结合M-Copula理论与半不变量的随机潮流方法
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摘要
随着光伏等可再生能源越来越多地并入电力系统,电力系统运行的随机性问题越来越突出。传统的确定性潮流将无法准确描述电力系统的实际运行状态,而随机潮流能充分考虑电力系统的各种随机波动,从而为电力系统的规划和运行提供指导。然而,新能源出力由于自然条件的时空关联性存在复杂的非线性相关性;为处理该非线性相关性,提出了一种基于M-Copula理论的半不变量随机潮流计算方法,将Copula理论与半不变量法结合起来,同时选择多个Copula函数模型来充分描述变量之间的复杂相关性。该方法既考虑了电力系统输入变量之间广泛存在的非线性相关性,又充分利用了半不变量法计算速度较快的优点,从而实现随机潮流的快速准确计算。以修改的IEEE 14系统为例,与蒙特卡洛方法进行的对比,仿真验证了所提方法的快速性与准确性。
With more and more renewable energy, such as photovoltaic and wind power, integrated into power systems, random problem of power system operation becomes increasingly prominent. Traditional deterministic power flow will not reflect actual operation status of power systems, while probabilistic load flow can fully consider various kinds of operating conditions of power systems and provide a guidance for power system planning and operation. However, nonlinear correlation with renewable energy is complex due to time and spatial coupling of natural conditions. In order to deal with this nonlinear correlation, a new cumulant method based on M-Copula theory combining cumulants for probabilistic load flow is proposed, and multiple Copula function models are chosen to describe complex correlation between random variables. The proposed method can deal with the nonlinear correlation with renewable energy and maintain fast computation speed of cumulant method. The fast computation speed and high accuracy of this algorithm is proved with case study in a modified IEEE 14 system by comparing with Monte Carlo simulations.
With more and more renewable energy, such as photovoltaic and wind power, integrated into power systems, random problem of power system operation becomes increasingly prominent. Traditional deterministic power flow will not reflect actual operation status of power systems, while probabilistic load flow can fully consider various kinds of operating conditions of power systems and provide a guidance for power system planning and operation. However, nonlinear correlation with renewable energy is complex due to time and spatial coupling of natural conditions. In order to deal with this nonlinear correlation, a new cumulant method based on M-Copula theory combining cumulants for probabilistic load flow is proposed, and multiple Copula function models are chosen to describe complex correlation between random variables. The proposed method can deal with the nonlinear correlation with renewable energy and maintain fast computation speed of cumulant method. The fast computation speed and high accuracy of this algorithm is proved with case study in a modified IEEE 14 system by comparing with Monte Carlo simulations.
引文
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[10]胡泽春,王锡凡.基于半不变量法的随机潮流误差分析[J].电网技术,2009,33(18):32-37.Hu Zechun,Wang Xifan.Error analysis of the probabilistic load flow based on cumulant method[J].Power System Technology,2009,33(18):32-37(in Chinese).
[11]黎静华,文劲宇,程时杰,等.考虑多风电场出力Copula相关关系的场景生成方法[J].中国电机工程学报,2013,33(16):30-36.Li Jinghua,Wen Jinyu,Cheng Shijie,et al.A scene generation method considering copula correlation relationship of multi-wind farms power[J].Proceeding of the CSEE,2013,33(16):30-36(in Chinese).
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[14]刘丹.关于几何分布数字特征的研究[D].沈阳:东北大学,2007.
[15]李斌,吕林,刘友波,等.考虑光伏接入不确定性的主动配电网有功-无功可控资源优化配置[J].电网技术,2017,41(2):355-362.Li Bin,LüLin,Liu Youbo,et al.Optimal configuration of controllable active-reactive power resources in active distribution network considering photovoltaic access uncertainty[J].Power System Technology,2017,41(2):355-362(in Chinese).
[16]王成山,郑海峰,谢莹华,等.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化,2005,29(24):39-44.Wang Chengshan,Zheng Haifeng,Xie Yinghua,et al.Probabilistic power flow containing distributed generation in distribution system[J].Automation of Electric Power Systems,2005,29(24):39-44(in Chinese).
