The penetration of Variable Renewable Energies (VREs) in the electricity mix poses serious challenges in terms of management of the electrical grids, as the associated variability and non-dispatchability are in contrast with the requirement that the load be instantaneously equalized by the generation. One of the goals of Integrated Assessment Models (IAMs) is to simulate the evolution of electricity demand and generation mix over time, therefore a proper modeling of VRE system integration is crucial. In this paper we discuss how different modeling mechanisms can profoundly impact the evolution of the electricity mix, and specifically renewable penetration. In particular, we focus on the effects of introducing a set of explicit system integration constraints in a model, WITCH, characterized by a Constant Elasticity of Substitution (CES) framework.