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Research Papers

# Influence of Atmospheric Stability on Wind Turbine Power Performance Curves

[+] Author and Article Information
Jonathon Sumner

Canadian Research Chair—Nordic Environment Aerodynamics of Wind Turbines, École de technologie superiéure, Department of Mechanical Engineering, 1100, rue Notre-Dame Ouest, Montreal, Quebec, H3C 1K3, Canadajonathon.sumner.1@etsmtl.ca

Christian Masson

Canadian Research Chair—Nordic Environment Aerodynamics of Wind Turbines, École de technologie superiéure, Department of Mechanical Engineering, 1100, rue Notre-Dame Ouest, Montreal, Quebec, H3C 1K3, Canadachristian.masson@etsmtl.ca

J. Sol. Energy Eng 128(4), 531-538 (Feb 14, 2006) (8 pages) doi:10.1115/1.2347714 History: Received November 15, 2005; Revised February 14, 2006

## Abstract

The impact of atmospheric stability on vertical wind profiles is reviewed and the implications for power performance testing and site evaluation are investigated. Velocity, temperature, and turbulence intensity profiles are generated using the model presented by Sumner and Masson. This technique couples Monin-Obukhov similarity theory with an algebraic turbulence equation derived from the $k-ϵ$ turbulence model to resolve atmospheric parameters $u*$, $L$, $T*$, and $z0$. The resulting system of nonlinear equations is solved with a Newton-Raphson algorithm. The disk-averaged wind speed $u¯disk$ is then evaluated by numerically integrating the resulting velocity profile over the swept area of the rotor. Power performance and annual energy production (AEP) calculations for a Vestas Windane-34 turbine from a wind farm in Delabole, England, are carried out using both disk-averaged and hub height wind speeds. Although the power curves generated with each wind speed definition show only slight differences, there is an appreciable impact on the measured maximum turbine efficiency. Furthermore, when the Weibull parameters for the site are recalculated using $u¯disk$, the AEP prediction using the modified parameters falls by nearly 5% compared to current methods. The IEC assumption that the hub height wind speed can be considered representative tends to underestimate maximum turbine efficiency. When this assumption is further applied to energy predictions, it appears that the tendency is to overestimate the site potential.

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## Figures

Figure 1

Layout of the Delabole wind farm (14)

Figure 2

Wind rose at 44m measured at M1

Figure 3

Wind frequency distribution and Weibull fit at 33m measured at M1

Figure 4

Mathematical representation of swept area

Figure 5

Frequency distribution of percent error in estimate of u(44m)

Figure 6

Histogram of lost data by wind speed

Figure 7

Measured power performance curve for Windane-34 (Turbine 9)

Figure 8

Measured power coefficient for Windane-34 (Turbine 9)

Figure 9

Measured power coefficient for Windane-34 (Turbine 9)

Figure 13

Histogram of lost data by wind speed

Figure 14

Comparison of Weibull curves (a) using u(H) and (b) using u¯disk

Figure 15

Percent difference in AEP estimates for different (a) diameters and (b) hub heights

Figure 10

Measured power performance curve for Windane-34 (Turbine 7)

Figure 11

Measured power coefficient for Windane-34 (Turbine 7)

Figure 12

Measured power coefficient for Windane-34 (Turbine 7)

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