Identification de Modèles de Rayonnement Solaire en Zone Tropicale par Critères d’Information

Identification de Modèles de Rayonnement Solaire en Zone Tropicale par Critères d’Information

Laurent Linguet Yannis Pousset  Christian Olivier 

Laboratoire UMR Espace-DEV, Université de la Guyane IRD, 275 route de Montabo, BP 165, 97323 Cayenne cedex, Guyane française

Laboratoire SIC, Université de Poitiers Département SIC (Signal, Images et Communication) Institut XLIM, 86962 Futuroscope Cedex, France

Page: 
363-381
|
DOI: 
https://doi.org/10.3166/TS.31.363-381
Received: 
N/A
|
Accepted: 
N/A
|
Published: 
31 December 2014
| Citation

OPEN ACCESS

Abstract: 

The aim of this article is to improve the knowledge of the solar radiation in the tropics through the analysis of irradiance measurements at ground. For this, we identify probability distributions introduced in some synthetic solar radiation models, using information criteria. Validation is conducted through different tests and measures between real data distributions and synthesized data distribution. 

Extended Abstract 

The aim of this article is to improve the knowledge of the solar radiation in the tropical areas, through the analysis of irradiance measurements. For that, we dispose of solar radiation time series. They are obtained from measured data at ground or transmitted by satellite. These data or samples are obviously incomplete, no totally representative, and subject to perturbation. 

All these constraints lead to introduce statistical models generating the time series of data. Among several models proposed in literature, we choose the TAG model (for Time dependent Autoregressive Gaussian) of Aguiar and CollaresPereira in 1992, and the model with high temporal resolution given by Polo and al. in 2011. These model generating sequences present random terms with probability density function which are a priori chosen. 

The originality of this paper consists in reconsidering the nature of these probability laws. We dispose of a great number of data. So, to select the best probability law we use a statistical tool based on Information Criteria, also referred as penalized log-likelihood criteria. We retain BIC and Φβ criteria for their strong consistence. 

Among retained probability law candidates, the BIC and Φβ criteria agree to give the same law for the TAG and the Polo models, and this, whatever the different sky conditions. These conclusions differ in part of the literature. 

Then we compare the two probability density functions between solar radiation measured and solar radiation generated from previously elected probability laws. An exact concordance is observed for the TAG model and for the Polo model, except for partially cloud cover case. For this case, the very close values of criteria and the similarity of Nakagami and Beta cumulative functions could explain this discordance. 

RÉSUMÉ

L’objet de cet article est d’améliorer la connaissance du rayonnement solaire en zone tropicale à travers l’analyse des données de mesures d’irradiance au sol. Pour cela nous identifions, à l’aide de critères d’information, les distributions de probabilité introduites dans quelques modèles de génération de rayonnement solaire synthétique. Puis, nous validons les résultats à partir de différentes mesures et différents tests entre distributions issues des données réelles et celles synthétisées. 

Keywords: 

criteria, synthetic solar radiation model, model selection.

MOTS-CLÉS

critères d’information, modèles de rayonnement solaire synthétique, sélection de modèle. 

1. Introduction
2. Rappel de Quelques Concepts Statistiques et Physiques
3. Identification des Lois
4. Validations des Modèles
5. Conclusion
Remerciements
  References

Aguiar R.J., Collares-Pereira M., Conde J.P. (1988). Simple procedure for generating sequences of daily radiation values using a library of Markov transition matrices, Solar Energy, vol. 40, n°3, p. 269-279.  

Aguiar R.J., Collares-Pereira M. (1992). TAG: A time-dependent, autoregressive, Gaussian model for generating synthetic hourly radiation, Solar Energy, vol. 49, n°3, p. 167-174. 

Akaike H. (1974). A new look at the statistical model identification, IEEE Transactions on Automatic Control, vol. 19, n°6, p. 716-723.  

Alata O., Olivier C., Pousset Y. (2013). Law recognitions by information criteria for the statistical modeling of small scale fading of the radio mobile channel. Signal Processing, vol. 93, n°5, p. 1064-1078. 

