基于双变量经验模态分解和最小二乘支持向量机的风电功率区间预测
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摘要
准确的功率预测是应对大规模风电并网问题的重要方法,但目前风电功率预测精度仍存在较大误差。为了更精确地对风电功率进行超短期预测,提出一种基于双变量经验模态分解技术和最小二乘支持向量机的组合区间预测方法。首先,通过比例系数法构造复值区间,解决了区间构造的难题;其次,利用双变量经验模态分解和样本熵分别将上、下限结果分解重构,凸显了数据的特征信息;再次,针对各特征分量分别建立基于深度信念网络和最小二乘支持向量机的组合预测模型进行预测;最后,将各分量的预测结果组合得到一定置信率下的预测区间。实际算例表明,与现有的区间预测方法比,所提区间预测方法有效提高了区间覆盖率,达到了更准确的预测精度。
Accurate prediction of wind power is an important measure to solve the problem that large-scale wind power accesses in power grid. At present, there are still large errors in the wind power prediction. An interval prediction method of wind power based on bivariate empirical mode decomposition and least squares support vector machine is proposed to help solve the problem. Firstly, a scale factor rule is proposed to build complex-valued power intervals. Then, the upper and lower bound of wind power are decomposed by bivariate empirical mode decomposition and reconstructed by sample entropy to extract main features. In addition, a model combined least squares support vector machine with deep belief network of each component is established. Finally, the overall interval prediction with a certain confidence level is obtained by superimposing the corresponding results. Taking real power data of a wind farm as examples, the results demonstrate that the proposed method can carry out power interval prediction, improving the interval coverage probability to get higher accuracy compared with the existing interval prediction methods.
Accurate prediction of wind power is an important measure to solve the problem that large-scale wind power accesses in power grid. At present, there are still large errors in the wind power prediction. An interval prediction method of wind power based on bivariate empirical mode decomposition and least squares support vector machine is proposed to help solve the problem. Firstly, a scale factor rule is proposed to build complex-valued power intervals. Then, the upper and lower bound of wind power are decomposed by bivariate empirical mode decomposition and reconstructed by sample entropy to extract main features. In addition, a model combined least squares support vector machine with deep belief network of each component is established. Finally, the overall interval prediction with a certain confidence level is obtained by superimposing the corresponding results. Taking real power data of a wind farm as examples, the results demonstrate that the proposed method can carry out power interval prediction, improving the interval coverage probability to get higher accuracy compared with the existing interval prediction methods.
引文
[1] ZHANG Y,WANG J,WANG X.Review on probabilistic forecasting of wind power generation[J].Renewable and Sustainable Energy Reviews,2014,32(5):255-270.
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[4] 彭小圣,熊磊,文劲宇,等.风电集群短期及超短期功率预精度改进方法综述[J].中国电机工程学报,2016,36(23):6315-6327.PENG Xiaosheng,XIONG Lei,WEN Jinyu,et al.A summary of the state of the art for short-term and ultra-short-term wind power prediction of regions[J].Proceedings of the CSEE,2016,36(23):6315-6327.
[5] HU J,WANG J,ZENG G.A hybrid forecasting approach applied to wind speed time series[J].Renewable Energy,2013,60(4):185-194.
[6] YE W,YE Y,CHANG P.Forecasting wind power in the Mai Liao wind farm based on the multi-layer perceptron artificial neural network model with improved simplified swarm optimization[J].International Journal of Electrical Power and Energy Systems,2014,55 (2):741-748.
[7] TASCIKARAOGLU A,UZUNOGLU M.A review of combined approaches for prediction of short-term wind speed and power[J].Renewable and Sustainable Energy Reviews,2014,34(6):243-254.
[8] KHOSRAVI A,NAHAVANDI S,CREIGHTON D.Quantifying uncertainties of neural network-based electricity price forecasts[J].Applied Energy,2013,112(4):120-129.
[9] HUSSAINI E,HAMID A,HASHEM A.Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution[J].Journal of the Egyptian Mathematical Society,2015,23(1):190-196.
[10] LYDIA M,SURESH S K,IMMANUE S.A comprehensive review on wind turbine power curve modeling techniques[J].Renewable and Sustainable Energy,2014,30(2):452-460.
[11] QUAN H,SRINIVASAN D,KHOSRAVI A.Short-term load and wind power forecasting using neural network-based prediction intervals[J] .IEEE Transactions on Neural Networks and Learning Systems,2014,25(2):303-315.
