Simulating clear-sky index increment correlations under mixed sky conditions using a fractal cloud model

Modelling clear-sky index increments (i.e. changes in normalized surface irradiance over specified intervals of time) and their spatial autocorrelation structures is important for the reliable grid integration of photovoltaic power systems. In order to capture increment correlation structures under mixed sky conditions, we apply a fractal cloud model. First, we use thousands of fish-eye sky camera and satellite images to estimate cloud edge fractal dimension D on scales between tens of meters and hundreds of kilometers. Box-counting analyses of cloud edges extracted from these images result in best-fit estimates of fractal dimension between 1.4 and 1.6, with satellite approximations being consistently higher than sky camera estimates. Contrary to previous studies, we find no evidence of any scale break and attribute the systematic discrepancy between the two estimates of D to intrinsic differences in the instrument-specific techniques of cloud detection. Next, we synthesize small-scale fractal cloud fields, with D=1.5 and satellite-derived cloud images as input. Using cloud motion vectors from the same satellite images, we then translate the small-scale cloud fields across a set of model pyranometer locations to obtain corresponding clear-sky index time series. From the simulated time series we calculate increment correlation structures for distances between tens of meters and about ten kilometers, and compare them to observation-based results from 1 Hz measurements of up to 99 pyranometers. The observed isotropic, along-wind, and across-wind spatial autocorrelation structures of clear-sky index increments are captured well by the model, both in terms of overall value and shape. While there are some systematic differences between modelled and observed structures (e.g. underevaluation for very small time scales of a few seconds), the differences are essentially small. In general, the simulated correlations are not strongly sensitive to variations in the fractal model parameters.