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[Display omitted] • Easy-to-use machine learning model for hourly renewable production and load profile modeling. • Novel variance-correction method to improve the reliability of the modeled profiles. • Probabilistic energy supply simulation based on 42 years of meteorological data. • Detailed evaluation and novel categorization of Dunkelflaute events. • Uncertainty analysis of the share of photovoltaic, wind and nuclear electricity. The increasing penetration of weather-dependent renewable energy generation calls for high-resolution modeling of the possible future energy mixes to support the energy strategy and policy decisions. Simulations relying on the data of only a few years, however, are not only unreliable but also unable to quantify the uncertainty resulting from the year-to-year variability of the weather conditions. This paper presents a new method based on artificial neural networks that map the relationship between the weather data from atmospheric reanalysis and the photovoltaic and wind power generation and the electric load. The regression models are trained based on the data of the last 3 to 6 years, and then they are used to generate synthetic hourly renewable power production and load profiles for 42 years as an ensemble representation of possible outcomes in the future. The modeled profiles are post-processed by a novel variance-correction method that ensures the statistical similarity of the modeled and real data and thus the reliability of the simulation based on these profiles. The probabilistic modeling enabled by the proposed approach is demonstrated in two practical applications for the Hungarian electricity system. First, the so-called Dunkelflaute (dark doldrum) events, are analyzed and categorized. The results reveal that Dunkelflaute events most frequently happen on summer nights, and their typical duration is less than 12 h, even though events ranging through multiple days are also possible. Second, the renewable energy supply is modeled for different photovoltaic and wind turbine installed capacities. Based on our calculations, the share of the annual power consumption that weather-dependent renewable generation can directly cover is up to 60% in Hungary, even with very high installed capacities and overproduction, and higher carbon-free electricity share targets can only be achieved with an energy mix containing nuclear power and renewable sources. The proposed method can easily be extended to other countries and used in more detailed electricity market simulations in the future. [ABSTRACT FROM AUTHOR]