Post on 26-Mar-2023
Citation: Li, X.; Li, C.; Bai, F.; Cao, F.
Study on the Interference
Distribution Characteristics of the
HVDC Grounding Electrode Current
with Buried Pipelines Based on MoM
and FEM. Appl. Sci. 2022, 12, 4433.
https://doi.org/10.3390/
app12094433
Academic Editor: Gilsoo Jang
Received: 4 April 2022
Accepted: 25 April 2022
Published: 27 April 2022
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applied sciences
Article
Study on the Interference Distribution Characteristics of theHVDC Grounding Electrode Current with Buried PipelinesBased on MoM and FEMXiong Li 1,*, Chengrong Li 1, Feng Bai 2 and Fangyuan Cao 2
1 State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North ChinaElectric Power University, Beijing 102206, China; crl@ncepu.edu.cn
2 China Electric Power Research Institute, Beijing 100192, China; baifeng@epri.sgcc.cn (F.B.);caofangyuan@epri.sgcc.com.cn (F.C.)
* Correspondence: leex@ncepu.edu.cn
Abstract: It is very important to calculate the interference of high voltage direct current (HVDC)grounding current with pipelines accurately and take proper protective measures to ensure energytransmission safety. There is still a lack of systematic research into related prediction methods thatconsider the nonlinear polarization on the interface between the soil and pipelines. In this paper,a methodology is proposed for calculating the coupling voltage and current on buried pipelinesinduced by grounding currents that accounts for nonlinear polarization based on the method ofmoments (MoM) and the finite element method (FEM). The validity of the proposed mathematicalmodel is verified by a scale experiment. The interference distribution characteristics under differentparameters are analyzed using the proposed method. The results show that the relationship betweenthe maximum leakage current density and the electrode grounding current satisfy the linear function.The corrosion area becomes more concentrated as the grounding current increases. The corrosionarea range increases substantially as the distance increases, whereas the influence degree decreasessubstantially. Both the maximum leakage current density and corrosion risk area are positivelycorrelated with the soil resistivity.
Keywords: HVDC grounding electrode; buried pipelines; nonlinear polarization; method of moments (MoM);finite element method (FEM); pipe-to-soil potential; leakage current density; distribution characteristics
1. Introduction
High voltage direct current (HVDC) transmission technology has been widely used inthe power system for its advantages in large transmission capacity and long transmissiondistance. The grounding electrode current can reach several kilo-amperes when the HVDCtransmission project is under monopole operation [1]. This current may cause severeinterference with buried pipelines in the vicinity of the electrode [2–4]. The currents canflow into the pipeline at one point and flow out at another point. Metal corrosion can occurat 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 veryimportant to determine the interference characteristics of the electrode current with buriedpipelines for pipeline risk assessment and safety protection.
In pipeline engineering, pipe-to-soil potential (PSP) and leakage current density areoften used to indicate the DC interference degree [7]. In the past, numerous tests wereneeded to obtain these two indicators along the pipelines [8,9]. In situ measurement isoften costly and time-consuming so simulations represent an interesting option for thestudy of such phenomena. Many calculation methods have been proposed to determinethe interference under different conditions. Lagace et al. used the transmission line modelto simulate long pipelines by applying the pipeline conductor parameters and coating
Appl. Sci. 2022, 12, 4433. https://doi.org/10.3390/app12094433 https://www.mdpi.com/journal/applsci
Appl. Sci. 2022, 12, 4433 2 of 13
parameters to the transmission line equations [10]. Yu et al. extended the simulationmethodology by adding a local damage equivalent branch and cathodic protection branchfor more practical engineering applications [11]. Giao et al. first calculated the currentdistribution of the HVDC grounding electrode by the method of moments (MoM) [12]. ThenDawalibi et al. developed the multi-step method to calculate the interaction of the multi-electrodes based on MoM [13,14]. Zhang et al. proposed a field-circuit coupling model toconsider the impacts of different protective measures [15]. However, the above-mentionednumerical methods cannot consider the nonlinear electrochemical polarization effectively,which may lead to inaccurate results for density and PSP calculations [16]. The PSP deviatesfrom the equilibrium potential when polarization occurs. This deviation becomes greateras the leakage current density increases. Besides, the polarization relationship is nonlinearand it can result in improper protective measures for pipeline safety.
There are many parameters that can influence the calculation results, such as theelectrode grounding current, soil resistivity, soil structures, pipeline coating characteristics,and the distance between the electrode and pipeline. Differences in these parameterscan lead to different pipeline safety assessments and protective measures. Therefore, it isnecessary 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 proposedto calculate the pipeline interference caused by HVDC electrode current. The proposedmethod takes into account the pipe-soil interface polarization by introducing a nonlinearboundary condition which is difficult to consider for traditional methods. Then the interfer-ence distribution characteristics under different parameters are studied using the proposedmethod. These characteristics can be used to develop guidelines for practical engineering.
2. Interference Mechanism of the Grounding Current
The high-voltage DC grounding electrode is a grounding facility that provides a lowresistance path during the operation of the HVDC transmission system [17]. Figure 1 showsthe interference process of the DC grounding electrode current on the buried metallicpipelines. The earth currents flow into the pipeline in the area close to the groundingelectrode when the electrode is under anode operation. The currents flow out of the pipelineat the two ends which are far away from the electrode. As we can see, electrochemicalcorrosion occurs in the area currents flow out. The pipe-soil potential also has an obviouspositive shift.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 2 of 13
the interference under different conditions. Lagace et al. used the transmission line model
to simulate long pipelines by applying the pipeline conductor parameters and coating pa-
rameters to the transmission line equations [10]. Yu et al. extended the simulation meth-
odology by adding a local damage equivalent branch and cathodic protection branch for
more practical engineering applications [11]. Giao et al. first calculated the current distri-
bution of the HVDC grounding electrode by the method of moments (MoM) [12]. Then
Dawalibi et al. developed the multi-step method to calculate the interaction of the multi-
electrodes based on MoM [13,14]. Zhang 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 devi-
ates 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 elec-
trode 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 nec-
essary to study the interference distribution characteristics under the various above-men-
tioned 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 inter-
ference distribution characteristics under different parameters are studied using the pro-
posed method. These characteristics can be used to develop guidelines for practical engi-
neering.
