Abstract—In this paper, nineteen models were used to estimate the monthly average hourly global solar irradiation from the daily global irradiation value; at the “Cirque de Mafate” which is an isolated high mountain and rugged relief site in Reunion Island. These models are divided into three groups; the first depends on solar parameters like hour angle or solar time, the second implies that the estimation function follows a Gaussian distribution, and the third is a simplified form of the first. The main target is to find, for the site, the best model to estimate the abovementioned monthly average hourly irradiation. The measured data used to validate the models are from an in situ weather station. The following statistical criteria; normalized mean bias error, normalized absolute mean bias error, normalized root mean square, t-statistical test, correlation coefficient, relative standard error and Nash-Sutcliffe Equation were used to evaluate the performance for each model. To rank and compare the nineteen models by the abovementioned seven criteria, the Multi-Criteria Decision Making (MCDM) approach has been used and especially the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). The basic principle of TOPSIS is to define the ideal model and the worst model by the set of the statistical criteria’s value for all models. Then the Euclidian distance to the ideal model and/or the worst model is calculated. The best model is the one that is nearest the ideal model and farthest the worst model. To use the TOPSIS, a normalized weight, that indicates the importance or priority, for each statistical criterion has been calculated by objective and subjective way. As result, it was found that the best model came from the first group and it is the Collares-Pereira and Rabl model modified by Gueymard (CPRG) and in second position is the Gueymard model.

Keywords—Clearness index, mean hourly irradiation from daily value, objective and subjective weight, Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS)

Cite: Tovondahiniriko Fanjirindratovo, Didier Calogine, Oanh Chau, Olga Ramiarinjanahary, "Using TOPSIS to Find the Best Model to Estimate Mean Hourly Irradiation at the “Cirque de Mafate” in Reunion Island," International Journal of Smart Grid and Clean Energy, Vol. 13, No. 3, pp. 65–93, 2024.

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