Probabilistic optimal power flow considering dependences of wind speed among wind farms by pair-copula method

Abstract This paper aims at exploring the impacts of high dimensional dependences of wind speed among wind farms on probabilistic optimal power flow (POPF). Kernel density estimate method is employed to estimate probability distribution of wind speed. A joint probability distribution function of wind speed among wind farms is obtained by pair-copula method, which can use variational bivariate copula functions to consider dependences of wind speed between two arbitrary wind farms and overcome the constraints of high dimensional copula function, not taking the mutual dependences of wind speed into account. Finally, the POPF calculation is operated by monte carlo simulation method under four cases to consider high dimensional dependences of wind speed among wind farms. Simulation results show that the impacts of dependences of wind speed on the POPF results exist and that cannot be ignored. Based on the pair-copula method to construct high dimensional dependences, the average relative errors of POPF results is smaller than that by other methods. Besides, the distribution curve of output variables is also close to that obtained by using actual wind speed data. Under the case of high requirements for calculation accuracy, it is a feasible scheme for using pair-copula method to construct dependences of wind speed to calculate POPF.

[1]  David McMillan,et al.  Power Engineering Letter A Copula Model of Wind Turbine Performance , 2011 .

[2]  Dajun Du,et al.  Two-Point Estimate Method for Probabilistic Optimal Power Flow Computation Including Wind Farms with Correlated Parameters , 2012 .

[3]  B. Stephen,et al.  Wind Turbine Condition Assessment Through Power Curve Copula Modeling , 2012, IEEE Transactions on Sustainable Energy.

[4]  Xue Li,et al.  Comparison of Levenberg-Marquardt Method and Path Following Interior Point Method for the Solution of Optimal Power Flow Problem , 2012 .

[5]  Antonio J. Conejo,et al.  Probabilistic power flow with correlated wind sources , 2010 .

[6]  Bin Zou,et al.  Probabilistic load flow computation using univariate dimension reduction method , 2014 .

[7]  A. Frigessi,et al.  Pair-copula constructions of multiple dependence , 2009 .

[8]  J. Usaola.  Probabilistic load flow in systems with wind generation , 2009 .

[9]  Claudia Czado,et al.  Pair-Copula Constructions of Multivariate Copulas , 2010 .

[10]  Zheng Yan,et al.  Probabilistic load flow evaluation considering correlated input random variables , 2016 .

[11]  Bin Zou,et al.  The Point Estimate Method Using Third-Order Polynomial Normal Transformation Technique to Solve Probabilistic Power Flow with Correlated Wind Source and Load , 2012, 2012 Asia-Pacific Power and Energy Engineering Conference.

[12]  Xiaofu Xiong,et al.  Estimating wind speed probability distribution using kernel density method , 2011 .

[13]  B Stephen,et al.  A Copula Model of Wind Turbine Performance , 2011, IEEE Transactions on Power Systems.

[14]  Xue Li,et al.  Probabilistic optimal power flow for power systems considering wind uncertainty and load correlation , 2015, Neurocomputing.

[15]  Zheng Yan,et al.  Estimating wind speed probability distribution by diffusion-based kernel density method , 2015 .

[16]  Yang Zi-qiang.  You Need Monte Carlo Method——Techniques for Enhancing Applications , 2007 .

[17]  Chen Qing.  A Study on Pair-copula Constructions of Multiple Dependence , 2013 .

[18]  Qing Xiao,et al.  Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation , 2014, IEEE Transactions on Power Systems.

[19]  Gregor N. F. Weiß,et al.  Mixture Pair-Copula-Constructions , 2015 .

[20]  Xue Li,et al.  Probabilistic load flow computation in power system including wind farms with correlated parameters , 2013 .

[21]  Johan Segers,et al.  Nonparametric estimation of pair-copula constructions with the empirical pair-copula , 2012, Comput. Stat. Data Anal..

[22]  M. Mohammadi,et al.  Probabilistic Load Flow by Using Nonparametric Density Estimators , 2013, IEEE Transactions on Power Systems.

[23]  G. Papaefthymiou,et al.  Stochastic Modeling of Power Demand Due to EVs Using Copula , 2012, IEEE Transactions on Power Systems.

[24]  C. Delgado,et al.  Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources , 2014 .

[25]  G. Papaefthymiou,et al.  Using Copulas for Modeling Stochastic Dependence in Power System Uncertainty Analysis , 2009 .

[26]  Cai De-f,et al.  Probabilistic load flow considering correlation between input random variables based on Copula theory , 2013 .

[27]  Longbing Cao,et al.  Model the complex dependence structures of financial variables by using canonical vine , 2012, CIKM.

[28]  Zhe Chen,et al.  Aggregated models and transient performances of a mixed wind farm with different wind turbine generator systems , 2012 .

[29]  Julio Usaola,et al.  Probabilistic load flow with correlated wind power injections , 2010 .