2. Interference Mechanism of the Grounding Current
The high-voltage DC grounding electrode is a grounding facility that provides a low
resistance path during the operation of the HVDC transmission system [17]. Figure 1
shows the interference process of the DC grounding electrode current on the buried me-
tallic pipelines. The earth currents flow into the pipeline in the area close to the grounding
electrode when the electrode is under anode operation. The currents flow out of the pipe-
line at the two ends which are far away from the electrode. As we can see, electrochemical
corrosion occurs in the area currents flow out. The pipe-soil potential also has an obvious
positive shift.
Grounding Electrode
Pipeline
PSPAnode zone Anode zone
Cathode zone
Figure 1. Interference process of HVDC electrode currents on pipelines. Figure 1. Interference process of HVDC electrode currents on pipelines.
Different electrochemical reactions occur for different interference areas [18]. The elec-trochemical reaction for the anode interference area is usually described by:
2Fe → 2Fe2++4e
Appl. Sci. 2022, 12, 4433 3 of 13
For the cathode interference area, hydrogen evolution reaction or oxygen absorptionreactions dominate under different soil medium environments. In general, it can be shownas follows:
2H+ + 2e− → H2 acid oxygen-free conditionH2O+2e− → 2OH− + H2 neutral or alkaline oxygen-free conditionO2 + 4H+ + 4e− → 2H2O acid aerobic conditionO2 + 2H2O+4e− → 4OH− alkaline aerobic condition
The above electrochemical reactions can finally lead to a specific relationship betweenthe PSP and the leakage current which can be defined as follows:
J = fp(ϕp − ϕs) (1)
where J, ϕp and ϕs are the leakage current density, the pipe-side potential and the soil-sidepotential interface between the soil and pipe, respectively. The nonlinear function f p, whichdescribes the relationship between the pipe-to-soil potential and the leakage current density,can be measured by experiment. The three-electrode system is often used to measure thepolarization curves with the potential sweep method [19]. Figure 2 shows the typicalthree-electrode system for measuring polarization curves.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 3 of 13
Different electrochemical reactions occur for different interference areas [18]. The
electrochemical reaction for the anode interference area is usually described by:
2+e e2F 2F +4e
For the cathode interference area, hydrogen evolution reaction or oxygen absorption
reactions dominate under different soil medium environments. In general, it can be shown
as follows:
2
2 2
2 2
2 2
2H 2e H acid oxygen-free condition
H O+2e 2OH H neutral or alkaline oxygen-free condition
O 4H +4e 2H O acid aerobic condition
O 2H O+4e 4OH alkaline aerobic condition
The above electrochemical reactions can finally lead to a specific relationship be-
tween the PSP and the leakage current which can be defined as follows:
p p s( )J f (1)
where J, p and s are the leakage current density, the pipe-side potential and the soil-side
potential interface between the soil and pipe, respectively. The nonlinear function fp,
which describes the relationship between the pipe-to-soil potential and the leakage cur-
rent density, can be measured by experiment. The three-electrode system is often used to
measure the polarization curves with the potential sweep method [19]. Figure 2 shows the
typical three-electrode system for measuring polarization curves.
Luggin capillary
Electrochemical workstation
CE WE RE
Counter electrode
Workingelectrode
Reference electrode
V
A
Figure 2. Typical three-electrode system for measuring polarization curves.
The discrete measurement data can be fitted by the Butler-Volmer equation which is
one of the most fundamental equations in electrochemical kinetics. Equation (2) shows the
typical Butler-Volmer equation [20]:
P ( ) (exp( ) exp( ))corr corrcorr
a c
E E E EJ f E J
(2)
where J and E are current density and PSP, respectively, and are obtained by measure-
ment. corr corr, , ,a cE J are the metal self-corrosion potential, self-corrosion current den-
sity, Tafel slope of the anode reaction and Tafel slope of the cathode reaction, respectively.
The four parameters to be fitted can be obtained using the least square method. Then, the
fitted functions can be used in the proposed methodology. The methodology must
Figure 2. Typical three-electrode system for measuring polarization curves.
The discrete measurement data can be fitted by the Butler-Volmer equation which isone of the most fundamental equations in electrochemical kinetics. Equation (2) shows thetypical Butler-Volmer equation [20]:
J = fP(E) = Jcorr(exp(E− Ecorr
βa)− exp(−E− Ecorr
βc)) (2)
where J and E are current density and PSP, respectively, and are obtained by measurement.Ecorr, Jcorr, βa, βc are the metal self-corrosion potential, self-corrosion current density, Tafelslope of the anode reaction and Tafel slope of the cathode reaction, respectively. The fourparameters to be fitted can be obtained using the least square method. Then, the fittedfunctions can be used in the proposed methodology. The methodology must consider thenonlinear polarization to calculate the current and potential distribution accurately.
3. Mathematical Model Combining MoM with FEM
Pipeline corrosion is mainly caused by the resistive coupling of the grounding currentson the pipeline metal. The computation domain includes the soil area, the pipeline con-ductor area, as well as the infinite air-earth boundary, the grounding conductor boundary,and the interface boundary between the soil area and the pipeline conductor area. Figure 3
Appl. Sci. 2022, 12, 4433 4 of 13
shows the boundary value problem of the resistive coupling model between the groundingelectrode and pipelines.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 4 of 13
consider the nonlinear polarization to calculate the current and potential distribution ac-
curately.
3. Mathematical Model Combining MoM with FEM
Pipeline corrosion is mainly caused by the resistive coupling of the grounding cur-
rents on the pipeline metal. The computation domain includes the soil area, the pipeline
conductor area, as well as the infinite air-earth boundary, the grounding conductor
boundary, and the interface boundary between the soil area and the pipeline conductor
area. Figure 3 shows the boundary value problem of the resistive coupling model between
the grounding electrode and pipelines.
Figure 3. Schematic diagram of the boundary value problem.
