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.

1.
Borg, J. P., 1996, “The Nonlinear Effect of Dynamic and Aerodynamic Imbalance on the Harmonic and Chaotic Motion of a Horizontal Axis Wind Turbine,” Ph.D. dissertation, Mechanical Engineering, University of Massachusetts, Amherst, MA.
2.
Borg, J. P., and Kirchhoff, R. H., 1996, “The Effect of Aerodynamic Imbalance on a Horizontal Axis Wind Turbine,” Proceedings of the 16th ASME Wind Energy Symposium, Houston, TX, pp. 180–189.
3.
Borg
J. P.
, and
Kirchhoff
R. H.
,
1997
, “
The Effects of Static and Dynamic Imbalance on a Horizontal Axis Wind Turbine
,”
ASME JOURNAL OF SOLAR ENERGY ENGINEERING
, Vol.
113
, pp.
261
262
.
4.
Butterfield, C. P., Musial, W. P., and Simms, D. A., 1992, “Combined Experiment Phase I Final Report” National Renewable Energy Laboratory, NREL/TP-257-4655, Oct.
5.
Butterfield, C. P., et al., 1992, “NREL Combined Experiment Final Report—Phase II,” U.S. National Renewable Energy Laboratory, NREL 1 TP-442-4807, Aug.
6.
Carter, J., 1992, “A Dynamic Analysis of a Horizontal Axis Wind Turbine,” M.S. thesis. Mechanical Engineering, University of Massachusetts, Amherst, MA.
7.
Cohen, R. D., 1979, “Yaw Dynamic Analysis of a Horizontal Axis Wind Turbine,” M.S. thesis, Mechanical Engineering, University of Massachusetts, Amherst, MA.
8.
de Vries, O., 1979, “Fluid Dynamic Aspects of Wind Energy Conversion,” Advisory Group of Aerospace Research and Development, North Atlantic Treaty Organization, AGARD-AG-243.
9.
Eggleston, D. M., and Stoddard, F. S., 1987, Wind Turbine Engineering Design, Van Nostand Reinhold Company, New York.
10.
Kirchhoff, R. H., and Borg, J. P., 1994, “The Effect of Mass Imbalance on Azimuthal and Yaw Motion of a HAWT: Theory and Experiment,” EWEC Thessaloniki, Greece.
11.
Manwell, J. F., 1990, “A Simplified Method for Predicting the Performance of a Horizontal Axis Wind Turbine Rotor,” AWEA Conference.
12.
Manwell, J. F., Jefferies, W. Q., and McGowan, J. G., 1991, “Power Fluctuations from a Horizontal Axis wind Turbine,” Proceedings of the 10th ASME Wind Energy Symposium, ASME, New York.
13.
Van Dyke, M., 1975, Perturbation Methods in Fluid Mechanics, The Parabolic Press, Stanford, CA.
14.
Wolfram, S., 1991, MATHEMATICA: A System for doing Mathematics by Components, 2nd Ed., Addison-Wesley, Redwood City, CA.
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