[12] PINSON P,TASTU J.Discussion of “prediction intervals for short-term wind farm generation forecasts” and “combined nonparametric prediction intervals for wind power generation”[J].IEEE Transactions on Sustainable Energy,2014,5(3):1019-1020.
[13] 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 quantileregression[J].Automation of Electric Power Systems,2011,35(3):83-87.
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[15] 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 interval estimation based on beta distribution[J].Electric Power Automation Equipment,2014,34(12):26-30.
[16] 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 forecasts errors based on beta distribution[J].Proceedings of the CSEE,2015,35(9):2135-2142.
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[18] JEON J,TAYLOR J W.Using conditional kernel density estimation for wind power density forecasting[J].Journal of the American Statistical Association,2012,107(497):66-79.
[19] HODGE M.B,MILLIGAN M.Wind power forecasting error distributions over multiple timescales[C]//IEEE Power Energy Society General Meeting.San Deigo,USA:IEEE,2011:1-11.
[20] ZHANG Z S,SUN Y Z,LIN J,et al.Versatile distribution of wind power output for a given forecast value[C]//2012 IEEE Power and Energy Society General Meeting.San Deigo,USA:IEEE,2012:1-7.
[21] MAIA A L S,CARVALHO F A T,LUDERMIR T B.Forecasting models for interval-valued time series [J].Neurocomputing,2008,71(16):3344-3352.
[22] ARROYO J,MUNOZ A,ROQUE S,et al.Exponential smoothing methods for interval time series[C]//Proceedings of the 1st European Symposium on Time Series.Otaniemi,Finland:ESTSP,2007:231-240.
[23] RILLING G,FLANDRIN P,GONALVES P,et al.Bivariate empirical mode decomposition[J].IEEE Signal Processing Letters,2007,14(12):936-939.
[24] 朱文龙,周建中,肖剑,等.独立分量分析-经验模态分解特征提取在水电机组振动信号中的应用[J].中国电机工程学报,2013,33(29):95-101.ZHU Wenlong,ZHOU Jianzhong,XIAO Jian,et al.An ICA-EMD feature extraction method and its application to vibration signals of hydroelectric generating units[J].Journal of Chinese Electrical Engineering Science,2013,33(29):95-101.
[25] 季峰,蔡兴国,王俊.基于混合Copula函数的风电功率相关性分析[J].电力系统自动化,2014,38(2):1-6.JI Feng,CAI Xingguo,WANG Jun.Wind power correlation analysis based on hybrid Copula[J].Automation of Electric Power Systems,2014,38(2):1- 6.
[26] 张学清,梁军,张熙,等.基于样本熵和极端学习机的超短期风电功率组合预测模型[J].中国电机工程学报,2013,33(25):33-40.ZHANG Xueqing,LIANG Jun,ZHANG Xi,et al.Combined model for ultra short-term wind power prediction based on sample entropy and extreme learning machine[J].Proceedings of the CSEE,2013,33(25):33-40.
[27] KHOSRAVI A,NAHAVANDI S,CREIGHTON D,et al.Lower upper bound estimation method for construction of neural network-based prediction intervals[J].IEEE Transactions on Neural Networks,2011,22(3):337-346.
[28] KHOSRAVI A,NAHAVANDI S,CREIGHTON D.Prediction intervals for short-term wind farm power generation forecasts[J].IEEE Transactions on Sustainable Energy,2013,4(3):602-610.
[29] 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(S1):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(S1):146-153.
[30] YAN J,LIU Y Q,HAN S,et al.Reviews on uncertainty analysis of wind power forecasting[J].Renewable and Sustainable Energy Reviews,2015,52(12):1322-1330.
[31] JULIJA T,PIERRE P,EWELINA K,et al.Spatio-temporal analysis and modeling of short-term wind power forecast errors[J].Wind Energy,2011,14(1):43-60.
[32] 刘蓓,汪沨,陈春,等.和声算法在含 DG 配电网故障定位中的应用[J].电工技术学报,2013,28(5):280-284.LIU Bei,WANG Feng,CHEN Chun,et al.Harmony search algorithm for solving fault location in distribution networks with DG[J].Transactions of China Electrotechnical Society,2013,28(5):280-284.
[33] ASKARZADEH A,REZAZADEH A.An innovative global harmony algorithm for parameter identification of a PEM fuel cell model [J].IEEE Transactions on Industrial Electronics,2012,59(9):3473-3480.
[34] ZHENG J,CHENG J,YANG Y.Partly ensemble empirical mode decomposition:An improved noise-assisted method for eliminating mode mixing[J].Signal Processing,2014,96(B):362-374.
