# Short-term solar radiation forecasting by using an iterative combination of wavelet artificial neural networks

## Main Article Content

## Abstract

The information provided by accurate forecasts of solar energy time series are considered essential for performing an appropriate prediction of the electrical power that will be available in an electric system, as pointed out in Zhou *et al.* (2011). However, since the underlying data are highly non-stationary, it follows that to produce their accurate predictions is a very difficult assignment. In order to accomplish it, this paper proposes an iterative *Combination of Wavelet Artificial Neural Networks *(CWANN) which is aimed to produce short-term solar radiation time series forecasting. Basically, the CWANN method can be split into three stages: at first one, a decomposition of level *p*, defined in terms of a wavelet basis, of a given solar radiation time series is performed, generating *r+1 **Wavelet Components* (WC); at second one, these* r+1* WCs are individually modeled by the *k* different ANNs, where *k>5*, and the *5* best forecasts of each WC are combined by means of another ANN, producing the combined forecasts of WC; and, at third one, the combined forecasts WC are simply added, generating the forecasts of the underlying solar radiation data. An iterative algorithm is proposed for iteratively searching for the optimal values for the CWANN parameters, as we will see. In order to evaluate it, ten real solar radiation time series of Brazilian system were modeled here. In all statistical results, the CWANN method has achieved remarkable greater forecasting performances when compared with a traditional ANN (described in Section 2.1).

### Downloads

### Metrics

## Article Details

**1. Proposal of Policy for Free Access Periodics**

Authors whom publish in this magazine should agree to the following terms:

a. Authors should keep the copyrights and grant to the magazine the right of the first publication, with the work simultaneously permitted under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 that allows the sharing of the work with recognition of the authorship of the work and initial publication in this magazine.

b. Authors should have authorization for assuming additional contracts separately, for non-exclusive distribution of the version of the work published in this magazine (e.g.: to publish in an institutional repository or as book chapter), with recognition of authorship and initial publication in this magazine.

c. Authors should have permission and should be stimulated to publish and to distribute its work online (e.g.: in institutional repositories or its personal page) to any point before or during the publishing process, since this can generate productive alterations, as well as increasing the impact and the citation of the published work (See The Effect of Free Access).

**Proposal of Policy for Periodic that offer Postponed Free Access**

Authors whom publish in this magazine should agree to the following terms:

a. Authors should keep the copyrights and grant to the magazine the right of the first publication, with the work simultaneously permitted under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 [SPECIFY TIME HERE] after the publication, allowing the sharing of the work with recognition of the authorship of the work and initial publication in this magazine.

b. Authors should have authorization for assuming additional contracts separately, for non-exclusive distribution of the version of the work published in this magazine (e.g.: to publish in institutional repository or as book chapter), with recognition of authorship and initial publication in this magazine.

c. Authors should have permission and should be stimulated to publish and to distribute its work online (e.g.: in institutional repositories or its personal page) to any point before or during the publishing process, since this can generate productive alterations, as well as increasing the impact and the citation of the published work (See The Effect of Free Access).

d. They allow some kind of open dissemination. Authors can disseminate their articles in open access, but with specific conditions imposed by the editor that are related to:

Version of the article that can be deposited in the repository:

Pre-print: before being reviewed by pairs.

Post-print: once reviewed by pairs, which can be:

The version of the author that has been accepted for publication.

The editor's version, that is, the article published in the magazine.

At which point the article can be made accessible in an open manner: before it is published in the magazine, immediately afterwards or if a period of seizure is required, which can range from six months to several years.

Where to leave open: on the author's personal web page, only departmental websites, the repository of the institution, the file of the research funding agency, among others.

## References

ADAMOWSKI, J.; KARAPATAKI, C. (2010) Comparison of Multivariate Regression and Artificial Neural Networks for Peak Urban Water-Demand Forecasting: Evaluation of Different ANN Learning Algorithms. Journal of Hydrological Engineering, ASCE, v. 15, p. 729-743.

CAO, S.; WENG, W.; CHEN, J.; LIU, W.; YU, G.; CAO, J. (2009) Forecast of Solar Irradiance Using Chaos Optimization Neural Networks. POWER AND ENERGY ENGINEERING CONFERENCE. ASIA-PACIFIC. Shanghai. Proceedings. Shanghai: IEEE, 2009.

CATALÃO, J. P. S.; POUSINHO, H. M. I.; MENDES, V. M. F. (2011) Short-Term Wind Power Forecasting in Portugal by Neural Networks and Wavelet Transform. Renewable Energy, v. 36, p. 1245-1251.

CHAABENE, M.; AMMAR, B. M. (2008) Neuro-Fuzzy Dynamic Model with Kalman Filter to Forecast Irradiance and Temperature for Solar Energy Systems. Renewable Energy. v. 33, n. 7, p. 1435-1443.

CYBENKO, G. (1989) Approximation by Superpositions of a Sigmoidal Function. Mathematics of Control, Signals, and Systems. v. 2, p. 303-314.

DAUBECHIES, I. (1988) Orthonormal Bases of Compactly Supported Wavelet. Communications Pure and Applied Math. v. 41, n. 7, p. 909-996.

DAUBECHIES, I. (1992) Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series In Applied Mathematics: SIAM.

DENG, F.; SU, G.; LIU, C.; WANG, Z. (2010) Global Solar Radiation Modeling Using The Artificial Neural Network Technique. POWER AND ENERGY ENGINEERING CONFERENCE. ASIA-PACIFIC. Chengdu. Proceedings. Beijing: IEEE, 2010.

