Statistical characterization of aggregated wind power from small clusters of generators

• We describe a procedure to aggregate wind power production in small wind sites.
• The procedure accounts for any level of correlation; not only perfect dependence/independence.
• We employ copula theory to cope with the involved formulation of random wind power.
• A real case analysis shows the remarkable error that may occur when using extreme dependence.

In this paper we address the problem of aggregating wind power. The purpose of the methodology presented here is to avoid the assumption of extreme values of correlation, meaning perfect dependence or perfect independence of the production. That is, we accept intermediate values of correlation, which we argue is of special interest for small-scale siting analysis, where the fluctuations of wind power production affect the capacity value or the size of energy storage.We provide a formulation that is based on the integration of the joint probability density function (PDF) of the wind power. We formulate this PDF by means of copula theory in order to cope with the involved representation of the marginal PDFs.As a result, we characterize the PDF of the aggregated wind power and the associated duration curve. We also present a simple formulation of the joint forced outage rate. These serves us for verifying, through a case analysis based on NREL datasets, that in some cases the assumption of extreme dependence in small-scale sites does not hold.