基于Copula理论的相关随机变量模拟方法  

A Simulation Method of Correlated Random Variables Based on Copula

作　　者：王俊[1] 蔡兴国[1] 季峰[1] 

机构地区：[1]哈尔滨工业大学电气工程及自动化学院,黑龙江省哈尔滨市150001

出　　处：《中国电机工程学报》2013年第22期75-82,13,共8页Proceedings of the CSEE

基　　金：高等学校博士学科点专项科研基金资助项目(20050213006);黑龙江省科技攻关项目(GD07A304)~~

摘　　要：电力系统中诸多随机变量彼此间存在相关性,忽视相关性将可能造成计算误差,甚至对电力系统安全、经济运行造成直接影响。然而,现有的理论计算方法存在对随机变量描述不够准确、难以处理其相关性以及运算耗时等问题。基于此,提出一种基于Copula理论的相关随机变量模拟方法。首先基于秩相关系数概念、蒙特卡洛(Monte Carlo,MC)模拟法以及Copula理论建立考虑随机变量相关性的样本抽样方法,该方法既能处理正态分布随机变量间相关性又能处理非正态随机变量间的相关性;然后,将中值超拉丁方采样技术融入到提出的方法中,提高运算效率,改善方法的精确性和稳定性;最后,以可用输电能力评估为例,利用风险概念通过改进的IEEE 30节点测试系统,验证所提方法的有效性。In power system,many random variables are correlated with each other,so ignoring correlation may cause calculation errors,even have a direct impact on safe and economic operation of the power system.However,existing method of theoretical calculation is not accurate enough to describe random variables,difficult to deal with its correlation and consuming computing time.Thus,random variables simulation based on Copula theory was put forward.Based on the concept of rank correlation coefficient,Monte Carlo（MC） simulation method,and Copula theory,it built sample sampling method considering random variables correlation.This method can deal with the correlation between random variables of normal and non-normal distribution.Then,the median Latin hypercube sampling techniques were put into the method proposed which raised calculation efficiency,and improved accuracy and robustness of the method.Finally,we can take the evaluation of available transfer capability（ATC） as an example,and used risk concept to verify the effectiveness of the method by improved IEEE 30 test system.

关 键 词：相关性 蒙特卡洛 COPULA 超拉丁方采样 可用输电能力 

分 类 号：TM74[电气工程—电力系统及自动化]