A Versatile Mixture Distribution and Its Application in Economic Dispatch with Multiple Wind Farms

An improved versatile distribution for wind power is proposed, with higher representation accuracy and more suitable applications in economic dispatch (ED) compared with Versatile distribution. Further, versatile mixture distribution (VMD) is proposed to represent all possible wind power distribution with customized arbitrary errors. Compared with Gaussian Mixture distribution (GMD), it has more flexible forms and can represent wind power more accurately. Its cumulative distribution function has analytical forms with higher computational efficiency. Then, real-time dynamic ED model and algorithm based on VMD with multiple wind farms (WFs) is proposed. Based on the VMD model, the probability distributions of wind power of each WF and the summation of all WFs are modeled. The ED model and algorithm solve the problem of the correlation of multiple renewable energy random variables with high computation efficiency for real-time ED. The results show that compared with GMD or unimodal distributions, VMD can represent wind power more accurately and can greatly simplify and speed up the ED model and algorithm. Compared with other methods for multiple renewable energy random variables, the proposed model and algorithm can improve economy significantly.