Intelligent techniques, harmonically coupled and SARIMA models in forecasting solar radiation data: A hybridization approach
The unsteady and intermittent feature (mainly due to atmospheric mechanisms and diurnal cycles) of solar energy resource is often a stumbling block, due to its unpredictable nature, to receiving high-intensity levels of solar radiation at ground level. Hence, there has been a growing demand for accurate solar irradiance forecasts that properly explain the mixture of deterministic and stochastic characteristic (which may be linear or nonlinear) in which solar radiation presents itself on the earth’s surface. The seasonal autoregressive integrated moving average (SARIMA) models are popular for accurately modelling linearity, whilst the neural networks effectively capture the aspect of nonlinearity embedded in solar radiation data at ground level. This comparative study couples sinusoidal predictors at specified harmonic frequencies with SARIMA models, neural network autoregression (NNAR) models and the hybrid (SARIMA-NNAR) models to form the respective harmonically coupled models, namely, HCSARIMA models, HCNNAR models and HCSARIMA-NNAR models, with the sinusoidal predictor function, SARIMA, and NNAR parts capturing the deterministic, linear and nonlinear components, respectively. These models are used to forecast 10-minutely and 60-minutely averaged global horizontal irradiance data series obtained from the RVD Richtersveld solar radiometric station in the Northern Cape, South Africa. The forecasting accuracy of the three above-mentioned models is undertaken based on the relative mean square error, mean absolute error and mean absolute percentage error. The HCNNAR model and HCSARIMA-NNAR model gave more accurate forecasting results for 60-minutely and 10-minutely data, respectively.Highlights
- HCSARIMA models were outperformed by both HCNNAR models and HCSARIMA-NNAR models in the forecasting arena.
- HCNNAR models were most appropriate for forecasting larger time scales (i.e. 60-minutely).
- HCSARIMA-NNAR models were most appropriate for forecasting smaller time scales (i.e. 10-minutely).
- Models fitted on the January data series performed better than those fitted on the June data series.
Akaike, H. (1983). Information measures and model selection. Bulletin of the International Statistical Institute, 50: 277-290.
Baridam, B., and Irozuru, C. (2012). The prediction of prevalence and spread of HIV/AIDS using artificial neural network: The case of Rivers State in the Niger Delta, Nigeria. International Journal of Computer Applications, 44 (2): 0975-8887. https://doi: 10.5120/6239-8584.
Brooks, M. J., du Clou, S., van Niekerk, J. L., Gauche, M. J., Leonard, P., Mouzouris, C., Meyer, A. J., van der Westhuizen, E. E., van Dyk, N., and Vorster, F. (2015). SAURAN: A new resource for solar radiometric data in Southern Africa. Journal of Energy in Southern Africa, 26 (1): 2-10. https://doi.org/10.17159/2413-3051/2015/v26i1a2208.
Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time series analysis, forecasting and control (3rd Edition). New Jersey: Prentice Hall.
Box, G. E. P, and Jenkins G. M. (1976). Time series analysis: Forecasting and control. Operational Research Quarterly, 22: 199-201.
Bozkurt, O. O., Biricik, G., and Tayşi, C. Z. (2017). Artificial neural network and SARIMA based models for power load forecasting in Turkish electricity market. PloS one, 11: e0175915. https://doi.org/10.1371/journal.pone.0175915.
Chaturvedi, D. K., and Isha, I. (2016). Solar power forecasting: A review. International Journal of Computer Applications (0975 - 8887), 145: 28-50. https://doi:110.5120/ijca2016910728.
Chu, Y., Urquhart, B., Gohari,S. M., Pedro, H. T., Kleissl, J., and Coimbra, C. F. (2015). Short-term reforecasting of power output from a 48 mwe solar PV plant. Solar Energy, 112: 68-77. http://dx.doi.org/10.1016/j.solener.2014.11.017.
Diagne, H. M., David, M., Lauret, P., Boland, J., and Schmutz, N. (2013). Review of solar irradiance forecasting methods and a proposition for small-scale insular grids. Renewable and Sustainable Energy Reviews, 27: 65-76. https://doi: 10.1016/j.rser.2013.06.042.
Fonseca Jr., J. G. S., Oozeki, T., Takashima, T., and Ogimoto, K. (2011). Analysis of the use of support vector regression and neural networks to forecast insolation for 25 locations in Japan. In: Proceedings of ISES Solar World Congress. Kassel, Germany.
Govindasamy, T. R., and Chetty, N (2019). Non-linear multivariate models for the estimation of global solar radiation received across five cities in South Africa. Journal of Energy in Southern Africa, 30 (2) : 38-51. https://orcid.org/0000-0002-9809-4230.
Hyndman, R. J., and Athanasopoulos, G. (2013). Forecasting: Principles and practice. Retrieved from https://otexts.com.
