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We introduce a top-down stylized model to analyse the impact of a transition to a European power system based only on wind and solar power. Wind and solar power generation is calculated from high-resolution weather data and based on the country specific electricity demand alone, we introduce a model of the conventional power system that facilitates simple spatio-temporal modelling of its macroscopic behavior without direct reference to the underlying technological, economical, and political development in the system. Using this model, we find that wind and solar power generation can replace conventional power generation and power capacity to a large degree if power transmission across the continent is made possible.