Cophase traction power system has high potential to be power supply for high-speed railway. However, the dc operation voltage of conventional power quality compensation device within, such as railway power quality conditioner, is high and may limit its application and development. The hybrid power quality conditioner (HPQC), in which a capacitive coupled $LC$ structure is added, is thus proposed for lower operation voltage. However, there is less investigation and study on the HPQC parameter design for minimum operation voltage when harmonic compensation is concerned. In this paper, the HPQC design for minimum dc operation voltage under comprehensive fundamental and harmonic compensation is being proposed and introduced. Analysis and case study are also performed to show the advantage of the proposed HPQC design. Simulation and laboratory-scaled experimental results are presented to show effective reduction in dc operation voltage using the proposed HPQC design. Through the simulation and experimental case study and verification, there is a reduction of 15% in operation voltage using the proposed hybrid $LC$ structure design compared with the conventional design. The proposed design does not add much additional cost and can also reduce the coupling inductance value. Similar analysis procedure may be also applied to other $LC$ hybrid-structured active power compensators.