Theoretical derivation of wind plant power distribution with the consideration of wind turbine reliability

Highlights: • The wind plant power distribution is derived. • Reliability values of the turbines are taken into account. • Wind speed distribution is utilized. -- Abstract: The wind power generated by a wind plant has a stochastic nature due to randomness in the wind speed. Although the empirical distribution of the wind power has been extensively studied by using data sets in different regions, several works focused on theoretical distribution of the wind power produced by wind turbines. In this paper, the theoretical distribution of the wind plant power is obtained. In the derivation of the distribution of the wind plant power, wind turbine reliability is taken into account. The wind plant power distribution can be effectively used if the wind speed probability distribution is known. Theoretical results are illustrated for Weibull and Birnbaum–Saunders wind speed distributions which have been found to be suitable for real data collected at two different locations.