[17]宋元峰,万凌云,刘涌,等.基于核密度估计的概率分布函数拟合方法[J].电网与清洁能源,2016(6):85-88.Song Yuanfeng,Wan Lingyun,Liu Yong,et al.Coarse-to-fine detection for nests on pylon[J].Power System and Clean Energy,2016(6):85-88(in Chinese).
[18]梁浩,张沛,贾宏杰,等.基于概率潮流的未来输电线路经济评估[J].电网技术,2014,38(3):675-680.Liang Hao,Zhang Pei,Jia Hongjie,et al.Economic assessment of future transmission line base on probabilistic power flow[J].Power System Technology,2014,38(3):675-680(in Chinese).
[19]Sklar M.Fonctions de répartitionàn dimensions et leurs marges[D].Paris:UniversitéParis,1959.
[20]韦艳华,张世英.Copula理论及其在金融分析上的应用[M].北京:清华大学出版社,2008:71-76.
[21]张玥,王秀丽,曾平良,等.基于Copula理论考虑风电相关性的源网协调规划[J].电力系统自动化,2017,41(9):102-108.Zhang Yue,Wang Xiuli,Zeng Pingliang,et al.Copula theory based generation and transmission co-planning considering wind power correlation[J].Automation of Electric Power Systems,2017,41(9):102-108(in Chinese).
[22]易文德.基于Copula理论的金融风险相依结构模型及应用[M].北京:中国经济出版社,2011:40-48.
[23]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):1-5.Ji Feng,Cai Xingguo,Wang Jun.Wind power correlation analysis based on hybrid copula[J].Automation of Electric Power Systems,2014,38(2):1-5(in Chinese).
[24]Hsu T M,Emura T,Fan T H.Reliability inference for a copula-based series system life test under multiple type-I censoring[J].IEEE Transactions on Reliability,2016,65(2):1069-1080.
[25]邱小霞,刘次华,吴娟,等.Copula函数中参数的矩估计方法[J].应用数学,2009,22(2):448-451.Qiu Xiaoxia,Liu Cihua,Wu Juan,et al.Moment estimation of parameters on Copulas[J].Mathematica Applicata,2009,22(2):448-451(in Chinese).
[26]潘雄,王莉莉,徐玉琴,等.基于混合Copula函数的风电场出力建模方法[J].电力系统自动化,2014,38(14):17-22.Pan Xiong,Wang Lili,Xu Yuqin,et al.A wind farm power modeling method based on mixed Copula[J].Automation of Electric Power Systems,2014,38(14):17-22(in Chinese).
[27]陈涵,刘会金,李大路,等.非均匀采样和最小二乘法在间谐波检测中的应用[J].中国电机工程学报,2009,29(10):109-114.Chen Han,Liu Huijin,Li Dalu,et al.Application of nonuniformly sampling and least square technique in interharmonic measurement[J].Proceeding of the CSEE,2009,29(10):109-114(in Chinese).
[28]高阳,张碧玲,毛京丽,等.基于机器学习的自适应光伏超短期出力预测模型[J].电网技术,2015,39(2):307-311.Gao Yang,Zhang Biling,Mao Jingli,et al.Machine learning-based adaptive very-short-term forecast model for photovoltaic power[J].Power System Technology,2015,39(2):307-311(in Chinese).
[29]蔡德福,陈金富,石东源,等.风速相关性对配电网运行特性的影响[J].电网技术,2013,37(1):150-155.Cai Defu,Chen Jinfu,Shi Dongyuan,et al.Impact of wind speed correlation on operation characteristics of distribution network[J].Power System Technology,2013,37(1):150-155(in Chinese).
[2]丁明,李生虎,黄凯.基于蒙特卡罗模拟的概率潮流计算[J].电网技术,2001,25(11):10-14.Ding Ming,Li Shenghu,Huang Kai.Probabilistic load flow analysis based on Monte-Carlo simulation[J].Power System Technology,2001,25(11):10-14(in Chinese).
