Ion‐flow field calculation of HVDC overhead lines using a high‐order stabilisation technique based on Petrov–Galerkin method

The ion‐flow environment is an important corona design factor of HVDC transmission lines. The space charges generated by corona form a typical convection‐dominated ion‐flow field. For this special transport phenomenon, however, standard Galerkin FEM always presents serious deficiencies. In this study, a new approach is used to solve ion‐flow field based on Petrov–Galerkin method derived from the theory of fluid computation. A high‐order stabilisation technique is used to overcome the non‐physical oscillations in the presence of highly convective effects. This algorithm is equivalent to the proper modification of weight function according to the direction and magnitude of local drift velocity. It reflects the characteristic of information propagation in flow problem. The establishment procedure of weak form and matrix gives a further explanation on the deficiency of Galerkin method. Moreover, to guarantee convergence of the iteration for this fully‐coupled non‐linear problem, a relaxation method is introduced in the iterative loop. Calculations with the Petrov–Galerkin least square method are in good agreement with analytical solution and experiment values of ground‐level values and corona losses. Results show that the proposed stabilisation technique is able to preclude the numerical spurious oscillation and has a higher‐order accuracy than the fully‐upwind treatment.