主元分析结合Cornish-Fisher展开的概率潮流三点估计法
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摘要
传统点估计概率潮流计算(Probabilistic Load Flow Calculation Based on Point Estimate Method, PLF-PEM)没有考虑输入随机变量相关系数矩阵非正定之情形。为克服上述不足,更准确地描述输出变量的统计特性,提出一种主元分析结合Cornish-Fisher级数展开的PLF-PEM算法。利用主元分析处理相关性输入随机变量,通过点估计方法得到输出变量的各阶矩。结合半不变量理论与Cornish-Fisher级数展开,利用输入变量的离散样本数据求得输出随机变量的数字特征和概率统计信息。算例表明所提算法能适应新能源发电高渗透电力系统的快速概率潮流计算。
The existing Probabilistic Load Flow Calculation based on Point Estimate Method(PLF-PEM) does not consider the case where the correlation matrix of random input variables is non-positive definite. To overcome the deficiency and describe the statistical characteristics of the outputs more accurately, a PLF-PEM computing method based on Principal Component Analysis(PCA) and Cornish-Fisher series expansion is suggested. The proposed method uses the PCA theory to deal with the correlated random inputs and applies the PEM to obtain the moments of the outputs. Then, based on the cumulant theory and the Cornish-Fisher expansion and by using the discrete sample data of the input variables, the digital characteristics and probability statistical properties of the outputs are obtained. Test examples show that the method is appropriate for fast PLF calculation of power systems with high penetrations of new energy power generations.
The existing Probabilistic Load Flow Calculation based on Point Estimate Method(PLF-PEM) does not consider the case where the correlation matrix of random input variables is non-positive definite. To overcome the deficiency and describe the statistical characteristics of the outputs more accurately, a PLF-PEM computing method based on Principal Component Analysis(PCA) and Cornish-Fisher series expansion is suggested. The proposed method uses the PCA theory to deal with the correlated random inputs and applies the PEM to obtain the moments of the outputs. Then, based on the cumulant theory and the Cornish-Fisher expansion and by using the discrete sample data of the input variables, the digital characteristics and probability statistical properties of the outputs are obtained. Test examples show that the method is appropriate for fast PLF calculation of power systems with high penetrations of new energy power generations.
引文
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[15]艾小猛,文劲宇,吴桐,等.基于点估计和GramCharlier展开的含风电电力系统概率潮流实用算法[J].中国电机工程学报,2013,33(16):16-22.AI Xiaomeng,WEN Jinyu,WU Tong,et al.A practical algorithm based on point estimate method and Gram-Charlier expansion for probabilistic load flow calculation of power systems incorporating wind power[J].Proceedings of the CSEE,2013,33(16):16-22.
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[17]HONG H P.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59(3):261-267.
[18]ABDI H,WILLIAMS L J.Principal component analysis[J].Wiley Interdisciplinary Reviews Computational Statistics,2010,2(4):433-459.
[19]CHRISTIE B R.Power systems test case archive[EB/OL].[2010-01-10].http://www.ee.washington.edu/research/pstca/.
[20]GALICIA S.The real time data for wind speed of the Galician wind farm[EB/OL].[2016-04-01].http://www.sotaventogalicia.com/en/real-time-data/historical.
[21]张涛,张东方,王凌云,等.计及电动汽车充电模式的主动配电网多目标优化重构[J].电力系统保护与控制,2018,46(8):1-9.ZHANG Tao,ZHANG Dongfang,WANG Lingyun,et al.Multi-objective optimization of active distribution network reconfiguration considering electric vehicle charging mode[J].Power System Protection and Control,2018,46(8):1-9.
[22]IQBA F,SIDDIQUI A S.Optimal configuration analysis for a campus microgrid-a case study[J].Protection and Control of Modern Power Systems,2017,2(2):245-256.DOI:10.1186/s41601-017-0055-z.
[2]方斯顿,程浩忠,徐国栋,等.基于Nataf变换含相关性的扩展准蒙特卡洛随机潮流方法[J].电工技术学报,2017,32(2):255-263.FANG Sidun,CHENG Haozhong,XU Guodong,et al.ANataf transformation based on extended quasi Monte Carlo simulation method for solving probabilistic load flow problems with correlated random variables[J].Transactions of China Electrotechnical Society,2017,32(2):255-263.
[3]徐潇源,严正,冯冬涵,等.基于输入变量秩相关系数的概率潮流计算方法[J].电力系统自动化,2014,38(12):54-61.XU Xiaoyuan,YAN Zheng,FENG Donghan,et al.Probabilistic load flow calculation based on rank correlation coefficient of input random variables[J].Automation of Electric Power Systems,2014,38(12):54-61.
[4]宣锐峰,王亚楠,万要军,等.基于Faure序列的电力系统概率潮流计算[J].电力系统保护与控制,2015,43(20):15-20.XUAN Ruifeng,WANG Yanan,WAN Yaojun,et al.Probabilistic power flow calculation based on Faure sequence with wind farms[J].Power System Protection and Control,2015,43(20):15-20.