The conductivities are assumed to be homogeneous. Then, the soil field Ωs and pipe
conductor field Ωp belong to the constant current field so the potential satisfies Laplace’s
equations. The air can be considered as electrical insulating medium so the current flow-
ing out of the air-earth boundary (Sg) is zero. The total leakage current of the grounding
electrode should equal the injected current in the HVDC transmission system based on
the charge conservation law. According to the interface conditions for electric field vec-
tors, the current density on the soil side should equal the current density on the pipe con-
ductor side. Besides, the leakage current density also should satisfy the polarization rela-
tionship with the pipe-to-soil potential ( s p ). The theoretical equations for the above
three-dimensional boundary value problem can be formulated as follows:
ele
s s
p p
sg
ss hvdc ele
p sp s
p
2
s p
2
p
( ) 0,
( ) 0
( )
( ),
( ) ( )
0,
( ),( ) ( )
S
r r
r r
rr S
n
rI r S
n
r r
n n
r r r S
ds
f
,
(3)
where r
is an arbitrary coordinate in the computation domain, Ihvdc is the grounding cur-
rent of the HVDC grounding electrode, and p and s are the conductivity of the pipe
conductor and soil medium, respectively. A numerical method combining MoM and FEM
is proposed to solve the above equations. The Laplace equation in the soil area is discre-
tized by MoM which is suitable for open-domain problems. The Laplace equation in pipe
conductor area is discretized by FEM which is suitable for enclosure domain problems.
By applying the nonlinear polarization boundary conditions between the two areas, the
two methods can be coupled for solving.
The potential of an arbitrary point in the soil area can be expressed as follows:
Figure 3. Schematic diagram of the boundary value problem.
The conductivities are assumed to be homogeneous. Then, the soil field Ωs and pipeconductor field Ωp belong to the constant current field so the potential satisfies Laplace’sequations. The air can be considered as electrical insulating medium so the current flowingout of the air-earth boundary (Sg) is zero. The total leakage current of the groundingelectrode should equal the injected current in the HVDC transmission system based on thecharge conservation law. According to the interface conditions for electric field vectors,the current density on the soil side should equal the current density on the pipe conductorside. Besides, the leakage current density also should satisfy the polarization relationshipwith the pipe-to-soil potential (ϕs − ϕp). The theoretical equations for the above three-dimensional boundary value problem can be formulated as follows:
∇2 ϕs(→r ) = 0,
→r ∈ Ωs
∇2 ϕp(→r ) = 0,
→r ∈ Ωp
∂ϕs(→r )
∂n = 0,→r ∈ Sg∫
Seleσs
∂ϕs(→r )
∂n ds = Ihvdc,→r ∈ Sele
σp∂ϕp(
→r )
∂n = σs∂ϕs(
→r )
∂n= − fp(ϕp(
→r )− ϕs(
→r )),
→r ∈ Sp
(3)
where→r is an arbitrary coordinate in the computation domain, Ihvdc is the grounding
current of the HVDC grounding electrode, and σp and σs are the conductivity of the pipeconductor and soil medium, respectively. A numerical method combining MoM andFEM is proposed to solve the above equations. The Laplace equation in the soil area isdiscretized by MoM which is suitable for open-domain problems. The Laplace equation inpipe conductor area is discretized by FEM which is suitable for enclosure domain problems.By applying the nonlinear polarization boundary conditions between the two areas, thetwo methods can be coupled for solving.
The potential of an arbitrary point in the soil area can be expressed as follows:
ϕs(→r ) =
x
sG(→r ,→r′) · Jleak(
→r′)ds, s ∈ Sele, Sp (4)
where→r′
is the current source coordinate in the soil area, Jleak(→r ) is the leakage current
density for the buried conductor, and G(→r ,→r′) is the Green’s function for the above
boundary problem. The electrode conductor and pipe conductor are divided into M and
Appl. Sci. 2022, 12, 4433 5 of 13
N segments, respectively. The basis function for different segment current density can beexpressed as follows:
vi =
1→r′∈ ∆i
0→r′
/∈ ∆i(5)
where ∆i is the definitional domain of the buried conductors so Jleak(→r ) can be expressed
as follows:
Jleak(→r′) =
M+N
∑i=1
civi (6)
c1, c2, · · · cM are the current density of the electrode conductor segments. cM+1, cM+2 · · ·cM+N are the current density of the pipe conductor segments. Based on the MoM and pointmatch method the following algebraic equation set can be formed.
G(r1,1) · · · G(r1,M) G(r1,M+1) · · · G(r1,M+N)...
. . ....
.... . .
...G(rM,1) · · · G(rM,M) G(rM,M+1) · · · G(rM,M+N)
G(rM+1,1) · · · G(rM+1,M) G(rM+1,M+1) · · · G(rM+1,M+N)...
. . ....
.... . .
...G(rM+N,1) · · · G(rM+N,M) G(rM+N,M+1) · · · G(rM+N,M+N)
c1...
cMcM+1
...cM+N
=
ϕ(e,0)...
ϕ(e,0)ϕ(s,1)
...ϕ(s,N)
(7)
The electrode is considered as an equipotential ϕ(e,0). The pipe potential on the soilside is ϕ(s,1), ϕ(s,2), · · · ϕ(s,N).
Using the finite element Galerkin method for the pipe conductor area, another equationset can be formed as follows:
K1,1 · · · K1,N K1,N+1 · · · K1,N+P...
. . ....
.... . .
...KN,1 · · · KN,N KN,N+1 · · · KN,N+P
KN+1,1 · · · KN+1,1 KN+1,N+1 · · · KN+1,N+P...
. . ....
.... . .
...KN+P,1 · · · KN+P,N KN+P,N+1 · · · KN+P,N+P
ϕ(p,1)...
ϕ(p,N)
ϕ(p,N+1)...
ϕ(p,N+P)
=
F(
ϕ(p,1) − ϕ(s,1)
)...
F(
ϕ(p,N) − ϕ(s,N)
)0...0
(8)
K is the Stiffness matrix element for different nodes. ϕ(p,1), ϕ(p,2), · · · ϕ(p,N) are thepipe potential on the pipe side. ϕ(p,N+1), ϕ(p,N+2), · · · ϕ(p,N+P) are the non-boundary nodepotentialin the pipe conductor area. F(ϕ(p,i) − ϕ(s,i)), i = 1, 2, · · ·N are the load elementswhich depend on the nonlinear polarization function. According to charge conservation,the electrode segment currents obey the following equation:
M
∑i=1
ci∆si = Ihvdc (9)
By combining Equations (7)–(9), the distribution of the PSP and leakage current alongthe pipeline can be solved with the Newton–Raphson Method.