[35] CHEN K L,YU J.Short-term wind speed prediction using an unscented Kalman ?lter based state-space support vector regression approach[J].Applied Energy,2014,113:690-705.
[36] WANG J,HU J,MA K,et al.A self-adaptive hybrid approach for wind speed forecasting[J].Renewable Energy,2015,78(6):374-385.
[37] MAHDAVI M,FESANGHARY M,DAMANGIR E.An improved harmony search algorithm for solving optimization problems[J].Applied Mathematics and Computation,2007,188(2):1567-1579.
[38] OMRAN M G H,MAHDAVI M.Global-best harmony search [J].Applied Mathematics and Computation,2008,198(2):643-656.
[39] CHATTERJEE A,GHOSHAL S P,MUKHERJEE V.Solution of combined economic and emission dispatch problems of power systems by an opposition-based on search algorithm[J],International Journal of Electrical Power & Energy Systems,2012,39(1):9-20.
[2] 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.
[3] 牛东晓,李建锋,魏林君,等.跨区电网中风电消纳影响因素分析及综合评估方法研究[J].电网技术,2016,40(4):1087-1093.NIU Dongxiao,LI Jianfeng,WEI Linjun,et al.Study on technical factors analysis and overall evaluation method regarding wind power integration in trans-provincial power grid[J].Power System Technology,2016,40(4):1087-1093.
[4] 彭小圣,熊磊,文劲宇,等.风电集群短期及超短期功率预精度改进方法综述[J].中国电机工程学报,2016,36(23):6315-6327.PENG Xiaosheng,XIONG Lei,WEN Jinyu,et al.A summary of the state of the art for short-term and ultra-short-term wind power prediction of regions[J].Proceedings of the CSEE,2016,36(23):6315-6327.
[5] HU J,WANG J,ZENG G.A hybrid forecasting approach applied to wind speed time series[J].Renewable Energy,2013,60(4):185-194.
[6] YE W,YE Y,CHANG P.Forecasting wind power in the Mai Liao wind farm based on the multi-layer perceptron artificial neural network model with improved simplified swarm optimization[J].International Journal of Electrical Power and Energy Systems,2014,55 (2):741-748.
[7] TASCIKARAOGLU A,UZUNOGLU M.A review of combined approaches for prediction of short-term wind speed and power[J].Renewable and Sustainable Energy Reviews,2014,34(6):243-254.
[8] KHOSRAVI A,NAHAVANDI S,CREIGHTON D.Quantifying uncertainties of neural network-based electricity price forecasts[J].Applied Energy,2013,112(4):120-129.
[9] HUSSAINI E,HAMID A,HASHEM A.Bayesian prediction intervals of order statistics based on progressively type-II censored competing risks data from the half-logistic distribution[J].Journal of the Egyptian Mathematical Society,2015,23(1):190-196.
[10] LYDIA M,SURESH S K,IMMANUE S.A comprehensive review on wind turbine power curve modeling techniques[J].Renewable and Sustainable Energy,2014,30(2):452-460.
[11] QUAN H,SRINIVASAN D,KHOSRAVI A.Short-term load and wind power forecasting using neural network-based prediction intervals[J] .IEEE Transactions on Neural Networks and Learning Systems,2014,25(2):303-315.
[12] PINSON P,TASTU J.Discussion of “prediction intervals for short-term wind farm generation forecasts” and “combined nonparametric prediction intervals for wind power generation”[J].IEEE Transactions on Sustainable Energy,2014,5(3):1019-1020.
[13] 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 quantileregression[J].Automation of Electric Power Systems,2011,35(3):83-87.
[14] JUNG J,BROADWATER R P.Current status and future advances for wind speed and power forecasting[J].Renewable and Sustainable Energy Reviews,2014,31:762-777.
[15] 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 interval estimation based on beta distribution[J].Electric Power Automation Equipment,2014,34(12):26-30.
[16] 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 forecasts errors based on beta distribution[J].Proceedings of the CSEE,2015,35(9):2135-2142.
[17] KOU P,GAO F,GUAN X H,et al.Prediction intervals for wind power forecasting:using sparse warped Gaussian process[C]//Proceedings of 2012 IEEE Power and Energy Society General Meeting.San Diego,CA:IEEE,2012:1-8.
[18] JEON J,TAYLOR J W.Using conditional kernel density estimation for wind power density forecasting[J].Journal of the American Statistical Association,2012,107(497):66-79.
[19] HODGE M.B,MILLIGAN M.Wind power forecasting error distributions over multiple timescales[C]//IEEE Power Energy Society General Meeting.San Deigo,USA:IEEE,2011:1-11.
