An efficient equivalent-boundary method for 3-D ion-flow field analysis of HVDC bundled conductors at different altitudes

Corona-generated ions around high-voltage direct-current (HVDC) transmission lines form ion-flow fields that are costly to resolve in three dimensions because bundled conductors require fine near-surface meshes. This study develops an equivalent-boundary method for three-dimensional upstream finite element calculations. Potential and ion-density distributions from a refined two-dimensional bundled-conductor model are mapped to a circular boundary in the three-dimensional domain, replacing the explicit subconductor geometry while retaining the external ion-transport solution. For the investigated six-bundle ±800 kV line, the method reduces the mesh from 48.72 million to 1.763 million elements (96.4%) and the computation time from 19,853 to 237.1 s (83.7-fold speedup), with a 1.07% deviation in the building-roof electric field relative to direct three-dimensional modeling. Reduced-scale climate-chamber experiments covering quad- and six-bundle configurations, multiple voltages, and simulated altitudes of 0–5000 m yield overall mean relative errors of 2.93% and 4.64% at representative rooftop and outer ground locations. Applications to sloped terrain and residential buildings show that slope inclination, slope truncation, and building edges redistribute and locally enhance the total electric field, with stronger effects at high altitude. The method therefore provides a computationally efficient means of assessing three-dimensional ion-flow fields in the evaluated complex environments.