Modeling the Effects of Electromagnetic Interference from Multi-Wire Traction Networks on Pipelines

Abstract

The 25 kV traction network creates highly intensive electromagnetic fields. These fields affect the long conductive structures located near railway lines and can induce voltage, posing a danger for maintenance personnel. Typical examples of such structures are pipelines, which are used to transport liquid and gaseous products. In addition to compromising electrical safety, the induced voltage can result in dangerous densities of corrosion currents in pipe insulation defects. Therefore, the determination of the induced voltage and current in the pipes is undoubtedly relevant. An analysis of existing literature on the electromagnetic compatibility of traction networks and pipelines indicates that important aspects regarding the effects of traction networks and high-voltage power lines on extended conductive structures have been addressed. However, these works do not present a unified method to determine the induced voltage on parts of the structures and the current flowing through the pipeline. Such a method could be based on a technology that models the operation of electric power systems in phase coordinates. This paper presents the development of a method and the results of the studies aimed at modeling the voltage induced by complex traction networks. The developed digital models make it possible to adequately determine the induced voltage created by multi-wire traction networks and the current flowing through the pipes. Using these models, one can make an informed decision regarding the appropriate measure to ensure the safety of personnel working on these structures, as well as the development of corrosion prevention methods and measures.

1. Introduction

The fundamental difference between three-phase transmission lines and single-phase traction networks (TNs) is the electromagnetic imbalance of the latter. This feature of TNs leads to significant effects [1] on the metal structures positioned along the railway route, such as pipelines through which liquid and gaseous products are transported. The electromagnetic interference from TNs can result in induced voltage on the components of these structure, with levels exceeding those set by electrical safety standards [2]. In addition, the induced voltage can create increased densities of corrosion currents in pipe insulation defects [3]. It should be noted that in high-voltage three-phase power lines, electromagnetic imbalance can manifest itself under special conditions caused by phase failures, single-phase, and two-phase short circuits, and others [4,5].

To ensure the safety of personnel working on pipelines located in areas with increased electromagnetic interference from the traction network, it is necessary to use organizational and technical measures. The choice of these measures should be based on the results of computer modeling in the present context. Such modeling should involve digital models that adequately factor in all influencing factors, including:

• Magnitudes and phases of current flowing through the wires of contact suspensions, 6-10-25 kV power lines laid on the supports of the contact network, and rail lines.
• Similar parameters for voltage at the nodal points of the traction network.
• Approach width when pipes are laid parallel to the railway track.
• Parameters of the approach in the case of non-parallel sections.
• Electrical parameters of soils on the approach path.

The relevance of the electromagnetic compatibility issue between traction networks (power lines) and pipelines is confirmed by an analysis of related studies. The main theoretical provisions and analytical expressions that make it possible to calculate the voltage induced by the traction network on metal structures are presented in [6,7]. The influence of harmonics on the levels of electromagnetic effects on pipelines caused by the traction network is assessed in [8]. The optimal design of pipeline routes near high-voltage power lines is discussed in [9]. The effect of electromagnetic fields of power transmission lines on pipelines is analyzed in [10]. In [11], the authors solved the problem of pipeline screening and presented a method for determining the induced potentials on different parts of the structure. A technique for assessing the induced voltage on pipelines located at short distances from an ultra-high voltage transmission line is presented in [12]. The inductive effects of overhead power lines on pipelines are considered in [13]. Efficient algorithms for analyzing the electromagnetic effects of power transmission lines on oil and gas pipelines are described in [14]. The influence of electromagnetic fields on a parallel pipelines is considered in [15]. The problem of determining the induced voltage on pipelines due to the magnetic effects of power lines is solved in [16]. The paper [17] analyzed the levels of induced voltage on pipelines equipped with insulating flanges. The studies in [18] aimed to analyze the electromagnetic fields of a 380 kV power transmission line located near pipelines. The work in [19] focused on determining the induced voltage on different parts of pipes laid along ultra-high voltage power lines. An analysis of the effects resulting from the proximity of high-voltage electrical networks and pipelines is presented in [20]. The results of a study on the effect of the electromagnetic interference of 750 kV AC power lines on several underground pipelines are presented in [21]. Ref. [22] presents the results of the analysis of mutual electromagnetic interference between the power line and the underground pipeline. The research presented in [23] is concerned with the study of the processes of electromagnetic induction in pipelines due to the influence of high-voltage overhead power lines. Methods for reducing the effect of electromagnetic interference on underground metal pipelines near overhead AC power lines are considered in [24]. The study discussed in [25] examines the interference generated by power lines on an underground pipeline. The electromagnetic impact of a lightning strike on underground metal pipelines connected to a UHV AC double-circuit transmission tower is studied in [26]. Ref. [27] proposes ways to detect electromagnetic effects on metal pipelines near overhead power lines. References [28,29] address the issues of electromagnetic effects on underground pipelines during a lightning strike on the wires of high-voltage power lines. In [30], the electromagnetic interference on a gas pipeline caused by critical faults in a wind farm was analyzed. The practical results of analyzing the electrical and magnetic field coupling between power transmission lines and pipelines are presented in [31]. Ref. [32] focuses on a method for calculating the electromagnetic interference on a gas pipeline from a 1000 kV power transmission line in the case of a single-phase ground fault. The authors of [33] describe a circuit model of underground metallic pipelines used to evaluate the shielding effectiveness of nearby communication lines.

