Modeling Wind Direction Randomness and Correlation Using a Probabilistic Approach

Accurate modeling of wind speed and direction plays a significant role in wind energy research. This paper proposes a probabilistic approach to model the randomness and correlation of wind direction at two nearby wind sites. Such an approach introduces mixture Wrapped Cauchy distribution to fit the marginal wind direction probability distribution at each location. The circular correlation coefficient is applied to measure the correlation between wind directions at two nearby sites. The analytical relationship between the circular correlation coefficient and the copula parameter is derived, which facilitates the determination of the appropriate copula parameter using the bisection method. The joint wind direction probability distribution with the appropriate copula parameter could preserve the circular correlation coefficient at a desirable level. A sampling procedure that produces random and correlated wind directions has also been developed. The collected wind direction data from two wind sites in the U.S are used to verify the proposed approach. The results show that the proposed method can appropriately model the randomness and correlation of collected wind direction data. Furthermore, the produced wind direction samples share similar circular mean value, circular standard deviation, and the circular correlation coefficient with those of collected wind direction samples.