A continuous form of the Perez diffuse sky model for forward and reverse transposition

The Perez 1990 transposition model has emerged as the preferred choice for estimating global tilted irradiance, also known as plane-of-array irradiance. One notable drawback is the Perez model's reliance on empirical coefficients assigned to discrete bins of the sky clearness parameter, resulting in discontinuities in the calculated tilted irradiance. In this study, we present a novel method to eliminate the discontinuities of the Perez model by replacing the empirical look-up table with a set of six quadratic splines. This is facilitated by transforming the unbounded sky clearness parameter (epsilon) to an equivalent bounded parameter (zeta). Transposition using the original Perez model and continuous Perez-Driesse model are compared for multiple orientations at two locations. The two models produce very similar deviation statistics, meaning the continuous version can be used as a plug-in replacement for the original. Reverse transposition is demonstrated using the Perez-Driesse model together with a new continuous version of the Erbs diffuse fraction model and a simple bisection solution search. This combination achieves a substantially higher success rate than the GTI-DIRINT algorithm in our tests.