Geographic Dependence of the Solar Irradiance Spectrum at Intermediate to High Frequencies

Temporal fluctuations in the solar irradiance are important for renewable-energy harvesting, as well as for climate and ecological-systems analysis. Environmental studies usually focus on slow fluctuations of the solar irradiance, assuming that fast fluctuations are averaged out, while studies of solar power generation emphasize the role of faster fluctuations, due to their effect on grid stability. Several analyses have reported a power-law dependence of the generated-power spectrum for frequencies ranging from 1/min to 1/year. However, both the origin of this power law and its geographic dependence are not fully understood, an issue of significance when one considers smoothing of solar-photovoltaic-power fluctuations by combining geographically distributed generation sources. Here we show that the power law appears in the global and direct components of the solar radiation and not only in the generated power. We also show that the exponent of the power law has a clear latitudinal dependence. At most locations, the spectral power-law dependence of the intermediate (1/day < f < 1/h) frequencies is different from that of the high (f > 1/h) frequencies. Using a simple model, we explain the origin of the power-law spectra and the latitudinal dependence. The implications of the power law for photovoltaic power generation and grid stability are discussed. We also suggest that the analysis of solar power generation should consider the power spectrum of the clear-sky irradiance at the location of interest in order to separate atmospheric effects from geographical ones.