A Probabilistic Power Flow Algorithm Based on Edgeworth Series and Multiple Linearization

doi:10.11985/2018.02.006

Abstract

Abstract:

On the problem of large-scale probabilistic power flow problems with random variables, if the Gram-Charlier series expansion was used to approximate the cumulative distribution of random variables, the amount of calculation was large. In order to reduce the computational complexity of higher order expansion by using the recurrence of Hermite orthogonal matrix of edgeworth, a probabilistic power flow model considering the randomness of wind power output and load fluctuation is established. According to the method of high-order series transform is eliminated the influence of calculation accuracy, the method of multiple linear systems by uniform division of the total active power is used to reduce the truncation error caused by the large variation range of the input random variables due to linearization of the power flow equation. Simulation results of IEEE 39 system verify the effectiveness of the proposed method.

Key words: Probabilistic power flow, multiple linearization, recursive, Edgeworth series

CLC Number:

TM711

Jie Liang. A Probabilistic Power Flow Algorithm Based on Edgeworth Series and Multiple Linearization[J]. Journal of Electrical Engineering, 2018, 13(2): 36-40.

Figures/Tables 4

References 12

[1]	文旭, 颜伟, 郭琳 , 等. 计及风电和负荷不确定性的日调度计划节能效益概率评估方法[J]. 电网技术, 2014,38(4):959-966.
	Wen Xu, Yan Wei, Guo Lin , et al. A probabilistic assessment method for energy saving benefit of daily scheduling plan considering wind power and load uncertainty[J]. Power Grid Technology, 2014,38(4):959-966.
[2]	刘建坤, 周前 , 等. 基于半不变量和Gram-Charlier级数展开法的随机潮流算法[J]. 电力工程技术, 2017,36(1):34-38.
	Liu Jiankun, Zhou Qian , et al. Random flow algorithm based on semi invariants and Gram-Charlier series expansion method[J]. Power Engineering Technology, 2017,36(1):34-38.
[3]	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(19):110-115.
	Yang Huan, Zou Bin . Monte Carlo simulation method for probabilistic optimal power flow problem with correlation random variables[J].Power System Protection and Control, 2012(19):110-115.
[4]	刘怡芳, 张步涵, 李俊芳 , 等. 考虑电网静态安全风险的随机潮流计算[J]. 中国电机工程学报, 2011,31(1):59-64.
	Liu Yifang, Zhang Buhan, Li Junfang , et al. Random flow calculation considering static security risk of power grid[J]. Journal of China Electrical Engineering, 2011,31(1):59-64.
[5]	靳冰洁 . 基于信息熵的电力系统潮流均衡度分析及应用[D]. 武汉:华中科技大学, 2015.
[6]	姚玉平 . 概率潮流在地区电网中的应用[D]. 吉林:东北电力大学, 2007.
[7]	张文婷, 范立新 . 基于直流概率潮流的风电穿透功率极限计算[J]. 电力工程技术, 2014,33(4):1-4.
	Zhang Wenting, Fan Lixin . Calculation of wind power penetration limit based on direct current probability flow[J]. Power Engineering Technology, 2014,33(4):1-4.
[8]	杜春燕, 周溪召 . 基于Edgeworth级数的行程时间可靠性的计算与实证[J]. 公路交通科技, 2015,32(7):127-133.
	Du Chunyan, Ma Hongwei, Zhou Xizhao . Calculation and empirical analysis of travel time reliability based on Edgeworth series[J]. Journal of Highway and Transportation Research and Development, 2015,31(7):127-133.
[9]	Magnus Perninge . Stochastic optimal power ﬂow by multi-variate Edgeworth expansions[J]. Electric Power Systems Research, 2014,109(2):90-100.
[10]	大规模风力发电机组间歇性动态随机过程研究[D]. 规模风力发电机组间歇性动态随机过程研究[D]. 北京:华北电力大学, 2016.
[11]	隋冰彦, 侯恺, 贾宏杰 , 等. 基于最大熵原理的含风电和电动汽车电力系统概率潮流[J]. 电网技术, 2016,40(12):3696-3705.
	Sui Yanyan, Hou Kai, Jia Hongjie , et al. The probabilistic power flow of wind power and electric vehicle power system based on the maximum entropy principle[J]. Power Grid Technology, 2016,40(12):3696-3705.
[12]	郭效军, 蔡德福 . 不同级数展开的半不变量法概率潮流计算比较分析[J]. 电力自动化设备, 2013,33(12):85-90.
	Guo Xiaojun, Cai Defu . Comparison and analysis of the probabilistic power flow calculation of the semi invariants method of different series expansion[J]. Power Automation Equipment, 2013,33(12):85-90.

	本文方法	Gram-Charlier级数	MCS
ARMS(%)	1.34	1.3	/
计算耗时/s	14.04	17.87	64.54

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