The Mu3e experiment under construction at the Paul Scherrer Institute, Switzerland, aims to search for the lepton flavour violating decay of a muon into one electron and two positrons with an ultimate sensitivity of one in $10^{16}$ muon decays. The detector for the Mu3e experiment consists of High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) combined with scintillating tiles and fibres for precise timing measurements. The entire detector and front-end electronics are located in the 1m diameter bore of a 1T superconducting magnet. A compact power distribution system based on custom DC-DC converters provides the detector ASICs and readout FPGAs with supply voltages of 1.1V to 3.6V with currents up to 30A per channel. These converters are placed as close as possible to the detector and provide 10kW of power in total. For the whole experiment a total of 126 DC-DC converters is required. The paper presents the results of recent prototype tests and the path to the production of the full power system.