Short Term Wind Power Prediction Based on Improved Kriging Interpolation, Empirical Mode Decomposition, and ClosedLoop Forecasting Engine
Abstract
:1. Introduction
 (1)
 A new version of KIM, named Improved KIM (IKIM), is presented. The proposed IKIM includes the von Karman covariance model whose settings are optimized based on error variance minimization by an evolutionary algorithm.
 (2)
 An improved version of EMD is introduced. Cubic spline fitting of conventional EMD is replaced by IKIM in the proposed EMD. It is shown that the proposed EMD alleviates the problems of conventional EMD.
 (3)
 A new closedloop forecasting engine is proposed for wind power prediction. This forecasting engine is based on NN trained by Levenberg–Marquardt learning algorithm.
 (4)
 A new wind power prediction approach is presented, which is composed of the proposed EMD, an informationtheoretic feature selection method, and the proposed forecasting engine.
2. Empirical Mode Decomposition (EMD)
EMD Algorithm: 

 Set x1(t) = x(t).
 Find the maxima of the signal x1(t) and obtain the upper envelope ue(t) using the proposed IKIM.
 Find the minima of the signal x1(t) and obtain the lower envelope le(t) using the proposed IKIM.
 Find the local mean m(t) = [ue(t) + le(t)]/2.
 Set x1(t) = x1(t) − m(t) and determine if x1(t) is an IMF or not by checking the properties of IMF. Repeat steps 2 to 5 until x1(t) becomes an IMF. Store the obtained IMF.
 Set x(t) = x(t) − x1(t).
 Repeat steps 1 to 6 until all IMFs and residual of signal x(t) are obtained.
3. Proposed Wind Power Prediction Approach
4. Numerical Results
4.1. Sotavento Wind Farm in Spain
4.2. Alberta Test Case
4.3. Blue Canyon Wind Farm
5. Discussion
6. Conclusions
Author Contributions
Conflicts of Interest
Abbreviations
KIM  Kriging Interpolation Method 
EMD  Empirical Mode Decomposition 
IKIM  Improved KIM 
CS  Cubic Spline 
NN  Neural Network 
HIFM  Hybrid Iterative Forecast Method 
ARMA  AutoRegressive Moving Average 
RNN  Ridgelet Neural Network 
DE  Differential Evolution 
EPSO  Enhanced Particle Swarm Optimization 
RBF  Radial Basis Function 
LM  LevenbergMarquardt 
BFGS  Broyden, Fletcher, Goldfarb, Shannon 
BR  Bayesian Regularization 
FT  Fourier Transform 
STFT  ShortTime FT 
WT  Wavelet Transform 
IMF  Intrinsic Mode Function 
NWP  Numerical Weather Prediction 
MRMRMS  Maximum Relevancy, Minimum Redundancy and Maximum Synergy 
MLP  MultiLayer Perceptron 
RMSE  Root Mean Squared Error 
BPNN  Back Propagation NN 
RBFNN  Radial Basis Function NN 
ANFIS  Adaptive NeuroFuzzy Inference System 
NNPSO  NN based Particle Swarm Optimization 
MIIG  Mutual InformationInteraction Gain 
SSO  Shark Smell Optimization 
CSSO  Chaotic SSO 
MAPE  Mean Absolute Percentage Error 
NMAE  Normalized Mean Absolute Error 
NRMSE  Normalized RMSE 
WNN  Wavelet Neural Network 
MSE  Mean Squared Error 
MCC  Maximum Correntropy Criterion 
CA  Correlation Analysis 
BCD  Bayesian Clustering by Dynamics 
SVR  Support Vector Regression 
MHNN  Modified Hybrid Neural Network 
Indexes  
i, j  Index of neighboring points in KIM 
v  Index of order 
t  Index of time 
Superscripts  
T  Transpose sign 
Variables  
$\widehat{x}(t)$  KIM estimation of time series x(t) 
t_{i}  Neighboring point i of time t 
w_{i}  Weight of neighboring point i in KIM 
M  Number of neighboring points in KIM 
e(.)  Error function of KIM 
$Var(.)$  Variance function 
Cov(.,.)  Covariance function 
λ  Lagrange multiplier 
d_{ij}  Euclidean distance between t_{i} and t_{j} 
C(.)  Covariogram function 
Γ(.)  Gamma function 
${K}_{v}(.)$  Modified Bessel function of the second type of order v 
r  Lag in the anisotropic von Karman function 
a  Correlation length in the anisotropic von Karman function 
σ^{2}  Variance in the anisotropic von Karman function 
X_{ACT}_{(t)}  Actual values of the time series 
X_{FOR}_{(t)}  Forecast values of the time series 
N  Number of hours in the forecast horizon 
${\overline{X}}_{ACT(t)}$  Average of X_{ACT}_{(t)} over the forecast horizon 
X_{N}  Aggregated nameplate capacity of the wind farms 
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Test Week  Correlation Analysis + HIFM [8]  MIMR Feature Selection + MLP [8]  MIMR Feature Selection + HIFM [8]  EMD + Cubic Spline  KIM + Gaussian Model  KIM + Exponential Model  KIM + Linear Model  KIM + Spherical Model  Proposed 

