Evaluation of Electromagnetic Interferences Affecting Metallic Pipelines

Abstract

This chapter presents some analysis of the modeling techniques used to evaluate the effects of electromagnetic interference phenomena that could occur when metallic pipelines are placed close to high-voltage power lines. The electric and magnetic fields produced by overhead power lines could perturb the normal operation of the metallic pipelines through induced currents and voltages. These perturbations could be dangerous for both pipeline operating personnel (as electrical hazard) and pipeline structural integrity (due to accelerated electrochemical corrosion phenomena). The chapter depicts the electromagnetic coupling mechanisms behind the abovementioned interference phenomena and how the induced voltages could be evaluated. A parametric analysis is showcased to highlight the influence of various geometrical and electrical parameters.

1. Introduction

European regulations regarding environmental protection, as well as economic reasons aimed to reduce construction costs, have determined a significant decrease in the access of energy carrier (like oil products, electricity, methane gas, or/and water) infrastructure to new right of ways. Therefore, the transport and distribution network of water, natural gas, or crude oil pipelines must share on long distances (for several kilometers) the same distribution corridors with high-voltage power lines (HVPL) (see Figure 1).

Figure 1.

Cross section of a common HVPL-MP right-of-way.

Studies on high-voltage AC power lines operating in steady state or fault regime identified the presence of electromagnetic interferences in nearby metallic structures due to the electric and magnetic fields generated by the currents flowing through the HVPL conductors [1, 2, 3, 4].

Therefore, in many situations, the metallic pipeline (MP) used for the transport and distribution of liquid or gaseous substances may be exposed to induced currents or voltages. These could be dangerous on one side for operating personnel, who coming into contact with the pipeline may be exposed to electrocution, and on the other hand, to the structural integrity of the pipeline due to accelerated corrosion phenomena [5, 6, 7].

In 1995, within the CIGRE Working Group 36.02, the document entitled Guide Concerning Influence of High Voltage AC Power Systems on Metallic Pipelines [8] has been developed, which addresses the influence of high-voltage energy devices on nearby metallic pipelines. It is a reference document in the field of electromagnetic interferences and summarizes the following aspects:

• presentation of different categories of electromagnetic disturbances and the problems arising from them

• description of simple methods for evaluating electromagnetic interference phenomena and their measurement methods

• presentation of main ways and means of reducing their influences, as well as the description of the most important protection systems.

Regarding the protection of underground MP against electrochemical corrosion processes, a special attention has been paid to the effects caused by AC systems. Previously, AC corrosion was considered negligible compared to the interferences in DC state. But research in the field proved the opposite, resulting in pipeline protection guidelines [9, 10] and a European regulatory standard [11]. The main causes of AC corrosion are the leakage current densities from the pipeline into the surrounding soil. The source of leakage currents is the AC voltages induced in the pipelines due to various electromagnetic coupling mechanisms [6, 7].

To comply with the European norms and regulations, it is necessary to investigate the electromagnetic interference phenomena in detail and to precisely determine the magnitude of the voltages induced in MPs exposed to nearby power lines, both under normal and HVPL fault operating conditions. To identify and apply the proper protection techniques for the metallic pipelines, the geometrical and electrical parameters that influence the level of induced voltages must be determined. The difficulty in accessing buried MPs not only requires mathematical models for the numerical evaluation of induced voltages, instead of on-site measurements [12].

2. Electromagnetic interference phenomena

At low frequencies, when the wavelength of the electrical signal is long compared to the size of the perturbation source, the electromagnetic interference propagates through capacitive (electric), inductive (magnetic), or conductive (galvanic) couplings [8, 11, 13]. Conversely, at high frequencies when the wavelength is comparable to the dimensions of the perturbation source, electromagnetic radiation appears. The radiation transition limit is variable, but in most practical cases, it is approximately 10 m, which corresponds to a frequency of 30 MHz. Therefore, in case of interference problems between HVPL and neighboring metallic structures, only conductive, capacitive, and inductive couplings should be considered [8, 11].

2.1 Galvanic coupling

Galvanic (conductive) couplings occur when two electrical circuits have a common portion of the circuit. In this situation, electromagnetic interference propagates in the receiver (victim) through conduction, through one or more conductors (power line, cable shield, etc.), or even through passive elements (capacitors, transformers, etc.).

The energy transported through power lines can be transmitted conductively to adjacent metallic structures (underground metallic pipes, etc.) if these structures are connected to the AC circuit (the grounding grid of a power line tower or any other device that has a network extended earthing), either directly (metallic connection) or through the proximity of the pipeline and the grounding grid (see Figure 2).

Figure 2.

Galvanic coupling between a HVPL and a MP.

The occurrence of a ground fault in the power system corresponds to a high-value short-circuit current flowing through earth. The electrical potential of the soil (close to the grounding grid) will increase considerably in relation with the pipeline potential (assumed to be at a reference potential) [14]. Any element connected between MP and the ground will be subject to this potential difference; in other words, the fault currents that flow through the earthing electrode of an HVPL tower, or substation, produce an increase in the potential of the electrode as well as the potential of the soil in its vicinity compared to the reference potential. Under these conditions, the metallic structures (pipelines) will be influenced if they are directly connected to the grounding grid of the electric energy transport/distribution system (for example, of a transformer station), or if they cross the influence zone near the grounding sockets. In these cases, the potential of the pipeline increases and can be transmitted over a relatively large distance (several km), depending on the degree of electrical insulation of the interfered metallic structure and the resistivity of the soil in the respective area.

