The utilization of a DC-link transmission corridor of embedded VSC HVDC for a DC power injection from renewable energy sources to increase the power flow capability and AC network stability support is a promising technology. However, DC faults on the DC transmission line are likely to threaten the system's operation and stability, especially when the DC power injection exceeds certain limits. A DC single line-to-earth fault is the most likely fault scenario and its effect on the VSC HVDC operation will depend on the earth-loop impedance. Adding an injection point on the DC-link will reduce the earth-loop impedance, hence imposing a danger of increasing the earth fault current. Therefore, in this paper, a VSC HVDC with a DC power injection on the DC-link is studied, the DC-line-to-earth fault is analyzed in the time domain, and its effects on the DC and AC sides of the system are presented. The analysis is based on a developed state-space representation of the system under a single-line-to earth fault. The zero-input zero-state (ZIZS) response is used to find the solution of the state-space representation. In order to correlate the state-space solution with a simulation, the system is modeled in MATLAB/Simulink. Interestingly, it was observed that a quick recharging of the DC-link capacitor due to a power injection created an additional damping of the postfault oscillations