[20] ZHANG Z S,SUN Y Z,LIN J,et al.Versatile distribution of wind power output for a given forecast value[C]//2012 IEEE Power and Energy Society General Meeting.San Deigo,USA:IEEE,2012:1-7.
[21] MAIA A L S,CARVALHO F A T,LUDERMIR T B.Forecasting models for interval-valued time series [J].Neurocomputing,2008,71(16):3344-3352.
[22] ARROYO J,MUNOZ A,ROQUE S,et al.Exponential smoothing methods for interval time series[C]//Proceedings of the 1st European Symposium on Time Series.Otaniemi,Finland:ESTSP,2007:231-240.
[23] RILLING G,FLANDRIN P,GONALVES P,et al.Bivariate empirical mode decomposition[J].IEEE Signal Processing Letters,2007,14(12):936-939.
[24] 朱文龙,周建中,肖剑,等.独立分量分析-经验模态分解特征提取在水电机组振动信号中的应用[J].中国电机工程学报,2013,33(29):95-101.ZHU Wenlong,ZHOU Jianzhong,XIAO Jian,et al.An ICA-EMD feature extraction method and its application to vibration signals of hydroelectric generating units[J].Journal of Chinese Electrical Engineering Science,2013,33(29):95-101.
[25] 季峰,蔡兴国,王俊.基于混合Copula函数的风电功率相关性分析[J].电力系统自动化,2014,38(2):1-6.JI Feng,CAI Xingguo,WANG Jun.Wind power correlation analysis based on hybrid Copula[J].Automation of Electric Power Systems,2014,38(2):1- 6.
[26] 张学清,梁军,张熙,等.基于样本熵和极端学习机的超短期风电功率组合预测模型[J].中国电机工程学报,2013,33(25):33-40.ZHANG Xueqing,LIANG Jun,ZHANG Xi,et al.Combined model for ultra short-term wind power prediction based on sample entropy and extreme learning machine[J].Proceedings of the CSEE,2013,33(25):33-40.
[27] KHOSRAVI A,NAHAVANDI S,CREIGHTON D,et al.Lower upper bound estimation method for construction of neural network-based prediction intervals[J].IEEE Transactions on Neural Networks,2011,22(3):337-346.
[28] KHOSRAVI A,NAHAVANDI S,CREIGHTON D.Prediction intervals for short-term wind farm power generation forecasts[J].IEEE Transactions on Sustainable Energy,2013,4(3):602-610.
[29] 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(S1):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(S1):146-153.
[30] YAN J,LIU Y Q,HAN S,et al.Reviews on uncertainty analysis of wind power forecasting[J].Renewable and Sustainable Energy Reviews,2015,52(12):1322-1330.
[31] JULIJA T,PIERRE P,EWELINA K,et al.Spatio-temporal analysis and modeling of short-term wind power forecast errors[J].Wind Energy,2011,14(1):43-60.
[32] 刘蓓,汪沨,陈春,等.和声算法在含 DG 配电网故障定位中的应用[J].电工技术学报,2013,28(5):280-284.LIU Bei,WANG Feng,CHEN Chun,et al.Harmony search algorithm for solving fault location in distribution networks with DG[J].Transactions of China Electrotechnical Society,2013,28(5):280-284.
[33] ASKARZADEH A,REZAZADEH A.An innovative global harmony algorithm for parameter identification of a PEM fuel cell model [J].IEEE Transactions on Industrial Electronics,2012,59(9):3473-3480.
[34] ZHENG J,CHENG J,YANG Y.Partly ensemble empirical mode decomposition:An improved noise-assisted method for eliminating mode mixing[J].Signal Processing,2014,96(B):362-374.
[35] CHEN K L,YU J.Short-term wind speed prediction using an unscented Kalman ?lter based state-space support vector regression approach[J].Applied Energy,2014,113:690-705.
[36] WANG J,HU J,MA K,et al.A self-adaptive hybrid approach for wind speed forecasting[J].Renewable Energy,2015,78(6):374-385.
[37] MAHDAVI M,FESANGHARY M,DAMANGIR E.An improved harmony search algorithm for solving optimization problems[J].Applied Mathematics and Computation,2007,188(2):1567-1579.
[38] OMRAN M G H,MAHDAVI M.Global-best harmony search [J].Applied Mathematics and Computation,2008,198(2):643-656.
[39] CHATTERJEE A,GHOSHAL S P,MUKHERJEE V.Solution of combined economic and emission dispatch problems of power systems by an opposition-based on search algorithm[J],International Journal of Electrical Power & Energy Systems,2012,39(1):9-20.