Electric power supply system for a vehicle including a heat engine able to propel the vehicle, comprising: - a network of at least one electricity consuming member, - a first electric accumulator battery connected to the network, - a controllable alternator connected to the network, driven by the engine, and able to deliver electric power to the network at a setpoint voltage controllable to at least a strictly positive low alternator voltage (Valt_basse), and to a high alternator voltage (Valt_haute) strictly higher than the low alternator voltage, - an ammeter making it possible to measure the instantaneous intensity (I res) consumed by the power network, - an estimator of the state of charge of the first battery making it possible to estimate the intensity (I) of the potential recharging current that the first battery would be capable of absorbing if it was at that instant powered at the high alternator voltage (Valt_haute), characterized in that the system also comprises: - a meter of the speed of rotation of the alternator, - an electronic control unit linked to the meter, to the state of charge estimator and to the ammeter, and linked to a map of the alternator yield as a function of the alternator speed and of the intensity output by the alternator, the electronic control unit being configured to estimate a first alternator yield (Rend 1) corresponding to the current speed of rotation (ω) of the alternator, and to the intensity of current (I res) consumed actually drawn from the network, to estimate a second alternator yield (Rend 2) corresponding to the current speed of rotation of the alternator and to the sum (I +I res) of the intensities of the potential recharging current of the first battery (I) and of said current consumed (I res), and to impose the high alternator voltage (Valt_haute) if the difference between the second yield and the first yield is higher than a first threshold (Δ). - a network of at least one electricity consuming member, - a first electric accumulator battery connected to the network, - a controllable alternator connected to the network, driven by the engine, and able to deliver electric power to the network at a setpoint voltage controllable to at least a strictly positive low alternator voltage (Valt_basse), and to a high alternator voltage (Valt_haute) strictly higher than the low alternator voltage, - an ammeter making it possible to measure the instantaneous intensity (I res) consumed by the power network, - an estimator of the state of charge of the first battery making it possible to estimate the intensity (I) of the potential recharging current that the first battery would be capable of absorbing if it was at that instant powered at the high alternator voltage (Valt_haute), characterized in that the system also comprises: - a meter of the speed of rotation of the alternator, - an electronic control unit linked to the meter, to the state of charge estimator and to the ammeter, and linked to a map of the alternator yield as a function of the alternator speed and of the intensity output by the alternator, the electronic control unit being configured to estimate a first alternator yield (Rend 1) corresponding to the current speed of rotation (ω) of the alternator, and to the intensity of current (I res) consumed actually drawn from the network, to estimate a second alternator yield (Rend 2) corresponding to the current speed of rotation of the alternator and to the sum (I +I res) of the intensities of the potential recharging current of the first battery (I) and of said current consumed (I res), and to impose the high alternator voltage (Valt_haute) if the difference between the second yield and the first yield is higher than a first threshold (Δ).