2.2 Capacitive coupling

Capacitive (electric) coupling occurs between two circuits whose conductors are at different potentials. As a result of the potential difference between the conductors, an electric field is produced and modeled in an equivalent electrical scheme by a parasitic capacitance. Figure 3 presents an example of electrical coupling of two circuits (1) and (2) by means of a quasi-stationary electric field, respectively, through parasitic capacities.

Figure 3.

(a) Field model, and (b) network model for capacitive coupling.

In the case of capacitive coupling, determined by the electric field of the high-voltage power line, the hypothesis that the soil is a perfect conductor, of infinite conductivity, can be used, because its conductivity is much higher than that of air (see Figure 4).

Figure 4.

Capacitive coupling between HVPL and metallic pipeline.

Therefore, only aboveground metallic structures located in the vicinity of HVPL are subject to capacitive coupling perturbations; this effect appears both in normal operating conditions and power line fault conditions [15].

2.3 Inductive coupling

Inductive (magnetic) couplings occur between two or more circuits passed by electric currents producing time-varying magnetic fields that induce in the victim circuit a voltage that disturbs the desired signal (if exists). The action of the magnetic field of the disturbing circuit on the perturbed one can be represented in the equivalent electric circuit model by a mutual inductance or by an induced voltage source (see Figure 5).

Figure 5.

(a) Field model, and (b) network model for inductive coupling.

A metallic pipeline near a high-voltage power line (as shown in Figure 6) is subject to induced voltages by magnetic coupling. In other words, a significant part of the energy transmitted through power lines surrounds the conductors and extends over large distances from their center. The nearby metallic pipelines, which have a common path with HVPL, can capture this energy in unfavorable parallelism and/or power line operation conditions (high zero-sequence currents, phase to ground faults, unbalanced loads, non-symmetric current system, etc.)

Figure 6.

Inductive coupling between HVPL and metallic pipeline.

As shown in some previous works, such as [16, 17, 18], the inductive influence from 50 Hz or 60 Hz electric power systems on pipeline networks is related to the time-varying magnetic field generated by the electric currents flowing in power lines conductors. The main parameters generally considered for this type of influence are the electric power system’s current load level, the ground wire current, the exposure length, the separation distance between involved structures of both systems, and the soil model resistivity [19, 20].

Given that the pipeline is buried and assuming that the ground permittivity can be neglected, there is no capacitive influence between the overhead transmission line and the buried pipeline. In this regard, the next chapters emphasize aspects related to investigation of the induced AC voltage effects on a buried pipeline due to the currents in an overhead transmission line.

3. Modeling techniques of the electromagnetic interference problems

Numerous numerical simulations have been carried out over the past few decades to analyze interference problems involving power lines and earth-return conductors. There are two main approaches for assessing such phenomena: transmission line theory [1, 21, 22, 23] and a hybrid approach based on finite element method (FEM) and circuit analysis [2, 3, 24, 25, 26]. The first approach has the advantage that it can be used for any operation state, while the other is only applicable to steady-state conditions.

In either case, a fundamental requirement of such modeling technique is that they should consider soil resistivity variations [24, 27, 28], non-parallel pipeline-power line right of ways, and multiple metallic conductors, such as sky wires and/or mitigation wires. Various commercial computer software are available to assess the influence of electric power systems on pipeline systems, but their licensing and annual renewal fees could be very high.

The analytical forms of the solutions of the electromagnetic field problems, related to the cylindrical current-carrying conductors in the presence of the ground, are a rather laborious problem, even when the geometry of the conductor network is simple. There are several difficulties with buried pipelines:

• Underground MPs can be long or short, but they cannot be infinitesimal or infinitely long.

• MPs are generally insulated and are in direct contact with the ground, so longitudinal (axial) and transversal (leakage) currents must be considered.

• Conductors with semi-insulating coating, such as pipelines, must also be analyzed.

• The most important results related to underground pipeline networks are related to the near field generated by these conductors.

In many cases [3, 15, 19, 20, 26, 28], the pipeline network is analyzed for low-frequency energizing currents conditions, but problems could arise when the performance of the network at high frequency should be investigated and transient state studies are required [18, 21, 23]. For both situations, an equivalent electrical circuit model of the investigated interference problem (like the one in Figure 7) must be constructed and analyzed considering all the present metallic conductors and all the coupling mechanisms.

Figure 7.

Equivalent circuit model for a general case of HVPL–MP interference.

By solving the equivalent electric circuit model of the entire right-of-way for the proper HVPL operating conditions, the induced currents and voltages could be evaluated along the pipeline length, and it could be determined if the pipeline would operate normally or mitigation measures should be applied.

3.1 Transmission line approach

The transmission line approach is the most general and complex formulation of an HVPL-MP interference problem that could be applied for both steady state and transient state studies. It has been developed from the well-known lumped-element model for an infinitesimal ($\mathit{\Delta x}$ length) single-wire conductor presented in Figure 8.

