The need for decarbonization and diversification of energy resources has led to the development of integrated energy systems (IESs), where multiple resources supply more than one energy sector. One such IES with small modular nuclear reactors and renewables (wind and solar) as generating resources, catering to the demand of the electric grid while producing hydrogen for industries, is modeled in this paper. The physics-based component models are represented using the Modelica language and interconnected to form the IES. The control and coordination of the overall system are ensured by designing a suitable control architecture composed of individual subsystem-level controls and supervisory control. The dynamic performance and the load-following capability of the IES are evaluated, while satisfying the safe operational limits of the components. Different configurations and modes of IES operation are considered, where the adaptability of the control system in the presence of varying demands and renewable generations is validated. The simulation results indicate that hydrogen as a flexible load facilitates the supply of varying grid demand. Additionally, the renewables are also accommodated into the IES owing to the flexibility of the balance of plant associated with the nuclear reactors.