New formulas generalized to the evaluations of solar irradiations captured on horizontal surfaces and optimal inclinations

Abstract

This work offers two significant contributions. The first concerns the proposal of a new formula for evaluating solar radiation on a horizontal plane in the sense of Joseph Fourrier's thermal equation. From which we deduce the characterization of solar radiation under overcast and almost overcast conditions. The second approach is dedicated to the calculation of solar irradiation captured on a fixed inclined surface. This consists of adding the expression of solar radiation coming from the horizontal plane with the overall balance of losses along the path of solar radiation. It appears that, contrary to the results of the models resulting from the Angstrom Prescott formula, the coefficients R= 0.9972, R<sup>2</sup>= 0.9952, and MAPE= 0.061 for the Garoua data and R= 0.8849, R<sup>2</sup>= 0.9407, and MAPE= 0.05, for the El Jadida data show that the results of the first proposed formula are well correlated with the measured values. Furthermore, using the optimal tilt angles, the second formula we proposed presents well-correlated results, such that: R= 0.9997, R<sup>2</sup>= 0.9978, and MAE= 4.1470 for Garoua data and R= 0.9994, R<sup>2</sup>= 0.9959, and MAE= 7.7742 for El Jadida data.