Developing new models for estimating solar radiation by using Fourier series

Solar energy (SE) is one of the most important energy sources. Being aware of the global solar radiation (GSR) levels in a specific region is crucial for the efficient utilization of SE. Over the years, numerous methods and approaches have been developed to estimate GSR. The accuracy of these models has been assessed using various statistical tests, and their performance or relative superiority has been widely studied. Fourier series are widely used in the analysis and solution of various engineering problems. However, a review of the literature reveals that no GSR prediction model has been developed using Fourier series. In this study, new models were developed by using the different degrees of Fourier series. The performances of all developed prediction models were examined and compared for different years in detail. The curve-fitting graphs and required calculations were made by using the Matlab program. In order to decide the success of these developed models, six different statistical metrics (R2, MPE, RPE, SSRE, t-stat and MAPE) were discussed in this article. Overall, the evaluation of the results indicates that all three models exhibit satisfactory and reliable performance. In the R2, MPE, SSRE and MAPE tests, Model 2 showed the best performance with 0.9705, 0.6187, 0.1450 and 8.4492 values, respectively. In the RPE and t-stat tests, model 3 showed the best performance with 0.7256 and 0.1751 values, respectively.