HAMILTON, J. D. (1994) Time Series Analysis. Princeton University Press.

HAYKIN, S. S. (2001) Redes Neurais Princípios e Aplicações. 2ª Ed. Porto Alegre: Bookman.

KRISHNA, B.; SATYAJI RAO Y. R.; NAYAK P. C. (2011) Time Series Modeling of River Flow Using Wavelet Neural Networks. Journal of Water Resource and Protection. v. 3, p. 50-59.

KUBRUSLY, C. S. (2012) Spectral Theory of Operators on Hilbert Spaces. New York: Birkhäuser.

KUBRUSLY, C. S.; LEVAN, N. (2006) Abstratc Wavelets Generated By Hilbert Space Shift Operators. Advances in Mathematical Sciences and Applications. v. 16, p. 643-660.

LEVAN, N.; KUBRUSLY, C. S. (2003) A Wavelet “Time-Shift-Detail” Decomposition. Mathematics and Computers in Simulation. v. 63, n. 2, p. 73-78.

LIU, H.; TIAN, H. Q.; CHEN, C.; LI, Y. (2010) A Hybrid Statistical Method to Predict Wind Speed and Wind Power. Renewable Energy. v. 35, p. 1857-1861.

MALLAT, S. (2009) A Wavelet Tour of Signal Processing. 3rd ed. Burlington: Academic Press.

MINU, K.K.; LINEESH, M. C.; JESSY, J. C. (2010) Wavelet Neural Networks for Nonlinear Time Series Analysis. Applied Mathematical Sciences. v. 4, n. 50, p. 2485-2495.

MORRIS, J. M.; PERAVALI, R. (1999) Minimum-bandwidth discrete-time wavelets. Signal Processing. v. 76, n. 2, p. 181-193.

PERDOMO, R.; BANGUERO, E.; GORDILLO, G. (2010) Statistical Modeling for Global Solar Radiation Forecasting in Bogotá. PHOTOVOLTAIC SPECIALISTS CONFERENCE (PVSC). Honolulu. Proceedings. Honolulu: IEEE, 2010.

SINGH, C.; CHAUDHARY, R.; THAKUR, R. S. (2011) Performance of advanced photocatalytic detoxification of municipal wastewater under solar radiation – A mini review. International Journal of Energy and Environment. v. 2, n. 2, p. 337-350.

TEIXEIRA JUNIOR, L. A.; MENEZES, M. L.; CASSIANO, K. M.; PESSANHA, J. F. M.; SOUZA, R. C. (2013) Residential Electricity Consumption Forecasting Using a Geometric Combination Approach. International Journal of Energy and Statistics. v. 1, n. 2, p. 113-125.

TEIXEIRA JUNIOR, L. A.; SOUZA, R. M.; MENEZES, M. L.; CASSIANO, K. M.; PESSANHA, F. M. P.; SOUZA, R. C. (2015) Artificial Neural Network and Wavelet Decomposition in the Forecast of Global Horizontal Solar Radiation. Brazilian Operations Research Society. v. 35, n. 1, p. 1-16.

WITTMANN, M.; BREITKREUZ, H.; SCHROEDTER-HOMSCHEIDT, S.; ECK, M. (2008) Case Studies on the Use of Solar Irradiance Forecast for Optimized Operation Strategies of Solar Thermal Power Plants. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. v.1, n. 1, p. 18-27.

YANLING, G.; CHANGZHENG, C.; BO, Z. (2012) Blind Source Separation for Forecast of Solar Irradiance. INTERNATIONAL CONFERENCE ON INTELLIGENT SYSTEM DESIGN AND ENGINEERING APPLICATION. Sanya, Hainan. Proceedings. Sanya, Hainan: IEEE, 2012.

YONA, A.; SENJYU, T. (2009) One-Day-Ahead 24-Hours Thermal Energy Collection Forecasting Based on Time Series Analysis Technique for Solar Heat Energy Utilization System. TRANSMISSION AND DISTRIBUTION CONFERENCE AND EXPOSITION: ASIA AND PACIFIC. Seoul. Proceedings. Seoul: IEEE, 2009.

ZERVAS, P. L.; SARIMVEIS, H.; PALYVOS, J. A.; MARKATOS, N. C. G. (2008) Prediction of Daily Global Solar Irradiance on Horizontal Surfaces Based on Neural-Network Techniques. Renewable Energy. v. 33, n. 8, p. 1796-1803.

ZHANG, N.; BEHERA, P. K. (2012) Solar Radiation Prediction Based on Recurrent Neural Networks Trained by Levenberg-Marquardt Backpropagation Learning Algorithm. INNOVATIVE SMART GRID TECHNOLOGIES (ISGT). Washington, DC. Proceedings. Washington, DC: IEEE, 2012.

ZHANG, P. G. (2003) Time Series Forecasting Using a Hybrid ARIMA and Neural Network Model. Neurocomputing. v. 50, p. 159-175.

ZHOU, H.; SUN, W.; LIU, D.; ZHAO, J.; YANG, N. (2011) The Research of Daily Total Solar-Radiation and Prediction Method of Photovoltaic Generation Based on Wavelet-Neural Network. POWER AND ENERGY ENGINEERING CONFERENCE (APPEEC). Wuhan. Proceedings. Wuhan: IEEE, 2011.