This work introduces a model of Future Technology Transformations for the power sector (FTT:Power), a representation of global power systems based on market competition, induced technological change (ITC) and natural resource use and depletion. It is the first component of a family of sectoral bottom-up models of future technology transformations, designed to be integrated into the global macroeconometric model E3MG. ITC occurs as a result of technological learning as given by cumulative investment and leads to highly nonlinear, irreversible and path dependent technological transitions. The model makes use of a dynamic coupled set of logistic differential equations. As opposed to traditional bottom-up energy models based on systems optimisation, logistic equations offer an appropriate treatment of the times and rates of change involved in sectoral technology transformations. Resource use and depletion are represented by local cost-supply curves, which give rise to different regional energy landscapes. The model is explored using two simple scenarios, a baseline and a mitigation case where the price of carbon is gradually increased. While a constant price of carbon leads to a stagnant system, mitigation produces successive technology transitions leading towards the gradual decarbonisation of the global power sector.