Empirical models for growth of renewable power are compared; the exponential, logistic, and power-law models. It is shown that the latter is a natural model for growth that slows down due to various constraints, yet not experiencing the effect of an upper limit defined by physical boundaries. One cannot conclude that this model is preferable based on the historical data only, but the predictions also align well with scenarios based on macroeconomic modelling that meet the two-degree target.