A system supplying electrical power to a vehicle including: a network of electricity consuming units; a first electrical accumulation battery connected to the network, exhibiting a first maximum voltage when unloaded less than a maximum network voltage; a second electrical accumulation battery connected to the network, exhibiting a second maximum voltage when unloaded greater than the maximum voltage when unloaded of the first battery, and a minimum acceptable voltage when unloaded below the maximum network voltage; a drivable alternator connected to the network, configured to deliver to the second battery an electrical energy under a setpoint voltage drivable to various setpoint values; an electronic management facility, configured to impose at least two different setpoint voltages successively on the alternator when the vehicle is running, a low alternator voltage greater than the first maximum voltage, and a high alternator voltage greater both than the minimum voltage and than the low alternator voltage.