An Improved Calculation Method Based on Newton–Raphson Method for Ion Flow Field of UHVDC Transmission Lines at High Altitude

Abstract

The fast and accurate solution of the total electric field and ion current density is crucial for the electromagnetic environment of ultra high voltage direct current (UHVDC) transmission lines. In this article, an improved method based on Newton–Raphson method (NRM) and upstream finite element method (UFEM) is proposed to calculate the ion flow field under complex conditions. According to the gas motion theory, the corona-onset electric field, ion mobility, and recombination coefficient are obtained at high altitude and put into the ion flow field model in this article. Subsequently, the charge density is used to solve Poisson’s equation, and the current continuity equations are calculated by UFEM. After that, the charge density of the conductor surface is updated based on NRM. These three parts are iterated repeatedly until the convergence conditions are met. According to the test results of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm$</tex-math> </inline-formula> 800-kV UHVDC transmission line at high altitude, the validity and rationality of the proposed method are verified. The result demonstrates that due to the reduction of atmospheric pressure at the high altitude, the corona-onset electric field decreases, and the ion mobility and recombination coefficient increase, which makes the total electric field and ion current density at ground level increase. Compared with the traditional methods, the improved method is insensitive to the initial value of the surface charge density. Moreover, this proposed method can effectively improve the convergence ability and achieve the stable and fast calculation of the ion flow field at high altitude.