Figure 8.

Lumped-element equivalent circuit transmission line model.

Imposing $\mathit{\Delta x}\to 0$ the following telegrapher’s equations can be written:

$$-\frac{\partial u\left(x,t\right)}{\partial x}=R_0·i\left(x,t\right)+L_0·\frac{\partial i\left(x,t\right)}{\partial t}$$E1

$$-\frac{\partial i\left(x,t\right)}{\partial x}=G_0·u\left(x,t\right)+C_0·\frac{\partial u\left(x,t\right)}{\partial t}$$E2

where $R_0$ is per-unit length resistance, $L_0$ per-unit length inductance, $G_0$ per-unit length conductance, and $C_0$ per-unit length capacitance. If Laplace transformation ($s=\mathit{j\omega }$) is applied to the above equations, we will obtain:

$$-\frac{\partial u\left(x,s\right)}{\partial x}=\left(R_0+{\mathit{sL}}_0\right)·i\left(x,s\right)=Z_0·i\left(x,s\right)$$E3

$$-\frac{\partial i\left(x,s\right)}{\partial x}=\left(G_0+{\mathit{sC}}_0\right)·u\left(x,s\right)=Z_0=Y_0·u\left(x,s\right)$$E4

where $Z_0$ is the longitudinal impedance, and $Y_0$ is the shunt admittance

The solution of Eqs. (3) and (4) can be written as:

$$u\left(x,s\right)=e^{-\gamma ·x}·u^{+}+e^{\gamma ·x}·u^{-}$$E5

$$i\left(x,s\right)=\frac{1}{Z_C}{\left(e\right.}^{-\gamma ·x}·u^{+}-e^{\gamma ·x}·u^{-})$$E6

where $u^{+}$ and $u^{-}$ denote the voltage as incident and reflect waves, respectively, $\gamma$ is the propagation constant, and $Z_C$ is the characteristic impedance, defined as:

$$\gamma =\sqrt{Z_0·Y_0}$$E7

$$Z_C=\sqrt{\frac{Z_0}{Y_0}}$$E8

The substitution of boundary conditions $x=0$ and $x=l$ where $l$ denotes the length, into (5) and (6) leads to the following line terminals equations:

$$u_k-Z_C·i_k=e^{-\gamma ·x}·\left(u_m+Z_C·i_m\right)$$E9

$$u_k+Z_C·i_k=e^{\gamma ·x}·\left(u_m-Z_C·i_m\right)$$E10

where $k$ and $m$ denote the terminals of the line corresponding to $x=0$ and $x=l$, respectively. The currents $i_k$ and $i_m$ are entering the line at both ends. The above equations are rewritten to:

$$i_k=Y_C·u_k-H\left(Y_C·u_m+i_m\right)$$E11

$$i_m=Y_C·u_m-H\left(Y_C·u_k+i_k\right)$$E12

where $Y_C=1/Z_C$ is the characteristic admittance, and $H=e^{\gamma ·l}$ is the propagation function. Eqs. (11) and (12) can be rewritten using vector and matrices for a multi-conductor system:

$$\left[{\mathit{I}}_{\mathit{k}}\right]=\left[{\mathit{Y}}_{\mathit{C}}\right]·\left[{\mathit{U}}_{\mathit{k}}\right]-H\left(\left[{\mathit{Y}}_{\mathit{C}}\right]·\left[{\mathit{U}}_{\mathit{k}}\right]+\left[{\mathit{I}}_{\mathit{m}}\right]\right)$$E13

$$\left[{\mathit{I}}_{\mathit{m}}\right]=\left[{\mathit{Y}}_{\mathit{C}}\right]·\left[{\mathit{U}}_{\mathit{m}}\right]-H\left(\left[{\mathit{Y}}_{\mathit{C}}\right]·\left[{\mathit{U}}_{\mathit{k}}\right]+\left[{\mathit{I}}_{\mathit{k}}\right]\right)$$E14

To determine the frequency-dependent characteristic impedances and admittances required for transient state analysis, Figure 9 illustrates the transition from a linear earth electrode to an equivalent transmission line with complex values, for the frequency-dependent parameters ${\underset{\_}{Z}}_C\left(\omega \right)$ and $\underset{\_}{\gamma }\left(\omega \right)$, which denote the characteristic impedance and propagation function, respectively:

Figure 9.

Characteristic impedance of a linear earth electrode.

$${\underset{\_}{Z}}_C\left(\omega \right)=\sqrt{\frac{R_0+\mathit{j\omega }{L}_0}{G_0+\mathit{j\omega }{C}_0}}=\sqrt{\frac{{\underset{\_}{Z}}_0\left(\omega \right)}{{\underset{\_}{Y}}_0\left(\omega \right)}},\underset{\_}{\gamma }\left(\omega \right)=\sqrt{{\underset{\_}{Z}}_0\left(\omega \right)·{\underset{\_}{Y}}_0\left(\omega \right)}$$E15

$${\underset{\_}{\Gamma }}_0\left(\omega \right)=\mathit{j\omega }\sqrt{{\mu }_0·{\epsilon }_0}$$E16

