**1. Introduction**

252 Recurrent Neural Networks and Soft Computing

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European ecological regulations meant to protect nature and wild life along with construction cost reduction policies generated a set of government regulations that limit the access to new transmission and distribution corridors. As a result, gas, water or oil supply pipelines are forced to share the same distribution corridors with Electrical Power Lines (EPL), AC Railway Systems or Telecommunication Lines (figure 1).

Fig. 1. Common distribution corridor. Right of way.

The electromagnetic fields generated by high voltage electrical power lines produce AC interference in the nearby metallic structures. Therefore, in many cases these underground or above ground utilities supply Metal Pipelines (MP) are exposed to effects of induced AC currents and voltages (CIGRÉ 1995, Dawalibi & Southey 1989). Especially in case of power line faults, the resulting AC voltage in unprotected pipelines may reach thousands of volts.

Artificial Intelligence Techniques Applied to

Electromagnetic Interference Problems Between Power Lines and Metal Pipelines 255

To evaluate the self and mutual impedance between the conductors (phase wires, sky wires and pipelines) the magnetic vector potential has to be evaluated on the cross section

Thus, taking into account the cross section of the studied problem, the *z*-direction component of the magnetic vector potential *Az* and of the total current density *Jz* are

<sup>1</sup> <sup>0</sup>

*jAJ J J ds I*

where *σ* is the conductivity, *ω* is the angular frequency, *µ0* is the magnetic permeability of free

current density in the *z*-direction and *Ii* is the imposed current on conductor *i* of *Si* cross section. To solve this differential equation system, the finite element method (FEM) is recommended to be used. FEM effectively transforms the electromagnetic interference problem into a numerical one. Although FEM yielded solutions are very accurate, regarding to the problem complexity, the computing time of this method increases with the geometry, its mesh,

The FEM calculations are used in the described method, as a means of calculating the self and mutual impedances of the conductors present in the configuration. Generally, if there exist *n* conductors in the configuration and assuming that the per unit length voltage drop on every conductor is known for a specific current excitation, the mutual complex impedance between conductor *i* and another conductor *j* carrying a certain current, where

, 1,2, , *<sup>i</sup>*

*<sup>V</sup> Z ij n <sup>I</sup>* (2)

*A A jAJ*

*z z z sz*

H/m), *µr* is the relative permeability of the environment, *Jsz* is the source

(1)

*z sz z z i*

(figure 2) of these conductors as presented in (Christoforidis et al. 2003, 2005).

2 2 2 2

*x y*

 

*i*

*S*

described by the following system of differential equations:

0

material characteristics and requested evaluation parameters.

all other conductors are imposed to carry zero currents, is given by:

The procedure is summarized below (Papagiannis et. al. 2000):

*ij*

*j*

Similarly, the self-impedance of conductor *i* may be calculated using (2), by setting *i=j*.

The self and mutual impedances of the j conductor may be calculated using (2).

conductor *i* having a conductivity of *σi* are obtained. Therefore, equation (2) becomes:

 By applying a sinusoidal current excitation of arbitrary magnitude to each conductor, while applying zero current to the other conductors, the corresponding voltages are

The above procedure is repeated *n* times, so as to calculate the impedances for *n* conductors. Applying FEM calculations for the solution of linear electromagnetic diffusion equation (first relation from system (1)), the values for source current density in the *z*-direction *(Jszi*) on each

 

 

space (*µ0*= <sup>7</sup> 4 10 

calculated.

*r*

This could be dangerous on both the operating personnel (that may be exposed to electric shocks), and to the structural integrity of the pipeline, due to corrosion. Underground steel pipelines are in permanent contact with the electrolyte solution from the soil, so proper protection measures are necessary in order to limit the induced current densities, which are the cause of electrochemical corrosion. Uncontrolled corrosion of supply pipelines may cause gas or/and oil spills with very serious ecological and economic implications. (Baboian 2002, Collet et al. 2001)

In order to provide proper protection for pipelines the AC interference has to be well known. Normally, the electromagnetic interference between electrical power lines and nearby metallic pipelines could be generated by any of the following three types of couplings (CIGRÉ 1995):


In case of interferences between EPLs under normal operating conditions and underground pipelines, only the inductive coupling described by the self and mutual impedance matrix has to be taken into consideration. Conductive and capacitive interference may be, also, neglected when a ground fault happens significantly away from the common corridor.

Fig. 2. Cross section of an interference problem between an EPL and an underground MP.

