The purpose of this paper is to investigate the shortterm wind power forecasting. STWPF is a typically complex issue, because it is affected by many factors such as wind speed, wind direction, and humidity. This paper attempts to provide a reference strategy for STWPF and to solve the problems in existence. The two main contributions of this paper are as follows. (1) In data preprocessing, each encountered problem of employed real data such as irrelevant, outliers, missing value, and noisy data has been taken into account, the corresponding reasonable processing has been given, and the input variable selection and order estimation are investigated by Partial least squares technique. (2) STWPF is investigated by multiscale support vector regression (SVR) technique, and the parameters associated with SVR are optimized based on Gridsearch method. In order to investigate the performance of proposed strategy, forecasting results comparison between two different forecasting models, multiscale SVR and multilayer perceptron neural network applied for power forecasts, are presented. In addition, the error evaluation demonstrates that the multiscale SVR is a robust, precise, and effective approach.
Compared to the traditional thermal power [
Shortterm wind distribution is essentially a random one although it can be described by a continuous probability distribution named Weibull distribution in a long term. It is hard to obtain the intrinsic regulation of wind speed in a shortterm; thus, the soft computing can play a significant role in shortterm wind power forecasting. SVR technique has already been employed for the short energy forecasting in the existing literatures; however, many of them assume that the employed data have good quality. In fact, it is impossible to acquire the data without noise because there are many reasons that are sometimes beyond the control of human operators [
Algorithm flow.
Figure
The quality of data samples plays an important role in wind power forecasting because it has a direct impact on forecasting performance. The data quality is the fundamental issue for the data analysis; in particular, data do not exist without noise in the real application. The main objective of data analysis is to discover knowledge which will be used to solve real problem and make decisions [
In this paper, the shortterm wind forecasting issue is formulated as a regression problem. The time series is denoted by
Shortterm wind power forecast has attracted more and more attention in recent decades. Alessandrini et al. [
Data analysis is the fundamental approach for the knowledge investigation [
In the data preprocessing, the issues that must be considered are about the irrelevant, missing value, and noisy data. The data with poor quality will result from the poor performance of final employed approaches. In this case, the data are not complete because there are missing values which cannot be eliminated because of the requirement for time continuity as well as they may contain useful information [
Median absolute deviation from the median
Unlike the MAD filter, the wavelet decomposition and denoising analysis for data is localized in both time domain and frequency domain, and it can be used to decompose the original data into highfrequency component (HFC) and lowfrequency component (LFC). Typically, the HFC denotes the detailed information such as mutant value, while the LFC usually represents the generalized or stationary characteristic related to employed data. The more detailed discussion of wavelet decomposition and denoising can be founded in [
Comparing to the continuous wavelet transform, the discrete wavelet transform (DWT) is more commonly used in real application and defined by
Swedish statistician named Herman Wold first introduces Partial least squares (PLS) technique which is used to find the fundamental relations between two variables (
Data order reflects the intrinsic relationship between past data and current data, which is derived through the autocorrelation function (ACF) for one data sequence and crosscorrelation function (CCF) for two different data sequences. Autocorrelation (is also sometimes called “lagged correlation” or “serial correlation”) refers to the correlation of a time series with its own past and future values, which relate to the correlation between members of a series of numbers arranged in time. CCF is a measure of similarity of two given date as a function of a time lag, and it is commonly used for the replacement of a long data by a shorter and suitable length. In the discrete domain, ACF and CCF for two real time series
In MATLAB, ACF and CCF are computed with the function “xcorr” which are defined by (
SVM for regression was proposed in 1996 by Drucker et al. in [
The basic task of regression is to establish the nonlinear function
Moreover, the
Consider
In this section, the numerical simulation is constructed for each part of Section
In this section, the data interpolation, MAD filter, wavelet decomposition, and denoising technique which correspond to the theory analysis in Sections
State trajectories refer to the 1st variable and 2nd variable.
State trajectories refer to the 3rd variable and 4th variable.
State trajectories refer to the 11th variable.
Figures
This section provides the simulation results with respect to the theory analysis of Section
PLS coefficients refer to eleven variables.
Variables  11  1  2  3  4  5 

