TY - JOUR

T1 - Theoretical derivation of wind power probability distribution function and applications

AU - Altunkaynak, Abdüsselam

AU - Erdik, Tarkan

AU - Dabanli, Ismail

AU - Şen, Zekai

PY - 2012/4

Y1 - 2012/4

N2 - The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.

AB - The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.

KW - Perturbation

KW - Power

KW - Statistical parameter

KW - Weibull distribution

KW - Wind

UR - http://www.scopus.com/inward/record.url?scp=84855272234&partnerID=8YFLogxK

U2 - 10.1016/j.apenergy.2011.08.038

DO - 10.1016/j.apenergy.2011.08.038

M3 - Article

AN - SCOPUS:84855272234

SN - 0306-2619

VL - 92

SP - 809

EP - 814

JO - Applied Energy

JF - Applied Energy

ER -