Analysis of the above publications allows for the conclusion that they address significant aspects of determining the induced voltage on pipelines. However, the objectives of studying the effects of electromagnetic interference caused by traction networks on extended metal structures have not been fully achieved. Moreover, the considered works do not present a unified procedure for determining the induced voltage on different parts of structures and the current flowing through the pipeline. Such a procedure could be implemented based on methods that model the behavior of electric power systems in phase coordinates, as described in [34,35,36]. In the following sections, we present the development of this procedure and the results of studies aimed at modeling the effects of electromagnetic interference from multi-wire traction networks and power lines on pipelines.

Determining the voltage induced by the electromagnetic fields of a power transmission line or traction network on a pipeline is a very complex task that requires the consideration of many factors. These factors include the operating conditions of the influencing line, the approach trajectory, the groundings of the metal structure, the length of the approach area, and the conductivity of the soils in this area.

The primary mechanism that affects the induced voltage on the parts of a grounded pipeline and the currents flowing within pipes is magnetic influence. Calculating these parameters relies on approximation formulas for mutual inductance, which work effectively in the near and remote zones determined by the approach width and soil resistance. These formulas are based on the Carson integral. However, there is an intermediate zone where the use of approximations leads to unacceptable errors. In this zone, it is necessary to use the expansion of the integral in a series [35].

The proposed method, implemented in the industrial software Fazonord [34], possesses features that significantly distinguishes it from the aforementioned methods used to determine the electromagnetic effects of power transmission lines and traction networks on extended metal structures:

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The method can determine electromagnetic influences in any technically feasible situations. For example, overhead and cable lines of various designs, current ducts, bus ducts, contact networks of railways, and other elements can act as influencing factors.

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The method employs a systems approach to model electromagnetic influences by calculating power flows within a complex electric power system.

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The adequacy of determining electromagnetic influences is achieved through correct operation in the near, intermediate, and remote zones of the Carson integral.

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The method calculates the induced voltage while considering harmonic distortions of current and voltage in the influencing power transmission line or traction network.

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The method can account for the heterogeneity of electrical parameters of soils along the approach path between the influencing power transmission line (traction network) and the pipeline.

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The approach path of the influencing power transmission line and the affected pipeline can be parallel, converging, or complex.

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The method enables the determination of the technical performance of devices used to reduce induced voltage, such as shielding wires.

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The method can accurately consider dedicated means of pipeline grounding, which minimizes the impact on corrosion protection systems.

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In addition to surface pipelines, underground structures can also be properly taken into account.

2. Problem Statement

The above analysis of publications focusing on electromagnetic compatibility of traction networks, power transmission lines, and pipelines highlights the need for further research on adequately detecting the induced voltage caused by traction networks and power transmission lines on extended metal structures. Additionally, the most urgent objective is to design efficient computer models that meet the following requirements:

• Adequately consider all factors affecting the levels of induced voltage on the components of the structure and the current passing through the pipes.
• Ensure high accuracy of calculations for the near, intermediate, and remote zones, which are determined by the width of the pipe approach and the route of the electrified railway [33,34].
• Calculate induced voltage and current based on the operational parameters of the traction network and the power supply system [34].
• Such models rely on modeling methods in phase coordinates, which are implemented in the Fazonord software [35]. Below are the results of modeling the voltage induced by multi-wire traction networks on pipelines.