11  1.0000  −0.7644  −0.7185  −0.6779  −0.7602  −0.7214 
6  −0.7595  0.9848  0.5741  0.8837  0.9815  0.5689 
7  −0.7191  0.5944  0.9437  0.6413  0.5906  0.9228 
8  −0.9648  0.8005  0.7235  0.7718  0.7949  0.7259 
9  −0.9732  0.6883  0.6697  0.5516  0.6854  0.6705 
10  −0.9998  0.7621  0.7174  0.6748  0.7579  0.7205 
Lower and upper bound related to Table
Variables  11  1  2  3  4  5  

11  UB  1.0000  −0.7434  −0.6942  −0.6508  −0.7389  −0.6973 
LB  1.0000  −0.7838  −0.7412  −0.7033  −0.7799  −0.7439  


6  UB  −0.7382  0.9862  0.6058  0.8939  0.9832  0.6009 
LB  −0.7793  0.9832  0.5406  0.8726  0.9796  0.5352  


7  UB  −0.6948  0.6249  0.9488  0.6690  0.6213  0.9297 
LB  −0.7417  0.5621  0.9381  0.6118  0.5580  0.9152  


8  UB  −0.9613  0.8173  0.7458  0.7907  0.8121  0.7481 
LB  −0.9680  0.7824  0.6995  0.7514  0.7763  0.7021  


9  UB  −0.9705  0.7130  0.6956  0.5845  0.7103  0.6964 
LB  −0.9757  0.6619  0.6420  0.5169  0.6588  0.6429  


10  UB  −0.9998  0.7818  0.7402  0.7004  0.7779  0.7430 
LB  −0.9998  0.7410  0.6930  0.6475  0.7365  0.6963 
Based on the discussion of Section
Based on the discussion of Section
ACF discrete trajectory.
CCF discrete trajectory.
From Figures
The following simulation is based on [
Simulation results refer to multiscale SVR.
Item  BCVM  Bc  Bg  Foin  RM  RS  

RBF(3)  O  0.00121642  1024  0.00195313  3465  0.00383891  0.943034 
M  0.00118972  64  0.015625  1756  0.00194981  0.972598  
W  0.00217458  0.5  1  1628  0.0211323  0.897533  


PF(3)  O  0.00121642  1024  0.00195313  4365  0.00383891  0.943034 
M  0.00118972  64  0.015625  2756  0.00194981  0.972598  
W  0.00217458  0.5  1  1628  0.0211323  0.897533  


RBF(6)  O  0.00117004  1024  0.00390625  4562  0.00381612  0.94281 
M  0.0010876  128  0.00390625  2810  0.00189855  0.972905  
W  0.0021321  0.5  1  1534  0.0219367  0.895725  


PF(6)  O  0.00117004  1024  0.00390625  4562  0.00381612  0.94281 
M  0.0010876  128  0.00390625  2810  0.00189855  0.972905  
W  0.0021321  0.5  1  1534  0.0219367  0.895725  


RBF(10)  O  0.0011804  512  0.00195313  5366  0.00381804  0.94289 
M  0.00107203  128  0.00390625  2441  0.00191227  0.972918  
W  0.00217458  0.5  1  1534  0.0219367  0.895725  


