Abstract: Recently, flexible DC traction power supply systems have developed rapidly and gained widespread attention for its advantages in optimizing system power flow and improving the utilization of regenerative energy. The ultimate supply capacity (USC), which directly reflects the system's output capability, requires precise evaluation. Given the non-convex nature of the USC model and the associated challenges in finding solutions, this study focuses a novel approach for establishing the USC model of the flexible DC traction power supply system based on second order cone programming (SOCP). First, the branch power flow model is employed to enhance the system's power flow modeling technique, while the rail potential modeling is achieved by introducing a virtual zero potential and a virtual current source. Subsequently, the Taylor expansion method is utilized to linearize the rail potential expression, and the SOCP relaxation method is employed to transform and relax the USC model into a convex optimization model. In conclusion, an case study is specifically devised using Beijing Metro Line 13 A to empirically verify the effectiveness of the proposed method. The findings indicate that through the utilization of the enhancement model described in this study, a significantly accurate result of the USC is achieved, resulting in a reduction of approximately 1 MW in the numerical value, as well as a 5.4-fold increase in the calculation speed. The method proposed in this paper holds profound significance for informing the meticulous planning and design stages of flexible DC traction power supply systems.