Probability Density Prediction Method Of Renewable Energy Based On B-spline Quantile Regression

At present,the problem of environmental pollution and energy shortage has been widely concerned in the world.Compared with the highly polluted and non-renewable fossil energy,the development and utilization of clean energy is the general trend of the times.Hydroelectric power,photovoltaic power and wind power are the most common renewable power used in the process of power generation.The application of renewable energy needs accurate prediction to reduce the uncertainty of power generation process.Therefore,accurate runoff prediction,reliable photovoltaic power prediction and wind power prediction are very important.In order to better measure the uncertainty of renewable energy prediction,this paper combined B-spline method and quantile regression method to construct a B-spline quantile regression(BSQR)probability density prediction method.The method includes three steps.Firstly,B-spline function is used to process the training a nd test data of the selected runoff,photovoltaic and wind power;Secondly,the training data after spline processing is input into quantile regression model to calculate the parameters of BSQR model,then the BSQR model is combined with the kernel density estimation method based on Epanechnikov kernel function and Silverman's rule of thumb to construct a BSQR probability density prediction method;Finally,the runoff,photovoltaic and wind power data after spline processing are inputted into the BSQR probability density prediction model to calculate the future runoff,photovoltaic and wind power.This method can obtain the conditional probability density of runoff,photovoltaic and wind power,so as to quantitatively analyze the uncertainty of prediction,thus obtaining more useful information than point prediction and interval prediction.In order to verify the validity of the model,the method is applied to the runoff data of Shigu station of Jinsha River,the photoelectric data of Germany and the photoelectric data of Canada.The results show that the point prediction and probability prediction results of this method are better than the existing quantile regression method(QR),quantile regression neural network method(QRNN)method and nonlinear quantile regression(NLQR),which can well measure the uncertainty of prediction.Therefore,the BSQR model provides an advanced probabilistic prediction method for renewable energy predictions such as runoff,photovoltaic and wind power.In addition,the directly used BSQR probability density prediction method can not determine which of the mode and median prediction results is better,and the evaluation indexes prediction interval coverage probability(PICP)and prediction interval normalized average width(PINAW)in interval prediction also can not be fully optimal.In order to solve those above problems,this paper proposes a combined model based on variable order BSQR and grid search(BSQR-GS).This method uses the mode-optimal and coverage width-based criterion(MCWC)as the objective function,then the best parameters df and p of MCWC can be calculated by grid searching.In this paper,the BSQR-GS method is applied to the wind power data of four seasons in Canada in 2018,which proves that the method can achieve the minimum bandwidth on the basis of satisfying the mode point prediction results better than the median prediction results,and obtain the equilibrium solution of PINAW and PICP,which weigh the prediction results of mode points.