An electric power supply network includes at least one connection point with an upstream electrical network delivering useful power to at least one input of a first electric power supply network of an electrically powered transport system, such as trolley buses, trams, metro, train, or other transport, the first electrical network presenting peak power fluctuations as a function of variable energy needs depending on traffic associated with the transport system. The first electrical network includes at least one power output capable of distributing energy, in particular recovered from the transport system and from the upstream electrical network, to at least a second electrical network, enabling energy to be supplied to electrical consumption points. At least one supervision unit monitors distribution of energy from the power output whenever at least the peak power required by the first transport system is below the useful power available upstream.