Wind Power Estimation Using Generalized Gamma Distribution and Logistic Power Curve Approximations

Abstract

Accurate wind energy prospective calculation is essential for forecasting, turbine efficiency studies, and wind farm design. Nevertheless, the inherent randomness of wind velocity along with the nonlinearity of turbine power conversion make the problem of energy production estimates difficult due to its uncertainty. The traditional approaches to the problem of wind resource assessment are mainly based on the usage of two-parameter distributions like Weibull. Furthermore, wind-speed variation analysis and wind-turbine power-curve assessment are typically carried out independently. In this research, an integrated method for wind power estimation is suggested, based on the combination of a three-parameter Generalized Gamma (GG) distribution for the description of wind speed and four-parameter (4PL) and five-parameter logistic (5PL) approximations of turbine power curves. Data of hourly wind speed from four different sites (Altamont, Iowa, Massachusetts, and Texas) were used in the analysis of this approach with a Vestas V90-3.0 MW turbine. Maximum Likelihood Estimation (MLE) was used to estimate the Generalized Gamma distribution's parameters, and the fitted wind speed distributions as well as Power Curves (PC) were numerically integrated to determine the expected power output. The evaluation of the performance of the proposed method was performed based on the indicators of capacity factor, annual energy production, RMSE, MAE, MAPE, and goodness of fit. The results show that the proposed model captures the wind regimes properly and gives capacity factors from 25.95% up to 43.83%. Slightly higher fitting accuracy was reached by the 5PL curve compared to the 4PL curve, whereas there is less than a 0.5% discrepancy between the predicted power output estimates. According to sensitivity analysis, the Generalized Gamma distribution's scale parameter has the biggest impact on the accuracy of energy estimation, followed by the shape parameter a. The second shape parameter has very little effect.