基于L2范数组合云的风电场短期风速–功率拟合方法
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摘要
为解决大型风电场运行分散性引起的风速–功率拟合误差较大的问题,提出一种基于L2范数组合云的风电场短期风速–功率拟合方法。首先,针对不同风速下风电场功率概率密度曲线峰值特性不同问题,以其概率密度曲线峰值点为边界点,建立组合云拟合模型;其次,为了避免样本峰值扰动引起的组合云模型拟合误差升高,基于L2范数理论对风电场特定风速下的功率离散点进行多项式拟合,以该多项式的峰值点作为边界,对上述组合云拟合模型进行修正;最后,采用贝叶斯法对上述组合云拟合模型参数进行计算。经仿真验证:对具有不确定性的不规则单峰或多峰风速–功率概率分布,所提组合云拟合方法均能获得较高的拟合精度,拟合误差较小。
In order to solve the large wind speed-power fitting error problem caused by the dispersion and uncertainty of wind farm operation, a novel short-term fitting method based on L2 norm combination cloud model was proposed.Firstly, a combination cloud model was established with the peak point of the curve as boundary point, to solve the problem that power probability density distributions differ from each other under different wind speeds. Secondly, in order to reduce the fitting error caused by the disturbance of sample peak, the L2 norm theory was used to fit the power discrete point, and the combination cloud model was modified with L2 norm peak instead of the original peak point. Finally, the Bayesian method was used to calculate the parameters of the combination cloud fitting model. It is verified by simulation that the proposed combination cloud fitting method can get higher fitting accuracy and smaller fitting error for the wind-power curve either with single or multi-peak characteristic.
In order to solve the large wind speed-power fitting error problem caused by the dispersion and uncertainty of wind farm operation, a novel short-term fitting method based on L2 norm combination cloud model was proposed.Firstly, a combination cloud model was established with the peak point of the curve as boundary point, to solve the problem that power probability density distributions differ from each other under different wind speeds. Secondly, in order to reduce the fitting error caused by the disturbance of sample peak, the L2 norm theory was used to fit the power discrete point, and the combination cloud model was modified with L2 norm peak instead of the original peak point. Finally, the Bayesian method was used to calculate the parameters of the combination cloud fitting model. It is verified by simulation that the proposed combination cloud fitting method can get higher fitting accuracy and smaller fitting error for the wind-power curve either with single or multi-peak characteristic.
引文
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[21]刘建伟,李双成,罗雄麟.p范数正则化支持向量机分类算法[J].自动化学报,2012,38(1):76-87.Liu Jianwei,Li Shuangcheng,Luo Xionglin.Classification algorithm of support vector machine via p-norm regularization[J].Acta Automatica Sinica,2012,38(1):76-87(in Chinese).
[22]Solak S,Bahsi M.On the spectral norms of hankel matrices with fibonacci and Lucas numbers[J].Sel?uk Journal of Applied Mathematics,2011,12(1):71-76.
[23]马腾跃.带有解释变量的一阶自回归模型的贝叶斯估计[D].长春:吉林大学,2015.Ma Tengyue.Bayesian estimation for first-order autoregressive model with explanatory variables[D].Changchun:Jilin University,2015(in Chinese).
[24]黄琴.基于贝叶斯估计与分布的关联分析方法研究[D].广州:华南理工大学,2016.Huang Qin.The research of associative analysis method based on Bayesian estimation and distribution[D].Guangzhou:South China University of Technology,2016(in Chinese).
[25]Marcel S,Millan J D R.Person authentication using brainwaves(EEG)and maximum a posteriori model adaptation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(4):743-752.
[26]ROBERTSON,HOEHER,VILLEBRUN.Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding[J].Transactions on Emerging Telecommunications Technologies,2010,8(2):119-125.
[2]Ucar A,Balo F.Evaluation of wind energy potential and electricity generation at six locations in Turkey[J].Applied Energy,2009,86(10):1864-1872.
[3]谢宇翔,张雪敏,罗金山,等.新能源大规模接入下的未来电力系统演化模型[J].中国电机工程学报,2018,38(2):421-430.Xie Yuxiang,Zhang Xuemin,Luo Jinshan,et al.Evolution model for future power system under massive penetration of renewable energy[J].Proceedings of the CSEE,2018,38(2):421-430(in Chinese).
[4]Mu Gang,Yang Mao,Wang Dong,et al.Spatial dispersion of wind speeds and its influence on the forecasting error of wind power in a wind farm[J].Journal of Modern Power Systems and Clean Energy,2016,4(2):265-274.
[5]郎斌斌,穆钢,严干贵,等.联网风电机组风速-功率特性曲线的研究[J].电网技术,2008,32(12):70-74.Lang Binbin,Mu Gang,Yan Gangui,et al.Research on wind speed vs output power characteristic curve of wind power generator interconnected with power grid[J].Power System Technology,2008,32(12):70-74(in Chinese).
[6]Jaramillo O A,Borja M A.Wind speed analysis in La Ventosa,Mexico:a bimodal probability distribution case[J].Renewable Energy,2014,29(10):1613-1630.
[7]鲍海波,韦化,郭小璇,等.考虑风电不确定性的概率区间潮流模型与算法[J].中国电机工程学报,2017,37(19):5633-5642.Bao Haibo,Wei Hua,Guo Xiaoxuan,et al.Model and algorithm of probabilistic interval power flow considering wind power uncertainty[J].Proceedings of the CSEE,2017,37(19):5633-5642(in Chinese).
[8]Chang T P.Estimation of wind energy potential using different probability density functions[J].Applied Energy,2011,88(5):1848-1856.
