,2016,36(4):145-150.GAN Di,KE Deping,SUN Yuanzhang,et al.Short-term probabilistic wind power forecast considering ramp characteristics[J].Electric Power Automation Equipment,2016,36(4):145-150.
[38]朱思萌,杨明,韩学山,等.多风电场短期输出功率的联合概率密度预测方法[J].电力系统自动化,2014,38(19):8-15.DOI:10.7500/AEPS20130507013.ZHU Simeng,YANG Ming,HAN Xueshan,et al.Joint probabilistic density forecast of short-term multiple wind farms output power[J].Automation of Electric Power Systems,2014,38(19):8-15.DOI:10.7500/AEPS20130507013.
[39]李德毅,孟海军,史雪梅.隶属云和隶属云发生器[J].计算机研究与发展,1995(6):15-20.LI Deyi,MENG Haijun,SHI Xuemei.Membership clouds and membership cloud generators[J].Computer Research and Development,1995(6):15-20.
[40]王惠中,刘轲,杨世亮.基于云模型的电力系统负荷组合预测[J].计算机系统应用,2016,25(5):209-212.WANG Huizhong,LIU Ke,YANG Shiliang.Load forecasting of power system based on cloud model SVM[J].Computer Systems and Applications,2016,25(5):209-212.
[41]栗然,崔天宝,肖进永.基于云模型的短期电价预测[J].电网技术,2009,33(17):185-190.LI Ran,CUI Tianbao,XIAO Jinyong.Short-term electricity price forecasting based on cloud model[J].Power System Technology,2009,33(17):185-190.
[42]刘树洁,赖旭,邹金,等.基于云模型理论的短期风速预测方法[J].武汉大学学报(工学版),2017,50(1):69-74.LIU Shujie,LAI Xu,ZOU Jin,et al.Cloud model based short-term wind speed prediction method[J].Engineering Journal of Wuhan University,2017,50(1):69-74.
[43]凌武能,杭乃善,李如琦.基于云支持向量机模型的短期风电功率预测[J].电力自动化设备,2013,33(7):34-38.LING Wuneng,HANG Naishan,LI Ruqi.Short-term wind power forecasting based on cloud SVM model[J].Electric Power Automation Equipment,2013,33(7):34-38.
[44]阎洁,许成志,刘永前,等.基于风速云模型相似日的短期风电功率预测方法[J].电力系统自动化,2018,42(6):53-59.DOI:10.7500/AEPS20170605001.YAN Jie,XU Chengzhi,LIU Yongqian,et al.Short-term wind power prediction based on daily similar wind speed cloud model[J].Automation of Electric Power Systems,2018,42(6):53-59.DOI:10.7500/AEPS20170605001.
[45]MADSEN H,PINSON P,KARINIOTAKIS G,et al.Standardizing the performance evaluation of short term wind power prediction models[J].Wind Engineering,2005,29(6):475-489.
[46]PINSON P,NIELSEN H A,MLLER J K,et al.Nonparametric probabilistic forecasts of wind power:required properties and evaluation[J].Wind Energy,2010,10(6):497-516.