A power supply of equipment onboard a motor vehicle equipped with a micro-hybrid system that can operate in a regenerative braking mode during which the energy recovered by a reversible rotary machine (1) of the micro-hybrid system is stored in an auxiliary energy storage unit (4). The micro-hybrid system provides a dual-voltage network including, on the one hand, a low voltage (Vb) for supplying a battery (3) of the vehicle and, on the other hand and at the terminals of said auxiliary energy-storage unit, a floating voltage (Vb+X) higher than the low voltage. The floating voltage (Vb+X) is used for powering the onboard equipment of the vehicle that may require high currents during short periods of time for the dynamic operation thereof. The power supply is particularly useful for powering an electric-assistance turbocharger.