Co-phase traction power supply system provides the insights for solving the existing power quality and electrical sectioning issues in high-speed railways, and the flexible control of co-phase traction substation (CTSS) with the integration of photovoltaic (PV) and hybrid energy storage system (HESS) attracts widespread attention. However, the strong volatilities and uncertainties of PV and traction load introduce challenges to the reliable and economic operation of CTSS. In this study, the energy management of CTSS aims at minimizing the operating cost of CTSS by coordinating PV, HESS, power flow controller (PFC) and the energy transactions with the power grid, where the three-phase voltage unbalance constraint is taken into account in particular. Furthermore, to handle the uncertainties of PV and traction load, a two-stage robust optimization model is proposed. The first stage determines the operating status of HESS and energy transaction status with grid, and the second stage aims at finding the optimal scheduling power of CTSS and the worst-case scenario with maximized operating cost of CTSS. A column-and-constraint generation algorithm is employed to solve this robust optimization model, along with efficient linearization approaches for the formulation of mixed-integer linear programming. The proposed methodology is tested with a real high-speed railway line case in China.