To achieve the efficient application of impedance analysis in the stability assessment and enhancement of multi-terminal DC distribution systems, this paper proposes the DC-side reduced-order impedance models with power control and AC voltage control, respectively, by taking the load converter station as the object. By using the DC-side current as the feedforward state, the active compensator applied to the load converter station with two control modes is also derived as well as the corresponding reduced-order impedance models. Combined with the reduced-order impedance models, a method based on damping factor sensitivity is further proposed to design the parameters of the derived active compensators. The verification results in the frequency domain and time domain demonstrate the accuracy of the reduced-order impedance and the effectiveness of the proposed compensator parameter design method.