[3]王秀丽,张择策,侯雨伸.基于拟蒙特卡罗模拟法的主动配电网随机潮流计算[J].电力自动化设备,2017,37(3):7-12.Wang Xiuli,Zhang Zece,Hou Yushen.Stochastic load flow calculation based on quasi-Monte Carlo method for active distribution network[J].Electric Power Automation Equipment,2017,37(3):7-12(in Chinese).
[4]Zhang P,Lee S T.Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion[J].IEEE Transactions on Power Systems,2004,19(1):676-682.
[5]Liu J,Hao X,Cheng P,et al.A parallel probabilistic load flow method considering nodal correlations[J].Energies,2016,9(12):1041.
[6]戎晓雪,别朝红,石文辉,等.考虑风电场相关性的含风电电力系统随机潮流分析[J].电网技术,2014,38(8):2161-2167.Rong Xiaoxue,Bie Zhaohong,Shi Wenhui,et al.Analysis on probabilistic load flow in power gird integrated with wind farms considering correlativity among different wind farms[J].Power System Technology,2014,38(8):2161-2167(in Chinese).
[7]Usaola J.Probabilistic load flow with correlated wind power injections[J].Electric Power Systems Research,2010,80(5):528-536.
[8]邓威,李欣然,徐振华,等.考虑风速相关性的概率潮流计算及影响分析[J].电网技术,2012,36(4):45-50.Deng Wei,Li Xinran,Xu Zhenhua,et al.Calculation of probabilistic load flow considering wind speed correlation and analysis on influence of wind speed correlation[J].Power System Technology,2012,36(4):45-50(in Chinese).
[9]徐青山,黄煜,刘建坤,等.采用混合高斯模型及边缘变换技术的蒙特卡洛随机潮流方法[J].电力系统自动化,2016,40(16):23-30.Xu Qingshan,Huang Yu,Liu Jiankun,et al.Probabilistic load flow method using Monte Carlo simulation based on gaussian mixture model and marginal transformation[J].Automation of Electric Power Systems,2016,40(16):23-30(in Chinese).
[10]胡泽春,王锡凡.基于半不变量法的随机潮流误差分析[J].电网技术,2009,33(18):32-37.Hu Zechun,Wang Xifan.Error analysis of the probabilistic load flow based on cumulant method[J].Power System Technology,2009,33(18):32-37(in Chinese).
[11]黎静华,文劲宇,程时杰,等.考虑多风电场出力Copula相关关系的场景生成方法[J].中国电机工程学报,2013,33(16):30-36.Li Jinghua,Wen Jinyu,Cheng Shijie,et al.A scene generation method considering copula correlation relationship of multi-wind farms power[J].Proceeding of the CSEE,2013,33(16):30-36(in Chinese).
[12]蔡德福,石东源,陈金富.基于Copula理论的计及输入随机变量相关性的概率潮流计算[J].电力系统保护与控制,2013,41(20):13-19.Cai Defu,Shi Dongyuan,Chen Jinfu.Probabilistic load flow considering correlation between input random variables based on Copula theory[J].Power System Protection and Control,2013,41(20):13-19(in Chinese).
[13]周宜广,刘天琪.基于混合Copula和均匀设计采样的电力系统随机潮流[J].中国电力,2016,49(2):109-113.Zhou Yiguang,Liu Tianqi.Probabilistic load flow based on mixed copula and uniform design sampling[J].Electric Power,2016,49(2):109-113(in Chinese).
[14]刘丹.关于几何分布数字特征的研究[D].沈阳:东北大学,2007.
[15]李斌,吕林,刘友波,等.考虑光伏接入不确定性的主动配电网有功-无功可控资源优化配置[J].电网技术,2017,41(2):355-362.Li Bin,LüLin,Liu Youbo,et al.Optimal configuration of controllable active-reactive power resources in active distribution network considering photovoltaic access uncertainty[J].Power System Technology,2017,41(2):355-362(in Chinese).
