In order to realize the rapid and accurate closed-loop calculation of high-voltage direct-current (HVDC) system under multiple fault types, dynamic phasor method is used to model the complete HVDC system including converter transformers. Firstly, in the case of AC asymmetry, the deviation of the actual firing angle and the unbalance of each commutation process are analyzed. Then, an advanced dynamic phasor model for converter, which is suitable for asymmetric faults, is proposed. Subsequently, the ideal converter transformer model is replaced with a new one that considers voltage loss, which improves the calculation accuracy of the AC voltage on the valve side. By combing it with the dynamic phasor model of DC line, the simulation process of HVDC system is reconstructed and closed loop calculation is realized. Based on the CIGRE Benchmark standard system, the proposed model is compared with the simulation results from PSCAD, and the result further proves the effectiveness.