|
|
|
| A Three-Point Estimate Method for Solving Probabilistic Load Flow Based on Inverse Nataf Transformation |
| Zhang Libo1, Cheng Haozhong1, Zeng Pingliang2, Yao Liangzhong2, Masoud Bazargan3 |
1. Key Laboratory of Control of Power Transmission and Conversion of Ministry of Education Shanghai Jiao Tong University Shanghai 200240 China;
2. China Electric Power Research Institute Beijing 100192 China;
3. ALSTOM Grid Research & Technology Stafford ST17 4LX UK |
|
|
|
|
Abstract With the increasing penetration of wind sources, not only the fluctuation and intermittency of wind power, but also the correlations among wind farms should be considered in power system analysis. Nataf transformation and inverse Nataf transformation establish the relationship between independent standard normal space and correlated non-normal space. By incorporating inverse Nataf transformation, this paper proposed a novel three-point estimate method to solve the probabilistic load flow problems considering correlations among input variables. Accuracy and efficiency of the proposed algorithm has been validated by the comparative tests in a modified IEEE RTS 24 bus system and a modified IEEE 118 bus system.
|
|
Received: 07 April 2014
Published: 01 April 2016
|
|
|
|
|
|
[1] Borkowska B. Probabilistic load flow[J]. IEEE Transa- ctions on Power Apparatus and Systems, 1974, 93(3): 752-759.
[2] Allan R N, Dasilva A M L, Burchett R C. Evaluation methods and accuracy in probabilistic load flow solutions[J]. IEEE Transactions on Power Apparatus and Systems, 1981, 100(5): 2539-2546.
[3] 董雷, 杨以涵, 张传成, 等. 综合考虑网络结构不确定性的概率潮流计算方法[J]. 电工技术学报, 2012, 27(1): 210-216.
Dong Lei, Yang Yihan, Zhang Chuancheng, et al. Probabilistic load flow considering network configur- ation uncertainties[J]. Transactions of China Electro- technical Society, 2012, 27(1): 210-216.
[4] Zhang P, Lee S T. Probabilistic load flow com- putation using the method of combined cumulants and Gram-Charlier expansion[J]. IEEE Transactions on Power Systems, 2004, 19(1): 676-682.
[5] 刘小团, 赵晋泉, 罗卫华, 等. 基于TPNT和半不变量法的考虑输入量相关性概率潮流算法[J]. 电力系统保护与控制, 2013, 41(22): 13-18.
Liu Xiaotuan, Zhao Jinquan, Luo Weihua, et al. A TPNT and cumulants based probabilistic load flow approach considering the correlation variables[J]. Power System Protection and Control, 2013, 41(22): 13-18.
[6] 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. Probabi- listic load flow calculation based on cumulant method considering correlation between input vari- ables[J]. Proceedings of the CSEE, 2012, 32(28): 104-113.
[7] Leite da Silva A M, Arienti V L, Allen R N. Probabilistic load flow considering dependence between input nodal powers[J]. IEEE Transactions on Power Apparatus and Systems, 1984, 103(6): 1524- 1530.
[8] Yu H, Chung C Y, Wong K P, et al. Probabilistic load flow evaluation with hybrid Latin hypercube sam- pling and Cholesky decomposition[J]. IEEE Transac- tions on Power Systems, 2009, 24(2): 661-667.
[9] 杨欢, 邹斌. 含相关性随机变量的概率最优潮流问题的蒙特卡罗模拟方法[J]. 电力系统保护与控制, 2012, 40(19): 110-115.
Yang Huan, Zou Bin. A Monte Carlo simulation method for probabilistic optimal power flow with correlated stochastic variables[J]. Power System Protection and Control, 2012, 40(19): 110-115.
[10] 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.
[11] 茆美琴, 周松林, 苏建徽. 基于风光联合概率分布的微电网概率潮流预测[J]. 电工技术学报, 2014, 29(2): 55-63.
Mao Meiqin, Zhou Songlin, Su Jianhui. Probabilistic power flow forecasting of microgrid based on joint probability distribution about wind and irradiance[J]. Transactions of China Electrotechnical Society, 2014, 29(2): 55-63.
[12] Chen Y, Wen J, Cheng S. Probabilistic load flow method based on Nataf transformation and Latin hypercube sampling[J]. IEEE Transactions on Sustainable Energy, 2013, 4(2): 294-301.
[13] Su C L. Probabilistic load-flow computation using point estimate method[J]. IEEE Transactions on Power Systems, 2005, 20(4): 1843-1851.
[14] Morales J M, Perez-Ruiz J. Point estimate schemes to solve the probabilistic power flow[J]. IEEE Transa- ctions on Power Systems, 2007, 22(4): 1594-1601.
[15] Caramia P, Carpinelli G, Varilone P. Point estimate schemes for probabilistic three-phase load flow[J]. Electric Power Systems Research, 2010, 80(2): 168- 175.
[16] Rosenblatt M. Remarks on a multivariate transfor- mation[J]. Annals of Mathematical Statistics, 1952, 23(3): 470-472.
[17] Liu P L, Der K A. Multivariate distribution models with prescribed marginals and covariances[J]. Pro- babilistic Engineering Mechanics, 1986, 1(2): 105-112.
[18] Chen X, Tung Y K. Investigation of polynomial normal transform[J]. Structural Safety, 2003, 25(4): 423-445.
[19] Lebrun R, Dutfoy A. Do Rosenblatt and Nataf isoprobabilistic transformations really differ?[J]. Probabilistic Engineering Mechanics, 2009, 24(4): 577-584.
[20] Morales J M, Baringo L, Conejo A J, et al. Pro- babilistic power flow with correlated wind sources[J]. IET Generation Transmission & Distribution, 2010, 4(5): 641-651.
[21] 朱星阳, 刘文霞, 张建华, 等. 电力系统随机潮流及其安全评估应用研究综述[J]. 电工技术学报, 2013, 28(10): 257-270.
Zhu Xingyang, Liu Wenxia, Zhang Jianhua, et al. Reviews on power system stochastic load flow and its applications in safety evaluation[J]. Transactions of China Electrotechnical Society, 2013, 28(10): 257- 270.
[22] Zhao Y G, Ono T. New point estimates for pro- bability moments[J]. Journal of Engineering Mech- anics, 2000, 126(4): 433-436.
[23] 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 Elec- tric Power Systems, 2012, 36(15): 51-56.
[24] Hong H P. An efficient point estimate method for probabilistic analysis[J]. Reliability Engineering & System Safety, 1998, 59(3): 261-267.
[25] Power Systems Test Case Archive[OL]. Available: http://www.ee.washington.edu/research/pstca |
|
|
|
2016, Vol. 31 
