Evaluation of the performance of three diffuse hourly irradiation models on tilted surfaces according to the utilizability concept R. Posadillo * , R. López Luque Research Team of Physics for Renewable Energies and Resources, Dept. of Applied Physics, Edificio C2 Campus de Rabanales, 14071 Córdoba, Spain article info Article history: Received 20 October 2008 Accepted 24 May 2009 Available online 21 June 2009 Keywords: Hourly diffuse tilted surfaces Model Utilizability abstract The performance of three diffuse hourly irradiation models on tilted surfaces was evaluated by making a database of hourly global and diffuse solar irradiation on a horizontal surface, as well as global solar irra- diation on a tilted surface, recorded in a solar radiation station located at Córdoba University (Spain). The method for a comparison of the performance of these models was developed from a study of the ‘‘utilizable energy” statistics, a value representing, for a specific period of time, the mean monthly radi- ation that exceeded a critical level of radiation. This model comparison method seemed to us to be highly suitable since it provides a way of comparing the capacity of these models to estimate, however, much energy is incident on a tilted surface above a critical radiation level. Estimated and measured values were compared using the normalized RMBE and RRMSE statistics. According to the results of the method let us verify that, of the three models evaluated, one isotropic and two anisotropic, the Reindl et al. anisotropic model was the one giving the best results. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction For any study of the behaviour of both active and passive solar systems, and particularly for our area of interest, such as the anal- ysis of the optimal dimensioning of a photovoltaic installation [1,2], it is necessary to find out the hourly irradiation received on the panel situated in a geographical area with a specific orientation and tilt. When these data are not available, the irradiation incident on the panel is estimated by applying models which require the values of global and diffuse irradiation on a horizontal surface as input. It is well known that there is a shortage of sufficiently long ser- ies of data measured of these variables in Iberian countries [3], par- ticularly in Spain, as well as the intermittence in the functioning of these measurement stations. This lack of data implies that the irra- diation measurements compiles in the University over a long per- iod of time is highly valuable work, since this information is the basis for future use and validation of models. The radiometer sta- tion located in the Superior Polytechnic School (Córdoba, Spain) has been recording data of these variables since 1992. Another aspect is that, in calculating the global irradiation on tilted surfaces, the diffuse component of this irradiation is the most complicated one due to its almost generalized anisotropic behav- iour. Many authors have either obtained calculation models of this component or have reviewed the performance of existing models. In this article, the performance of three models for the estima- tion of hourly diffuse radiation on a tilted surface has been evalu- ated. The best one will be used to calculate the global irradiation on the collector. 2. Characterization of solar energy incident on a photovoltaic panel. Calculation of the tilted component of the diffuse irradiation The measured hourly global solar irradiation on a surface tilted toward the equator (surface azimuth angle c = 0) at an angle b to the horizontal is given by the following expression: H gb ¼ H bb þ H db þ H rb ð1Þ in which H bb , H db y and H rb are the direct, diffuse and ground-re- flected or albedo components, respectively. The most complex problem when evaluating how much irradi- ation will incidence on a panel with a specific orientation and tilt is the calculation of H db or hourly diffuse irradiation on a tilted sur- face. The reason for this complexity lies in the fact that this diffuse component, as mentioned previously, does not have an isotropic distribution in the sky and this distribution is not uniform over time. Based on the above premises, there is a classification of the models which permit the calculation of this component, taking into account the diffuse radiation distribution present over the sky. These are basically of three types: isotropic, circum-solar and anisotropic. Many authors have reviewed them, and, with 0196-8904/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2009.05.014 * Corresponding author. Tel.: +34 957212689; fax: +34 957212068. E-mail address: rposadillo@uco.es (R. Posadillo). Energy Conversion and Management 50 (2009) 2324–2330 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman