A model of spatially integrated solar irradiance variability based on logarithmic station-pair correlations

The opportunities for integrating large amounts of variable solar power generation into power systems depend on the degree of variability in the power generation and on the flexibility of the power system. To determine the need for increased system flexibility, methods for quantifying the smoothing effect on the aggregate power output of an arbitrary set of power plants are required. In this paper a mathematical model for spatially integrated variability in solar irradiance continuously distributed over a rectangular field is derived, based on the mathematical properties of so-called virtual radiation networks. The model yields the variance of the aggregate clear sky index step changes relative to the variance at a point location as a function of time resolution, field side length in the direction of cloud movement, cloud speed and a parameter representing the volatility of the irradiance fluctuations at a point location. The model is most suited for estimating the smoothing effect on short-term variability (spatial scales up to around 1 km and time scales up to a few minutes) in power generation from large photovoltaic (PV) fields or dense distributed PV fleets in the built environment. The paper concludes that the model, and the logarithmic station-pair correlation function that it is derived from, accurately describe the empirical variability and correlations in a virtual network. The paper also reproduces and explains certain previously reported empirical results from measurements of station-pair correlations over short distances.

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