[16]王成山,郑海峰,谢莹华,等.计及分布式发电的配电系统随机潮流计算[J].电力系统自动化,2005,29(24):39-44.Wang Chengshan,Zheng Haifeng,Xie Yinghua,et al.Probabilistic power flow containing distributed generation in distribution system[J].Automation of Electric Power Systems,2005,29(24):39-44(in Chinese).
[17]宋元峰,万凌云,刘涌,等.基于核密度估计的概率分布函数拟合方法[J].电网与清洁能源,2016(6):85-88.Song Yuanfeng,Wan Lingyun,Liu Yong,et al.Coarse-to-fine detection for nests on pylon[J].Power System and Clean Energy,2016(6):85-88(in Chinese).
[18]梁浩,张沛,贾宏杰,等.基于概率潮流的未来输电线路经济评估[J].电网技术,2014,38(3):675-680.Liang Hao,Zhang Pei,Jia Hongjie,et al.Economic assessment of future transmission line base on probabilistic power flow[J].Power System Technology,2014,38(3):675-680(in Chinese).
[19]Sklar M.Fonctions de répartitionàn dimensions et leurs marges[D].Paris:UniversitéParis,1959.
[20]韦艳华,张世英.Copula理论及其在金融分析上的应用[M].北京:清华大学出版社,2008:71-76.
[21]张玥,王秀丽,曾平良,等.基于Copula理论考虑风电相关性的源网协调规划[J].电力系统自动化,2017,41(9):102-108.Zhang Yue,Wang Xiuli,Zeng Pingliang,et al.Copula theory based generation and transmission co-planning considering wind power correlation[J].Automation of Electric Power Systems,2017,41(9):102-108(in Chinese).
[22]易文德.基于Copula理论的金融风险相依结构模型及应用[M].北京:中国经济出版社,2011:40-48.
[23]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):1-5.Ji Feng,Cai Xingguo,Wang Jun.Wind power correlation analysis based on hybrid copula[J].Automation of Electric Power Systems,2014,38(2):1-5(in Chinese).
[24]Hsu T M,Emura T,Fan T H.Reliability inference for a copula-based series system life test under multiple type-I censoring[J].IEEE Transactions on Reliability,2016,65(2):1069-1080.
[25]邱小霞,刘次华,吴娟,等.Copula函数中参数的矩估计方法[J].应用数学,2009,22(2):448-451.Qiu Xiaoxia,Liu Cihua,Wu Juan,et al.Moment estimation of parameters on Copulas[J].Mathematica Applicata,2009,22(2):448-451(in Chinese).
[26]潘雄,王莉莉,徐玉琴,等.基于混合Copula函数的风电场出力建模方法[J].电力系统自动化,2014,38(14):17-22.Pan Xiong,Wang Lili,Xu Yuqin,et al.A wind farm power modeling method based on mixed Copula[J].Automation of Electric Power Systems,2014,38(14):17-22(in Chinese).
[27]陈涵,刘会金,李大路,等.非均匀采样和最小二乘法在间谐波检测中的应用[J].中国电机工程学报,2009,29(10):109-114.Chen Han,Liu Huijin,Li Dalu,et al.Application of nonuniformly sampling and least square technique in interharmonic measurement[J].Proceeding of the CSEE,2009,29(10):109-114(in Chinese).
[28]高阳,张碧玲,毛京丽,等.基于机器学习的自适应光伏超短期出力预测模型[J].电网技术,2015,39(2):307-311.Gao Yang,Zhang Biling,Mao Jingli,et al.Machine learning-based adaptive very-short-term forecast model for photovoltaic power[J].Power System Technology,2015,39(2):307-311(in Chinese).
[29]蔡德福,陈金富,石东源,等.风速相关性对配电网运行特性的影响[J].电网技术,2013,37(1):150-155.Cai Defu,Chen Jinfu,Shi Dongyuan,et al.Impact of wind speed correlation on operation characteristics of distribution network[J].Power System Technology,2013,37(1):150-155(in Chinese).