基于三适应度粒子群算法的风速威布尔分布参数估计
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摘要
在传统粒子群算法的基础上,提出具有三适应度的粒子群算法来确定风速威布尔分布参数,其中适应度的函数分别根据风速拟合的相关程度、平均风能密度相对误差和方差3个指标进行定义。该方法具有收敛速度快综合考虑多方面指标的优点,能够确定对实际风频具有很好拟合效果的威布尔曲线参数,达到三适应度指标均最优的效果。利用三适应度粒子群算法对实例进行分析并与其他算法对比,结果表明该算法可较好估计威布尔参数,综合性能优点明显。
An accurate description of wind speed characteristics will directly affect the results of wind energy resource assessment of wind farms. On the basis of the traditional particle swarm optimization(PSO)algorithm,a three fitness of the PSO algorithm is proposed to determine the wind speed Weibull distribution parameters,fitness function respectively defined by the relevance of the wind speed fitting,the average relative error of wind energy density and variance of these three indicators. This method has fast convergence rate,considering the advantages of the various indicators,to determine the actual wind frequency has the very good fitting effect curve of Weibull parameters,to achieve the effect of three fitness indicators are all optimal. Three fitness particle swarm optimization(PSO)algorithm is used to analyze the instance analysis and comparison with other algorithms,the results showet that the algorithm can be well estimated Weibull parameters,comprehensive performance advantage is obvious.
An accurate description of wind speed characteristics will directly affect the results of wind energy resource assessment of wind farms. On the basis of the traditional particle swarm optimization(PSO)algorithm,a three fitness of the PSO algorithm is proposed to determine the wind speed Weibull distribution parameters,fitness function respectively defined by the relevance of the wind speed fitting,the average relative error of wind energy density and variance of these three indicators. This method has fast convergence rate,considering the advantages of the various indicators,to determine the actual wind frequency has the very good fitting effect curve of Weibull parameters,to achieve the effect of three fitness indicators are all optimal. Three fitness particle swarm optimization(PSO)algorithm is used to analyze the instance analysis and comparison with other algorithms,the results showet that the algorithm can be well estimated Weibull parameters,comprehensive performance advantage is obvious.
引文
[1]华泽嘉,闫少军,杨振华.风资源评估方法的研究[J].技术与市场,2012,19(11):33—35.[1] Hua Zejia,Yan Shaojun,Yang Zhenhua. Study of thewind resource assessment method[J]. Technology andMarket,2012,19(11):33—35.
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[3]方华元,胡昌华,曹小平,等.含约束条件遗传算法在三参数威布尔分布参数估计中的应用[J].战术导弹技术,2006,(6):32—35,44.[3] Fang Huayuan,Hu Changhua,Cao Xiaoping,et al.Optimal estimation of three parameters Weibulldistribution based on genetic algorithm with constrains[J]. Tactical Missile Technology,2006,(6):32—35,44.
[4]董胜,韩意,陶山山,等. Weibull分布参数的粒子群算法估计[J].中国海洋大学学报,2012,42(6):120—125.[4] Dong Sheng,Han Yi,Tao Shanshan,et al. Parametersestimation for Weibull distribution with particle swarmoptimization[J]. Periodical of Ocean University ofChina,2012,42(6):120—125.
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[6]罗航,王厚军,黄建国,等.基于PSO的三参数威布尔分布参数的联合估计方法[J].仪器仪表学报,2009,30(8):1604—1611.[6] Luo Hang, Wang Houjun, Huang Jianguo, et al.Method of united estimation to the parameters of three-parameter Weibull distribution based on PSO[J].Chinese Journal of Scientific Instrument,2009,30(8):1604—1611.
[7]贺德馨.风工程与工业空气动力学[M].北京:国防工业出版社,2006,23—24.[7] He Dexin. Wind engineering and industrial aerodynamics[M]. Beijing:National Defense Industry Press,2006,23—24.
[8]徐卫民,孔新红,桂保玉.三种风速威布尔分布参数算法的比较[A].第26届中国气象学会年会气候资源应用研究分会场论文集[C],杭州,2009.[8] Xu Weimin, Kong Xinhong, Gui Baoyu. Thecomparation of three methods to calculate the Weibullparameters of wind speed[A]. Proceedings of the 26thChinese Meteorology Conference[C],Hangzhou,2009.
[9]包小庆,刘志强,吴永忠,等.双参数威布尔分布函数的确定及曲线拟合[J].能源与环境,2007,(4):4—9.[9] Bao Xiaoqing,Liu Zhiqiang,Wu Yongzhong,et al. Thedetermination of double parameters Weibull distributionfunction and curve fitting[J]. Energy and Environment,2007,(4):4—9.
[10]龚伟俊,李为相,张广明.基于威布尔分布的风速概率分布参数估计方法[J].可再生能源,2011,29(6):20—23.[10] Gong Weijun,Li Weixiang,Zhang Guangming. Theestimation algorithm on the probabilistic distributionparameters of wind speed based on Weibull distribution[J]. Renewable Energy Resources,2011,29(6):20—23.
