Improved methodology to evaluate clear-sky direct normal irradiance with a multi-pyranometer array

Based on the general expressions for the solar radiation on each of the MPA sloped surfaces and using a hybrid model that includes an anisotropic sky diffuse component, in this work an improved procedure is presented that estimate the normal direct solar irradiance by grouping two expressions of a couple of MPA sensors and analytically look for a satisfactory solution; one set for the horizontal and south sensors, and another for the east and west sensors. The solution for the east and west sensors is expanded to two new solutions by mirroring their readings according to the solar noon. A final switching scheme based on the expressions denominator size provides the satisfactory direct normal irradiance estimation. The analysis of the results for the analyzed days showed that the root mean square error (RMSE) decreased by around 14-43% in comparison with previous results reported in the literature. The proposed methodology is a promising new approach for MPA.