This form corresponds to any two-conductor transmission line. Sunde derived equivalent expressions for a single conductor in contact to the soil, with a current returning through the earth [29, 30]. Both the complex longitudinal impedance per unit length, ${\underset{\_}{Z}}_0$, and the complex transversal admittance per unit length ${\underset{\_}{Y}}_0$, of a horizontal conductor consist of an internal term and an earth return term in the following manner:

$${\underset{\_}{Z}}_0\cong {\underset{\_}{Z}}_{0i}+\frac{\mathit{j\omega }{\mu }_0}{2\pi }·\mathit{ln}\frac{1.85}{\sqrt{{\underset{\_}{\gamma }}^2+{\underset{\_}{\Gamma }}^2}·\sqrt{2\mathit{ah}}}$$E17

$${\left({\underset{\_}{Y}}_0\right)}^{-1}\cong {\left({\underset{\_}{Y}}_{0i}\right)}^{-1}+\frac{\mathit{j\omega }{\mu }_0}{\pi ·{\underset{\_}{\Gamma }}^2}·\mathit{ln}\frac{1.12}{\underset{\_}{\gamma }·\sqrt{2\mathit{ah}}}$$E18

Here ${\underset{\_}{Z}}_{0i}$ denotes the internal complex impedance of a conductor of radius $a$, buried at depth $h$, and ${\underset{\_}{Y}}_{0i}$ stands for the insulation admittance of an eventual coating gap, through which the conductor is in contact to the surrounding medium. The latter is characterized by the earth conductivity ${\sigma }_E$, relative electric permittivity ${\epsilon }_{\mathit{rE}}$, and magnetic permeability ${\mu }_0$. All three lead to a propagation function [31, 32, 33]:

$$\underset{\_}{\mathrm{\Gamma }}\left(\omega \right)=\sqrt{\mathit{j\omega }{\mu }_0·\left({\sigma }_E+\mathit{j\omega }{\epsilon }_0{\epsilon }_{\mathit{rE}}\right)}$$E19

which would govern the transmission of impulses along the conductor if it were imbedded in a homogeneous soil with these parameters.

For a more complex geometry like the one from Figure 10, the generalized telegrapher’s equations for the case of multi-wire system along the $x$-axis above an imperfectly conducting ground and in the presence of an external electromagnetic excitation are [33]:

Figure 10.

Multiple conductors over a conductive earth.

$$\left\{\begin{array}{c}\frac{d}{\mathit{dx}}\left[{\underset{\_}{U}}_i\left(x\right)\right]+\left[\mathit{j\omega }{L}_{\mathit{ij}}\right]·\left[{\underset{\_}{I}}_i\left(x\right)\right]+\left[{\underset{\_}{Z}}_{\mathit{gij}}\right]·\left[{\underset{\_}{I}}_i\left(x\right)\right]=\left[{\underset{\_}{S}}_{1i}^e\left(x\right)\right]\\ \frac{d}{\mathit{dx}}\left[{\underset{\_}{I}}_i\left(x\right)\right]+\left[G_{\mathit{ij}}\right]·\left[{\underset{\_}{U}}_i\left(x\right)\right]+\left[\mathit{j\omega }{C}_{\mathit{ij}}\right]·\left[{\underset{\_}{U}}_i^s\left(x\right)\right]=\left[{\underset{\_}{S}}_{2i}^e\left(x\right)\right]\end{array}\right.$$E20

where:

• $\left[{\underset{\_}{U}}_i\left(x\right)\right]$, $\left[{\underset{\_}{I}}_i\left(x\right)\right]$ are vectors of voltage and current along the line, in the frequency domain

• $\left[L_{\mathit{ij}}\left(x\right)\right]$, $\left[G_{\mathit{ij}}\left(x\right)\right]$, and $\left[C_{\mathit{ij}}\left(x\right)\right]$ are the matrices of per unit length line inductance, transverse conductance, and capacitance, respectively

• $\left[{\underset{\_}{Z}}_{\mathit{gij}}\right]$ is the matrix of ground impedance

• $\left[{\underset{\_}{S}}_{1i}^e\left(x\right)\right]$ and $\left[{\underset{\_}{S}}_{2i}^e\left(x\right)\right]$ are the vectors of distributed source terms representing the effect of an external exciting electromagnetic field. These terms are equal to zero in the absence of an external exciting electromagnetic field.

In (20), there are neglected the terms corresponding to wire impedance and the ground admittance. Indeed, it has been shown in literature [30, 31, 32, 33] that for a typical frequency range of interest (bellow 10 MHz) and for typical overhead lines, these parameters can be disregarded with reasonable approximation.

The expression for the mutual ground impedance between two conductors $i$ and $j$ has been derived by Sunde and is given by:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·{\int }_0^{\infty }\frac{e^{-\left(h_i+h_j\right)·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{cos}\left(r_{\mathit{ij}}x\right)\mathit{dx}$$E21

where:

$${\underset{\_}{\gamma }}_g=\sqrt{\mathit{j\omega }{\mu }_0·\left({\sigma }_g+\mathit{j\omega }{\epsilon }_0{\epsilon }_{\mathit{rg}}\right)}$$E22

in which ${\sigma }_g$ and ${\epsilon }_{\mathit{rg}}$ are the ground conductivity and relative permittivity.