3. Determination of Induced Voltage Based on Phase Coordinates

The determination of operating parameters can be represented by a functional transformation as follows:

$$A:D\Rightarrow X,$$

(1)

where A is a general nonlinear operator; $D=S\cup Y$ is a set of initial data; X is the desired vector of operating parameters, the components of which are the magnitudes and phases of voltage at the network nodes; $S$ is a set of data describing the structure and parameters of network components; and $Y$ is the parameters that characterize generators and loads.

The transformations (1) correspond to a system of steady-state equations, which are generally nonlinear [34]:

$$F\left(X,Y\right)=0,$$

(2)

where X is the nodal voltage vector in Cartesian or polar coordinates, and Y is a vector that includes the active P_k and reactive Q_k power of generators and loads.

The models and methods proposed in this paper for determining electromagnetic effects rely on an approach based on the use of phase coordinates [32]. In this approach, lattice equivalent circuits (LEC) are used, which have a fully connected topology, represented as:

$$TEC:hub\cup con,\forall i,j\subset hub\to co{n}_{i,j}\subset con,$$

where TEC is the LEC designation, hub is a set of LEC nodes, and con is a set of LEC branches.

The set of power components of the electric power system can be represented as a union of two subsets:

$$EPS=Power\cup Conv.$$

The first subset includes the electricity transport components: overhead and cable power lines, current ducts, and traction networks. The second subset consists of transformation components, including transformers of various designs.

Despite the significant design differences of the devices included in electric power systems, they can be generally considered as static multi-wire components consisting of a set of wires or windings with electromagnetic coupling.

At the beginning of the last century, single-line power system models based on several simplifying assumptions were proposed to calculate steady-state conditions. The introduction of these assumptions was justified since, at that time, there were no adequate means to solve high-dimensional problems numerically. Today, the use of single-line models has become impractical, and the main focus for developing technologies for modeling operating conditions should be based on a multi-phase representation.

Based on the phase coordinates, it is possible to implement models that adequately determine the effects of electromagnetic interference caused by high-voltage and high-ampere power lines on adjacent metal structures. Below is a brief description of the methodology for modeling electric power systems and traction power supply systems (TPS) in phase coordinates.

The generation of a LEC for power lines or traction networks involves the following steps:

• Construction of a conductivity matrix without considering capacitive couplings between wires.
• Addition of capacitive couplings.

The first stage involves the construction of a conductivity matrix of an LEC with dimensions n = 2r, which does not factor in capacitive couplings between individual wires or between wires and the ground:

$${\underset{¯}{Y}}_{PC}=-M{\underset{¯}{Z}}^{-1}{M}_{}^{\mathrm{T}}=\left[\begin{array}{cc}-\underset{¯}{D}& \underset{¯}{D}\\ \underset{¯}{D}& -\underset{¯}{D}\end{array}\right],$$

where $\underset{¯}{D}={\underset{¯}{Z}}^{-1}$, $\underset{¯}{Z}$ is an impedance matrix of dimension $r\times r$, and ${\underset{¯}{z}}_{ik}={\underset{¯}{z}}_{ki}$; $r$ is the number of power line wires.

The matrix M is formed as follows:

$$M=\left[\begin{array}{c}{E}_r\\ -E_r\end{array}\right],$$

where $E_r$ is an identity matrix with dimension $r\times r$.

Capacitive couplings are taken into account based on the relation:

$${\underset{¯}{Y}}_C={\underset{¯}{Y}}_{PC}+j\mathsf{\omega }{C}_Y,$$

where $C_Y=\frac{1}{2}\left[\begin{array}{cc}B& 0\\ 0& B\end{array}\right]$, $\mathsf{\omega }$ = 314 rad/s, $B=A^{-1}$, and $A$ is a matrix of potential coefficients of dimension $r\times r$.

The elements of matrix A are calculated using the following formulas:

$${\mathsf{\alpha }}_{ii}=\frac{1}{2\mathsf{\pi }{\mathsf{\epsilon }}_0}\ln \frac{2h}{r_w};\to {\mathsf{\alpha }}_{ij}=\frac{1}{2\mathsf{\pi }{\mathsf{\epsilon }}_0}\ln \frac{D_{ij}}{d_{ij}},$$

where ${\mathsf{\epsilon }}_0$ is an electric constant, h is an equivalent wire suspension height in terms of sag, $D_{ij}$ is a distance between wire i and a mirror image of wire j, $d_{ij}$ is the distance between wires i and j, and $r_w$ is the wire radius.

