This paper seeks to quantify the benefits of a flexible energy system in the context of enabling higher levels of variable renewable energy on the grid. We explore a nuclear hybrid energy system (NHES) consisting of a 300 MW small modular reactor, wind generation, battery storage, and a reverse osmosis desalination plant. A dispatch rule is constructed within the Risk Analysis Virtual Environment (RAVEN) to model the system. Stochastic optimization and parametric analysis are utilized to explore how increased volatility in the net demand resulting from higher levels of wind penetration affect the optimal solution, and the stability of the system's levelized cost of electricity (LCOE). In this study, net demand is the demand minus wind generation. This work contributes multi-objective analysis implemented through a supply-demand mismatch penalty to illustrate the financial stability and operational reliability benefits of the flexible energy system. In this context, we find that the additional up front cost of flexible loads and energy storage result in greater stability in LCOE as volatility in the demand increases. Additionally, the flexibility results in increased reliability in terms of meeting the demand. Although the analysis is conducted on a NHES, we emphasize the flexibility of the method applied here, in that the RAVEN platform and the multi-objective strategy are widely applicable to the analysis of energy systems faced with uncertainties in supply and demand.