A Two-Regime Statistical Framework for Wind-Power Distributions: From Wind-Speed Fluctuations to Turbine Control

Abstract

Wind-power variability is a major challenge for the reliable integration of utility-scale wind energy into modern power systems. Although wind-speed statistics are often described by simple parametric distributions, translating these statistics into turbine-level power fluctuations is nontrivial because the relationship between wind speed and power is highly nonlinear and changes across different turbine operating regimes. Here, we develop a two-regime statistical framework for wind-power distributions. In the aerodynamic operating regime, between the cut-in and rated speeds, the turbine power follows an approximate cubic dependence on wind speed. Starting from a physically motivated Rician model for the wind-speed magnitude, we derive an analytical expression for the corresponding wind-power distribution using a nonlinear change of variables. In the control-dominated near-rated regime, where active blade-pitch and generator control regulate the turbine output, the aerodynamic transformation is no longer applicable. Instead, we characterize the power deficit relative to the rated power and show empirically that its continuous tail is well described by a bounded stretched-exponential distribution for both individual turbines and wind-farm ensembles. These results provide a physically interpretable statistical description of wind-power fluctuations across the full operational range of utility-scale wind turbines.