4. Experimental Verification4.1. Experiment System
To verify the effectiveness of the proposed methodology, a scale problem experimentwas conducted. Figure 4 shows the experiment system layout for the scale groundingelectrode and pipeline.
Appl. Sci. 2022, 12, 4433 6 of 13
Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 13
4. Experimental Verification
4.1. Experiment System
To verify the effectiveness of the proposed methodology, a scale problem experiment
was conducted. Figure 4 shows the experiment system layout for the scale grounding elec-
trode and pipeline.
Electrode
Auxiliary grounding electrode
DC Source
pipeline
Cable
Cable28m
Figure 4. Layout of the scale experiment system.
The scale electrode was a 30 m diameter steel circle buried at a depth of 1.5 m. The
pipeline was buried 28 m away from the electrode at a depth of 1 m. The grounding cur-
rent was supplied by a current generator with 300 A maximum output current. The pipe
material was X80 steel. The soil was considered as a homogeneous medium and the soil
resistivity is r, pH = 8. The leakage current density and PSP along the pipeline were meas-
ured with the test coupons. The test points layout is shown in Figure 5.
Test Pile
200m
Insulated joint Test point
P
−100 −82.5 −65 −47.5 −30 −15 0 15 30 47.5 65 82.5 100
Figure 5. Test points layout along the pipeline.
For each test point, the test circuit is shown in Figure 6. based on the external coupon
method [21].
Figure 4. Layout of the scale experiment system.
The scale electrode was a 30 m diameter steel circle buried at a depth of 1.5 m.The pipeline was buried 28 m away from the electrode at a depth of 1 m. The groundingcurrent was supplied by a current generator with 300 A maximum output current. The pipematerial was X80 steel. The soil was considered as a homogeneous medium and the soilresistivity is r, pH = 8. The leakage current density and PSP along the pipeline weremeasured with the test coupons. The test points layout is shown in Figure 5.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 13
4. Experimental Verification
4.1. Experiment System
To verify the effectiveness of the proposed methodology, a scale problem experiment
was conducted. Figure 4 shows the experiment system layout for the scale grounding elec-
trode and pipeline.
Electrode
Auxiliary grounding electrode
DC Source
pipeline
Cable
Cable28m
Figure 4. Layout of the scale experiment system.
The scale electrode was a 30 m diameter steel circle buried at a depth of 1.5 m. The
pipeline was buried 28 m away from the electrode at a depth of 1 m. The grounding cur-
rent was supplied by a current generator with 300 A maximum output current. The pipe
material was X80 steel. The soil was considered as a homogeneous medium and the soil
resistivity is r, pH = 8. The leakage current density and PSP along the pipeline were meas-
ured with the test coupons. The test points layout is shown in Figure 5.
Test Pile
200m
Insulated joint Test point
P
−100 −82.5 −65 −47.5 −30 −15 0 15 30 47.5 65 82.5 100
Figure 5. Test points layout along the pipeline.
For each test point, the test circuit is shown in Figure 6. based on the external coupon
method [21].
Figure 5. Test points layout along the pipeline.
For each test point, the test circuit is shown in Figure 6. based on the external couponmethod [21].
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 13
uDL2 Data Logger
Terminal
Reference electrode Coupon
Pipeline
Test pile
Soil
Figure 6. Test circuit based on external coupon method.
Figure 7 shows the polarization relationship for the above-mentioned soil and pipe
material. The current density is plotted with logarithmic coordinates for a better view.
“log J” means the common logarithm of the leakage current density.
- 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3
- 4
- 3
- 2
- 1
0
1
2
3
pola
riza
tion
pot
enti
al(V
CS
E)
current density (logJ A/m2)
Figure 7. The relationship between polarization potential and current density for the X80 pipe steel
under 100 m , pH = 8 soil condition.
4.2. Verification of Calculation Method with Expriments Results
The buried conductors was subdivided into about 3000 segments. Boundary condi-
tions were considered in the Green’s function when applying MoM. The pipeline conduc-
tor domain was subdivided into 45,800 tetrahedron elements. The nonlinear polarization
conditions can be treated as a Neumann boundary in each iterative computation when
applying FEM. The leakage current density and PSP were measured under 100 A and 150
A grounding current, respectively. The results of the experiment and calculation are
shown in Figure 8.
Figure 6. Test circuit based on external coupon method.
Appl. Sci. 2022, 12, 4433 7 of 13
Figure 7 shows the polarization relationship for the above-mentioned soil and pipematerial. The current density is plotted with logarithmic coordinates for a better view.“log J” means the common logarithm of the leakage current density.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 13
uDL2 Data Logger
Terminal
Reference electrode Coupon
Pipeline
Test pile
Soil
Figure 6. Test circuit based on external coupon method.
Figure 7 shows the polarization relationship for the above-mentioned soil and pipe
material. The current density is plotted with logarithmic coordinates for a better view.
“log J” means the common logarithm of the leakage current density.
- 6 - 5 - 4 - 3 - 2 - 1 0 1 2 3
- 4
- 3
- 2
- 1
0
1
2
3
pola
riza
tion
pot
enti
al(V
CS
E)
current density (logJ A/m2)
Figure 7. The relationship between polarization potential and current density for the X80 pipe steel
under 100 m , pH = 8 soil condition.
4.2. Verification of Calculation Method with Expriments Results
The buried conductors was subdivided into about 3000 segments. Boundary condi-
tions were considered in the Green’s function when applying MoM. The pipeline conduc-
tor domain was subdivided into 45,800 tetrahedron elements. The nonlinear polarization
conditions can be treated as a Neumann boundary in each iterative computation when
applying FEM. The leakage current density and PSP were measured under 100 A and 150
A grounding current, respectively. The results of the experiment and calculation are
shown in Figure 8.
Figure 7. The relationship between polarization potential and current density for the X80 pipe steelunder 100 Ω ·m, pH = 8 soil condition.
