Hybrid energy systems consisting of multiple energy inputs and multiple energy outputs have been proposed to be an effective element to enable ever increasing penetration of clean energy. In order to better understand the dynamic and probabilistic behavior of hybrid energy systems, this paper proposes a model combining Fourier series and autoregressive moving average (ARMA) to characterize historical weather measurements and to generate synthetic weather (e.g., wind speed) data. In particular, Fourier series is used to characterize the seasonal trend in historical data, while ARMA is applied to capture the autocorrelation in residue time series (e.g., measurements minus seasonal trends). The generated synthetic wind speed data is then utilized to perform probabilistic analysis of a particular hybrid energy system con guration, which consists of nuclear power plant, wind farm, battery storage, natural gas boiler, and chemical plant. As a result, requirements on component ramping rate, economic and environmental impacts of hybrid energy systems, and the effects of deploying different sizes of batteries in smoothing renewable variability, are all investigated.