A fractional frequency transmission system (FFTS) is the most competitive choice for long distance transmission of offshore wind power, while the Hexverter, as a newly proposed direct AC/AC converter, is an attractive choice for its power conversion. This paper proposes a novel control scheme characterizing the global stability and strong robustness of the Hexverter in FFTS applications, which are based on the interconnection and damping assignment passivity-based control (IDA-PBC) methodology. Firstly, the frequency decoupled model of the Hexverter is studied and then a port-controlled Hamiltonian (PCH) model is built. On this basis, the IDAPB control scheme of the Hexverter is designed. Considering the interference of system parameters and unmodeled dynamics, integrators are added to the IDA-PB controller to eliminate the steady-state error. In addition, the voltagebalancing control is applied in order to balance the capacitor DC voltages to obtain a better performance. Finally, the simulation results and experimental results are presented to verify the effectiveness and superiority of the IDA-PB controller.