The dramatic evidence of climate change is making the transition to more renewable energy systems an urgent global priority. As energy planners normally look 20-50 years ahead, it is crucial to consider the key uncertainties stemming from inaccurate forecasts (e.g. of fuel prices, investment costs, etc.) in energy models to ensure making robust investment decisions. Nonetheless, uncertainty is to date seldom accounted for in energy planning models. In this paper, we challenge the general perception that the transition to a more renewable energy system always comes at a higher price; to do this, we analyze the impact of uncertainty on the cost of this transition for a real-world national energy system. Concretely, we first generate a set of energy planning scenarios with increasing renewable energy penetration (REP); in a second stage, we perform an uncertainty analysis to compare the cost of these scenarios and thus to determine the significance of the difference in their total cost in presence of uncertainty. Our results show that increasing the amount of renewable energy in a national energy system is not necessarily as- sociated to a higher cost, and can even lead to a cost reduction for some specific realizations of the uncertain parameters.