balance, and also takes the form of an exponential function depending on variable renewable energy E shares and parameterized to the Ueckerdt _et al._ data.

- In the MESSAGE model (Messner and Strubegger, 1995, Riahi _et al._ , 2012), region- and sharedependent residual load duration curves (Ueckerdt _et al._ , 2017) are used to parameterize how flexibility of the residual non- variable renewable energy system, variable renewable energy curtailment, and wind and solar PV capacity values change with increasing variable renewable energy share (Johnson et al., 2017--in this issue). These equations are translated into step-wise linear functions that describe the contribution of variable renewable energy to capacity adequacy and system flexibility constraints, where increasing deployment requires more firm (backup) capacity and increasing flexibility from the non- variable renewable energy portion of generation. In addition, electricity storage and hydrogen electrolysis technologies are included as options for repurposing both variable renewable energy and non-variable renewable energy production that would otherwise be curtailed. Thermoelectric technologies are represented in two modes of operation, baseload and flexible, to better account for the cost, efficiency, and availability penalties associated with flexible operation and the consequences of variable renewable energy deployment for non-variable renewable energy plant utilization. Since MESSAGE is a least-cost optimization model with perfect foresight, the additional electricity system requirements for integrating variable renewable energy endogenously influence investment decisions within the power sector.

- The energy-economy-climate model REMIND (Luderer _et al._ , 2013, Luderer _et al._ , 2015) is a Ramsey-type general equilibrium growth model of the macro-economy in which inter-temporal global welfare is maximized, combined with a technology-rich representation of the energy system. Its power sector implementation is based on the region-specific residual load duration curves developed in Ueckerdt _et al._ (2017), which capture the effects of adding wind and solar power to the power sector on a) capacity adequacy, b) dispatch, c) storage and d) curtailment. The residual load duration curves are represented by four load bands plus a capacity adequacy equation. The height of these load bands is a polynomial function of wind and solar share, so their height endogenously adjusts with changing variable renewable energy shares. Investments into the different power technologies are optimized with perfect foresight over the full time horizon of the model. Dispatch is represented through the residual load bands. Short-term storage deployment and curtailment are prescribed by polynomial fits of the variable renewable energy-share-dependent residual load duration curves. As the model uses an optimization framework for investments into dispatchable and variable renewable energy technologies, the share-dependent polynomial residual load duration curves formulation enables the model to fully account for the changing marginal value of variable renewable energy in the investment procedure.

- WITCH (Bosetti _et al._ , 2006, Emmerling _et al._ , 2016) is a hybrid model that combines an aggregated, top-down inter-temporal optimal growth Ramsey-type model (with perfect foresight) with a detailed description of the energy sector. Energy technologies – divided between the electric and the non-electric sectors – are nested in a Constant Elasticity of Substitution (CES) framework, which represents the many economic and non-economic drivers leading to limited technology substitution in a stylized way. Energy demand is modeled in average terms over the year. System integration of variable renewable energies is explicitly modeled through two constraints, related to the flexibility and the capacity adequacy of the power generation fleet. A simple modeling of the electric infrastructure and a generic storage technology are implemented as well (Carrara and Marangoni, 2017).

Among general equilibrium models: 27