The diagonal terms of the ground impedance matrix are given by:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·{\int }_0^{\infty }\frac{e^{-2h_i·x}}{\sqrt{x^2+\underset{\_}{{\gamma }^2}}+x}·\mathit{dx}$$E23

Eqs. (22) and (23) are not suitable for a numerical evaluation since they involve Sommerfeld integrals. Several approximate expressions for ${\underset{\_}{Z}}_{\mathit{gij}}$ have been presented in literature, but one of the simplest forms was proposed by Sunde himself and is given by the following logarithmic function [29]:

$${\underset{\_}{Z}}_{\mathit{gij}}\cong \frac{\mathit{j\omega }{\mu }_0}{2\pi }·\mathit{ln}\frac{1+{\underset{\_}{\gamma }}_g·h_i}{{\underset{\_}{\gamma }}_g·h_i}$$E24

It has been shown [33] that (24) is an excellent approximation of the general expression (23).

In the following, the logarithmic approximation is extended also to off-diagonal terms. Using Euler relation in (21) and after some simple mathematical manipulations, we can obtain [33]:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·\left(\frac{1}{2}{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}+\frac{1}{2}{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}^{\ast }·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}\right)$$E25

in which ${\underset{\_}{h}}_{\mathit{ij}}$ is a complex quantity, and ${\underset{\_}{h}}_{\mathit{ij}}^{\ast }$ is its complex conjugate [31]:

$${\underset{\_}{h}}_{\mathit{ij}}=\frac{h_i+h_j}{2}+j·\frac{r_{\mathit{ij}}}{2}$$E26

Using the earlier mentioned approximate identity between expressions (23) and (24) we can express:

$$\frac{\mathit{j\omega }{\mu }_0}{2\pi }·{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}\cong \frac{\mathit{j\omega }{\mu }_0}{4\pi }\mathit{ln}\left(\frac{1+{\underset{\_}{\gamma }}_g·{\underset{\_}{h}}_{\mathit{ij}}}{{\underset{\_}{\gamma }}_g·{\underset{\_}{h}}_{\mathit{ij}}}\right)$$E27

$$\frac{\mathit{j\omega }{\mu }_0}{2\pi }·{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}^{\ast }·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}\cong \frac{\mathit{j\omega }{\mu }_0}{4\pi }\mathit{ln}\left(\frac{1+{\underset{\_}{\gamma }}_g·{\underset{\_}{h}}_{\mathit{ij}}^{\ast }}{{\underset{\_}{\gamma }}_g·{\underset{\_}{h}}_{\mathit{ij}}^{\ast }}\right)$$

Introducing (27) in (25), the following approximation can be derived for the general term ${\underset{\_}{Z}}_{\mathit{gij}}$ of the ground impedance matrix:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·\left(\frac{1}{2}{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}+\frac{1}{2}{\int }_0^{\infty }\frac{e^{-2{\underset{\_}{h}}_{\mathit{ij}}^{\ast }·x}}{\sqrt{x^2+{\underset{\_}{\gamma }}_g^2}+x}·\mathit{dx}\right)$$E28

By introducing another type of approximation called the low-frequency approximation $\left({\sigma }_g>>\omega {\epsilon }_0{\epsilon }_{\mathit{rg}}\right)$, valid for low-frequency analysis, the general expression will become [33]:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·{\int }_0^{\infty }\frac{e^{-\left(h_i+h_j\right)·x}}{\sqrt{x^2+\mathit{j\omega }{\mu }_0{\sigma }_g}+x}·\mathit{cos}\left(r_{\mathit{ij}}·x\right)\mathit{dx}$$E29

And in particular, the diagonal terms will be given by:

$${\underset{\_}{Z}}_{\mathit{gij}}=\frac{\mathit{j\omega }{\mu }_0}{\pi }·{\int }_0^{\infty }\frac{e^{-2h_i·x}}{\sqrt{x^2+\mathit{j\omega }{\mu }_0{\sigma }_g}+x}·\mathit{dx}$$E30

Therefore, the general expressions for the elements of the ground impedance matrix in the multi-conductor transmission line equations are in terms of infinite integrals. Accurate approximations for the diagonal terms of the ground impedance matrix have already been presented in the literature [30, 31, 32, 33] and that proposed by Sunde is the most accurate and simple.

3.2 Combined field and circuit method for evaluating inductive and capacitive matrices

In case of steady state or phase to ground fault HVPL operating conditions when the fault is far away of the common HVPL-MP right-of-way and a single frequency analysis is enough (no transients study is required), a simpler distributed elements equivalent electrical circuit approach could be implemented. At the same time for more complex conductor shapes (not only cylindrical/cable type conductors), a hybrid/combined field and circuit method should be applied [2, 3, 5, 25].

The hybrid method [2] was developed for single frequency analysis but could be extended to multiple frequency studies also if necessary. It combines the finite element method (FEM) analysis of the electromagnetic field in the common distribution corridor, with Faraday’s law and with electric circuits theory respectively to determine the self and mutual inductances/capacitances between any metallic structures present in a HVPL-MP interference problem [5].