[11]纪震,廖慧连,吴青华.粒子群算法及应用[M].北京:科学出版社,2009,16—21.[11] Ji Zhen,Liao Huilian,Wu Qinghua. Particle swarmoptimization algorithm and application[M]. Beijing:Science Press,2009,16—21.
[12]李宁,孙德宝,邹彤,等.基于差分方程的PSO算法粒子运动轨迹分析[J].计算机学报,2006,29(11):2052—2061.[12] Li Ning,Sun Debao,Zou Tong,et al. An analysis for aparticle’s trajectory of PSO based on difference equation[J]. Chinese Journal of Computers,2006,29(11):2052—2061.
[13]姜海燕.数值法与群智能算法在低风速分布模型优化中的对比研究[D].兰州:兰州大学,2015.[13] Jiang Haiyan. Comparative study of numerical methodsand swarm intelligence algorithms on optimizing lowwind speed distribution models[D]. Lanzhou:LanzhouUniversity,2015.
[2]史景钊,杨星钊,陈新昌. 3参数威布尔分布参数估计方法的比较研究[J].河南农业大学学报,2009,43(4):405—409.[2] Shi Jingzhao, Yang Xingzhao, Chen Xinchang.Comparative study on parameter estimation methods for3-parameter Weibull distribution[J]. Journal of HenanAgricultural University,2009,43(4):405—409.
[3]方华元,胡昌华,曹小平,等.含约束条件遗传算法在三参数威布尔分布参数估计中的应用[J].战术导弹技术,2006,(6):32—35,44.[3] Fang Huayuan,Hu Changhua,Cao Xiaoping,et al.Optimal estimation of three parameters Weibulldistribution based on genetic algorithm with constrains[J]. Tactical Missile Technology,2006,(6):32—35,44.
[4]董胜,韩意,陶山山,等. Weibull分布参数的粒子群算法估计[J].中国海洋大学学报,2012,42(6):120—125.[4] Dong Sheng,Han Yi,Tao Shanshan,et al. Parametersestimation for Weibull distribution with particle swarmoptimization[J]. Periodical of Ocean University ofChina,2012,42(6):120—125.
[5]于赞梅,刘观起,刘森.基于双适应度微粒群优化算法的最优潮流计算[J].电气应用,2007,26(4):25—29.[5] Yu Zanmei, Liu Guanqi, Liu Sen. Optimal powersystem calculation based on particle swarm optimizationof double fitness[J]. Electrotechnical Application,2007,26(4):25—29.
[6]罗航,王厚军,黄建国,等.基于PSO的三参数威布尔分布参数的联合估计方法[J].仪器仪表学报,2009,30(8):1604—1611.[6] Luo Hang, Wang Houjun, Huang Jianguo, et al.Method of united estimation to the parameters of three-parameter Weibull distribution based on PSO[J].Chinese Journal of Scientific Instrument,2009,30(8):1604—1611.
[7]贺德馨.风工程与工业空气动力学[M].北京:国防工业出版社,2006,23—24.[7] He Dexin. Wind engineering and industrial aerodynamics[M]. Beijing:National Defense Industry Press,2006,23—24.
[8]徐卫民,孔新红,桂保玉.三种风速威布尔分布参数算法的比较[A].第26届中国气象学会年会气候资源应用研究分会场论文集[C],杭州,2009.[8] Xu Weimin, Kong Xinhong, Gui Baoyu. Thecomparation of three methods to calculate the Weibullparameters of wind speed[A]. Proceedings of the 26thChinese Meteorology Conference[C],Hangzhou,2009.
[9]包小庆,刘志强,吴永忠,等.双参数威布尔分布函数的确定及曲线拟合[J].能源与环境,2007,(4):4—9.[9] Bao Xiaoqing,Liu Zhiqiang,Wu Yongzhong,et al. Thedetermination of double parameters Weibull distributionfunction and curve fitting[J]. Energy and Environment,2007,(4):4—9.
[10]龚伟俊,李为相,张广明.基于威布尔分布的风速概率分布参数估计方法[J].可再生能源,2011,29(6):20—23.[10] Gong Weijun,Li Weixiang,Zhang Guangming. Theestimation algorithm on the probabilistic distributionparameters of wind speed based on Weibull distribution[J]. Renewable Energy Resources,2011,29(6):20—23.
[11]纪震,廖慧连,吴青华.粒子群算法及应用[M].北京:科学出版社,2009,16—21.[11] Ji Zhen,Liao Huilian,Wu Qinghua. Particle swarmoptimization algorithm and application[M]. Beijing:Science Press,2009,16—21.
[12]李宁,孙德宝,邹彤,等.基于差分方程的PSO算法粒子运动轨迹分析[J].计算机学报,2006,29(11):2052—2061.[12] Li Ning,Sun Debao,Zou Tong,et al. An analysis for aparticle’s trajectory of PSO based on difference equation[J]. Chinese Journal of Computers,2006,29(11):2052—2061.
[13]姜海燕.数值法与群智能算法在低风速分布模型优化中的对比研究[D].兰州:兰州大学,2015.[13] Jiang Haiyan. Comparative study of numerical methodsand swarm intelligence algorithms on optimizing lowwind speed distribution models[D]. Lanzhou:LanzhouUniversity,2015.
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