[5]邱宜彬,欧阳誉波,李奇,等.考虑多风电场相关性的场景概率潮流计算及无功优化[J].电力系统保护与控制,2017,45(2):61-68.QIU Yibin,OUYANG Yubo,LI Qi,et al.Scenario probabilistic load flow calculation and reactive power optimization considering wind farms correlation[J].Power System Protection and Control,2017,45(2):61-68.
[6]USAOLA J.Probabilistic load flow with correlated wind power injections[J].Electric Power Systems Research,2010,80(5):528-536.
[7]石东源,蔡德福,陈金富,等.计及输入变量相关性的半不变量法概率潮流计算[J].中国电机工程学报,2012,32(28):104-113.SHI Dongyuan,CAI Defu,CHEN Jinfu,et al.Probabilistic load flow calculation based on cumulant method considering correlation between input variables[J].Proceedings of the CSEE,2012,32(28):104-113.
[8]杨欢,邹斌.含相关性随机变量的概率潮流三点估计法[J].电力系统自动化,2012,36(15):51-56.YANG Huan,ZOU Bin.A three-point estimate method for solving probabilistic power flow problems with correlated random variables[J].Automation of Electric Power Systems,2012,36(15):51-56.
[9]韩海腾,高山,吴晨,等.基于Nataf变换的电网不确定性多点估计法[J].电力系统自动化,2015,39(7):28-34.HAN Haiteng,GAO Shan,WU Chen,et al.Uncertain power flow solved by multi-point estimate method based on Nataf transformation[J].Automation of Electric Power Systems,2015,39(7):28-34.
[10]尹青,杨洪耕,马晓阳.考虑多重不确定参数的配电网概率无功优化[J].电力系统保护与控制,2017,45(7):141-147.YIN Qing,YANG Honggeng,MA Xiaoyang.Probabilistic reactive power optimization for distribution network considering multiple uncertainties[J].Power System Protection and Control,2017,45(7):141-147.
[11]陈璨,吴文传,张伯明,等.考虑光伏出力相关性的配电网概率潮流[J].电力系统自动化,2015,39(9):41-47.CHEN Can,WU Wenchuan,ZHANG Boming,et al.Probabilistic load flow of distribution network considering correlated photovoltaic power output[J].Automation of Electric Power Systems,2015,39(9):41-47.
[12]张立波,程浩忠,曾平良,等.基于Nataf逆变换的概率潮流三点估计法[J].电工技术学报,2016,31(6):187-194.ZHANG Libo,CHENG Haozhong,ZENG Pingliang,et al.A three-point estimate method for solving probabilistic load flow based on inverse Nataf transformation[J].Transactions of China Electrotechnical Society,2016,31(6):187-194.
[13]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,LIN Tao,XU Xialing,et al.An algorithm based on 2m+1 point estimate method for harmonic probabilistic load flow calculation of power systems incorporating wind power[J].Power System Technology,2015,39(11):3260-3265.
[14]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):62-68,120.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):62-68,120.
[15]艾小猛,文劲宇,吴桐,等.基于点估计和GramCharlier展开的含风电电力系统概率潮流实用算法[J].中国电机工程学报,2013,33(16):16-22.AI Xiaomeng,WEN Jinyu,WU Tong,et al.A practical algorithm based on point estimate method and Gram-Charlier expansion for probabilistic load flow calculation of power systems incorporating wind power[J].Proceedings of the CSEE,2013,33(16):16-22.
[16]MORALES J M,BARINGO L,CONEJO A J,et al.Probabilistic power flow with correlated wind sources[J].IET Generation Transmission&Distribution,2010,4(5):641-651.
[17]HONG H P.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59(3):261-267.
[18]ABDI H,WILLIAMS L J.Principal component analysis[J].Wiley Interdisciplinary Reviews Computational Statistics,2010,2(4):433-459.
[19]CHRISTIE B R.Power systems test case archive[EB/OL].[2010-01-10].http://www.ee.washington.edu/research/pstca/.
[20]GALICIA S.The real time data for wind speed of the Galician wind farm[EB/OL].[2016-04-01].http://www.sotaventogalicia.com/en/real-time-data/historical.
[21]张涛,张东方,王凌云,等.计及电动汽车充电模式的主动配电网多目标优化重构[J].电力系统保护与控制,2018,46(8):1-9.ZHANG Tao,ZHANG Dongfang,WANG Lingyun,et al.Multi-objective optimization of active distribution network reconfiguration considering electric vehicle charging mode[J].Power System Protection and Control,2018,46(8):1-9.
[22]IQBA F,SIDDIQUI A S.Optimal configuration analysis for a campus microgrid-a case study[J].Protection and Control of Modern Power Systems,2017,2(2):245-256.DOI:10.1186/s41601-017-0055-z.