Renewable energy systems with x% renewable penetration reveal a cusp singularity at x=100% for the required back-up storage energy capacity. It will be shown that this phenomenon is related to a phase transition, with x being the control parameter and the average storage filling level being the order parameter. Simplified stochastic processes lead to a scaling exponent of one. Based on weather-driven renewable power generation data, a Markov process is proposed, which is also able to describe the temporal correlations in the mismatches between power generation and load, and which is able to reproduce the non-scaling cusp singularity behavior.