Using measured daily meteorological parameters to predict daily solar radiation

doi:10.1016/j.measurement.2015.08.004

Measurement

Volume 76, December 2015, Pages 148-155

https://doi.org/10.1016/j.measurement.2015.08.004 Get rights and content

Abstract

A major factor for an efficient design of solar energy systems is to provide accurate estimations of the solar radiation. Many of the existing studies are focused on the analysis of monthly or annual solar radiation. This is while less attention has been paid to the determination of daily solar radiation. Accordingly, the main goal of this paper is to develop a robust machine learning approach, based on genetic programming (GP), for the estimation of the daily solar radiation. The solar radiation is formulated in terms of daily air temperature, relative humidity, atmospheric pressure, wind speed, and earth temperature. A comprehensive database containing about 7000 records collected for about 20 years (1995–2014) in a nominal city in Iran is used to develop the GP model. The performance of the derived model is verified using different criteria. A multiple linear regression analysis is performed to benchmark the GP model with a classical technique. The influences of the input variables on the solar energy are evaluated through a sensitivity analysis. The proposed model has a very good prediction performance and significantly outperforms the traditional regression model.

Introduction

Renewable energy sources such as solar have emerged as effective alternatives to fossil fuels. Optimal design of solar systems requires exact prediction of the solar energy [1], [2], [3], [4]. To this aim, several empirical methods have been developed to avoid performing costly in-situ solar radiation measurements [5], [6]. Some of the well-known methods in this area are auto-regression, Markov chain, or robust optimization techniques [7], [8], [9]. Among the empirical methods, machine learning has been widely used to solve real world problems [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28]. Artificial neural networks (ANNs) are well-known machine learning systems that have been utilized to predict the solar radiation [2], [3], [4], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. As typical examples in this context, Rahimikhoob [41] successfully applied ANN for predicting the global solar radiation. Alam et al. [42] employed ANN to predict beam solar radiation. Mellit et al. [43] conducted a comprehensive study on application multi-layer perceptron of ANN for estimating total solar radiation data. However, a limitation of ANNs is that they cannot always be converted into explicit forms to provide the details of the prediction process [44].

Genetic programming (GP) [45] is a new approach with notable simulation capabilities. It is a division of genetic algorithms (GA) that generates computer programs rather [44]. For the last decade, GP has been used to formulate complicated engineering problems [44], [46], [47], [48], [49], [50], [51], [52]. Gene expression programming (GEP) [53], [54] is a recent branch of GP evolving programs of various sizes and shapes. Compared to other soft computing methods, it has been barely applied to energy related problems [2], [3], [55], [56], [57]. Although ANNs are used to predict the “daily” solar radiation [41], [58], [59], [60], [61], [62], none of the existing studies have focused on GP-based analysis of daily solar radiation. Therefore, this study presents the GEP technique for predicting the daily solar radiation in Iran. A regression analysis was later preformed to benchmark the proposed model.

Section snippets

Methodology

GP is an optimization technique to create computer programs. The process is inspired by the biological evolution of living organisms [45]. Generally, in GP, the main goal is to find a program that connects inputs to outputs (see Fig. 1) [55]. The solutions derived by conventional GP are shown as tree structures [63]. However, there are other branches of GP that produce models in different shapes (see Fig. 2) [44], [55]. Among different variants, linear variants have a higher speed permitting

The methodology for predicting daily solar radiation

The soft computing tools commonly follow similar steps to develop a prediction model for the daily solar radiation [3], [55], [67]. A similar approach was also considered herein.

Performance verification

It is known that |R| > 0.8 is a good indicator of accuracy of a regression model [69]. Moreover, the values of RMSE and MAE should be minimum. It can be observed from Fig. 5 that the GEP model has acceptable performance both for the training (R_Training = 0.866, RMSE_Training = 1.032 kW h/m²/d, MAE_Training = 0.817 kW h/m²/d) and testing (R_testing = 0.881, RMSE_testing = 1.202 kW h/m²/d, MAE_testing = 0.940 kW h/m²/d) data. Besides, new measures were checked for more verification of the models on the testing [70], [71].

Sensitivity analysis

As discussed before, the effect of all of the considered parameters (i.e., T_ave, T_min, T_max, H, P, W, and E) on DS is well understood. Ignoring any of these three parameters for the model development resulted in a model with poor performance. Herein, a sensitivity analysis was conducted to provide a more in depth understanding of the contribution of these important parameters to the prediction of DS. A common approach for the sensitivity analysis in the GP-based modeling is to obtain the input

Conclusion

In this study, a new GEP approach is presented for the prediction of the daily solar radiation. A comprehensive database containing data collected for about 20 years was used to develop the GEP model. The model predicts the daily solar radiation with an acceptable accuracy and outperforms the developed regression-based model. GEP does not need a predefined function for the modeling of the solar radiation. As expected, the solar radiation is more affected by average of air temperature, wind speed

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