Inanlougani, A., Reddy, T. A., and Katiamula, S. (2017). Evaluation of time-series, regression and neural network models for solar forecasting: Part I: One-hour horizon, 1–20.
IRENA [International Renewable Energy Agency]. (2016). The power to change: Solar and wind cost reduction potential to 2025. Retrived from: https://www.irena.org/-/media/Files/IRENA/Agency/Publication/2016/IRENA Power to Change 2016.pdf.
Khalek, A., and Ali, A. (2015). Comparative study of Wavelet-SARIMA and Wavelet- NNAR models for groundwater level in Rajshahi District. IOSR Journal of Environmental Science, Toxicology and Food Technology (IOSR-JESTFT), 10 (7): 2319-2399.
Kibirige, B. (2018). Monthly average daily solar radiation simulation in: northern KwaZulu-Natal: A physical approach. South African Journal of Science, 114: 1-8. https://doi. org/10.17159/sajs.2018/4452.
Liew, A. W.C., Law, N. F., Cao, X. Q. , and Yan, H. (2009). Statistical power of Fisher test for the detection of short periodic gene expression profiles. Pattern Recognition, 42: 549¬–556. https://doi.org/10.1016/j.patcog.2008.09.022.
Lorenz, E., Hammer, A., and Heinemann, D. (2004). Short term forecasting of solar radiation based on satellite data. In: Proceedings of EuroSun 2004 Congress. Freiburg, Germany: 841–848.
Martin, A., Kourentzes, A., and Trapero, J. R. (2015). Short-term solar irradiation forecasting based on dynamic harmonic regression. Energy, 84: 289-295. https://doi.org/10.1016 /j.energy.2015.02.100.
Mpfumali, P., Sigauke, C., Bere, A. and Mulaudzi, S. (2019). Day ahead hourly global horizontal irradiance forecasting-application to South African data. Energies, 12(18): 1-28. https://doi.org/10.3390/en12183569.
Mukaram, M. Z., and Yusof, F. (2017). Solar radiation forecast using hybrid SARIMA and ANN model: A case study at several locations in peninsular Malaysia. Malaysian Journal of Fundamental and Applied Sciences – Special Issue on Some Advances in Industrial and Applied Mathematics, 13 (4): 346-350. https://doi:10.11113/mjfas.v13n4-1.895.
Pavlovski, A., and Kostylev, V. (2011). Solar power forecasting performance towards industry standards. In: 1st International Workshop on the Integration of Solar Power into Power Systems. Aarhus, Denmark.
Pretorius, P., and Sibanda, W. (2012). Artificial neural networks: A review of applications of neural networks in the modeling of HIV epidemic. International Journal of Computer Applications, 44(16): 1-4.
Ranganai, E., and Nzuza, M. B. (2015). A comparative study of the stochastic models and harmonically coupled stochastic models in the analysis and forecasting of solar radiation data. Journal of Energy in Southern Africa, 26(1): 25-137.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6: 461–464.
Sena, D., and Nagwani, N. K. (2016). A neural network autoregression model to forecast per capita disposable income. ARPN Journal of Engineering and Applied Sciences, 11(22): 13123-13128.
Suleiman, E. A., and Adejumo, A. O. (2017). Application of ARMA-GARCH models on solar radiation for South Southern Region of Nigeria. Journal of Informatics and Mathematical Sciences, 9(2): 405-416. http://dx.doi.org/10.26713%2Fjims.v9i2.742.
Voyant, C., Notton, G., Kalogirou, S., Nivet, M., Paoli, C., Motte, F., and Fouilloy, A. (2017). Machine learning methods for solar radiation forecasting: A review. Renewable Energy, 105: 569-582.
Voyant, C., Muselli, M., Paoli, C., and Nivet, M. L. (2011). Optimization of an artificial neural network dedicated to the multivariate forecasting of daily global radiation. Energy, 36: 48-59.
Wei, W. (2006). Time series analysis: Univariate and multivariate methods (2nd Edition). Boston: Addison-Wesley.
Yarmohammadi, M. (2011). A filterbased Fisher g-test approach for periodicity detection in time series analysis. Scientific Research and Essays, 6: 7317-3723. https://doi: 10.5897/SRE11.802.
Zhang, G. P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50: 159-175.
Zhang, J., Hodge, B. M., Florita, A., Lu, S., Hamann, H. F., and Banunarayanan, V. (2013). Metrics for Evaluating the Accuracy of Solar Power Forecasting. In: Proceedings of the 3rd International Workshop on Integration of Solar Power into Power Systems. London, England.
Zhandire, E (2017). Predicting clear-sky global horizontal irradiance at eight locations in South Africa using four models. Journal of Energy in Southern Africa, 28: 77-86. https://doi.org/10.17159/2413-3051/2017/v28i4a2397.
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