Probabilistic load flow calculation of distribution network with wind power and electric vehicles based on space transform#br#

doi:10.12028/j.issn.2095-4239.2016.0075

Abstract

Abstract: The use of electric vehicles and distributed generation increases the complexity of modern distribution network. This is made more serious with more correlated input of random variables. In this study, we use the Nataf transformation, also called the third order polynomial normal transformations, to transform random variables from a correlated non-normal random vector space (CNNRVS) to a correlated standard normal random vector space (CSNRVS), and use the elementary transformation, also called the orthogonal transformation, to transform random variables from CSNRVS to independent standard normal random vector space (ISNRVS). These lead to the random independent input variables to execute the probabilistic load flow calculations using a 2m+1 point estimate method. Examples was made to simulate an IEEE-33 distribution network with wind power and electric vehicles. Comparison was made between four cases for the correlation among random input variables. The results showed that the Nataf transformation combined with elementary transformation gave the best accuracy.

Key words: electric vehicles, wind farm, distribution network, correlation, point estimate method, probabilistic load flow calculation

ZHU Zhangtao1, CHEN Haojie2, DAI Junjie1, LI Weibin1, LI Xue2 . Probabilistic load flow calculation of distribution network with wind power and electric vehicles based on space transform#br#[J]. Energy Storage Science and Technology, 2017, 6(1): 127-134.

References

[1] BORKOWSKA B. Probabilistic load flow[J]. IEEE Transactions on Power Apparatus and Systems, 1974, 93(3): 752-759.

[2] ROSIC D, ZARKOVIC M, DOBRIC G. Fuzzy-based monte carlo simulation for harmonic load flow in distribution networks[J]. IET Generation Transmission & Distribution, 2015, 9(3): 267-275.

[3] HONG H P. An efficient point estimate method for probabilistic analysis[J]. Reliability Engineering and System Safety, 1998, 59(3): 261-267.

[4] CHEN Y, WEN J Y, CHENG S J. Probabilistic load flow method based on Nataf transformation and latin hypercube sampling[J]. IEEE Transactions on Sustainable Energy, 2013, 4(2): 294-301.

[5] MORALES J M, BARINGO L, CONEJO A J, et al. Probabilistic power flow with correlated wind sources[J]. Institution of Engineering and Technology, 2010, 4(5): 641-651.

[6] 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 H, ZOU B. 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.

[7] 田立亭, 史双龙, 贾卓. 电动汽车充电功率需求的统计学建模方法[J]. 电网技术, 2010, 34(11): 126-130.

TIAN L T, SHI S L, JIA Z. A statistical model for charging power demand of electric vehicles[J]. Power System Technology, 2010, 34(11): 126-130.

[8] QIAN K E, ZHOU C K, ALLAN M, et al. Modelling of load demand due to EV battery charging in distribution systems[J]. IEEE Transaction on Power Systems, 2011, 26(2): 802-810.

[9] FRERIS L L. Wind energy conversion system[M]. Englewood Cliffs, NJ: Prentice-Hall, 1990.

[10] JIANG W, YAN Z, FENG D H. A review on reliability assessment for wind power[J]. Renewable and Suatainable Energy Reviews, 2009, 13(9): 2485-2494.

[11] 王海超, 鲁宗相, 周双喜. 风力发电容量可信度研究[J]. 中国电机工程学报, 2005, 25(10): 103-106.

WANG H C, LU Z X, ZHOU S X. Research on the capacity credit of wind energy resources[J]. Proceedings of the CSEE, 2005, 25(10): 103-106.

[12] HOHEBBICHLER M, RACKWITZ R. Non-normal dependent vectors in structural safety[J]. Journal of the Engineering Mechanics Dvivision, 1981, 107(6): 12-14.

[13] Nataf A. Détermination des distributions de probabilités dont les marges sont données[J]. Comptes Rendus de l’Académie des Sciences, 1962, 225: 3-42.

[14] XIAO Q. Evaluating correlation coefficient for Nataf transformation[J]. Probabilistic Engineering Mechanics, 2014, 37(4): 1-6.

[15] FLEISHMAN A. A method for simulating non-normal distributions[J]. Psychometrika, 1978, 43(4): 521-532.

[16] CAI D F, SHI D Y, CHEN J F. Probabilistic load flow computation with polynomial normal transformation and latin hypercube sampling[J]. IET Generation Transmission and Distribution, 2013, 7(5): 474-482.

[17] 张明. 结构可靠度分析——方法与程序[M]. 北京: 科学出版社，2009.

ZHANG M. Structural reliability analysis——Methods and procedures [M]. Beijing: Science Press, 2009.

[18] KNAPP A W. Advanced algebra[M]. Boston: Birkhauser, 2007.

[19] BAUER H. Probability theory[M]. Berlin: Gerike Gmbh, 1996.

[20] BARAN M E, WU F F. Network reconfiguration in distribution systems for loss reduction and load balancing[J]. IEEE transactions on Power Delivery, 1989, 4(2): 1402-1407.

[21] LI X, ZHANG X, WU L, et al. Transmission line overload risk assessment for power systems with wind and load-power generation correlation[J]. IEEE Transactions on Smart Grid, 2015, 6(3): 1233-1242.

[22] MORALES J M, PEREZ-RUIZ J. Point estimate schemes to solve the probabilistic power flow[J]. IEEE Transactions on Power Systems, 2007, 22(4): 1594-1601.