The technique used to determine the diagonal elements ${\mathsf{\alpha }}_{ii}$ of matrix A for grounded current-carrying parts, such as rails, is as follows: the capacitive currents of the rail thread with respect to the ground are significantly lower than the leakage current to the ground due to the ohmic contact resistance. This phenomenon is denoted as rails–ground. Therefore, for the calculation, it is sufficient to position the wire above the ground at a height greater than two times the radius of the equivalent wire that simulates the rail. The radius of this wire is determined by the cross-sectional area of the rail. The errors in the calculation of operating parameters and the electromagnetic field are small in this case.

With an ohmic contact resistance rail–ground below several hundred Ohm·km, the capacitance corresponding to its self-potential coefficient ${\mathsf{\alpha }}_{ii}$ at a frequency of 50 Hz exceeds the ohmic value by more than two orders of magnitude. The Fazonord software has control over the relationship between the wire radius and its height above the ground. For buried wires, the software employs an algorithm that takes into account the insulating cavity for the current-carrying part located in the ground.

A similar technique can be used for pipelines and for other metal structures located on the ground.

The resistances of the shunts that are added to the LEC nodes can be determined using the capacitance coefficients in matrix B. The procedure for constructing the matrices of LEC transformers is described in [34].

Matrices ${\underset{¯}{Y}}_{Ck}$, k = 1 … n that correspond to individual components are used to build a model of the network that corresponds to the conductivity matrix ${\underset{¯}{Y}}_{\Sigma }$. This matrix can be obtained through the following transformation:

$${\underset{¯}{Y}}_{\Sigma }=M_0{\underset{¯}{Y}}_V{M}_0^T,$$

where $M_0=\left[\begin{array}{ccc}-P& -P& 0\\ 0& P& -P\\ P& 0& P\end{array}\right]$ is a generalized incidence matrix comprising submatrices P.

The row blocks of submatrices P correspond to the nodes of a single-line network, and the single-line branches correspond to column blocks. The conductivity matrix of branches ${\underset{¯}{Y}}_V$ is block-diagonal:

$${\underset{¯}{Y}}_V=diag{\underset{¯}{Y}}_{Sk}.$$

The system of steady-state equations is formed on the basis of the obtained matrix ${\underset{¯}{Y}}_{\Sigma }$. This system can be represented as follows:

$${\underset{¯}{Y}}_{\Sigma }\dot{U}=\dot{I},$$

(3)

where $\dot{U}$ is a vector of phase voltage, and $\dot{I}$ is a vector of current.

After setting fixed values of voltage at the slack nodes, Equations (2) and (3) can be represented as follows:

$$\left[\begin{array}{cc}{\underset{¯}{Y}}_1& {\underset{¯}{Y}}_{1B}\\ {\underset{¯}{Y}}_{B1}& {\underset{¯}{Y}}_B\end{array}\right]\left[\begin{array}{c}\dot{U}\\ {\dot{U}}_B\end{array}\right]=\left[\begin{array}{c}\dot{I}\\ 0\end{array}\right],$$

where ${\dot{U}}_B$ is a voltage vector of slack nodes, and ${\underset{¯}{Y}}_{1B}={\underset{¯}{Y}}_{B1}^T$, ${\underset{¯}{Y}}_B$ are blocks corresponding to the branches associated with them.

After excluding the equations corresponding to the slack nodes, we can write ${\underset{¯}{Y}}_1\dot{U}=\dot{I}-{\underset{¯}{Y}}_{1B}{\dot{U}}_B$.

By replacing current with power, a system of non-linear steady-state equations can be obtained:

$${\underset{¯}{Y}}_1\dot{U}=diag\left(\frac{{\tilde{S}}_k}{{\tilde{U}}_k}\right)n-{\underset{¯}{Y}}_{1B}{\dot{U}}_B,$$

(4)

where ${\tilde{S}}_k$ is the conjugate complex of the k-th node power, n is a vector of dimension n − n_B consisting of units, n is the total number of network nodes, n_B is the number of slack nodes, and ${\tilde{U}}_k$ is a conjugate complex of the k-th node voltage. By separating the real and imaginary quantities, Equation (4) can be represented in the form (2).

If lines affected by influences are included in the individual LEC, then solving the equations will determine the induced voltage [36].