4.2. Verification of Calculation Method with Expriments Results
The buried conductors was subdivided into about 3000 segments. Boundary condi-tions were considered in the Green’s function when applying MoM. The pipeline conductordomain was subdivided into 45,800 tetrahedron elements. The nonlinear polarizationconditions can be treated as a Neumann boundary in each iterative computation whenapplying FEM. The leakage current density and PSP were measured under 100 A and 150 Agrounding current, respectively. The results of the experiment and calculation are shown inFigure 8.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 13
- 100 - 50 0 50 100
- 6
- 4
- 2
0
2
4
6
8
10
leak
age
curr
ent
den
sity
(mA
/cm
2 )
position relative to the pipeline midpoint (m)
100A test 100A Calculation 150A test 150A Calculation
- 100 - 50 0 50 100
- 6
- 4
- 2
0
2
4
6
8
10
pipe
-to-
soil
pot
enti
al(V
)
position relative to the pipeline midpoint (m)
100A test
100A Calculation 150A test 150A Calculation
(a) (b)
Figure 8. Results of test and calculation. (a) leakage current density along the pipeline; (b) pipe-to-
soil potential along the pipeline.
The results show that, the current density and PSP at the center point are the largest
along the pipeline for both test results and calculation results. The maximum test leakage
current density changed from 5.987 mA/cm2 to 8.719 mA/cm2 when the grounding current
changed from 100 A to 150 A. Accordingly, the maximum calculated leakage current den-
sity changed from 5.667 mA/cm2 to 8.604 mA/cm2. The relative error between the calcu-
lated results and the measured results for leakage current is 1.32–5.35%. In the same way,
the relative error for PSP can be obtained, that is 2.63–7.72%. As the grounding current
increases, the relative error becomes smaller. Therefore, the validity of the calculation
method is verified by experiment results.
5. Interference Distribution Characteristics
Based on the proposed calculation model, the interference distribution characteristics
were analyzed under different parameters. These parameters include the electrode cur-
rents, soil resistivity, and the distance between the electrode and pipelines. Considering
the following typical interference model, the length of the pipeline is L, and the distance
between the electrode and pipeline is d. The soil is considered as a homogeneous medium
and the soil resistivity is r, pH = 8. The pipe material was X80 steel. A schematic diagram
of the pipeline and HVDC grounding electrode arrangement is shown in Figure 9.
HVDCGrouding Electrode
L
dpipeline
Figure 9. Schematic diagram of the pipeline and HVDC grounding electrode arrangement.
Figure 8. Results of test and calculation. (a) leakage current density along the pipeline; (b) pipe-to-soilpotential along the pipeline.
The results show that, the current density and PSP at the center point are the largestalong the pipeline for both test results and calculation results. The maximum test leakagecurrent density changed from 5.987 mA/cm2 to 8.719 mA/cm2 when the grounding currentchanged from 100 A to 150 A. Accordingly, the maximum calculated leakage current densitychanged from 5.667 mA/cm2 to 8.604 mA/cm2. The relative error between the calculated
Appl. Sci. 2022, 12, 4433 8 of 13
results and the measured results for leakage current is 1.32–5.35%. In the same way,the relative error for PSP can be obtained, that is 2.63–7.72%. As the grounding currentincreases, the relative error becomes smaller. Therefore, the validity of the calculationmethod is verified by experiment results.
5. Interference Distribution Characteristics
Based on the proposed calculation model, the interference distribution characteristicswere analyzed under different parameters. These parameters include the electrode currents,soil resistivity, and the distance between the electrode and pipelines. Considering thefollowing typical interference model, the length of the pipeline is L, and the distancebetween the electrode and pipeline is d. The soil is considered as a homogeneous mediumand the soil resistivity is r, pH = 8. The pipe material was X80 steel. A schematic diagramof the pipeline and HVDC grounding electrode arrangement is shown in Figure 9.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 13
- 100 - 50 0 50 100
- 6
- 4
- 2
0
2
4
6
8
10
leak
age
curr
ent
den
sity
(mA
/cm
2 )
position relative to the pipeline midpoint (m)
100A test 100A Calculation 150A test 150A Calculation
- 100 - 50 0 50 100
- 6
- 4
- 2
0
2
4
6
8
10
pipe
-to-
soil
pot
enti
al(V
)
position relative to the pipeline midpoint (m)
100A test
100A Calculation 150A test 150A Calculation
(a) (b)
Figure 8. Results of test and calculation. (a) leakage current density along the pipeline; (b) pipe-to-
soil potential along the pipeline.
The results show that, the current density and PSP at the center point are the largest
along the pipeline for both test results and calculation results. The maximum test leakage
current density changed from 5.987 mA/cm2 to 8.719 mA/cm2 when the grounding current
changed from 100 A to 150 A. Accordingly, the maximum calculated leakage current den-
sity changed from 5.667 mA/cm2 to 8.604 mA/cm2. The relative error between the calcu-
lated results and the measured results for leakage current is 1.32–5.35%. In the same way,
the relative error for PSP can be obtained, that is 2.63–7.72%. As the grounding current
increases, the relative error becomes smaller. Therefore, the validity of the calculation
method is verified by experiment results.
5. Interference Distribution Characteristics
Based on the proposed calculation model, the interference distribution characteristics
were analyzed under different parameters. These parameters include the electrode cur-
rents, soil resistivity, and the distance between the electrode and pipelines. Considering
the following typical interference model, the length of the pipeline is L, and the distance
between the electrode and pipeline is d. The soil is considered as a homogeneous medium
and the soil resistivity is r, pH = 8. The pipe material was X80 steel. A schematic diagram
of the pipeline and HVDC grounding electrode arrangement is shown in Figure 9.
HVDCGrouding Electrode
L
dpipeline
Figure 9. Schematic diagram of the pipeline and HVDC grounding electrode arrangement.
Figure 9. Schematic diagram of the pipeline and HVDC grounding electrode arrangement.
5.1. Electrode Current
The relationship between the polarization potential and current density is the same asin Section 5.1 and shown in Figure 7. The other parameters are listed in Table 1.
Table 1. Parameters for the study model.
