Abstract This paper proposes a novel and hybrid intelligent algorithms to directly modelling prediction intervals (PIs), as an accurate, optimum, reliable and high efficient wind power generation prediction intervals (PIs) are developed by using extreme learning machines (ELM) and self-adaptive evolutionary extreme learning machines (SAEELM). Given significant of uncertainties existed in the wind power generation, SAEELM is the state-of-the-art technology to estimate and quantify the potential uncertainties that may result in risk facing the power system planning, economical operation, and control. In SAEELM, a single hidden layer extreme learning machine is constructed, where the output weight matrix is optimised by using the self-adaptive differential evolution (DE) optimisation method. Also, selecting and adjusting the control parameters and generation strategies involved in differential evolution algorithm to minimises the developed objective cost function. Different case studies using Australian real wind farms have been conducted and analysed. By comparing the statistical analysis and results to other models and methods, e.g. artificial neural networks (ANN), support vector machines (SVM), and Bootstrap, therefore, the proposed approach is an efficient, accurate, robust, and reliable for dealing with uncertainties involved in the integrated power systems, and generation of high-quality PIs. Moreover, the proposed SAEELM based algorithm has a better generalisation than other methods and has a high potential for practical applications.