This type of analysis consists of solving Maxwell’s equations in nonuniform three-dimensional space and consists of the following steps [5, 25]:

1. Step 1. A multi-conductor system that includes the pipeline, phase wires, and overhead ground wires together with electrical towers and grounding systems is modeled.

2. Step 2. A reference current/voltage is set on phase wire $A\left(0°\right)$ and zero value currents/voltages on the rest of the metallic conductors (including the other phases).

3. Step 3. The magnetic vector potential $\overrightarrow{A}$ on the cross sections of all the metallic structures (${\overrightarrow{A}}_{\mathit{\text{cond}}}$) that make up the studied problem is determined by FEM analysis.

4. Step 4. The electric charges $Q$, due to the imposed reference voltage, that appear on the surface of all the conductors, respectively on the surface of the ground, are determined by means of the FEM analysis.

5. Step 5. Self-inductance per unit length of the conductor on which the reference current $I_{\mathit{ref}}$ was imposed is determined, respectively, the mutual inductances per unit length given by this current in the rest of the metallic structures are computed.

   $$L_{\mathit{\text{self}}}\text{or}{L}_{\mathit{mut}}=\frac{{\overrightarrow{A}}_{\mathit{\text{cond}}}}{{\overrightarrow{I}}_{\mathit{ref}}}\left[\mathrm{H}/\mathrm{m}\right]$$E31

6. Step 6. Based on the determined electrical charges $Q$ or linear charge distributions ${\rho }_{\ell }$, the conductor-soil (self) capacity per unit length of the conductor on which the reference voltage $V_{\mathit{ref}}$ was imposed, respectively, the mutual capacities compared to the rest of the conductors per unit length, are evaluated

   $$C_{\mathit{\text{self}}}\text{or}{C}_{\mathit{mut}}=\frac{{\rho }_{\ell }}{U}=\frac{{\rho }_{\ell }}{V_{\mathit{ref}}-V_0}=\frac{{\rho }_{\ell }}{V_{\mathit{ref}}}\left[\mathrm{C}/\mathrm{m}\right]$$E32

7. Step 7. Steps 3 and 5 respectively 4 and 6 are repeated for the case where the imposed reference current/voltage is set one by one on all the metallic structures that constitutes the investigated interference problem.

Using this iterative algorithm [25], the matrixes of self and mutual inductances and capacities between all the present structures could be constructed. Thus, the obtained inductive and capacitive matrixes describe the inductive respectively the capacitive couplings mechanism between HVPL and MP. Therefore, they could be used to solve the equivalent electric circuit model [5, 25].

The FEM evaluates the total electromagnetic interference effect in a single step, avoiding the separation of the inductive, capacitive, and conductive components, which is necessary in the circuit model. However, the FEM limitation is that when the common corridor is very long and consists of many circuits, the modeling and computation can be extremely time-expansive.

Therefore, usually 2D cross-section FEM analysis is applied for HVPL-MP parallel exposures. The following system of equations describes the linear 2D electromagnetic diffusion problem for the z-direction (along the common right-of-way) components $A_z$ of the magnetic vector potential and $J_z$of the total current density vector [2]:

$$\left\{\begin{array}{c}\frac{1}{{\mu }_0{\mu }_r}·\left[\frac{{\partial }^2{A}_z}{\partial x^2}+\frac{{\partial }^2{A}_z}{\partial y^2}\right]-\mathit{j\omega \sigma }{A}_z+J_{\mathit{sz}}=0\\ -\mathit{j\omega \sigma }{A}_z+J_{\mathit{sz}}=J_z\\ {\iint }_{S_i}{J}_z\mathit{ds}=I_i\end{array}\right.$$E33

where $J_{\mathit{sz}}$ is the source current density in the $z$ direction, and $I_i$ is the imposed current on conductor $i$ of $S_i$ cross section.

Eq. (33) could be solved by any dedicated finite element calculation software to compute the magnetic vector potentials on the surface of each metallic structure (phase wires, sky wires and pipeline).

4. Analysis of main parameters that influence the induced voltages

For the numerical evaluation of the induced voltages in metallic pipelines exposed to the electromagnetic fields produced by nearby high-voltage power lines, several software applications and software packages that implement the above presented approaches or similar methodologies could be used. There are to main types of such software applications:

• Electromagnetic Transients Programs such as EMTP-RV, ATP-EMTP, or PSCAD, which are dedicated to steady-state and transient-state analysis of complex power networks and systems. These applications require the user to build up the circuit model of the analyzed system and to select the proper circuit elements and equipment.

• Partial Element Equivalent Circuit (PEEC) technique-based software packages such as CDGES or XGSLab that are dedicated for the investigation of multi-conductor or grounding grid system. These software packages usually require the user to draw the analyzed multi-conductor system and to set the corresponding material parameters.

To highlight the effect of the main parameters that could influence the level of induced voltages in metallic pipelines, a usual HVPL-MP electromagnetic interference problem is simulated and analyzed in the following using the EMTP-RV software, due to its user-friendly interface and high computational capabilities.

An underground metallic gas transportation pipeline is considered to share the same distribution corridor with a single circuit 220 kV/50 Hz overhead electrical power line.