The mutual inductance, which determines the magnetic interference, was calculated using Carson’s formulas [37], which take into account the return of currents through the earth. Approximation formulas were used to calculate inductances in the near and remote zones. The boundaries between the zones are defined by the parameter r, which depends on the distance between the wires, earth resistance, and frequency:

$$r=2.8099\cdot {10}^{-3}\cdot r_{ik}\prime \sqrt{\frac{f}{\mathsf{\rho }}},$$

where f is the frequency, Hz; $r_{ik}\prime =\sqrt{{\left(x_i-x_k\right)}^2+{\left(y_i+y_k\right)}^2}$; $\mathsf{\rho }$ is earth resistivity, Ohm·m; and (x_i, y_i), (x_k, y_k) are the coordinates of current-carrying parts, m.

The near zone satisfies the condition $r\le 0.25$, and the remote zone satisfies the condition $r\ge 5$. Many practically important cases require that the electromagnetic interference effects are determined for the intermediate zone, which is located within the range $0.25<r<5$. Approximation expressions for this zone can lead to significant errors; therefore, when solving this problem, one can use monograms [37] or calculate the series to which the Carson integral belongs.

The current and voltage of AC traction networks are characterized by considerable harmonic distortions, which must be taken into account when calculating the induced voltage.

Developing a model of the power supply system for the main railway to determine the dynamics of changes in traction loads during the movement of trains along real routes requires the construction of models of individual components and an algorithm for their interaction. This includes the following steps:

• modeling the train schedule,
• building instant diagrams that take into account the position of trains in space for the given moment of time and the magnitude of non-traction loads,
• identifying power flow for each instant diagram, and
• calculating the summary indicators of the modeling process.

Based on this approach, one can obtain information about the dynamics of changes in the operating conditions of the traction and external networks during the movement of trains and determine voltage deviations, asymmetry coefficients for the negative and zero sequences, non-sinusoidality indicators, active and reactive power consumption for connections, as well as the induced voltage values for adjacent lines and extended metal structures.

The values of traction loads can be determined through calculations or experimentation. Modeling of moving traction loads is based on a preset train schedule that relates the coordinate of the train’s position to time.

The algorithm for instant diagram generation includes the following steps:

• identifying the position of each train at the current moment of time based on the traffic schedule;
• calculating the active and reactive power of the load at the node corresponding to the train’s position based on information about traction currents, train weight, and railway milepost;
• redefining the lengths of the catenary system components according to the position of the trains;
• recalculating the models of the catenary system components and integrating them into the stationary part of the calculation scheme. Once this step is completed, the next instant diagram is prepared for the calculation of operating parameters.

The current version of the Fazonord software enables the modeling of active components of electric power systems built using smart grid technologies. These components include:

• Distributed generation
• FACTS devices
• Multiphase transmission lines
• Gas-insulated and cryogenic power lines
• Phase shifting devices
• Current limiters
• Controlled devices for unbalance elimination
• Active harmonic conditioners
• Surface and underground cable lines with insulation from highly cross-linked polyethylene

Below are the modeling results for the following facilities:

• The 25 kV traction network of a traditional design.
• The prospective traction network with balancing transformers [38].
• The multi-track traction network of a railway station.

In addition, the resultant electromagnetic interference effects of the traction network and high-voltage power lines on the pipeline were modelled.

Modeling was also performed for a facility that includes a 220 kV power line, a 25 kV traction network, and a 25 kV power line with a grounded phase.

4. The 25 kV Traction Network

For a typical 25 kV traction power supply system (Figure 1a), the operating conditions were modeled for the multi-wire system, including a pipeline with a pipe diameter of 250 mm. The design diagram includes models of three traction transformers and two inter-substation zones (ISZ). The left ISZ was divided into five sections with a length of 10 km. In addition, models of three 220 kV power lines were presented in this work. The distance a from the pipeline to the road axis (approach width) was assumed to be 100 m. The modeling took into account the distributed grounding of the pipeline with a conductivity of 0.002 S/km. In addition, the presence of stationary grounding with an impedance of 1 Ohm was assumed along the edges of the structure. To take into account the distributed parameters, the model of the traction network sections with a pipeline was built as a chain diagram.

The movement of six down trains with a mass of 5968 t and the same number of up trains with the same mass was modeled. The train schedule is shown in Figure 1b, and the current profiles for the trains are given in Figure 2. The modeling results are presented in Figure 3 and Figure 4.

Figure 3a shows the time dependencies of the induced voltage for six pipeline points corresponding to different coordinates along the x axis, directed parallel to the approach path (Figure 1a). Figure 3b shows similar graphs for the current flowing through the pipe.