Amado M., Poggi F. (2012). Towards Solar Urban Planning: A New Step for Better Energy Performance, Energy Procedia, vol. 30, p. 1261-1273.  

Bilbao J., Miguel A., Franco J.A. and Ayuso A. (2004). Test Reference Year Generation and Evaluation Methods in the Continental Mediterranean Area. Journal of Applied Meteorology, vol. 43, p. 390-400. 

Boland J. (1995). Time Series Analysis of Climatic variables, Solar Energy, vol. 55, n°5, p. 377-388. 

Boland J. (2008). Time Series Modelling of Solar Radiation. Modeling Solar Radiation at the Earth Surface – Recent Advances. Viorel Badescu Ed. Springer Verlag, Chapter 11.  

El Matouat A. and Hallin M. (1996). Order selection, stochastic complexity and KullbackLeibler information. Time Series Analysis, Springer Verlag, 2: 291-299. 

Graham V.A., Hollands K.G.T., Unny T.E. (1988). A time series model for Kt with application to global synthetic weather generation, Solar Energy, vol. 40, n°2, p. 83-92. 

Hannan E.J., Quinn B.G. (1979). The Determination of the Order of an Autoregression, Journal of the Royal Statistic Society, vol. 41, n°2, p. 190-195.  

Hansen C.W., Stein J.S. and Ellis A. (2010). Statistical Criteria for Characterizing Irradiance Time Series. Sandia Report, SAND2010-7314, October 2010. 

Jouzel F., Olivier C., El Matouat A. (1998). Information Criteria based edge Detection, EUSIPCO’98-Signal Processing IX, Rhodes (Greece), vol. 2, p. 997-1000, Sept 1998.  

Linares-Rodríguez A., Antonio Ruiz-Arias J., Pozo-Vázquez D., Tovar-Pescador J. (2011). Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks, Energy, vol. 36, n°8, p. 5356-5365. 

Marie-Joseph I., Linguet L., Gobinddass M.-L., Wald L. (2013). On the applicability of the Heliosat-2 method to assess surface solar irradiance in the Intertropical Convergence Zone, French Guiana, International Journal of Remote Sensing, vol. 34, n° 8, p. 30123027.  

Mellit A., Kalogirou S.A., Shaari S., Salhi H., Hadj A. (2008). Methodology for predicting sequences of mean monthly clearness index and daily solar radiation data in remote areas: Application for sizing a stand-alone PV system, Renewable Energy, vol. 33, n°7, p. 15701590. 

Muselli M., Poggi P., Notton G. Louche A. (1998). Improved procedure for stand-alone photovoltaic systems sizing using meteostat satellite images. Solar Energy, vol. 62, p. 429-444. 

Olivier C., Alata O. (2009). The Information Criteria: examples of applications in image and signal processing. Optimisation in Image and Signal Processing, Wiley Ed., Chapter 4, p. 79-110.  

Poggi P., Notton G., Muselli M. Louche A. (2000). Stochastic study of hourly total solar radiation in Corsica using a Markov model. International Journal of Climatology, vol. 20, p. 1843-1860. 

Polo J., Zarzalejo L.F., Marchante R. and Navarro A.A. (2011). A simple approach to the synthetic generation of solar irradiance time series with high temporal resolution, Solar Energy, vol. 85, p. 1164-1170. 

Remund J. and Page J. (2002). Integration and exploitation of networked Solar radiation Databases for environment monitoring, SODA Project Report. 

Rissanen J. (1989). Stochastic Complexity in Statistical Inquiry, World Scientific ed., New Jersey. Schwarz G. (1978). Estimating the dimension of a model. The Annals of Statistics, vol. 6, p. 461-464.

Stanhill G., Cohen S. (2001). Global dimming: a review of the evidence for a widespread and significant reduction in global radiation with discussion of its probable causes and possible agricultural consequences. Agricultural and Forest Meteorology, vol. 107, n° 4, p. 255-278. 

Tiba C., Fraidenraich N. (2004). Analysis of monthly time series of solar radiation and sunshine hours in tropical climates. Renewable Energy, vol. 29, n°7, p. 1147-1160.