We introduce a new method for incorporating short-term temporal variability of both power demand and VRE (variable renewables) into long-term energy-economy models: the RLDC approach. The core of the implementation is a representation of RLDCs (residual load duration curves), which change endogenously depending on the share and mix of VRE. The approach captures major VRE integration challenges and the energy system's response to growing VRE shares without a considerable increase of numerical complexity. The approach also allows for an endogenous representation of power-to-gas storage and the simultaneous optimization of long-term investment and short-term dispatch decisions of non-VRE plants. As an example, we apply the RLDC approach to REMIND-D, a long-term energy-economy model of Germany, which was based on the global model REMIND-R 1.2. Representing variability results in significantly more non-VRE capacity and reduces the generation of VRE in 2050 by about one-third in baseline and ambitious mitigation scenarios. Explicit modeling of variability increases mitigation costs by about one fifth, but power-to-gas storage can alleviate this increase by one third. Implementing the RLDC approach in a long-term energy-economy model would allow improving the robustness and credibility of scenarios results, such as mitigation costs estimates and the role of VRE.