Correlation modeling of instantaneous solar irradiance with applications to solar engineering

• Solar irradiance is modeled via convolution of beam and diffuse irradiance.
• The convolution is modeled with correlation using copulas.
• An Ångström-type equation is derived relating sunshine hours to average irradiance.

Estimating solar irradiance, in particular its variability, on Earth’s surface is paramount for solar engineering and for improving the utilization of solar energy. This paper presents a novel approach to statistical modeling of instantaneous solar irradiance by using a multivariate probability distribution—a copula—to describe the dependency between beam and diffuse indices. This approach significantly simplifies certain calculations for solar energy engineering, which is shown with simulated outputs for photovoltaic (PV) systems for different orientations. The PV power generation is expressed as probability distributions, which is directly applicable for power system operation and design. It is also shown that an Ångström-type equation, which is historically useful in relating time of bright sunshine to average solar radiation, is the statistical expectation of solar irradiance in this model.