Research PaperEmpirical modeling of solar radiation exergy for Turkey
Introduction
Solar radiation reaching the surface of the earth is the most fundamental renewable energy source in nature. Solar energy is one of the most important renewable energy sources such as wind energy, geothermal energy [1], [2], [3], [4], [5], [6]. The average daily global solar radiation is the most important parameter for solar energy applications, such as solar furnaces, concentrating collectors, interior illumination of buildings and thermoelectricity [1], [7]. In locations where no measured average daily global solar radiation values are available, a common application has been to obtain this parameter by appropriate regression models, which are established using the measured data [1].
Measured data are the best source for proper knowledge of global solar radiation. However, such data are not available to measure global solar radiation at every location. In contrast, the sunshine duration has been measured in almost all meteorological stations for many years. As a result, there have been many studies that have represented the relationship between and developed regression equations for average daily global solar radiation and sunshine duration [8], [9], [10], [11]. The first equation developed for predicting monthly average daily global radiation was carried out by Angstrom [12]. In this regression model, sunshine duration data for predicting the global radiation were used. Most of the sunshine based regression equations built to predict the monthly average daily global solar radiation are based on the Angstrom equation [13]. Because of the difficulty in determining clear sky global irradiance, Prescott [14] proposed extraterrestrial radiation intensity values instead of global irradiance [15]. Many types of regression models or methods have been proposed to estimate solar radiation in the literature [1], [2], [3], [4], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49].
As known, exergy is related to the work potential of the energy contained in a system at a specified state [50], and it is a concept that explicitly shows the ‘usefulness (quality)’ of energy and matter, in addition to ‘what is consumed’ in the course of energy transfer or conversion steps. The concept of ‘Energy’ does not show these quality and consumption aspects, because it is a concept aimed at ‘quantity’; this quantity, being subject to a conservation law, cannot be consumed according to the first law of thermodynamics. The concept of ‘Exergy’ provides further understanding of ‘how a system works’, by pinpointing the subsystems where energy is degraded. An understanding of exergy consumption principles will lead us to a better understanding of resource and environment issues [51], [52].
Currently, the conversion of solar energy into useful energy, such as mechanical and electrical energy, does not play a crucial role in the energy budget of most countries. However, this energy conversion will become more important in the future because of its environmentally friendly standing. Thus, it is crucial to have these thermodynamic tools ready for action when the demand increases. Given a fixed environment, exergy is the fraction of the incoming energy that is fully convertible into mechanical or electrical energy. Mechanical and electrical energy are completely exergy; they are fully convertible into all other energy types. Solar energy is not fully convertible because of its entropy content; therefore, its exergy content is less than 100%. Thus, the energetic conversion efficiency of a solar conversion device will not be 100%, even if there were an ideal, fully reversible conversion. The exergy content of solar radiation arriving on earth is between 50 and 80% of its energy flux, depending on the atmospheric conditions [53].
In analyzing solar energy application systems using an exergy analysis method, the calculation of the exergy of solar radiation is very important. Over a period of more than 20 years, many papers considering different approaches to this calculation have been published [53], [54], [55], [56]. For example, a thermodynamic model was developed by Zamfirescu and Dincer [57] to study the exergetic content of incident solar radiation reaching the Earth’s surface that can be used to produce work through a dually cascaded thermodynamic cycle. Joshi et al. [58] developed a solar exergy map concept and conduct a comprehensive case study to show how it is utilized and how it is significant for practical solar applications.
The aim of many papers in the literature is to estimate the global solar radiation using empirical models or methods. However, empirical models or methods have not been reported in literature only in relation to the estimation of solar radiation exergy. Therefore, the main objective of this study is to predict the global solar radiation exergy using sunshine duration based on the Angstrom–Prescott method in Turkey. Also, this study proves that regression modeling can be used prediction of solar exergy.
The advantage of proposed approach used this study, by the developed regression models in this study do not require exergy-to-energy ratio (ψ) and monthly average daily global solar radiation to calculate solar radiation exergy.
Section snippets
Modeling
Many empirical models have been found in the literature, such as linear, quadratic and cubic regression models, to estimate the solar irradiation on a horizontal surface from the observed the monthly average daily hours of bright sunshine and the calculated extraterrestrial radiation and monthly average day length. The first recommended regression model (Table 1) is the linear form known as the Angstrom-Prescott model, which is most commonly used model [12], [14]. The second quadratic and third
Statistical performance evaluation
In the literature, there are many statistical methods available to compare solar radiation models. In this study, seven performance indicators were used for model comparisons, namely, the coefficient of determination (R2), mean percent error (MPE), mean absolute percent error (MAPE), mean bias error (MBE), mean absolute bias error (MABE), root mean square error (RMSE), and t-statistic method (tsta).
The coefficient of determination (R2) can be utilized to obtain the linear relation between the
Results and discussion
For the seven locations studied, the following main results were obtained from the evaluation of the values found in Table 4, Table 5. The variations between the observed and predicted values are given in Fig. 2 for seven stations. Fig. 2 shows that there are no significant differences between the observed and the estimated values.
Istanbul station: The best result for R2 = 0.977 is obtained with the quadratic and cubic model. The computed lowest values of the statistical tests MBE, MABE, RMSE,
Conclusion
Global solar radiation exergy data are used in the design and study of solar energy application systems. In this respect, regression models have been developed to predict the monthly average daily global radiation exergy on a horizontal surface for Turkey. The main conclusions of this study can be summarized as follows:
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According to the R2 values, the use of all models for Turkey is recommended for academic and industrial users.
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The statistical analyses (MBE, MABE, RMSE, MPE, MAPE, and tsta)
Acknowledgement
The author thanks the Turkish State Meteorological Service for providing the solar radiation, the bright sunshine and air temperature data. I also wish to thank Prof. Abdulvahap Yigit and Associate Professor Erhan Pulat for his comments, which improved the manuscript.
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