This paper introduces the design of the CSIRO variant of the Global Trade and Environment model (GTEM-C). GTEM-C is a hybrid model that combines the top-down macroeconomic representation of a computable general equilibrium model with the bottom-up engineering details of energy production. The model features detailed accounting for global energy flows that are embedded in traded energy goods, and it offers a unified framework to analyse the energy-carbon-environment nexus. As an illustrative example, we present simulation results on global energy transformation under the Intergovernmental Panel on Climate Change's representative carbon pathways 4.5 and 8.5. By testing the model's sensitivity to the relevant parameter, we find that the pace of electrification will significantly contain the spiking of carbon prices because electricity can be produced from carbon-free or less carbon-intensive technologies. The decoupling of energy use and carbon footprint, due to the uptake of clean electricity technologies, such as nuclear, wind, solar, and carbon capture and storage, allows the world to maintain high level of energy consumption, which is essential to economic growth.