基于改进降维法的概率潮流计算Probabilistic Load Flow Calculation Based on Improved Dimension Reduction Method
肖青;周少武;
摘要(Abstract):
旨在建立一种高效、准确的概率潮流算法。在处理潮流方程中的相关随机变量时,选用高斯Copula和秩相关系数来建模,将相关随机变量表示成独立的标准正态随机变量,从而将概率潮流输出量的统计矩表示成关于独立标准正态随机变量的多维积分。沿用单维降维法的思想,提出了一种改进的降维模型,将概率潮流输出量的统计矩近似成多个低维积分之和,并基于容积量法求解积分权重和节点,用以计算低维积分。此外,文中方法也可与基于单维降维模型的点估计法相结合,用于求解概率潮流问题。对IEEE 30-节点和IEEE 118-节点系统的计算结果表明:与Hong的点估计和基于单维降维法的点估计相比,文中算法更加灵活,在提高精度的同时也可减小计算量。
关键词(KeyWords): 概率潮流;高斯Copula;秩相关系数;容积量法;降维模型
基金项目(Foundation): 国家自然科学基金项目(51577057)~~
作者(Author): 肖青;周少武;
Email:
DOI: 10.13335/j.1000-3673.pst.2017.2335
参考文献(References):
- [1]张楷旋,陈建英,郭创新,等.考虑天气因素的含风电场电力系统的概率潮流分析[J].电网技术,2014,38(12):3418-3423.Zhang Kaixuan,Chen Jianying,Guo Chuangxin,et al.Weather factor based analysis on probabilistic load flow of power grid containing wind farms[J].Power System Technology,2014,38(12):3418-3423(in Chinese).
- [2]柳志航,卫志农,孙国强,等.计及参数模糊性的含风电场电力系统概率潮流计算[J].电网技术,2017,41(7):2038-2315.Liu Zhihang,Wei Zhinong,Sun Guoqiang,et al.Probabilistic power flow calculation of power system with wind farms considering fuzzy parameters[J].Power System Technology,2017,41(7):2038-2315(in Chinese).
- [3]陈雁,文劲宇,程时杰.考虑输入变量相关性的概率潮流计算方法[J].中国电机工程学报,2011,31(22):80-87.Chen Yan,Wen Jinyu,Cheng Shijie.Probabilistic load flow analysis considering dependencies among input random variables[J].Proceedings of the CSEE,2011,31(22):80-87(in Chinese).
- [4]李俊芳,张步涵.基于进化算法改进拉丁超立方抽样的概率潮流计算[J].中国电机工程学报,2011,31(25):90-96.Li Junfang,Zhang Buhan.Probabilistic load flow based on improved Latin hypercube sampling with evolutionary algorithm[J].Proceedings of the CSEE,2011,31(25):90-96(in Chinese).
- [5]蔡德福,石东源,李高望,等.基于输入随机变量离散数据的概率潮流计算方法[J].电网技术,2013,37(9):2474-2479.Cai Defu,Shi Dongyuan,Li Gaowang,et al.A probabilistic load flow calculation method based on discrete data of input random variable[J].Power System Technology,2013,37(9):2474-2479(in Chinese).
- [6]丁明,王京景,李生虎.基于扩展拉丁超立方采样的电力系统概率潮流计算[J].中国电机工程学报,2013,33(4):163-170.Ding Ming,Wang Jingjing,Li Shenghu.Probabilistic load flow evaluation with extended Latin hypercube sampling[J].Proceedings of the CSEE,2013,33(4):163-170(in Chinese).
- [7]Zou Bin,Xiao Qing.Solving probabilistic optimal power flow problem using quasi Monte Carlo method and ninth-order polynomial normal transformation[J].IEEE Transactions on Power Systems,2014,29(1):300-306.
- [8]Fang Sidun,Cheng Haozhong,Xu Guodong.A modified Nataf transformation-based extended Quasi-Monte Carlo simulation method for solving probabilistic load flow[J].Electric Power Components and Systems,2016,44(15):1735-1744.
- [9]Usaola J.Probabilistic load flow with correlated wind power injections[J].Electric Power Systems Research,2010,80(5):528-536.
- [10]石飞,於益军,冯树海,等.计及多机平衡策略的半不变量法在线概率潮流[J].电网技术,2015,39(5):1337-1342.Shi Fei,Yu Yijun,Feng Shuhai,et al.Online probabilistic load flow based on cumulant method considering multi-slack strategy[J].Power System Technology,2015,39(5):1337-1342(in Chinese).
- [11]连浩然,周保荣,秦鹏,等.基于场景分区的随机潮流解析算法[J].电网技术,2017,41(10):3153-3160.Lian Haoran,Zhou Baorong,Qin Peng,et al.Probabilistic power flow analytic algorithm based on scenario partition[J].Power System Technology,2017,41(10):3153-3160(in Chinese).
- [12]Wu Wei,Wang Keyou,Li Guojie,et al.Probabilistic load flow calculation using cumulants and multiple integrals[J].IET Generation Transmission Distribution,2016,44(15):1735-1744.
- [13]Ren Zhouyang,Li Wenyuan,Roy Billinton.Probabilistic power flow analysis based on the stochastic response surface method[J].IEEE Transactions on Power Systems,2016,31(3):2307-2315.
- [14]Wu Hao,Zhou Yongzhi,Dong Shufeng,et al.Probabilistic load flow based on generalized polynomial chaos[J].IEEE Transactions on Power Systems,2017,32(1):820-821.
