Research On The Applicability Of Beta Distribution For Wind Power Forecast Conditional Error

The conditional error of wind power forecast refers to the error model based on the wind power forecast value.It is an important research direction extended on the basis of unconditional error.Studying the probability distribution of conditional error can estimate the confidence interval of real power more accurately and analyze the risk value of reserve capacity more credibly,which is helpful to improve the safe and economic operation level of power system.At present,most of the literatures chose Beta distribution modeling directly according to the morphological characteristics of conditional error,but have no study about its applicability in detail.Beta distribution is a double-parameters model,and its common statistical characteristics(including mean value,variance,skewness,kurtosis)have specific correlation.However,the basic statistical characteristics of conditional errors are determined by unconditional errors.Under the influence of factors such as predictive power value,partition numbers and anomaly detection,there are complex and changeable correlation.Under the influence of many factors,whether Beta distribution has consistent and universal applicability has become a practical problem that engineers paid more attention to.In addition,it is the premise of studying the conditional error to obtain the error set by partition method.And any partition method is to expand the accurate conditional error to the interval conditional error,which will inevitably result in the deviation of probability model.It is also a key problem that how to use the partition method to minimize the deviation of probability model.According to the current research status of conditional error,the following aspects are studied in this paper:(1)The definition and properties of Beta distribution,as well as two modeling methods are studied,including maximum likelihood and moment estimation,and the robustness and accuracy of these two modeling methods are studied by using simulation data.(2)The definition of unconditional error and conditional error and the relationship between them are expressed by standard and mathematical statistics,and a division method for obtaining the data set of conditional error is given.According to different real datasets,the change rule of common statistical characteristics of conditional error under different influence factors is studied by simulation.(3)In order to solve the problem of Beta distribution applicability,we defined an index Beta interval proportion to measure the applicability of Beta distribution;through simulation,we study the consistency of this index under the influence of the number of partitions,anomaly detection and modeling methods;for different data sets,we simulate and study the universality of Beta models of different data sets.Then,this paper studies the main reasons for the differences in applicability,and gives an empirical judgment criterion.(4)In order to solve the problem of optimal partition,the paper puts forward the concept of eigenvalue function;on the basis of analyzing the influence of partition mode on eigenvalue function,an optimization model is established with the minimum total error as the goal and the partition mode as the variable;for the unknown parameters in the model,a computable equivalent model is derived and the solution algorithm is given.In the simulation,the correctness of the model and method is verified by the simulation data,and the practicability of the model and method is verified by the actual data.