PF(10)  O  0.0011804  512  0.00195313  5366  0.00381804  0.94289 
M  0.00107203  128  0.00390625  2441  0.00191227  0.972918  
W  0.00214353  0.5  1  1534  0.0219367  0.895725 
O: original data; M: MAD filter; W: wavelet filter; RBF(3): number of crossvalidation for testing set is 3 by RBF, similar to RBF(6) and RBF(10); PF(3): number of crossvalidation for testing set is 3 by PF, similar to PF(6) and PF(10); BCVM: best crossvalidation mean squared error; Bc: best c; Bg: best g; Foin: finished optimization iteration number; RM: regression mean squared error; RS: regression squared correlation coefficient.
RMSE, MAE, and RMAE refer to SVR and MLP.
Item  RMSE  MAE  RMAE  Hn  Et  

RBF(3)  O  1.6044  1.0931  0.1094  NA  132.122945 
M  1.0887  0.6336  0.0638  NA  110.138815  
W  3.3950  2.3570  0.2375  NA  113.548014  


PF(3)  O  1.6044  1.0931  0.1094  NA  137.698291 
M  1.0887  0.6336  0.0638  NA  112.438881  
W  3.3950  2.3570  0.2375  NA  113.008574  


RBF(6)  O  1.5997  1.0888  0.1090  NA  374.338732 
M  1.0743  0.5767  0.0581  NA  309.984871  
W  3.4590  2.4161  0.2435  NA  288.569125  


PF(6)  O  1.5997  1.0888  0.1090  NA  346.989140 
M  1.0743  0.5767  0.0581  NA  280.287914  
W  3.4590  2.4161  0.2435  NA  284.077991  


RBF(10)  O  1.6001  1.0892  0.1090  NA  624.630533 
M  1.0782  0.5872  0.0591  NA  501.316555  
W  3.4590  2.4161  0.2435  NA  368.402477  


PF(10)  O  1.6001  1.0892  0.1090  NA  623.420666 
M  1.0782  0.5872  0.0591  NA  512.878352  
W  3.4590  2.4161  0.2435  NA  501.985355  


MLP neural network  11.6547  9.6265  0.9631  20  97.536770 
O: original data; M: MAD filter; W: wavelet filter; RBF(3): number of crossvalidation for testing set is 3 by RBF, similar to RBF(6) and RBF(10); PF(3): number of crossvalidation for testing set is 3 by PF, similar to PF(6) and PF(10); Hn: number of hidden layer; Et: elapsed time in seconds; RMSE: regression mean squared error for testing sample; MAE: MAE for testing sample; RMAE: RMAE for testing sample; NA: not available.
2D and 3D parameter selection results. (Gridsearch method and contours method, RBF).
Final forecasting results via RBF.
2D and 3D parameter selection results. (Gridsearch method and contours method, PF).
Final forecasting results via PF.
In this section, the error with respect to the forecasting results is given to evaluate the performance of multiscale SVR and MLP network of Section
Based on Tables
In this paper, the multiscale SVR technique is applied for the shortterm wind power forecasting. Firstly, we introduce a brief illustration for the main processing step and its corresponding theory analysis. Secondly, the data interpolation technique is used to fill the missing value of employed data. Thirdly, median absolute deviation filter and wavelet decomposition and denoising technique are applied to eliminate the irrelevant, noisy, and outlier value. Fourthly, Partial least squares technique, autocorrelation function, and crosscorrelation function are, respectively, employed to the input variable selection and order estimation. Fifthly, the multiscale SVR in combination with Gridsearch technique is utilized to forecast the shortterm wind power. Finally, the performance evaluation and error analysis are applied to evaluate the performance of multiscale SVR. Comparing to the multilayer perceptron (MLP) neural network, the performance demonstrates that SVR technique is a fast and robust time series forecasting approach. We believe that the proposed strategy has reference value for shortterm wind power forecasting and other energy consumption on the demand aspect.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors would like to thank the Professor Hongjie Jia and editor Dean who gave valuable comments by means of considerable suggestion and comments which improved highly the quality of this paper; the authors gratefully acknowledge Professor Xueliang Huang from the School of Electrical Engineering, Southeast University. This paper is partly supported by the National High Technology Research and Development Program (863 Program) (2011AA05A107).