A wireless power transmitting device may transmit power wirelessly to a wireless power receiving device. The wireless power receiving device may be a portable electronic device with an array of wireless power receiving coils that receive wireless power from wireless power transmitting coils in the wireless power transmitting device. Each receiving coil in the array of wireless power receiving coils may be coupled to a respective rectifier. Control circuitry of the wireless power receiving device may be configured to determine which rectifiers to enable for synchronous rectification. The control circuitry may be configured to enable at least one rectifier based on the alternating-current voltages produced by each coil in the array of receiving coils. The control circuitry may also be configured to enable at least one rectifier based on the output current from each rectifier.