Abstract. Three simple, empirical models for growth of power consumption in the renewable energy sector are compared. These are the exponential, logistic, and power-law models. The exponential model describes growth at a fixed relative growth rate, the logistic model saturates at a fixed limit, while the power-law model describes slowing, but unlimited, growth. The model parameters are determined by regression to historical global data for solar and wind power consumption, and model projections are compared to scenarios based on macroeconomic modelling that meet the 2° target. It is demonstrated that rational rejection of an exponential growth model in favour of a logistic growth model cannot be made from existing data for the historical evolution of global renewable power consumption y(t). It is also shown that the logistic model yields saturation of growth at unrealistic low levels. The power-law growth model is found to give very good fits to the data through the last decade, and the projections align very well with the scenarios. Power-law growth is equivalent to the simple law that the relative growth rate y′∕y decays inversely proportional to time. It is shown that this is a natural model for growth that slows down due to various constraints, yet not experiencing the effect of a strict upper limit defined by physical boundaries. If the actual consumption follows the power-law curve in the years to come the exponential-growth null hypothesis can be correctly rejected around 2020.