[9]叶林,朱远,赵永宁,等.风能资源分布特性的改进最大熵方法[J].中国电机工程学报,2014,34(34):6093-6100.Ye Lin,Zhu Yuan,Zhao Yongning,et al.An improved approach based on maximum entropy principle for wind resource distribution characteristics[J].Proceedings of the CSEE,2014,34(34):6093-6100(in Chinese).
[10]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-time-interval[J].Automation of Electric Power Systems,2013,37(10):23-28(in Chinese).
[11]叶林,张慈杭,汤涌,等.多时空尺度协调的风电集群有功分层预测控制方法[J].中国电机工程学报,2018,38(13):3767-3780.Ye Lin,Zhang Cihang,Tang Yong,et al.Active power stratification predictive control approach for wind power cluster with multiple temporal and spatial scales coordination[J].Proceedings of the CSEE,2018,38(13):3767-3780(in Chinese).
[12]吕晓禄,梁军,贠志皓,等.风电场出力的纵向时刻概率分布特性[J].电力自动化设备,2014,34(5):40-45.LüXiaolu,Liang Jun,Yun Zhihao,et al.Longitudinal instant probability distribution of wind farm output power[J].Electric Power Automation Equipment,2014,34(5):40-45(in Chinese).
[13]陈凡,卫志农,张小莲,等.计入风速与风电机组故障相关性的风电场可靠性建模及其应用[J].中国电机工程学报,2016,36(11):2900-2908.Chen Fan,Wei Zhinong,Zhang Xiaolian,et al.Reliability modeling of wind farms incorporating correlation between wind speed and failure of wind turbines and its application[J].Proceedings of the CSEE,2016,36(11):2900-2908(in Chinese).
[14]王松岩,于继来.短时风速概率分布的混合威布尔逼近方法[J].电力系统自动化,2010,34(6):89-93.Wang Songyan,Yu Jilai.Approximation of two-peak wind speed probability density function with mixed Weibull distribution[J].Automation of Electric Power Systems,2010,34(6):89-93(in Chinese).
[15]崔杨,杨海威,李鸿博.基于高斯混合模型的风电场群功率波动概率密度分布函数研究[J].电网技术,2016,40(4):1107-1112.Cui Yang,Yang Haiwei,Li Hongbo.Probability density distribution function of wind power fluctuation of a wind farm group based on the Gaussian mixture model[J].Power System Technology,2016,40(4):1107-1112(in Chinese).
[16]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,1995,32(6):15-20.Li Deyi,Meng Haijun,Shi Xuemei.Membership clouds and membership cloud generators[J].Journal of Computer Research and Development,1995,32(6):15-20(in Chinese).
[17]陈绍南,陈碧云,韦化,等.不规则风速概率分布的混合半云建模方法[J].中国电机工程学报,2015,35(6):1314-1321.Chen Shaonan,Chen Biyun,Wei Hua,et al.Mixed half-cloud modeling method for irregular probability distribution of wind speed[J].Proceedings of the CSEE,2015,35(6):1314-1321(in Chinese).
[18]蔡国伟,张斌,王建元,等.云模型理论在互联电力系统负荷频率控制中的应用[J].中国电机工程学报,2015,35(2):353-358.Cai Guowei,Zhang Bin,Wang Jianyuan,et al.Application of cloud model theory to the load frequency control in interconnected power systems[J].Proceedings of the CSEE,2015,35(2):353-358(in Chinese).
[19]王洪涛,李丹.基于二维正态云模型算法的红外图像弱小目标检测[J].红外技术,2013,35(10):646-649.Wang Hongtao,Li Dan.Detection of infrared dim and small target based on two-dimensional normal cloud model algorithm[J].Infrared Technology,2013,35(10):646-649(in Chinese).
[20]俞吉,周德云,周灿辉.基于云模型空空导弹攻击区的拟合方法[J].火力与指挥控制,2013,38(7):32-35.Yu Ji,Zhou Deyun,Zhou Canhui.A method for approximating allowable attack area for air-to-air missile based on cloud_model[J].Fire Control&Command Control,2013,38(7):32-35(in Chinese).
[21]刘建伟,李双成,罗雄麟.p范数正则化支持向量机分类算法[J].自动化学报,2012,38(1):76-87.Liu Jianwei,Li Shuangcheng,Luo Xionglin.Classification algorithm of support vector machine via p-norm regularization[J].Acta Automatica Sinica,2012,38(1):76-87(in Chinese).
[22]Solak S,Bahsi M.On the spectral norms of hankel matrices with fibonacci and Lucas numbers[J].Sel?uk Journal of Applied Mathematics,2011,12(1):71-76.
[23]马腾跃.带有解释变量的一阶自回归模型的贝叶斯估计[D].长春:吉林大学,2015.Ma Tengyue.Bayesian estimation for first-order autoregressive model with explanatory variables[D].Changchun:Jilin University,2015(in Chinese).
[24]黄琴.基于贝叶斯估计与分布的关联分析方法研究[D].广州:华南理工大学,2016.Huang Qin.The research of associative analysis method based on Bayesian estimation and distribution[D].Guangzhou:South China University of Technology,2016(in Chinese).
[25]Marcel S,Millan J D R.Person authentication using brainwaves(EEG)and maximum a posteriori model adaptation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2007,29(4):743-752.
[26]ROBERTSON,HOEHER,VILLEBRUN.Optimal and sub-optimal maximum a posteriori algorithms suitable for turbo decoding[J].Transactions on Emerging Telecommunications Technologies,2010,8(2):119-125.