The increasing integration of renewable energy sources into current power systems has posed the challenge of adequately representing the statistical properties associated with their variable power generation. In this paper, a novel procedure is proposed to select a proper synthetic time series generation model for renewable energy sources to analyze power system problems. The procedure takes advantage of the objective of the specific analysis to be performed and the statistical characteristics of the available time series. The aim is to determine the suitable model to be used for generating synthetic time series of renewable energy sources. A set of indicators is proposed to verify that the statistical properties of synthetic time series fit the statistical properties of the original data. The proposal can be integrated into systematic tools available for data analysis without compromising the representation of the statistical properties of the original time series. The procedure is tested using real data from the New Zealand power system in a mid-term analysis on integrating wind power plants into the power system. The results show that the proposed procedure reduces the error obtained in analyzing power systems compared with reference models.