Comparison of Three Methods for Wind Turbine Capacity Factor Estimation

Abstract

Three approaches to calculating capacity factor of fixed speed wind turbines are reviewed and compared using a case study. The first “quasiexact” approach utilizes discrete wind raw data (in the histogram form) and manufacturer-provided turbine power curve (also in discrete form) to numerically calculate the capacity factor. On the other hand, the second “analytic” approach employs a continuous probability distribution function, fitted to the wind data as well as continuous turbine power curve, resulting from double polynomial fitting of manufacturer-provided power curve data. The latter approach, while being an approximation, can be solved analytically thus providing a valuable insight into aspects, affecting the capacity factor. Moreover, several other merits of wind turbine performance may be derived based on the analytical approach. The third “approximate” approach, valid in case of Rayleigh winds only, employs a nonlinear approximation of the capacity factor versus average wind speed curve, only requiring rated power and rotor diameter of the turbine. It is shown that the results obtained by employing the three approaches are very close, enforcing the validity of the analytically derived approximations, which may be used for wind turbine performance evaluation.

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“…In similar manner, Weibull distribution [ 5 , 6 , 21 , 24 – 26 ] utilized for fitting variable of wind-speed data x in this study has its cumulative distribution function given by the following expression: where η is the shape and β is the scale parameters [ 21 , 23 , 27 – 29 ] that were evaluated, from n sample sized wind-speed data, from regression of the linearized cumulative distribution function in the following form: Estimated values of η and β obtained from this were also used for evaluating the Weibull mean, μ W , of the wind speed from the following expression [ 10 , 14 , 29 – 32 ]: where Γ(·) is the gamma function of (·).…”

“…Evaluation of the average power output P e ,ave of the wind turbine model, for determining total energy production and the total income from the wind-energy conversion system, was obtained from [ 5 ] It is worth noting that the simulation of electric-power output P e in 9 and average power output P e ,ave in 10 was for wind speed measured at height h 0 = 10 m. For simulating these quantities for different hub heights h of wind turbine model, the extrapolations of scale and shape parameters of the pdfs, β 0 and η 0 at the measurement height h 0 = 10 m, to the hub height h are required. This could be obtained from [ 5 , 35 ] where the exponent ε was evaluated from From the simulated wind-energy system, the capacity factor evaluation employs the ratio of the averaged turbine power to the turbine rated power [ 5 , 24 , 36 ]: …”

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“…In this atlas, this issue is overcomed using actual performance power-curve of the wind turbine and Weibull probability distribution function. This method for wind power calculation is known as quasi-exact method and used in studies [30,56]. The wind speed (v) is first calculated at 10 meters height from the u and v components of wind data available from the ECMWF data-set [44].…”

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“…In the literature, the probability distribution of wind speed is developed by the Weibull distribution and was accepted without any statistical survey [26]. it presents a better adjustment of the wind speed data.…”