Considerations regarding the roles of advanced technologies are crucial in energy-economic modeling, as these technologies, while usually not yet commercially viable, could substitute for fossil energy when relevant policies are in place. To improve the representation of the penetration of advanced technologies, we present a formulation that is parameterized based on observations, while capturing elements of rent and real cost increases if high demand suddenly appears due to large policy shock. The formulation is applied to a global economy-wide model to study the roles of low carbon alternatives in the power sector. While other modeling approaches often adopt specific constraints on expansion, our approach is based on the assumption and observation that these constraints are not absolute—the rate at which advanced technologies will expand is endogenous to economic incentives. The policy simulations are designed to illustrate the response under sudden increased demand for the advanced technologies, and are not intended to represent necessarily realistic price paths for greenhouse gas emissions.