A random number generator driven solar irradiance model is presented that simulates solar irradiance on a horizontal plane as a function of time. The model supposes three types of irradiance: beam irradiance, only present when the sun is shining; diffuse irradiance emanating from the clear part of the sky; and diffuse irradiance emanating from the cloud covered part of the sky. The model is divided into a stochastic and a deterministic part. In the stochastic part, a random number generator drives cloud cover, which is then used to stochastically determine whether the sun is shining or hidden behind clouds. The Angstrom-Prescott regression forms the bridge between stochastic properties and deterministic parameters of the model. Parameters derived by way of this regression are the diffuse and the direct component of clear sky global irradiance on a horizontal plane and the transmission factor for clear sky global irradiance on a horizontal plane passing through clouds. The model calculates beam irradiance in a strict on/off fashion. A filtering process is used to transform this raw output stream into a continuous signal that closely resembles real world irradiance. The upper frequency limit of solar irradiance is explored. Based on the model, a novel method for the calculation of the expectation of global irradiance on a horizontal plane is shown. The application of the model for the output power calculation of a geographically dispersed photovoltaic fleet is outlined. Cloud enhancement is explored. (C) 2012 Elsevier Ltd. All rights reserved.