Parameters Value
HVDC grounding current 100 A, 500 A, 1000 A, 2000 A, 5000 Apipeline length 100 km
distance between electrode and pipelines 10 kmsoil parameters 100 Ω·m, pH = 8
pipeline steel material X80pipeline coating resistivity 3.3 × 107 Ω·m
The distribution of the leakage current density and pip-to-soil potential under differentHVDC ground currents are shown in Figure 10.
Appl. Sci. 2022, 12, 4433 9 of 13
Appl. Sci. 2022, 12, x FOR PEER REVIEW 9 of 13
5.1. Electrode Current
The relationship between the polarization potential and current density is the same
as in Section 5.1 and shown in Figure 7. The other parameters are listed in Table 1.
Table 1. Parameters for the study model.
Parameters Value
HVDC grounding current 100 A, 500 A, 1000 A, 2000 A, 5000 A
pipeline length 100 km
distance between electrode and pipelines 10 km
soil parameters 100 Ω·m, pH = 8
pipeline steel material X80
pipeline coating resistivity 3.3 × 107 Ω·m
The distribution of the leakage current density and pip-to-soil potential under differ-
ent HVDC ground currents are shown in Figure 10.
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50- 2
- 1
0
1
2
3
4
5
leak
age
curr
ent
den
sity
(A/m
2)
position relative to the pipeline midpoint (km)
100A
500A 1000A
2000A 5000A
electorde current
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
- 1.5
- 1.0
- 0.5
0.0
0.5
1.0
pip
e-to
-so
il p
ote
nti
al(V
)
position relative to the pipeline midpoint (km)
100A
500A
1000A
2000A
5000A
electorde current
(a) (b)
Figure 10. Calculation results under different HVDC grounding currents. (a) leakage current den-
sity along the pipeline; (b) PSP along the pipeline.
As can be seen in Figure 10, the leakage current density and PSP reach 3.92 A/m2 and
0.89 V, respectively, when the grounding current is 5000 A. Both maximum leakage cur-
rent density and maximum PSP increase as the electrode grounding current increases.
Regression analysis shows that the relationship between the maximum leakage current
density Jmax and the electrode grounding current Ihvdc is linear, that is Jmax = a1·Ihvdc + b1 where
a1 and b1 are fitting constant coefficients.
The maximum value is located at the midpoint of the pipeline. When currents flow
out of the pipe, the pipeline faces corrosion risk, especially for the central area of the pipe-
line. Figure 11 shows the corrosion risk area distribution under different grounding cur-
rents.
Figure 10. Calculation results under different HVDC grounding currents. (a) leakage current densityalong the pipeline; (b) PSP along the pipeline.
As can be seen in Figure 10, the leakage current density and PSP reach 3.92 A/m2
and 0.89 V, respectively, when the grounding current is 5000 A. Both maximum leakagecurrent density and maximum PSP increase as the electrode grounding current increases.Regression analysis shows that the relationship between the maximum leakage currentdensity Jmax and the electrode grounding current Ihvdc is linear, that is Jmax = a1·Ihvdc + b1where a1 and b1 are fitting constant coefficients.
The maximum value is located at the midpoint of the pipeline. When currents flow outof the pipe, the pipeline faces corrosion risk, especially for the central area of the pipeline.Figure 11 shows the corrosion risk area distribution under different grounding currents.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 13
Figure 11. Corrosion risk area distribution under different grounding currents.
The length of anode area is 34.5 km under 100 A, whereas the length of anode area is
25.7 km under a 5000 A grounding current The result shows that the length facing corro-
sion risk decreases as the HVDC grounding current increases, which means the corrosion
area is becoming more concentrated. The effect of grounding current on the anode area
range is not very significant when the current exceeds 1000 A.
5.2. Distance between Electrode and Pipelines
The interference scope of the HVDC grounding current can reach tens of kilometers.
Therefore, the potential and density distribution characteristics were studied in the range
from 2 km to 50 km. A schematic diagram for the pipeline and HVDC grounding electrode
arrangement is shown in Figure 9. Five distance types (2 km, 5 km, 10 km, 20 km, 50 km)
were chosen for study. The HVDC grounding current is 3000 A. The other parameters are
the same as those listed in Table 1. The relationship between polarization potential and
current density is the same as in Section 5.1 and shown in Figure 7.
The results are shown in Figure 12 for different distances between the electrode and
pipelines.
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50- 5
0
5
10
15
20
25
leak
age
curr
ent
den
sity
(A/m
2)
position relative to the pipeline midpoint (km)
2km 5km
10km
20km 50km
distance betweenelectrode and pipeline
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
- 2
0
2
4
6
8
10
pip
e-to
-so
il p
ote
ntia
l(V
)
position relative to the pipeline midpoint (km)
2km 5km
10km 20km
50km
distance between
electrode and pipeline
(a) (b)
Figure 12. Calculation results under different distance between electrode and pipeline. (a) leakage
current density along the pipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP reach 25.2 A/m2 and 8.74 V, respec-
tively, when the distance between electrode and pipeline is 2 km. As the distance in-
creases, the maximum current density and PSP decrease gradually. Regression analysis
shows that the relationship between the maximum leakage current density Jmax and the
distance d satisfy negative exponential function, that is 2
max 2bJ a d (b2 < 0) where a2
Figure 11. Corrosion risk area distribution under different grounding currents.
The length of anode area is 34.5 km under 100 A, whereas the length of anode area is25.7 km under a 5000 A grounding current The result shows that the length facing corrosionrisk decreases as the HVDC grounding current increases, which means the corrosion areais becoming more concentrated. The effect of grounding current on the anode area range isnot very significant when the current exceeds 1000 A.
5.2. Distance between Electrode and Pipelines
The interference scope of the HVDC grounding current can reach tens of kilometers.Therefore, the potential and density distribution characteristics were studied in the rangefrom 2 km to 50 km. A schematic diagram for the pipeline and HVDC grounding electrodearrangement is shown in Figure 9. Five distance types (2 km, 5 km, 10 km, 20 km, 50 km)were chosen for study. The HVDC grounding current is 3000 A. The other parameters are
Appl. Sci. 2022, 12, 4433 10 of 13
the same as those listed in Table 1. The relationship between polarization potential andcurrent density is the same as in Section 5.1 and shown in Figure 7.
