Railway network of the type comprising: - a track, - a network power supply, and - a plurality of trains, each train comprising: - propulsion means capable of generating electrical energy by braking, - an internal electrical energy storage system designed to store electrical energy originating from the propulsion means of said train and from the network power supply, and to supply electrical energy to said train and to said supply, - a set of auxiliary equipment, and - means for connecting the train to the network power supply, each train being supplied with energy when it is connected to the network power supply via the connecting means, its internal electrical energy storage system then being connected to said supply, and powered off when it is not connected, each train being capable of passing between an operational state in which its set of auxiliary equipment is connected to the network power supply or to the internal electrical energy storage system of said train and the train is capable of moving on the track, and a stopped state in which said set of auxiliary equipment is disconnected from the network power supply and from the internal electrical energy storage system and the train is not capable of moving on the track, characterised in that at least one of the trains is both in the stopped state and supplied with energy, its internal electrical energy storage system being connected to the network power supply. - a track, - a network power supply, and - a plurality of trains, each train comprising: - propulsion means capable of generating electrical energy by braking, - an internal electrical energy storage system designed to store electrical energy originating from the propulsion means of said train and from the network power supply, and to supply electrical energy to said train and to said supply, - a set of auxiliary equipment, and - means for connecting the train to the network power supply, each train being supplied with energy when it is connected to the network power supply via the connecting means, its internal electrical energy storage system then being connected to said supply, and powered off when it is not connected, each train being capable of passing between an operational state in which its set of auxiliary equipment is connected to the network power supply or to the internal electrical energy storage system of said train and the train is capable of moving on the track, and a stopped state in which said set of auxiliary equipment is disconnected from the network power supply and from the internal electrical energy storage system and the train is not capable of moving on the track, - propulsion means capable of generating electrical energy by braking, - an internal electrical energy storage system designed to store electrical energy originating from the propulsion means of said train and from the network power supply, and to supply electrical energy to said train and to said supply, - a set of auxiliary equipment, and - means for connecting the train to the network power supply, each train being supplied with energy when it is connected to the network power supply via the connecting means, its internal electrical energy storage system then being connected to said supply, and powered off when it is not connected, each train being capable of passing between an operational state in which its set of auxiliary equipment is connected to the network power supply or to the internal electrical energy storage system of said train and the train is capable of moving on the track, and a stopped state in which said set of auxiliary equipment is disconnected from the network power supply and from the internal electrical energy storage system and the train is not capable of moving on the track,