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Title: Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime

Abstract

Average or expectation values for annual power of a wind turbine in a Rayleigh wind regime are calculated and plotted as a function of cut-out wind speed. This wind speed is expressed in multiples of the annual average wind speed at the turbine installation site. To provide a common basis for comparison of all real and imagined turbines, the Rayleigh-Betz wind machine is postulated. This machine is an ideal wind machine operating with the ideal Betz power coefficient of 0.593 in a Rayleigh probability wind regime. All other average annual powers are expressed in fractions of that power. Cases considered include: (1) an ideal machine with finite power and finite cutout speed, (2) real machines operating in variable speed mode at their maximum power coefficient, and (3) real machines operating at constant speed.

Authors:
Publication Date:
Research Org.:
National Renewable Energy Lab., Golden, CO (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Energy Efficiency and Renewable Energy, Washington, DC (United States)
OSTI Identifier:
420358
Report Number(s):
NREL/CP-440-21671; CONF-970135-8
ON: DE97000088; TRN: 97:000734
DOE Contract Number:
AC36-83CH10093
Resource Type:
Conference
Resource Relation:
Conference: 16. American Society of Mechanical Engineers wind energy symposium, Reno, NV (United States), 6-9 Jan 1997; Other Information: PBD: Dec 1996
Country of Publication:
United States
Language:
English
Subject:
17 WIND ENERGY; WIND POWER; CALCULATION METHODS; WIND TURBINES; MATHEMATICAL MODELS

Citation Formats

Carlin, P.W. Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime. United States: N. p., 1996. Web.
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Carlin, P.W. Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime. United States.
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Carlin, P.W. Sun . "Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime". United States. doi:. https://www.osti.gov/servlets/purl/420358.
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@article{osti_420358,
title = {Analytical expressions for maximum wind turbine average power in a Rayleigh wind regime},
author = {Carlin, P.W.},
abstractNote = {Average or expectation values for annual power of a wind turbine in a Rayleigh wind regime are calculated and plotted as a function of cut-out wind speed. This wind speed is expressed in multiples of the annual average wind speed at the turbine installation site. To provide a common basis for comparison of all real and imagined turbines, the Rayleigh-Betz wind machine is postulated. This machine is an ideal wind machine operating with the ideal Betz power coefficient of 0.593 in a Rayleigh probability wind regime. All other average annual powers are expressed in fractions of that power. Cases considered include: (1) an ideal machine with finite power and finite cutout speed, (2) real machines operating in variable speed mode at their maximum power coefficient, and (3) real machines operating at constant speed.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Dec 01 00:00:00 EST 1996},
month = {Sun Dec 01 00:00:00 EST 1996}
}
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Conference:
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  • In 1926 Albert Betz derived a one-dimensional stream tube theory for the maximum power that can be obtained from a wind turbine in a uniform flow. However, for modern large wind turbines there is a considerable velocity gradient in the approaching flow, since the wind flow field above the ground normally is a shear layer with a velocity profile reminding of that of a boundary layer of a wing or a flat plate. The present study extends Betz' theory to a two-dimensional case, where the undisturbed velocity field is given and allowed to vary arbitrarily vertically, and the location ofmore » the wind turbine is given. The maximum power is calculated by the method of calculus of variations. It is found that for common wind velocity profiles the maximum power is only slightly larger than the power, which is obtained by a constant relative wind speed retardation, equal to Betz' retardation, while for a linear velocity profile there is a considerable difference.« less

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    Abstract not provided.

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    Nontorque loads induced by the wind turbine rotor overhang weight and aerodynamic forces can greatly affect drivetrain loads and responses. If not addressed properly, these loads can result in a decrease in gearbox component life. This work uses analytical modeling, computational modeling, and experimental data to evaluate a unique drivetrain design that minimize the effects of nontorque loads on gearbox reliability: the Pure Torque drivetrain developed by Alstom. The drivetrain has a hub-support configuration that transmits nontorque loads directly into the tower rather than through the gearbox as in other design approaches. An analytical model of Alstom's Pure Torque drivetrainmore » provides insight into the relationships among turbine component weights, aerodynamic forces, and the resulting drivetrain loads. Main shaft bending loads are orders of magnitude lower than the rated torque and are hardly affected by wind speed and turbine operations.« less

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  • ; ; ; ...
    Nontorque loads induced by the wind turbine rotor overhang weight and aerodynamic forces can greatly affect drivetrain loads and responses. If not addressed properly, these loads can result in a decrease in gearbox component life. This work uses analytical modeling, computational modeling, and experimental data to evaluate a unique drivetrain design that minimizes the effects of nontorque loads on gearbox reliability: the Pure Torque(R) drivetrain developed by Alstom. The drivetrain has a hub-support configuration that transmits nontorque loads directly into the tower rather than through the gearbox as in other design approaches. An analytical model of Alstom's Pure Torque drivetrainmore » provides insight into the relationships among turbine component weights, aerodynamic forces, and the resulting drivetrain loads. Main shaft bending loads are orders of magnitude lower than the rated torque and are hardly affected by wind conditions and turbine operations.« less