The results are shown in Figure 12 for different distances between the electrode and pipelines.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 13
Figure 11. Corrosion risk area distribution under different grounding currents.
The length of anode area is 34.5 km under 100 A, whereas the length of anode area is
25.7 km under a 5000 A grounding current The result shows that the length facing corro-
sion risk decreases as the HVDC grounding current increases, which means the corrosion
area is becoming more concentrated. The effect of grounding current on the anode area
range is not very significant when the current exceeds 1000 A.
5.2. Distance between Electrode and Pipelines
The interference scope of the HVDC grounding current can reach tens of kilometers.
Therefore, the potential and density distribution characteristics were studied in the range
from 2 km to 50 km. A schematic diagram for the pipeline and HVDC grounding electrode
arrangement is shown in Figure 9. Five distance types (2 km, 5 km, 10 km, 20 km, 50 km)
were chosen for study. The HVDC grounding current is 3000 A. The other parameters are
the same as those listed in Table 1. The relationship between polarization potential and
current density is the same as in Section 5.1 and shown in Figure 7.
The results are shown in Figure 12 for different distances between the electrode and
pipelines.
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50- 5
0
5
10
15
20
25
leak
age
curr
ent
den
sity
(A/m
2)
position relative to the pipeline midpoint (km)
2km 5km
10km
20km 50km
distance betweenelectrode and pipeline
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
- 2
0
2
4
6
8
10
pip
e-to
-so
il p
ote
ntia
l(V
)
position relative to the pipeline midpoint (km)
2km 5km
10km 20km
50km
distance between
electrode and pipeline
(a) (b)
Figure 12. Calculation results under different distance between electrode and pipeline. (a) leakage
current density along the pipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP reach 25.2 A/m2 and 8.74 V, respec-
tively, when the distance between electrode and pipeline is 2 km. As the distance in-
creases, the maximum current density and PSP decrease gradually. Regression analysis
shows that the relationship between the maximum leakage current density Jmax and the
distance d satisfy negative exponential function, that is 2
max 2bJ a d (b2 < 0) where a2
Figure 12. Calculation results under different distance between electrode and pipeline. (a) leakagecurrent density along the pipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP reach 25.2 A/m2 and 8.74 V, respec-tively, when the distance between electrode and pipeline is 2 km. As the distance increases,the maximum current density and PSP decrease gradually. Regression analysis shows thatthe relationship between the maximum leakage current density Jmax and the distance dsatisfy negative exponential function, that is Jmax = a2 · db2 (b2 < 0) where a2 and b2 arefitting constant coefficients. That means that the interference current density increases aspower function when the distance between electrode and pipeline decreases.
Figure 13 shows the interference range for the anode area and cathode area along thepipeline for different distances between the electrode and pipeline.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 11 of 13
and b2 are fitting constant coefficients. That means that the interference current density
increases as power function when the distance between electrode and pipeline decreases.
Figure 13 shows the interference range for the anode area and cathode area along the
pipeline for different distances between the electrode and pipeline.
Figure 13. Corrosion risk area distribution for different distances between HVDC electrode and
pipeline.
The distance between the electrode and pipeline has a significant influence on the
anode area range. The anode area range increases as the distance increases. Although the
anode area range extends, the influence degree decreases substantially.
5.3. Soil Resistivity
Soil resistivity influences not only the grounding current flow path but also the po-
larization. Four soil resistivity types (10, 30, 100, 1300 Ω·m) were chosen for study. The
HVDC grounding current is 3000 A. The other parameters are the same as those listed in
Table 1. The polarization curves were measured under different soil conditions. Figure 14
shows the test polarization curve data.
- 5 - 4 - 3 - 2 - 1 0 1 2
- 4
- 3
- 2
- 1
0
1
2
3
pola
riza
tio
n po
tent
ial(
V)
leakage current density (logJ A/m2)
X80-10 m pH=8
X80-30 m pH=8
X80-100 m pH=8
X80-1300 m pH=8
Figure 14. Polarization curve under different soil resistivity.
The calculation results of leakage current density and PSP are shown in Figure 15.
Figure 13. Corrosion risk area distribution for different distances between HVDC electrodeand pipeline.
The distance between the electrode and pipeline has a significant influence on theanode area range. The anode area range increases as the distance increases. Although theanode area range extends, the influence degree decreases substantially.
5.3. Soil Resistivity
Soil resistivity influences not only the grounding current flow path but also the polar-ization. Four soil resistivity types (10, 30, 100, 1300 Ω·m) were chosen for study. The HVDC
Appl. Sci. 2022, 12, 4433 11 of 13
grounding current is 3000 A. The other parameters are the same as those listed in Table 1.The polarization curves were measured under different soil conditions. Figure 14 showsthe test polarization curve data.
Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 14
and b2 are fitting constant coefficients. That means that the interference current density
increases as power function when the distance between electrode and pipeline decreases.
Figure 13 shows the interference range for the anode area and cathode area along the
pipeline for different distances between the electrode and pipeline.
Figure 13. Corrosion risk area distribution for different distances between HVDC electrode and
pipeline.
The distance between the electrode and pipeline has a significant influence on the
anode area range. The anode area range increases as the distance increases. Although the
anode area range extends, the influence degree decreases substantially.
5.3. Soil Resistivity
Soil resistivity influences not only the grounding current flow path but also the
polarization. Four soil resistivity types (10, 30, 100, 1300 Ω·m) were chosen for study. The
HVDC grounding current is 3000 A. The other parameters are the same as those listed in
Table 1. The polarization curves were measured under different soil conditions. Figure 14
shows the test polarization curve data.
−5 −4 −3 −2 −1 0 1 2
−4
−3
−2
−1
0
1
2
3
po
lari
zati
on
po
ten
tial
(V)
leakage current density (logJ A/m2)
X80-10 m pH=8
X80-30 m pH=8
X80-100 m pH=8
X80-1300 m pH=8
Figure 14. Polarization curve under different soil resistivity.
The calculation results of leakage current density and PSP are shown in Figure 15.
Figure 14. Polarization curve under different soil resistivity.