To model the electromagnetic coupling between HVPL and the underground MP, the new Line/Cable Data component is used from EMTP-RV, which allows to combine overhead conductors (HVPL phase wires and sky wires) with above or underground cables (the pipeline is considered as an unenergized insulated hollow cable with the same geometrical dimensions).

Using this Line/Cable Data component, the equivalent wideband transmission line model of the common distribution corridor is created (see Figure 11). The wideband transmission line model is based on the Universal Line Model (ULM) introduced in [34] applying the transmission line approach described in section 3.1. The wideband model form EMTP-RV uses complex poles and zeros for the rational approximation of the frequency-dependent characteristic admittance and wave propagation matrices, while it also takes fully into account the frequency dependence of the modal transformation matrix [23]. Therefore, it can be considered the most accurate time-domain model, its applicability being extended to any type of overhead or underground transmission line.

Figure 11.

General overview of the HVPL-MP common distribution corridor implemented in EMTP-RV.

The HVPL consists of three phase wires in a horizontal layout with a 7.4 m spacing between each other placed at 24 m above ground and two sky wires placed at 26.5 m above ground with a 4.4 m spacing from HVPL axis. The metallic pipeline is buried at 1.2 m depth. The geometrical and electrical parameters of the conductors involved in the analyzed HVPL-MP common distribution corridor (phase wires, sky wires, and the metallic pipeline) are presented in Table 1.

Source phase voltage (kV)	220
Internal radius of the pipeline (cm)	38.1
External radius of the pipeline (cm)	39.1
Thickness of the pipeline’s coating (cm)	1
Resistivity of the pipeline’s metal (Ohm/m)	1.72E-7
Relative permeability of the pipeline’s metal	300
Relative permittivity of the pipeline’s coating	2.3

Table 1.

Parameters that describe the system under investigation.

Figure 11 presents the electrical circuit model implemented in the EMTP-RV software of the investigated HVPL-MP electromagnetic interference problem considering a single equivalent transmission line element for the entire common distribution corridor. Such an implementation allows us to evaluate only the maximum values of the induced voltage, which is reached at the ends of the analyzed pipeline.

To be able to evaluate the variation of the induce voltages along the pipeline length and not just the maximum values, the common distribution corridor must be divided into several consecutive transmission line sections (segments). Usually, the length of such a transmission line segment is considered equal the span between two consecutive power line towers. This approach allows also to investigate the influence of power line towers and their grounding in case of transient state faults like the ones generated by lightning strikes to HVPL. Figure 12 presents a detailed representation of a 1 km long HVPL-MP common right-of-way using 250 m transmission line segments as the distance between two consecutive power line towers.

Figure 12.

Detailed representation of a HVPL-MP common distribution corridor implemented in EMTP-RV.

To be as close as possible to real-life situations, at both ends of common distribution corridor, the pipeline is continued with 5 km long transmission line segments representing the pipeline outside of the HVPL zone of influence. Being an underground pipeline, the inductive coupling will prevail in the electromagnetic interference problem that occurs.

4.1 Steady-State operating condition

As a first step, the induced AC voltages are evaluated in the underground MP during power line steady-state conditions with a 300 A symmetrical current load (around 115 MVA power load with a 0.9 power factor). The HVPL-MP distribution corridor has a length of 2 km. The underground MP follows a parallel route within the right-of-way at 30 m separation distance from the power line axis on the right side. The HVPL phase wires are placed in the phase A (0°), phase B (−120°), and phase C (−240°) order on the power line towers. Therefore, phase C (−240°) is the nearest phase wire to the underground MP. The soil is considered uniform with a resistivity of 100 Ωm for the entire right-of-way.

The time-domain variation of the induced voltages at different locations along pipeline length in the investigated common distribution corridor evaluated through EMTP-RV simulation and modeling is showcased in Figure 13.

Figure 13.

Time-domain representation of the AC induced voltages in MP, for steady-state HVPL condition.

The graphical representation from Figure 13 highlights values around 6.5 V regarding the induced AC voltages, which are in dangerous range from corrosion point of view. The critical values of the induced voltages, regarding the start of electrochemical corrosion reaction, are around 1.2 V as in [9, 10, 22] are presented.

Due to the induced voltages in the metallic pipeline, leakage currents will appear that depend directly on the induced voltage levels, the pipeline conductivity, and its insulation. These leakage currents could highly increase if pipeline insulation defects are present, accelerating the corrosion process.

Figure 14 shows the variation of the induced AV voltages along the pipeline length as RMS values. It can be observed that the “V”-shaped curve as reported in several literature studies [3, 17, 23, 24, 25, 26], with the highest induced RMS voltage values recorded at right-of-way ends. It must be mentioned that at each time moment, the pipeline has opposite electrical potential at its end as in Figure 13 can be noticed.

Figure 14.

Induced voltages along the MP, in case of steady-state condition.

4.2 Parametric analysis

To highlight the effect that different geometric and electrical parameters can have on the values of the induced voltages in the case of a HVPL-MP interference problem, a parametric analysis is made, by taking into account: the length of the common distribution corridor, the HVPL-MP separation distance, the HVPL load current, and the soil resistivity variation.

