Mass and Aerodynamic Imbalance of a Horizontal Axis Wind Turbine

Abstract

It is very common among wind turbines of all designs that a spectral analysis of operating variables, such as yaw motion, torque, or electrical power output has a large concentration of variance at the rotational frequency of the low speed shaft. This spike in the spectrum of the operating variables has come to be known as the once per revolution response or 1P. In addition to this 1P spike, three-bladed wind turbine spectral signatures usually include the harmonic integers 2P and 3P. The two main sources of IP are mass imbalance in the rotor plane and various aerodynamic performance imbalances of the rotor blades. This paper is dedicated to determining the specific contribution of each of these sources to 1P as well as their effects on the 2P and 3P harmonics. Mass imbalance and aerodynamic imbalance issues are addressed separately so that the relative contribution of each can be quantified. The nonlinear differential equations describing the coupled azimuth and yaw motion with mass imbalance were analytically solved using a perturbation technique. A blade strip element technique was used to determine the effects of aerodynamic imbalance on 1P, 2P, and 3P fluctuations. It was found that 60 percent of the 1P low-speed shaft torque (LSST) fluctuation is due to mass imbalance and 40 percent due to aerodynamic imbalance. These results compare quite favorably with the NREL 15 kW Combined Experiment wind turbine data.