A power supply for a power line includes a synchronization module having a receiver configured for receiving a clock signal from a satellite-based positioning system and an oscillator configured for generating a periodic signal synchronized to the received clock signal. The power supply includes an inverter module having an inverter configured for supplying an AC voltage to the power line, receiving the periodic signal from the synchronization module, and controlling the inverter using the received periodic signal as a synchronization reference signal for the supplied AC voltage. The power supply further includes a power exchange control module configured for: monitoring an active power flow P from the inverter module to the power line, determining whether the active power flow P satisfies a reverse-flow condition, and when the reverse-flow condition is determined, adapting at least one of a phase and an output voltage of the supplied AC voltage.