Figure 15 highlights the induced voltages along the MP in the case of a right-of-way with a length that varies from 0.5 km to 10 km. It is found that the induced voltage increases quasi-proportionally with the length of the common distribution corridor, up to a “critical” (or characteristic) length that depends on the geometrical and electrical parameters of the pipeline, the insulation, and the surrounding environment (soil), being defined based on the propagation constant of the electromagnetic wave along the pipeline. Among these parameters, various studies have shown that soil resistivity has the least influence.

Figure 15.

(a) Induced voltages along pipeline length for different right-of-way length, and (b) Maximum induced voltage variation with right-of-way length.

Another important aspect in an HVPL-MP interference problem is the distance between the electrical line and the metallic structure. Figure 16.a highlights the induced voltage values in the MP if it is positioned at up to 1000 meters from the power line (on either side of it). While Figure 16.b is a more detailed representation of the induced voltages in MP recorded near the metallic towers of the power line, up to 100 m on either side HVPL axis.

Figure 16.

(a) Maximum induced voltage variation with HVPL-MP separation distance, and (b) Highlight for close HVPL-MP exposures (under 100 m).

To investigate the induced voltage levels that can occur for different power flows, the symmetrical current load on HVPL was considered in the range of 150–450 A. According to Figure 17, the levels of the induced voltages in MP increase with the value of current load (an increase from 300 A to 450 A of the load current leads to 50% increase of the maximum value of the induced AC voltage).

Figure 17.

(a) Induced voltages along pipeline length for different HVPL load currents, and (b) maximum induced voltage variation with HVPL load current.

Evaluation of induced voltages for different soil resistivity values has shown than even when the soil resistivity varies in a large range like from 10 Ωm to 10 kΩm, the maximum induced voltage values vary only with 2–3% with regard to the steady-state results. The soil resistivity has a higher influence on the pipeline leakage currents in case of insulation defects or in case of lighting generated HVPL faults when soil ionization phenomena could occur around power line tower groundings.

4.3 Oblique exposures and intersections HVPL-MP

The above-presented EMTP-RV implementation and the parametric analysis consider perfect parallel exposure between HVPL and MP. However, in practice [20, 35, 36], there are frequent situations in which above or underground MPs present oblique exposures to the HVPL axis (see Figures 18 and 19) [8].

Figure 18.

Oblique HVPL-MP exposure.

Figure 19.

Induced AC voltage in case of a real HVPL-MP right-of way [37].

Therefore, to analyze real-life HVPL-MP interference problems using electromagnetic transients programs like EMTP-RV, each oblique HVPL-MP exposure section has to be replaced with an equivalent parallel HVPL-MP exposure section for which the HVPL-MP separation distance $d_{\mathit{eq}}$ is given by the Eq. (34) as long as the ratio between $d_2$ and $d_1$ (see Figure 18) is less than or equal to 3 [8].

$$d_{\mathit{eq}}=\sqrt{d_1·d_2}$$E34

If the ratio between the distances at which the two ends of the oblique exposure $d_2/d_1$ is greater than 3, the oblique exposure must be divided into two subsections, both sections verifying the imposed condition:

$$\frac{d_3}{d_1}\le 3\text{and}\frac{d_2}{d_3}\le 3$$E35

On the other hand, if MP sub-crosses the HVPL, this section is replaced by an equivalent section, in which the MP is located at $d=6m$ distance from the HVPL, for a length equal to the length of the MP projection segment considered in around the crossing point up to a separation distance less than or equal to $10m$ on either sides of the HVPL.

Figure 19 presents the AC induce voltage variation along a complex real-life HVPL-MP common distribution corridor applying the abovementioned right-of-way segmentation procedure [37].

5. Conclusions

An evaluation of the electromagnetic interferences phenomena effects that affect metallic pipelines placed in the vicinity of high-voltage power lines is presented in this chapter highlighting different analyzing and modeling techniques.

As it is shown, the presence of AC power supply systems may cause voltages to build up in nearby metallic pipeline systems, due to one or more of the following mechanisms: inductive, conductive and capacitive coupling. Such voltages may put the pipeline operating personal in danger, damage the pipeline, disturb the electrical/electronic equipment connected to the pipeline.

The induced voltages and currents on the buried pipelines may be dangerous to pipeline security due to the AC corrosion and deteriorated the cathodic protection devices. Consequently, a mitigation system is required to be designed to reduce the effects of the corrosion of which main causes are the leakage current densities from the pipeline into the surrounding soil due to AC-induced voltages.

Since even very high-quality insulation of underground metal pipelines could present insulation defects, to reduce the probability of occurrence of corrosion phenomena, European standards [14] suggest limiting the induced voltages depending on the electrochemical characteristics of the soil, so that they do not exceed:

• 10 V if the soil resistivity is greater than 25 Ωm;

• 4 V if the soil resistivity is lower than 25 Ωm.

Different techniques can be applied to mitigate induced AC voltages and gas, such as cancelation wires, gradient control wires, and insulating joints [9, 10, 26].

Thanks

Energy Transition Research Center (EnTReC) of Technical University of Cluj-Napoca is an EMTP-RV official educational partner and would like to thank POWERSYS SOLUTIONS for offering the academic license of the software.