Feb.  7.56  7.68  5.71  5.08  5.37  2.26  2  1.56  0.98 
May  5.82  5.96  4.26  4.14  4.07  3.37  3.07  2.4  1.32 
Aug.  6.93  7.01  5.92  4.37  4.08  2.03  1.9  1.28  0.87 
Nov.  5.97  6.04  4.55  4.41  4.83  3.35  3.11  2.08  1.34 
Ave.  6.57  6.68  5.11  4.5  4.59  2.75  2.52  1.83  1.13 
Test Day  Error Criterion  Persistence [25]  BPNN [25]  RBFNN [25]  ANFIS [25]  NNPSO [25]  WT + BPNN [25]  WT + RBFNN [25]  WT + ANFIS [25]  WT + NNPSO [25]  MIIG + NN + CSSO [42]  Proposed 

3 December  MAPE  10.03  13.62  10.41  14.81  9.54  11.26  8.26  11.08  7.28  7.12  4.18 
NMAE  4.18  4.32  4.61  4.75  4.09  4.29  4.19  4.55  3.87  4.02  3.23  
NRMSE  5.41  5.73  5.84  6.13  5.38  5.44  5.43  5.91  5.07  4.86  3.32  
4 May  MAPE  11.31  12.42  11.07  13.51  11.41  11.73  9.22  11.76  8.73  8.50  5.43 
NMAE  4.58  4.88  4.61  4.71  4.51  4.67  4.18  4.39  4.11  4.12  3.12  
NRMSE  6.11  6.38  5.89  6.43  6.20  6.09  5.41  6.22  5.83  5.92  4.13  
7 July  MAPE  21.58  17.44  16.72  19.30  12.26  14.11  12.39  16.38  11.27  10.12  7.32 
NMAE  8.48  7.46  7.21  7.75  5.94  6.97  7.04  7.18  5.29  5.10  4.14  
NRMSE  11.25  9.23  8.88  10.16  7.33  8.96  8.36  9.63  7.02  6.76  5.44  
15 October  MAPE  14.79  13.93  12.73  12.04  12.82  11.67  14.86  11.08  5.48  5.63  4.07 
NMAE  7.48  7.26  7.31  7.76  6.85  7.14  7.08  7.32  6.17  6.08  5.21  
NRMSE  9.19  8.79  8.99  9.38  7.43  8.22  8.60  8.93  7.21  6.43  5.73  
Average  MAPE  14.43  14.35  12.73  14.91  11.51  12.19  11.18  12.57  8.19  7.84  5.25 
NMAE  6.18  5.98  5.93  6.24  5.35  5.77  5.62  5.86  4.86  4.83  3.92  
NRMSE  7.99  7.53  7.4  8.02  6.58  7.18  6.95  7.67  6.28  5.99  4.65 
Methods  Error Criterion  March Test Week  June Test Week  September Test Week  December Test Week  Ave. 

Persistence [43]  NRMSE  13.71  15.14  18.44  12.49  14.95 
NMAE  10.08  10.79  13.11  8.84  10.71  
RBF [43]  NRMSE  18.32  14.57  18.62  14.11  16.40 
NMAE  13.32  10.45  13.77  10.24  11.95  
MLP [43]  NRMSE  15.36  15.62  19.80  12.32  15.78 
NMAE  12.42  11.56  14.54  9.02  11.89  
WNN with MSE [43]  NRMSE  12.38  14.99  17.66  11.65  14.17 
NMAE  9.36  10.64  12.49  8.53  10.26  
WNN with MCC [43]  NRMSE  12.23  12.48  16.68  11.58  13.24 
NMAE  9.22  9.64  11.73  8.22  9.70  
Proposed  NRMSE  10.10  10.54  14.21  9.32  11.04 
NMAE  7.32  7.47  9.14  6.36  7.57 
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Amjady, N.; Abedinia, O. Short Term Wind Power Prediction Based on Improved Kriging Interpolation, Empirical Mode Decomposition, and ClosedLoop Forecasting Engine. Sustainability 2017, 9, 2104. https://doi.org/10.3390/su9112104
Amjady N, Abedinia O. Short Term Wind Power Prediction Based on Improved Kriging Interpolation, Empirical Mode Decomposition, and ClosedLoop Forecasting Engine. Sustainability. 2017; 9(11):2104. https://doi.org/10.3390/su9112104
Chicago/Turabian StyleAmjady, Nima, and Oveis Abedinia. 2017. "Short Term Wind Power Prediction Based on Improved Kriging Interpolation, Empirical Mode Decomposition, and ClosedLoop Forecasting Engine" Sustainability 9, no. 11: 2104. https://doi.org/10.3390/su9112104