doi:10.1016/j.neucom.2006.04.005 
Copyright © 2006 Elsevier B.V. All rights reserved.
Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting
aDepartment of Computer Science, College of Information Technology, Universiti Tenaga Nasional, Km7, Jalan Kajang-Puchong, 43009 Kajang, Selangor, Malaysia
bDepartment of Computer Science, Royal Holloway, University of London, Egham, Surrey TW20 0EX, England, UK
cDAPNIA/SEDI-SAP, CEA-Saclay, 91191 Gif sur Yvette, France
dFaculté de Psychologie et Sciences de l’Education, Université de Genève, 40 Bd. Du Pont d’Arve, 1211 Genève 4, Switzerland
Received 20 June 2005;
revised 17 January 2006;
accepted 23 April 2006.
Communicated by A. Zobaa.
Available online 6 June 2006.
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Abstract
We propose a wavelet multiscale decomposition-based autoregressive approach for the prediction of 1-h ahead load based on historical electricity load data. This approach is based on a multiple resolution decomposition of the signal using the non-decimated or redundant Haar à trous wavelet transform whose advantage is taking into account the asymmetric nature of the time-varying data. There is an additional computational advantage in that there is no need to recompute the wavelet transform (wavelet coefficients) of the full signal if the electricity data (time series) is regularly updated. We assess results produced by this multiscale autoregressive (MAR) method, in both linear and non-linear variants, with single resolution autoregression (AR), multilayer perceptron (MLP), Elman recurrent neural network (ERN) and the general regression neural network (GRNN) models. Results are based on the New South Wales (Australia) electricity load data that is provided by the National Electricity Market Management Company (NEMMCO).
Keywords: Wavelet transform; Load forecast; Scale; Resolution; Time series; Autoregression; Multi-layer perceptron; Recurrent neural network; General regression neural network
Fig. 1. Haar à trous wavelet transform of a sample set, 744-valued, electricity hourly load.
Fig. 2. Redundant Haar à trous wavelet transform—this shows which time steps of the signal data are used to compute the last wavelet coefficients at each different scale.
Fig. 3. Daily load pattern in different seasons.
Fig. 4. Fortnightly load pattern around Christmas and New Year Holidays.
Fig. 5. Ten wavelet coefficients, MAR(2) with 4 wavelet scales plus the smoothed array, that are used for the forecast of the next value XN+1.
Fig. 6. Wavelet based multilayer perceptron (MLP) neural network architecture.
Fig. 7. Plot of BIC against AR order.
Fig. 8. Example of daily electricity load forecasting for 1 day in April 2002.
Fig. 9. The difference between the actual and forecasted load by ERNw, MAR, MLPw, and MLP, respectively for a day of April 11, 2002.
Fig. 10. Example of daily electricity load forecasting for 1 day, January 3, 2002.
Fig. 11. The difference between the actual and forecasted load by ERNw, MLPw, MAR, and MLP, respectively for a day of January 3, 2002.
Fig. 12. Overall process flow of the computer system to derive load forecast from historical load data.
Fig. 13. Functional process flow of the way historical load data is explored, selected, and forecasted in our model.
Table 1.
New South Wales (NSW) load data used both to train and test the proposed forecasting models
Table 2.
Model architectures and parameter settings for 1-h ahead hourly load forecasting
Table 3.
CPU computing time for 1-h ahead hourly load forecast
a Input neurons are being fed by wavelet transformed data.
b This is an execution time when generating, on the fly, the training and testing file from a wavelet-transformed file where scale=3 and order=7. If the train-test file is separately generated by the data preparation module, the execution time becomes very much faster.
c MSE: mean-squared error.
d STDEV: standard deviation.
Table 4.
One-hour ahead hourly load forecasting results for a day of January 2002
a Input neurons are being fed by wavelet transformed data.
Table 5.
One-hour ahead hourly load forecasting results for a day of January 2002
a Input neurons are being fed by wavelet transformed data.
Table 6.
One-hour ahead hourly load forecasting results for a day of April 2002
a Input neurons are being fed by wavelet transformed data.
Table 7.
One-hour ahead hourly load forecasting results for a day of April 2002
a Input neurons are being fed by wavelet transformed data.
Table 8.
One-hour ahead hourly load forecasting results for a day of April 2002
a Input neurons are being fed by wavelet transformed data.
Table 9.
One-hour ahead hourly load forecasting results for a day of April 2002
a Input neurons are being fed by wavelet transformed data.
Table 10.
One-hour ahead hourly load forecasting results for a day of June 2002
a Input neurons are being fed by wavelet transformed data.
Table 11.
One-hour ahead hourly load forecasting results for a day of October 2002
a Input neurons are being fed by wavelet transformed data.
Table 12.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 13.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 14.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 15.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 16.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 17.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 18.
One-hour ahead hourly load forecasting results for a day of December 2002
a Input neurons are being fed by wavelet transformed data.
Table 19.
One-hour ahead hourly load forecasting results for a day of January 2002
a Input neurons are being fed by wavelet transformed data.
Abstract
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