Unified Impedance Model of Four-Port Network for Bipolar Overhead Lines in Parallel Multi-Terminal DC Transmission System

There are various operating modes of parallel bipolar multi-terminal DC transmission systems, among which there is an asymmetric condition of unipolar-bipolar hybrid form. In this case, the distribution of harmonics on the line is different from the normal case, and the equivalent impedance of the mode-domain loops obtained by pole-mode transformation is changed. To solve the problem of harmonic analysis on the DC side under asymmetric conditions, a unified impedance model for bipolar DC overhead lines applicable to various conditions is proposed. Firstly, the decoupling model and equivalent circuit of the mode domain of bipolar symmetrical lines are explained. Then, the limitations of the mode-domain component superposition calculation method in the analysis with asymmetric conditions are revealed. On this basis, from the perspective of the dual input and dual output port network of bipolar DC lines, the four-port pole-mode conversion relationship and fourth-order transformation matrix of bipolar DC lines are proposed. A unified impedance model of four-port network for bipolar overhead lines is established. Finally, the simulation results based on PSCAD show that the proposed model can solve the harmonic transfer analysis and exhibit good reliability, with at least 5% reduction in the average relative error under asymmetric conditions.