An electrical power supply system includes a battery of cells, the battery including an ammeter configured to measure battery current flowing through the battery, and at least one voltage sensor configured to measure voltage at terminals of a cell. An electronic control unit is configured to deliver a maximum permissible electrical power setpoint. The control unit is configured to calculate a maximum permissible electrical power associated with a cell by taking the minimum of at least two values, including a first electrical power and a second electrical power.