Research On Moment Estimation Method Of TLS Model For Wind Power Forecast Error

Accurately describing the probability distribution of wind power forecast error is of great significance to ensure the safe and economic operation of the power system.A large number of studies have shown that the wind power forecast error has different degrees of peak and thick tail characteristics.The existing research results show that the TLS(T-Location-Scale)distribution has very flexible thick-tail adaptability and is one of the widely used models.The commonly used parameter estimation method for TLS distribution is the maximum likelihood method,which solves the distribution parameters by maximizing the sample joint probability value.Since the optimal solution of parameters cannot be obtained by the analytical method of the derivative equation,an optimization method is needed to complete the search of the optimal solution.However,the optimal solution search process is not only time-efficient,but also easy to fall into local extreme points because of TLS distribution is a three-parameter model,which is difficult to apply in some special power systems.Therefore,finding a simple and fast parameter estimation method has great practical significance for the application of TLS distribution in wind power forecast error modeling.In view of the above problems,the following research is carried out: Firstly,the definition,properties of TLS distribution and the regular pattern of morphological changes for parameter changes are studied.At the same time,an algorithm for maximal likelihood method is given,which lays a theoretical foundation for further research;Secondly,the relationship between the commonly statistical moments and the parameters of TLS distribution is discussed.According to these relationships,the idea of moment estimation for TLS distribution parameters is proposed for the first time.At the same time,the theory formula and implementation algorithm of moment estimation which based on sample statistical features are derived,and the correctness of the method is verified by the random sample of standard distribution.Thirdly,the time efficiency and fitting precision of TLS distribution moment estimation method are researched.On the one hand,simulated to compares the time efficiency not only of the moment estimation method and the maximum likelihood method,but also of the moment estimation method combined with the maximum likelihood method and the maximum likelihood method.On the other hand,Comparing the error between the moment estimation method,the maximum likelihood method and its corresponding real value,discussing the relative errors between the moment estimation method and the maximum likelihood method,even the change laws of relative error along with the sample size and statistical characteristics are also studied.According to these changing laws,the equivalence method of moment estimation method and maximum likelihood method is considered.Fourthly,the TLS distribution,normal distribution,cauchy distribution and laplace distribution are simulated and compared on actual wind power curves of different capacity and different time scales,verifing the applicability of the TLS distribution in the actual wind power forecast error modeling.