A probability distribution model based on the maximum entropy principle for wind power fluctuation estimation

Abstract

Volatility is an inherent characteristic of wind power. The normal, Weibull, and other distributions are commonly used to describe the characteristics of wind power. However, many of these single distribution models are not suitable to characterize wind power, particularly those converging from multiple wind farm groups. In this study, the maximum entropy distribution model is utilized as probability density function to fit wind power fluctuations. To evaluate the effectiveness and performance of the model, we compared the probability density function curve and cumulative distribution function curve fitting with the mixed Gaussian, the mixed logistic, and the mixed Weibull distribution models using simulation experiments. We developed four scenarios with different numbers of wind farm groups and calculated the fitting error, determination coefficient, and K–S test value for the four models. The simulation results show that the maximum entropy distribution model has the best fitting effect in all four scenarios. Compared with the other three distribution models, the maximum entropy distribution model has clear advantages and is more suitable to describe the fluctuation characteristics of wind power. The parameter estimation of the maximum entropy distribution model can be transformed into a linear optimization problem to significantly reduce calculation complexity.

Keywords

• Wind power fluctuation
• Maximum entropy principle
• Probability density function
• Cumulative distribution function