Versatile distribution of wind power output for a given forecast value

Abstract

The wind power output distribution for a given forecast value is often described by a theoretical distribution, such as Gaussian, Beta and Cauchy. However, the theoretical distributions could hardly simulate the actual wind power uncertainty for all situations. Moreover, the cumulative distribution function (CDF) or quantile function is more concerned by system operators than the probability density function (PDF). Nonetheless, the CDF of a theoretical distribution usually could not be expressed in a closed form and is commonly derived from the numerical integral of PDF. The estimation error of PDF may hence be cumulatively enlarged through the numerical integral process. Given this background, this paper presents a versatile distribution model that can simulate any shape of the actual distributions of wind power forecast errors. The CDF of the versatile distribution could be written as a closed form so it can be directly applied on fitting the actual CDF. The mathematical feature of the versatile distribution can also facilitate the dispatching decision-making and benefit power system analysis. The results demonstrate the feasibility and effectiveness of the proposed distribution model.