An analytical approach for estimating the global horizontal from the global tilted irradiance

Knowledge of horizontal solar irradiance is crucial for the nowcasting and forecasting of generated photovoltaic (PV) power. High quality irradiance measurement devices, however, are typically not collocated with PV systems. The lack of measurements can be compensated by numerical weather models or satellite-derived products, but they provide only limited temporal and spatial resolutions. Another possibility is to directly use PV systems as irradiance sensors, since the measured PV power is a good indicator of incoming solar irradiance. The challenging part in this procedure is the computation of the global horizontal irradiance Gh from the global tilted irradiance Gc, because a combination of decomposition and transposition models is not analytically invertible. Hence, the majority of existing solutions to this problem are numerical procedures. In this paper, an analytical approach to compute Gh from Gc is presented. The comparison of the proposed approach with one of the existing iterative (numerical) approaches shows promising results. When applied to 1-min data at four different locations, the new approach outperforms the iterative procedure by up to 9% in terms of the relative root mean square error (rRMSE) for east/west module's orientations, and performs slightly better with the south orientation. Moreover, the new approach provides results in less than 1 s, whereas the iterative procedure requires more than 20 min for a one year of data. An open source R-script of the new approach is also publicly available and provided as supplementary material.