The use of variable renewable energy sources to generate electricity introduces a dependency on meteorological factors into power systems. With the renewables share growing globally, often driven by political pressures, the reliability and efficiency of power systems are increasingly affected by this dependency. In this paper, we investigate the impact of the natural variability of meteorological parameters on the European power system in 2030. We specifically focus on (1) analysing the main European weather patterns affecting renewable energy production and (2) understanding the co-variability of this production among European countries. The identification of a set of patterns in the behaviour of key power system operation indicators allows us to analyse the relationship between large-scale weather regimes and daily power system operations in a 2030 European energy context. Regarding renewable generation, analysis of the co-variability shows that European power systems tend to form two clusters, in each of which all the regions tend to show a positive correlation among themselves and a negative correlation with the other cluster. Our analysis of the most important large-scale weather regimes shows that during cyclonic patterns, the carbon intensity of all the European power systems is lower than normal, while the opposite happens during blocking regimes.