The distribution of wind power from a dispersed array of wind turbine generators and its reliability based applications

In this paper, the probability distribution of wind power from a dispersed array of wind turbine sites is studied considering forced outage rates of wind turbines. The wind speeds at distinct sites are assumed to be dependent and the dependence is modeled by copulas. In particular, the probability distribution of the aggregate power from two sites is exactly derived. The probability distribution of the aggregate power is also derived under the particular case when site 1 consists of n₁ identical wind turbines of type 1 and site 2 consists of n₂ identical wind turbines of type 2. Numerical results are presented to illustrate the theoretical findings for a chosen copula function.