Analytic model for correlations of cloud induced fluctuations of clear-sky index

We have derived an analytic model to describe the correlation of cloud-induced fluctuations on photovoltaic (PV) system power generation versus distance or time lag in terms of the parameters that describe the clouds (duration, opacity, ramp smoothness and lag). Clouds are modeled as clear-sky index deviations with sigmoidal ramps. The found auto-correlation function is suited to deterministically describe the correlation versus distance or time lag over a short period of recent time (up to several hours depending on the amount of clouds and the temporal resolution of the data) to a very high level of detail, as opposed to other methods that use a statistical approach. The sensor-pair cross-correlation of a cloud with variable width (and/or specified to a more complex or two-dimensional localized shape) can also be fully understood. Application of the model is investigated in terms of relative aggregate variability of an ensemble of (virtual) PV-systems for one, two or three subsequent clouds. This analysis explicitly relates the shape of clouds to the dimensions of a dense PV-network which is beneficial for understanding variability of PV-systems in a large plant or dense urban region.