We have recently developed a simple yet powerful method to identify key properties of electricity systems with a high share of renewables. Here, our weather-driven methodology is described and applied to model the Danish power system with combined wind and solar energy gross shares of up to 100% of the total demand. We show that in a wind only scenario, surplus energy grows rapidly beyond gross shares of about 50%, while the potential for arbitrage of surplus renewable energy, i.e. demand-side management or high-efficiency storage, is very limited in this case. A scenario with a wind-solar energy mix of 80/20, on the other hand, both decreases the total amount of surplus and has a significantly higher potential for arbitrage of the remaining surplus. However, beyond gross shares of about 75%, only large-scale seasonal storage of, e.g. hydrogen, enables the use of Danish surplus wind and solar energy to cover the residual Danish electricity demand in both scenarios. (C) 2014 Elsevier Ltd. All rights reserved.