Improved Flux Tracing Method Based on Parametric Curve for Calculating Ion Flow Field of HVDC Transmission Lines

An improved method for tracing electric flux lines in the vicinity of the overhead high voltage direct current (HVDC) transmission lines is developed by using parametric curves. Based on the geometric relation between the electric field vector and the derivative of the parametric curve function, the electric flux lines can be successfully traced without accumulation of the numerical error caused by the differentiation for calculating the electric potential. Considering the structural characteristics of the transmission line, the control points at both ends of the parametric curve can be easily located, and the remaining control points are modified to minimize an error function defined by the electric field vectors at nodes along the curve. Once the electric flux lines are traced, a series of flux tubes is created by bundling adjacent flux lines, and the nodal electric field vectors and space charge densities are iteratively updated. In order to consider the ionized space charge effect, new flux lines of modified electric field are traced, which in turn affects the existing space charge distribution. The process is repeated until the effect of the space charge is fully considered. The performance of the proposed algorithm is verified by comparing the resulting ground profiles of the ion flow field distribution with the result of the analytical model and the long-term measurement of the full-scale transmission line.