Modeling and Dynamics of a Horizontal Axis Wind Turbine

Abstract

In this paper, we develop a mathematical model of a horizontal axis wind turbine (HAWT) with flexible tower and blades. The model describes the flapping flexures of the tower and blades, and takes into account the nacelle pitch angle and structural damping. The eigenvalue problem is solved both analytically and numerically using the differential quadrature method (DQM). The closed-form and numerical solutions are compared, and the precision of the DQM-estimated solution with a low number of grid points is concluded. Next, we examine the effects of pitch angle and blade orientation on the natural frequencies and mode shapes of the wind turbine. We find that these parameters do not incur apparent alteration of the natural frequencies. Then, we examine the linear dynamics of the wind turbine subjected to persistent excitations applied to the tower. We investigate the effects of the pitch angle and blade orientation on the linear vibrations of the wind turbine. We demonstrate that the time response of the coupled system remain nearly unaffected. We show that small vibrations of the tower induce important blade deflections, and thus, the dynamic tower— blade coupling cannot be considered insignificant.