Amplitude-phase information of the voltage/current phasor, which is the prerequisite for grid-tied converter control and protection, can change almost instantaneously in lowvoltage distribution systems with small X/R ratios. However, the equivalent impedances of high-voltage power systems are usually inductive (with large X/R ratios), and the power flow of pertinent grids generates decaying DC (DDC) components with large amplitude and long duration during large disturbances. Therefore, the X/R ratios and DDC components must be fully considered in amplitude-phase detection to achieve effective converter control and protection. To this end, the main components present in the transient voltage/current of a high-voltage power system after unbalanced disturbance are first analyzed, and the general transient model is obtained by synthesizing multi-mode DDC components. Then, by resorting to waveform characteristics of different components, an amplitude-phase detection algorithm is proposed based on the multi-component parallel-detection structure. Compared to existing techniques, the detection time is reduced to half grid cycle. Finally, an iterative variable-interval integral algorithm is developed, improving the anti-noise ability of detection algorithm, and overcoming the computational burden issue. This enables the direct integration of algorithm into the converter's embedded processor. Experiment results verified the effectiveness and superiority of the proposed technique.