This paper introduces the Zero_Sequence Voltage_Injection(ZSVI) based Model Predictive_Control (MPC) to minimize the ripples in dc current & voltage and concurrently regulate the power_flow & dc_current. This paper takes the benefits to calculate and inject best possible zero_sequence_voltage_components to Parallel_Hybrid Modular Multilevel_Converter (PHMMC) dc bus voltage. Dc line current has been derived by discrete_time_dynamic model and also it expands the predictive_model. Required amount of zero sequence voltage is injected to reference voltage of dc bus by using predictive model. Compared to triplen_harmonic injection_method, the proposed scheme improves the PHMMC_performance by minimizing the ripples of dc_voltage ¤t. Execution of the proposed methodology of PHMMC-based HVDC system is done using SIMULINK/MATLAB