An iterative particle tracking method for steady-state surface charge calculation on HVDC GIL spacers

Steady-state surface charge calculation for high voltage direct current gas insulated line (HVDC GIL) spacers requires coupling gas ion transport with current continuity across gas–solid interfaces, often causing high computational cost and convergence difficulties. This study combines a particle tracking method (PTM) with an iterative gas–solid interface coupling scheme (IGSCS) to develop PTM-IGSCS for natural ionization, drift-dominated conditions. When space charge feedback, ion diffusion, and ion recombination are negligible, the electric field is solved independently from the Laplace equation, and ions are tracked along field lines. With constant ion mobility, the divergence-free drift velocity yields ion concentrations directly from travel time, and the mapped concentrations determine the gas drift conductivity for interface iteration. A 1D analytical solution verifies the coupling implementation, while two surface conductivity cases assess the accuracy of PTM-IGSCS against full Poisson–Nernst–Planck (PNP)-based IGSCS and transient analysis. PTM-IGSCS closely reproduces both reference solutions over most spacer surfaces, with the largest deviations confined to localized regions of steep gradient. Across four matched mesh resolutions, PTM-IGSCS with four workers was faster than IGSCS in the reported single run comparisons, whereas serial performance depended on mesh resolution. In two surface conductivity cases, the complete parallel PTM-IGSCS procedure achieved speedups of 17.4 and 201.1 over transient analysis. Sensitivity analyses identify particle-to-mesh transfer as a principal localized numerical difficulty, while particle tracking remains a substantial component of the computational cost. Under the conditions studied here, PTM-IGSCS lowers the cost of steady-state surface charge calculation while retaining the gas–solid interface coupling framework.