It has been well documented that population growth, development of biological subsystems and the utilization of resources in ecology and economy frequently follow a logistic or sigmoid time-development. In the context of oil and gas extraction such development is known as Hubbert's peak oil theory. We observe that the logistic equation describes the historic development of nuclear and hydroelectric energy production as well. Previous studies have hypothesized that the present time fastest growing renewable technologies, wind and Solar energy, will develop under similar constraints. Here, we provide evidence that the installation of these technologies follow a logistic curve. In contrast to what is commonly perceived, the specific growth rate in energy extraction from wind turbines and photovoltaics have decreased in recent years. In an optimistic scenario, where we have included forecasted data from the solar and wind associations four years into the future, the logistic model implies that the total installed capacity saturates at around 1.8 TW in 2030. This is in sharp contrast to the almost established belief that these energy technologies will experience an exponential growth far into this century.