Figure 4 shows the graphs illustrating the x-coordinate dependencies of the maximum and average values of voltage and current. These figures show the values of the resultant voltage and current in terms of harmonics, defined as follows:

$$U=U_1\sqrt{1+{\left(\frac{k_U}{100}\right)}^2}; I=I_1\sqrt{1+{\left(\frac{k_I}{100}\right)}^2},$$

where $U_1$, $I_1$ represent the voltage and current of the fundamental frequency 50 Hz, respectively, and $k_U$, $k_I$ are the total harmonic distortion of voltage and current in percent, respectively.

Analysis of the presented results leads to the following conclusions:

• The electromagnetically unbalanced 25 kV traction network has significant electromagnetic interference effects on the parallel pipeline. The maximum levels of induced voltage at individual points along the pipe were within the range of 300–670 V, with a peak approaching 700 V at the coordinate x = 10 km, which significantly exceeds the permissible level of 60 V [2]. It should be noted that these induced voltage values were obtained with an insulation conductivity of G = 0.002 S/km, which is typical for structures with short periods of operation. Over time, this parameter can decrease to 0.4 S/km [4]. In this case, the distributed grounding will be amplified, which will lead to a noticeable decline in the induced voltage. For example, calculations for a value of G = 0.05 S/km show that, with other factors held constant, the maximum induced voltage decreases to 170 V.
• The current flowing through the pipe, which exceeds 20 A, can have a negative effect on corrosion protection devices (CPD).
• Reducing in the electromagnetic interference effects of the traction network can involve the following measures: reducing the length of parallel sections between the pipeline and the railway line, increasing the width of the approach, and installing additional grounding (in this case, the pipe can be connected to additional grounding conductors through blocks of capacitors to exclude the CPD malfunction). The proposed method and developed digital models will enable the selection of the most rational measures to mitigate the electromagnetic interference effects of traditional traction networks.

5. Prospective Traction Power Supply Systems with Balancing Transformers

A prospective traction power supply system (Figure 5) involves the construction of master traction substations equipped with balancing transformers.

In this case, the distance between the master traction substations can reach 300 to 350 km [38]. The traction network is powered by single-phase transformers with a winding voltage of 93.9/27.5 kV, which are located at distances of 30 to 45 km from each other. The modeling considers similar movement parameters to those described in the previous section (Figure 1b and Figure 2). Figure 6 shows the x-coordinate dependencies of the maximum and average values of induced voltage and current, taking into account harmonic distortions.

Based on the analysis of the results presented in Figure 6, we can draw the following conclusions:

• The demagnetizing effect of supply wires in the prospective traction power supply system results in a more than two-fold decrease in the induced voltage maxima at the pipe points corresponding to x coordinates or 30 and 40 km. At points with x coordinates equal to 10 and 20 km, the voltage decreases by a factor of 1.6. The voltage along the edges of the structure increases by 27 to 60% but does not exceed the permissible values.
• The maximum current running through the pipe increases compared to the 25 kV traction network by 1.3 to 2.1 times.

6. Multi-Track Traction Network of a Railway Station

Modeling was carried out for an eight-track traction network (Figure 7). A portion of the traction network is shown in Figure 8.

The modeled network included the following components:

• The 220 kV high-voltage transmission line;
• The traction transformer TDTNZh-40000-230/27.5;
• The eight-track 25 kV traction network, which was 2.5 km long and had total loads equal to 9 + j9 MVA for the up-train direction and 10 + j10 MVA for the down-train direction.

The model of the traction network sections included a ground-based pipeline with a pipe diameter of 250 mm and distributed grounding of 0.05 S/km. In addition, the modeling factored in stationary grounding conductors along the edges of the structure with a spreading resistance of one Ohm. Part of the calculation model diagram is shown in Figure 9. To control the voltage along the length of the pipeline, the traction network was represented by five sections with a length of 500 m (Figure 10). The parameters of the traction transformer are given in

Table 1. Nominal winding voltage.

No.	Parameter	Phase A	Phase B	Phase C
1	UHV, kV	132.8	132.8	132.8
2	UMV, kV	27.5	27.5	27.5
3	ULV, kV	11	11	11

Notes: HV—high voltage; MV—medium voltage; LV—low voltage.

,

Table 2. Short-circuit voltage $U_k$ and losses $\mathsf{\Delta }{P}_k$.

