Wind direction and speed are both crucial factors for wind farm layout; however, the relationship between the two factors has not been well addressed. To optimize wind farm layout, this study aims to statistically explore wind speed characteristics under different wind directions and wind direction characteristics. For this purpose, the angular–linear model for approximating wind direction and speed characteristics were adopted and constructed with specified marginal distributions. Specifically, Weibull–Weibull distribution, lognormal–lognormal distribution and Weibull–lognormal distribution were applied to represent the marginal distribution of wind speed. Moreover, the finite mixture of von Mises function (FVMF) model was used to investigate the marginal distribution of wind direction. The parameters of those models were estimated by the expectation–maximum method. The optimal model was obtained by comparing the coefficient of determination value (R2
) and Akaike’s information criteria (AIC). In the numerical study, wind data measured at a featured wind farm in north China was adopted. Results showed that the proposed joint distribution function could accurately represent the actual wind data at different heights, with the coefficient of determination value (R2
) of 0.99.
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