Calculation of ion flow environment of DC transmission lines in the presence of charged aerosol particulates based on upwind-FEM

Highlights

• The solving algorithm for ion flow model in the presence of aerosol particulates is proposed.

• The ion-aerosol attachment coefficients are calculated by Fuchs theory.

• Application of the proposed approach to calculate monopolar and bipolar DC line.

• The charged particulate has a significant influence on the spatial distributions of charge density.

Abstract

Atmospheric environment has a significant influence on ion current, space charge and ground-level electric field profiles of HVDC transmission lines, which attracts a huge amount of interest already. This work presents that the upwind finite element method is applied to calculate the ion flow model in the presence of aerosol particulates. The ion-aerosol attachment coefficient, electrical mobility and diffusion coefficient of charged aerosol are calculated by Fuchs theory and Stokes–Einstein relation. Application of the proposed approach to calculate monopolar and bipolar DC line provides an insight into the physical mechanism of effect of aerosol. Making some appropriate assumptions, computational results present a reasonable agreement with the long-term measured data within a certain aerosol density. It is found that aerosol has a significant influence on the spatial distributions of charge density. In the downwind direction, the ground-level electric field increases significantly because of the dominant of charged aerosol particles.

Introduction

Accurately understanding and calculating the corona-generated charge electric field is a crucial issue for researchers in direct voltage electromagnetic environment and electric power planning research [1]. The ions generated from DC high voltage electric equipment and transmission line may bring about the environment intolerance and inconvenience [2]. It is imperative to understand the influencing factors of ion current environment, which would help avoid exceeding the threshold of design guideline [3].

Considerable efforts have been made to study the theory of ion flow models in the presence of space charge, solution techniques and applications. Fig. 1 presents the generally research progress of ion flow algorithms and its applications. It is found that ion flow theory provides an insight into the physical mechanism of monopolar and bipolar ion flow field.

Due to the strong coupling relation of model governing equations of ion flow, the numerical calculation technique is employed to solve the model. Specific numerical calculation techniques includes flux tracing method [4], finite element method [5], upstream finite element method [6], finite element-flux tracing method [7], charge simulation-weighted residual method [8], particle in cell [9], adaptive finite element method [10], finite volume method [11], Petrov–Galerkin finite element method [12], finite element-finite volume method [13], time-domain finite volume method [14], finite difference based flux tracing method [15], method of characteristics [16], FE-FDM with domain decomposition [17], high-order stabilisation method with Petrov–Galerkin [18] etc.

The theory and experiment pertaining to the main influence factors of ion current environment of DC transmission line have been studied in the past decades. The influencing factors consist the conductor surface condition, the corona inception gradient and ambient atmospheric conditions [1,3]. The influence of wind climate have always been meteorological condition of major concern [11]. However, the aerosol climate effect on the ion current environment is rarely involved. The diameter of aerosol (the suspended solid particulate or liquid naturally in air medium categorized as gaseous dispersion system) in ambient atmosphere is much larger (ranging from 0.001 to 100 μm) than the corona-generated ion or cosmic radiation originated ion. When the ion collides with aerosol particulate, the charge is transferred to the aerosol particulate. Due to the lower mobility of charged aerosol (approximately three to four orders of magnitude lower than the ion mobility), the space charge distribution in the ion drift region of DC line may be changed [19]. Central Research Institute of Electric Power had calculated the charged aerosol density and corona-generated ion density by finite difference method and measured the aerosol density and ion density in the monopolar and bipolar ion environment [20]. However, the aerosol effects on space charge distribution and ground-level total electric field have not been detailedly analyzed, and this is major concerns from the point of view of environmental effect.

In this paper, application of the upwind-finite element method to solve ironized field model in the presence of aerosol is proposed. The ion-aerosol attachment parameter and charge distribution on aerosol particle in monopolar and bipolar ion flow environment are calculated by Fush's theory. The electrical mobility and diffusion coefficient of charged aerosol are calculated by Stokes–Einstein relation. Application of the proposed approach to calculate±350 kV to ±750 kV DC lines is carried out. It indicates that the model considering aerosol solved by proposed technique can be estimate the ion flow environment of monopolar and bipolar HVDC transmission line under different aerosol densities.