HVDC additional transient control is an essential means to elevate the transient stability of AC/DC interconnected systems and the inevitable requirement of intelligent transmission. Two-stage transient additional control and a smooth switching strategy are proposed. By establishing an extended state observer for unbalanced power in the system disturbance, the real-time and accurate estimation of unstable power is realized, and an adaptive emergency power support controller is constructed. The mathematical model of the system is identified by using Total Least Squares-Estimation on Signal Parameters via Rotational Technique (TLS-ESPRIT). Based on the singular value reduction theory, the HVDC additional Active Disturbance Rejection Damping Controller (ADRDC) that can inhibit the low-frequency oscillation of the system is designed. Finally, two switching strategies are designed based on the change in the state of the network fault switch and the change in the power angle oscillation curve. The three-in-feed HVDC system is built in PSCAD, and the simulation analysis is carried out. The simulation results confirm the validity of the proposed method.