The transition towards a sustainable energy sector depends on how we safely manage the transport and storage of energy to keep up with the demand. Large storage (TWh) of renewable energy can be accomplished by producing an energy carrier like ammonia. This power-to-ammonia production process overly depends on the stability of the ammonia reactor where any variations induced by uncertainties could have a large impact on the performance during its dynamic operations. To determine the effect of these variations, we need to identify which of the uncertainties have to be scrutinized during model design. The current work carries out the development of a dynamic Haber-Bosch process, implementing uncertainties in the model and performing an uncertainty quantification analysis on the process. Subsequently, the sensitivity indices quantify the impact of these uncertainties on the design during ramp-up. The global sensitivity analysis indicated that the reactor inlet temperature has the most considerable impact on the performance during ramp-up, where the hydrogen/nitrogen ratio has the second most significant impact. We see that the uncertainty on the reactor inlet temperature dominates (87.8%) the overall standard deviation of the ammonia production. More precise control over the inlet temperature could reduce this impact on the standard deviation. The work can be extended by including a hydrogen and nitrogen production process while powering the full process with renewable power. We can then measure the effect of coupling renewables directly to the dynamic power-to-ammonia process and optimize the design under uncertainty.