FINITE DIFFERENCE AND MULTIPLE REGRESSION METHODS APPLIED IN DYNAMIC MODELING OF WIND ENERGY

Resumo

ABSTRACT The intermittency of wind energy poses challenges to the stability of the electrical grid, making the precise modeling of the relationship between wind speed and generated power crucial. Traditional models, based on static algebraic equations, are insufficient as they fail to capture the dynamics of the wind and the non-instantaneous responses of the turbine, such as inertia and elasticity. This paper aims to overcome these limitations by developing a dynamic model for wind power, based on a differential equation that describes the temporal evolution of the system. The methodology integrates physical modeling with rigorous statistical analysis, using the Finite Difference Method for the numerical solution of the differential equation, based on classic works in the field. For the calibration and validation of the model against empirical data, the Multiple Regression Method was employed, which allows for analyzing the relationship between power and multiple predictors and evaluating the residuals of the dynamic model. As a result, a particular differential equation describing the dynamic behavior of power was obtained, demonstrating superiority over the static approach, especially under transient wind conditions. The proposed hybrid approach not only offers a more accurate solution for generation forecasting but also establishes a foundation for optimizing control algorithms and future research in the field. Keywords: Wind Turbines; Differential Equations; Numerical Analysis; Power Forecasting; Computational Simulation.