Abstract We present two advances in representing variable renewables (VRE) in global energy-economy-climate models: accounting for region-specific integration challenges for eight world regions and considering short-term storage. Both advances refine the approach of implementing residual load duration curves (RLDCs) to capture integration challenges. In this paper we derive RLDCs for eight world regions (based on region-specific time series for load, wind and solar) and implement them into the REMIND model. Therein we parameterize the impact of short-term storage using the highly-resolved model DIMES. All RLDCs and the underlying region-specific VRE time series are made available to the research community. We find that the more accurate accounting of integration challenges in REMIND does not reduce the prominent role of wind and solar in scenarios that cost-efficiently achieve the 2 °C target. Until 2030, VRE shares increase to about 15–40% in most regions with limited deployment of short-term storage capacities (below 2% of peak load). The REMIND model's default assumption of large-scale transmission grid expansion allows smoothening variability such that VRE capacity credits are moderate and curtailment is low. In the long run, VRE become the backbone of electricity supply and provide more than 70% of global electricity demand from 2070 on. Integration options ease this transformation: storage on diurnal and seasonal scales (via flow batteries and hydrogen electrolysis) and a shift in the non-VRE capacity mix from baseload towards more peaking power plants. The refined RLDC approach allows for a more accurate consideration of system-level impacts of VRE, and hence more robust insights on the nature of power sector decarbonization and related economic impacts.