No.	Parameter	HV-MV	HV-LV	MV-LV
1	∆Pk, kW	220	220	200
2	$U_k,\%$	12.5	17	6

,

Table 3. Geometrical sizes.

S1, m2	S2, m2	l1, m	l2, m	l7, m
0.4	0.8	1.5	3	1.5

Notes: S₁ is the cross-sectional area of an equivalent non-magnetic rod replacing the magnetic flux closure through the tank walls; S₂ is the cross-sectional area of the central rod of the magnetic circuit; l₁ is the length of the average field line of the equivalent non-magnetic rod; l₂ is the length of the central rod; l₇ is the length of the average power line along the yoke from the central rod to the nearest lateral rod.

and

Table 4. Other parameters.

Winding	SH, MV·A	B2m, T	Ix, %	ΔPx, kW
HV	40	1.6	1.1	66
MV	40
LV	40

Note: S_H is the nominal power; I_x and ΔP_x are the no-load current and power losses, respectively; and B_2m is the nominal value of the induction amplitude in the rod of the magnetic circuit.

, and parameters of the traction network are given in

Table 5. Traction network parameters.

Name of Current-Carrying Part	R0, Ohm/km	Radius, cm	F, mm2	γ, S/km
Carrier cable	0.62	0.62	95	0
Contact wire	0.177	0.62	100	0
Rail	0.2	11.14	8290	0.5
Pipeline	0.1	12.5	50,000	0.05

Note: R₀ is resistivity; F is cross-sectional area; γ is rail-to-ground conductivity.

. The coordinates of the traction network current-carrying parts in space are shown in Figure 11.

The modeling results are shown in Figure 12, Figure 13, Figure 14 and Figure 15. Figure 12 shows the graphs of the x-coordinate dependences (Figure 10) of the induced voltage on the pipe due to the electromagnetic interference of the station’s traction network under the initial conditions, with total loads of 9 + j9 MV·A and 10 + j10 MV·A for the up-train and down-train direction, respectively. Figure 13 shows similar graphs representing the current flowing through the pipe.

Similar dependencies were obtained when modeling the conditions of contact-wire to rail short-circuit, which are shown in Figure 14 and Figure 15.

An analysis of the obtained relations U = U(x) and I = I(x) allows for the following conclusions:

• The levels of voltage induced on pipeline components under the load and emergency conditions do not exceed the permissible values established by the regulatory document [2].
• A significant current (155 A) flowing through the pipeline in the case of a short circuit can have a negative impact on the pipeline’s corrosion protection system. The main mechanism that determines the induced voltage and current flowing through the pipe is the magnetic effect, which depends on the distribution of the traction network’s magnetic field in space. Figure 16 shows the z-coordinate dependencies of the TN magnetic field strength, which are calculated at a height of 0.5 m for the axis located perpendicular to the railway track.

The calculations were performed for the initial conditions with total loads of 9 + j9 MV·A and 10 + j10 MV·A for the up-train and down-train directions, respectively. In addition, calculations were done for the short circuit of the catenary system’s contact wire to a rail.

The analysis of the presented dependencies indicates that short-circuit conditions can lead to significant levels of magnetic field strength above the pipe, exceeding 120 A/m on the axis of the structure. Magnetic fields with such strength levels can have a negative effect on electronic devices located near the pipeline.

The presented results suggest that, based on the operating parameters of traction power supply system, it is possible to solve the problems of modeling the effect of electromagnetic interference created by complex traction networks with a large number of contact wires in phase coordinates. The developed digital models make it possible to adequately determine the induced voltage caused by multi-wire traction networks and the current flowing through the pipes. With these models, it is possible to reasonably choose measures to ensure the safety of personnel serving the structure, and to develop corrosion prevention methods and means.

7. Modeling the Resulting Effects of Electromagnetic Interference Caused by the Traction Network and High-Voltage Power Lines on the Pipeline

The modeling was performed for a facility (Figure 17) that included a 220 kV power line, a 25 kV traction network, and a 25 kV power line with a grounded phase (LGP). The spatial arrangement of current-carrying parts is shown in Figure 18. The movement of six down trains weighing 6300 t was modeled (Figure 19). Part of the calculation model diagram is shown in Figure 20, and the modeling results are presented in Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25.