The calculation results of leakage current density and PSP are shown in Figure 15.Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 14
−50 −40 −30 −20 −10 0 10 20 30 40 50
−2
−1
0
1
2
3
4
5
leak
age
curr
ent
den
sity
(A/m
2)
position relative to the pipeline midpoint (km)
10 m
30 m
100 m
1300 m
soil resistivity
−50 −40 −30 −20 −10 0 10 20 30 40 50
−10
−5
0
5
10
pip
e-to
-so
il p
ote
nti
al (
V)
position relative to the pipeline midpoint (km)
10 m
30 m
100 m
1300 m
soil resistivity
(a) (b)
Figure 15. Calculation results under different soil resistivity. (a) leakage current density along the
pipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP increase as the soil resistivity
increases. Regression analysis shows that the relationship between the maximum leakage
current density Jmax and the soil resistivity ρs satisfy logarithmic function, that is
3max s3 ln( )J a b . a3 and b3 are fitting constant coefficients.
Figure 16 shows the interference range for the anode area and cathode area along the
pipeline for different distances between the electrode and pipeline.
Figure 16. Corrosion risk area distribution under different soil resistivity.
The results indicate that the anode area range extends as the soil resistivity becomes
higher. Both the maximum leakage current density and corrosion risk area are positively
correlated with the soil resistivity. Therefore, it is very important to evaluate the
interference level accurately when dealing with highly resistive soil conditions.
6. Conclusions
(1) A methodology based on a combination of MoM and FEM is proposed for calculating
the coupling voltage and current on buried pipelines induced by grounding currents
while taking into account nonlinear polarization. The validity of the calculation
method was verified by experiment.
(2) Both the maximum leakage current density and maximum PSP increase as the
grounding electrode current increases. The relationship between the maximum
leakage current density and the electrode grounding current is linear. The corrosion
area becomes more concentrated as the grounding current increases.
(3) The maximum leakage current density increases exponentially when the distance
between electrode and pipeline decreases. The distance between the electrode and
Figure 15. Calculation results under different soil resistivity. (a) leakage current density along thepipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP increase as the soil resistivity increases.Regression analysis shows that the relationship between the maximum leakage currentdensity Jmax and the soil resistivity ρs satisfy logarithmic function, that is Jmax = a3 ·ln(ρs) + b3. a3 and b3 are fitting constant coefficients.
Figure 16 shows the interference range for the anode area and cathode area along thepipeline for different distances between the electrode and pipeline.
Appl. Sci. 2022, 12, 4433 12 of 13
Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 13
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
- 2
- 1
0
1
2
3
4
5
leak
age
curr
ent
den
sity
(A/m
2)
position relative to the pipeline midpoint (km)
10 m
30 m
100 m
1300 m
soil resistivity
- 50 - 40 - 30 - 20 - 10 0 10 20 30 40 50
- 10
- 5
0
5
10
pipe
-to-s
oil
pote
nti
al (
V)
position relative to the pipeline midpoint (km)
10 m
30 m
100 m
1300 m
soil resistivity
(a) (b)
Figure 15. Calculation results under different soil resistivity. (a) leakage current density along the
pipeline; (b) PSP along the pipeline.
The maximum leakage current density and PSP increase as the soil resistivity in-
creases. Regression analysis shows that the relationship between the maximum leakage
current density Jmax and the soil resistivity ρs satisfy logarithmic function, that is
3m ax s3 ln ( )J a b . a3 and b3 are fitting constant coefficients.
Figure 16 shows the interference range for the anode area and cathode area along the
pipeline for different distances between the electrode and pipeline.
Figure 16. Corrosion risk area distribution under different soil resistivity.
The results indicate that the anode area range extends as the soil resistivity becomes
higher. Both the maximum leakage current density and corrosion risk area are positively
correlated with the soil resistivity. Therefore, it is very important to evaluate the interfer-
ence level accurately when dealing with highly resistive soil conditions.
6. Conclusions
(1) A methodology based on a combination of MoM and FEM is proposed for calculating
the coupling voltage and current on buried pipelines induced by grounding currents
while taking into account nonlinear polarization. The validity of the calculation
method was verified by experiment.
(2) Both the maximum leakage current density and maximum PSP increase as the
grounding electrode current increases. The relationship between the maximum leak-
age current density and the electrode grounding current is linear. The corrosion area
becomes more concentrated as the grounding current increases.
(3) The maximum leakage current density increases exponentially when the distance be-
tween electrode and pipeline decreases. The distance between the electrode and
Figure 16. Corrosion risk area distribution under different soil resistivity.
The results indicate that the anode area range extends as the soil resistivity becomeshigher. Both the maximum leakage current density and corrosion risk area are positivelycorrelated with the soil resistivity. Therefore, it is very important to evaluate the interferencelevel accurately when dealing with highly resistive soil conditions.
6. Conclusions
(1) A methodology based on a combination of MoM and FEM is proposed for calculatingthe coupling voltage and current on buried pipelines induced by grounding currentswhile taking into account nonlinear polarization. The validity of the calculationmethod was verified by experiment.
(2) Both the maximum leakage current density and maximum PSP increase as the ground-ing electrode current increases. The relationship between the maximum leakagecurrent density and the electrode grounding current is linear. The corrosion areabecomes more concentrated as the grounding current increases.
(3) The maximum leakage current density increases exponentially when the distancebetween electrode and pipeline decreases. The distance between the electrode andpipeline has a significant influence on the corrosion area range. The corrosion arearange increases substantially as the distance increases, whereas the influence degreedecreases substantially.
(4) The maximum leakage current density and PSP increase as the soil resistivity increases.The relationship between the maximum leakage current density and the soil resistivitysatisfies the logarithmic function. Both the maximum leakage current density andcorrosion risk area are positively correlated with the soil resistivity.
Author Contributions: X.L. conducted theoretical research, characteristics computation, and wrotethe paper; F.B. and F.C. are responsible for the experiment design and data analysis; C.L. gave somegood advice during the experiments and paper writing. All authors have read and agreed to thepublished version of the manuscript.
Funding: This research received no external funding.
Informed Consent Statement: Not applicable.
Acknowledgments: The authors would like to thank the State Grid UHVDC Test Site of China forproviding the experiment environment.
Conflicts of Interest: The authors declare no conflict of interest.
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