| For modern power systems,the load flow calculation is the basis for state analysis,optimal control,system planning,and stable operation.The target of load flow computation is to obtain the power flow distribution and the nodes voltages in a power system.In recent years,renewable energy sources including wind energy and solar energy are connected into power systems.For their inherent uncertainties,intermittences and fluctuations,the load flow problem in power system becomes more complex and it is difficult for traditional deterministic load flow method to solve this problem.Probabilistic load flow(PLF)can deal with the uncertainties caused by renewable energy and other stochastic factors in power systems.A lot of sucesses have been achieved since it was first proposed in 1974.The PLF computation methods can be grouped into Monte Carlo simulation methods(MCSM),analytical methods and point estimate methods(PEM).For the integration of wind generators,it is necessary to consider the correlation between random variables,including linear and nonlinear correlation,for probabilistic load flow computation.The traditional linear correlation coefficient cannot measure the nonlinear correlation between random variables.Therefore,a more accurate correlation modelling method should be applied.Copula function describes the correlation structure between random variables,and then the correlation between random variables can be modelled,accurately.Tranditional Copula theory becomes inflexible when dimension increases.Whereas vine Copula can flexibly construct high-dimensional correlation model and consider the correlation among random variables.In this paper,vine Copula method is applied to construct the dependence models of correlated wind speeds.Furthermore,nonparametric kernel density method is used to estimate the marginal distribution of wind speed.The kernel density estimation is not restricted by the parametric distribution of wind speed and it has a better fitting performance than parameter models.The computation efficiency of probabilistic load flow should be taken into account when modelling the correlation of random variables.Large-scale simple random sampling can provide high-precision computation results.However,it is timeconsuming and a more efficient calculation method that satisfies the accuracy requirements should be used.The main contribution of this paper is the probabilistic load flow method,which considers the correlation of multiple wind farms output.First,a D-vine Copula and improved Latin hypercube sampling(LHS)based PLF computation method is firstly proposed.This method considers the correlation among multiple wind speeds.Vine Copula is flexible to build a multivariate dependence by using bivariate Copula as building blocks.The nonparametric kernel density estimation is applied to estimate wind speed marginal distribution.Therefore,the proposed method is also suitable to other distributions besides the distribution of wind speed.Compared with simple random sampling(SRS)method,LHS method has the characteristic of higher efficiency.The accuracy and efficiency of the proposed method are verified by the corresponding numerical simulation experiments.Further,a quasi-Monte Carlo and truncated regular vine(R-vine)Copula based PLF computation method is proposed in this paper.For higher dimension dependence modelling,R-vine Copula is not restricted by the special cases such as D-vine and C-vine.In addition,this method considers the computation burden caused by building R-vine Copula.Truncation is adopted in constructing R-vine Copula to reduce the consumed time and memory size.Compared with Monte Carlo simulation method,the convergence rate of quasi-Monte Carlo method is much higher.Meanwhile,the performance of the proposed method is verified by IEEE 118-node system PLF computation.The two proposed methods are also suitable to deal with other correlations,for example,the correlation between wind powers and loads,the correlation between pthotovaoltaic powers and loads. |
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