The length of the approach was set to 10 km, and the route was divided into five sections, each spanning two kilometers. The modeling factored in the distributed grounding of the pipeline with a conductivity of 0.002 S/km. In addition, stationary groundings with a resistance of 1 Ohm were assumed along the edges of the structure. To take into account the distribution of the parameters, the models of traction network sections with a pipeline were built as chain diagrams in harmonic frequency calculations.

In addition to the normal operating conditions of the traction power supply system described above, the following emergency conditions were modeled:

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Two-phase short-circuit, single-phase short circuit, and two-phase-to-ground short circuit on a 220 kV power line.

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Single-phase short circuit on the 0.4 kV buses of the substation connected to the power line with a grounded phase.

The obtained results allow for the following conclusions to be drawn:

• Under normal conditions of the traction network and balanced loads of the 220 kV power line and 25 kV transmission line with a grounded phase, the maximum induced voltage does not exceed the permissible limit [2] and remains within the range of 5 to 12 V. A similar parameter for the current running through the pipe does not exceed 9 A.
• Under emergency conditions of the 220 kV transmission line, the induced voltage and current increase significantly. In the case of a single-phase short circuit, the highest induced voltage occurs at the edges of the structure and reaches 3.3 kV, which significantly exceeds the permissible value of 1000 V [2]. Current and voltage close to the indicated values occur with a two-phase-to-ground fault.
• Due to the different directions of the two-phase short-circuit currents, the induced voltage and current are much lower than the values indicated in the previous paragraph. The maximum induced voltage lies within the range of 100 to 520 V and does not exceed the permissible limit. The maximum current flowing through the pipe is within the range of 511 to 514 A.
• In the event of a single-phase short circuit on the 0.4 kV buses of the substation connected to the line with a grounded phase, the maximum induced voltage does not exceed the permissible value, ranging from 98 to 270 V. The range of 265 to 267 A corresponds to the similar parameter of induced current.

8. Discussion of Results

Modeling using the Fazonord software, which implements the proposed method for determining the effects of electromagnetic interference of power transmission lines and traction networks on pipelines, was carried out for four different facilities, confirming the universality of the proposed approach. This study examined the dynamics of changes in the induced voltage over time, which was obtained during the movement of trains along real-life railway sections.

The calculations of the induced voltage took into account the harmonic distortions created by AC rectifier locomotives [39]. Both normal operational situations and emergency conditions caused by short circuits were considered.

The levels of voltage induced by the interference effects of the 25 kV traction network significantly exceeded the permissible limits for the assumed values of the conductivity of the insulating coatings of the pipeline. A similar situation was observed for a traction network with balancing transformers, although the demagnetizing effect of the supply wires resulted in a reduction of induced voltage by more than one and a half times.

The induced voltage for the traction network of the station did not exceed the permissible values. This is due to the short length of the approach path and a higher level of insulation conductivity, which can occur during long-term operation of the structure.

Large values of induced voltage that significantly exceeded the permissible value of 1000 V were observed in emergency conditions when modeling the resulting electromagnetic interference effects of the traction network and high-voltage power lines on the pipeline.

In addition to analyzing the electromagnetic effects, the proposed method makes it possible to determine electromagnetic fields by considering the induced voltage on the pipeline and the currents flowing through the pipes.

9. Conclusions

The paper presents a method, algorithms, and digital models for determining the induced voltage on pipelines located in electromagnetic interference zones of traction networks and power lines, as well as calculating the current flowing through the pipe. This methodology differs from existing approaches due to its systematic approach, versatility, and universality. The systematic approach is achieved by calculating the induced voltage and current on the pipeline based on the operating parameters of a complex traction power supply system in phase coordinates, while also considering the external supply network. In addition, the dynamics of changes in traction loads over time is taken into account by modeling the movement of trains along real track profiles. Versatility is achieved through the possibility of modeling not only operating parameters, but also the electromagnetic fields created near the pipeline. Universality is ensured by the capability to model traction networks and transmission lines of any design.

It is possible to calculate the effects of electromagnetic interference for complex trajectories of power lines and traction networks, including non-parallel sections.

The modeling takes into account all significant factors that affect the levels of induced voltage, including:

• Operating conditions of the influencing transmission line or traction network
• Approach trajectory
• Approach width for parallel lines and approach corridor dimensions for complex trajectories
• Nature of pipeline grounding
• Length of the joint passage for the influencing transmission line and the affected pipeline
• Soil conductivity along the approach path
• Resistance of insulating coatings

The method demonstrates good performance in the near, intermediate, and remote zones of the Carson integral.