The Japan Aerospace Exploration Agency (JAXA) has developed a power processing unit (PPU) for a 6 kW Hall thruster system. The PPU is a candidate for future mission applications, such as all-electric satellites, exploration vehicles, and orbital transfer services. The PPU has to be small and still provide a wide output range of outputs, consider the in orbit and launch environments, and manage any instability in the Hall thruster's discharge. Specifically, the four converters that make up the anode power supply of the PPU is digitally controlled to reduce the size of the control circuit. It must operate stably despite small output capacitors and long dead times. This article clarifies the design criteria for the power supply, focusing on the size of capacitors and the PI control parameters to solve these problems. The result is a compact, high-performance PPU for the 6 kW Hall thruster. The power supply meets stringent design criteria and operates the thruster stably with an output voltage that can be varied between 200 and 730 V, provide a maximum power of 5.9 kW, and offer a maximum efficiency of 96.1% in the coupling test for the 6 kW Hall thruster. The proposed PPU, including the anode power supply, achieves a power density of 0.3 kW/kg, significantly higher than that of comparable PPUs.