## 1 Introduction  
High voltage direct current (HVDC) transmission technology has been widely used in the power system for its advantages in large transmission capacity and long transmission distance. The grounding electrode current can reach several kilo-amperes when the HVDC transmission project is under monopole operation [1]. This current may cause severe interference with buried pipelines in the vicinity of the electrode [2; 3; 4]. The currents can flow into the pipeline at one point and flow out at another point. Metal corrosion can occur at the current-in point, while hydrogen embrittlement may occur at the current-out point, which both threaten the operation safety of pipeline engineering [5; 6]. Therefore, it is very important to determine the interference characteristics of the electrode current with buried pipelines for pipeline risk assessment and safety protection.  
In pipeline engineering, pipe-to-soil potential (PSP) and leakage current density are often used to indicate the DC interference degree [7]. In the past, numerous tests were needed to obtain these two indicators along the pipelines [8; 9]. In situ measurement is often costly and time-consuming so simulations represent an interesting option for the study of such phenomena. Many calculation methods have been proposed to determine the interference under different conditions. [PERSON] et al. used the transmission line model to simulate long pipelines by applying the pipeline conductor parameters and coating parameters to the transmission line equations [10]. [PERSON] et al. extended the simulation methodology by adding a local damage equivalent branch and cathodic protection branch for more practical engineering applications [11]. [PERSON] et al. first calculated the current distribution of the HVDC grounding electrode by the method of moments (MoM) [12]. Then [PERSON] et al. developed the multi-step method to calculate the interaction of the multi-electrodes based on MoM [13; 14]. [PERSON] et al. proposed a field-circuit coupling model to consider the impacts of different protective measures [15]. However, the above-mentioned numerical methods cannot consider the nonlinear electrochemical polarization effectively, which may lead to inaccurate results for density and PSP calculations [16]. The PSP deviates from the equilibrium potential when polarization occurs. This deviation becomes greater as the leakage current density increases. Besides, the polarization relationship is nonlinear and it can result in improper protective measures for pipeline safety.  
There are many parameters that can influence the calculation results, such as the electrode grounding current, soil resistivity, soil structures, pipeline coating characteristics, and the distance between the electrode and pipeline. Differences in these parameters can lead to different pipeline safety assessments and protective measures. Therefore, it is necessary to study the interference distribution characteristics under the various above-mentioned parameters.  
In this paper, a methodology based on a combination of MoM and FEM is proposed to calculate the pipeline interference caused by HVDC electrode current. The proposed method takes into account the pipe-soil interface polarization by introducing a nonlinear boundary condition which is difficult to consider for traditional methods. Then the interference distribution characteristics under different parameters are studied using the proposed method. These characteristics can be used to develop guidelines for practical engineering.