- [15]李怡宁,吴浩,辛焕海,等.基于广义多项式混沌法的电力系统随机潮流[J].电力系统自动化,2015,39(7):14-20.Li Yining,Wu Hao,Xin Huanhai,et al.Power system probabilistic load flow based on generalized polynomial chaos methods[J].Automation of Electric Power Systems,2015,39(7):14-20(in Chinese).
- [16]孙明,吴浩,邱一苇,等.基于广义多项式混沌法的含风电电力系统随机潮流[J].电力系统自动化,2017,41(7):54-60.Sun Ming,Wu Hao,Qiu Yiwei,et al.Probabilistic load flow for wind power integrated system based on generalized polynomial chaos method[J].Automation of Electric Power Systems,2017,41(7):54-60(in Chinese).
- [17]孙英云,毛瑞,董雷,等.基于随机配置点法的概率潮流算法[J].电力系统自动化,2015,39(23):111-118.Sun Yunying,Mao Rui,Dong Lei,et al.Probabilistic load flow algorithm based on stochastic collocation method[J].Automation of Electric Power Systems,2015,39(23):111-118(in Chinese).
- [18]Tang Junjie,Ni Fei,Ferdinanda Ponci,et al.Dimension-adaptive sparse grid interpolation for uncertainty quantification in modern power systems:probabilistic power[J].IEEE Transactions on Power Systems,2016,31(4):907-919.
- [19]Ni Fei,Nguyen P H,Cobben J F G.Basis-adaptive sparse polynomial chaos expansion for probabilistic power flow[J].IEEE Transactions on Power Systems,2017,32(1):694-704.
- [20]余光正,林涛,徐遐龄,等.基于2m+1点估计法的考虑风力发电接入时电力系统谐波概率潮流算法[J].电网技术,2015,39(11):3260-3265.Yu Guangzheng,Li Tao,Xu Xialing,et al.An algorithm based on2m+1point estimate method for harmonic probabilistic load flow calculation of power systems incorporating wind power[J].Power System Technology,2015,39(11):3260-3265(in Chinese).
- [21]刘利民,刘俊勇,刘友波.Nataf变换三点估计分布式发电网络的概率潮流分析[J].电力系统自动化,2015,39(12):62-68.Liu Limin,Liu Junyong,Liu Youbo.Nataf transform based three point estimation algorithm for probabilistic load flow analysis of distributed power network[J].Automation of Electric Power Systems,2015,39(12):62-68(in Chinese).
- [22]楚云飞,孙国强,卫志农,等.基于无迹变换的含风电场电力系统可用输电能力计算[J].电网技术,2015,39(8):2122-2128.Chu Yunfei,Sun Guoqiang,Wei Zhinong,et al.An algorithm based on 2m+1point estimate method for harmonic probabilistic load flow calculation of power systems incorporating wind power[J].Power System Technology,2015,39(8):2122-2128(in Chinese).
- [23]Aien M,Fotuhi-Firuzabad M,Aminifar F.Probabilistic load flow in correlated uncertain environment using unscented transformation[J].IEEE Transactions on Power Systems,2012,27(4):2233-2241.
- [24]Zou Bin,Xiao Qing.Probabilistic load flow computation using univariate dimension reduction method[J].International Transactions on Electrical Energy Systems,2014,24(12):1700-1714.
- [25]Xiao Qing.Dimension reduction method for probabilistic power flow calculation[J].IET Generation Transmission Distribution,2016,44(15):1735-1744.
- [26]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).
- [27]熊强,陈维荣,张雪霞,等.考虑多风电场相关性的场景概率潮流计算[J].电网技术,2015,39(8):2154-2159.Xiong Qiang,Chen Weirong,Zhang Xuexia,et al.Scenario probabilistic load flow calculation considering wind farms correlation[J].Power System Technology,2015,39(8):2154-2159(in Chinese).
- [28]吴巍,汪可友,李国杰.计及光伏发电相关性的多重积分法概率潮流计算[J].中国电机工程学报,2015,35(3):568-575.Wu Wei,Wang Keyoug,LI Guojie.Probabilistic load flow calculation method based on multiple integral method considering correlation of photovoltaic generation[J].Proceedings of the CSEE,2015,35(3):568-575(in Chinese).
- [29]Liu Yu,Gao Shan,Cui Hantao,et al.Probabilistic load flow considering correlations of input variables following arbitrary distributions[J].Electric Power Systems Research,2016(140):354-362.
- [30]Morales J M,Conejo A J,Perz-Ruiz J.Simulating the impact of wind product on locational marginal prices[J].IEEE Transactions on Power Systems,2011,26(2):820-828.
- [31]Lebrun R,Dutfoy A.An innovating analysis of the Nataf transformation from the copula viewpoint[J].Probabilistic Engineering Mechanics,2009,24(3):312-320.
- [32]Wu Wei,Wang Keyoug,Li Guojie,et al.A multivariate dimension-reduction method for probabilistic power flow calculation[J].Electric Power Systems Research,2016(141):272-280.
- [33]潘雄,张龙,黄家栋,等.基于数字网系方法的概率最优潮流计算[J].电力系统自动化,2015,39(7):35-40.Pan Xiong,Zhang Long,Huang Jiadong,et al.Probabilistic optimal power flow calculation based on digital nets methods[J].Automation of Electric Power Systems,2015,39(7):35-40(in Chinese).