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2011 -12 Seminars


Atmospheric Turbulence and Geographic Diversity in Wind-Powered Electricity Generation

Dr. Mark Handschy
Partner
Enduring Energy, LLC

Abstract
Variability of electric generation from renewable wind and solar resources poses a challenge for regulation and stability of the electric grid. It has been widely suggested that this variability can be reduced by aggregating geographically diverse generators, with a benefit determined by the degree of correlation between sites. Here, we propose a general quantitative form for site-to-site correlation using a simple model that equates horizontal wind with fully developed turbulence. The proposed model shows how the geographic size of an aggregation region affects the time scale of electric-grid regulation requirements for wind and solar power. The model is based on the similarity of k‒5/3 Kolmogorov power spectra for wind and turbulence. This allows classic results for turbulence correlation functions to be carried over to wind. According to these results correlation falls off with distance between measurement sites according to a universal form, with a spectral cut-off at low wave number or outer scale determining the correlation length. Wind speed exhibits the same dependence on temporal frequency (f‒5/3) as on spatial wave number (k‒5/3), which suggests a characteristic velocity connects space and time domains even when atmospheric turbulence is not “frozen” as required by Taylor’s hypothesis. With this connection, the temporal cut-off frequency below which trends are removed from time-series data substitutes for the outer spatial scale in determining correlation length. Some previously published results for wind-speed correlations seem to agree with this conjecture. Data for solar irradiance also show similar scaling, indicating that wind influence on cloud size, shape, and motion may determine solar power variability statistics.