Integrated wind farm power curve and power curve distribution function considering the wake effect and terrain gradient

Abstract

This work presents a computational method for the simulation of wind speeds and for the calculation of the statistical distributions of wind farm (WF) power curves, where the wake effects and terrain features are taken into consideration. A three-parameter (3-P) logistic function is used to represent the wind turbine (WT) power curve. Wake effects are simulated by means of the Jensen's wake model. Wind shear effect is used to simulate the influence of the terrain on the WTs located at different altitudes. An analytical method is employed for deriving the probability density function (PDF) of the WF power output, based on the Weibull distribution for describing the cumulative wind speed behavior. The WF power curves for four types of terrain slopes are analyzed. Finally, simulations applying the Monte Carlo method on different sample sizes are provided to validate the proposed model. The simulation results indicate that this approximated formulation is a possible substitute for WF output power estimation, especially for the scenario where WTs are built on a terrain with gradient.