This could be dangerous on both the operating personnel (that may be exposed to electric shocks), and to the structural integrity of the pipeline, due to corrosion. Underground steel pipelines are in permanent contact with the electrolyte solution from the soil, so proper protection measures are necessary in order to limit the induced current densities, which are the cause of electrochemical corrosion. Uncontrolled corrosion of supply pipelines may cause gas or/and oil spills with very serious ecological and economic implications.

In order to provide proper protection for pipelines the AC interference has to be well known. Normally, the electromagnetic interference between electrical power lines and nearby metallic pipelines could be generated by any of the following three types of

 **Inductive Coupling**: Aerial and underground pipelines that run parallel to or in close proximity to transmission lines or cables are subjected to induced voltages by the time varying magnetic fields produced by the transmission line currents. The induced electromotive forces (EMF) causes current circulation in the pipeline and voltages

 **Conductive Coupling**: When a ground fault occurs in the electrical power system the current flowing through the grounding grid produce a potential rise on both the grounding grid and the neighbouring soil with regard to remote earth. If the pipeline goes through the "zone of influence" of this potential rise, then a high difference in the

 **Capacitive Coupling**: Affects only above ground pipelines situated next to overhead power lines. It occurs due to the capacitance between the power line and the pipeline. For underground pipelines the effect of capacitive coupling may be neglected, because

In case of interferences between EPLs under normal operating conditions and underground pipelines, only the inductive coupling described by the self and mutual impedance matrix has to be taken into consideration. Conductive and capacitive interference may be, also, neglected when a ground fault happens significantly away from the common corridor.

Fig. 2. Cross section of an interference problem between an EPL and an underground MP.

electrical potential can appear across the coating of the pipeline metal.

(Baboian 2002, Collet et al. 2001)

between the pipeline and surrounding earth.

of the screening effect of the earth.

couplings (CIGRÉ 1995):

To evaluate the self and mutual impedance between the conductors (phase wires, sky wires and pipelines) the magnetic vector potential has to be evaluated on the cross section (figure 2) of these conductors as presented in (Christoforidis et al. 2003, 2005).

Thus, taking into account the cross section of the studied problem, the *z*-direction component of the magnetic vector potential *Az* and of the total current density *Jz* are described by the following system of differential equations:

$$\begin{cases} \frac{1}{\mu\_0 \mu\_r} \cdot \left[ \frac{\partial^2 A\_z}{\partial x^2} + \frac{\partial^2 A\_z}{\partial y^2} \right] - j\alpha \sigma A\_z + J\_{sz} = 0\\\\ \qquad -j\alpha \sigma A\_z + J\_{sz} = I\_z\\ \qquad \qquad \iint\_S I\_z ds = I\_i \end{cases} \tag{1}$$

where *σ* is the conductivity, *ω* is the angular frequency, *µ0* is the magnetic permeability of free space (*µ0*= <sup>7</sup> 4 10 H/m), *µr* is the relative permeability of the environment, *Jsz* is the source current density in the *z*-direction and *Ii* is the imposed current on conductor *i* of *Si* cross section.

To solve this differential equation system, the finite element method (FEM) is recommended to be used. FEM effectively transforms the electromagnetic interference problem into a numerical one. Although FEM yielded solutions are very accurate, regarding to the problem complexity, the computing time of this method increases with the geometry, its mesh, material characteristics and requested evaluation parameters.

The FEM calculations are used in the described method, as a means of calculating the self and mutual impedances of the conductors present in the configuration. Generally, if there exist *n* conductors in the configuration and assuming that the per unit length voltage drop on every conductor is known for a specific current excitation, the mutual complex impedance between conductor *i* and another conductor *j* carrying a certain current, where all other conductors are imposed to carry zero currents, is given by:

$$Z\_{ij} = \frac{V\_i}{I\_j} \quad \left(i, j = 1, 2, \dots, n\right) \tag{2}$$

Similarly, the self-impedance of conductor *i* may be calculated using (2), by setting *i=j*.

The procedure is summarized below (Papagiannis et. al. 2000):


The above procedure is repeated *n* times, so as to calculate the impedances for *n* conductors.

Applying FEM calculations for the solution of linear electromagnetic diffusion equation (first relation from system (1)), the values for source current density in the *z*-direction *(Jszi*) on each conductor *i* having a conductivity of *σi* are obtained. Therefore, equation (2) becomes:

Artificial Intelligence Techniques Applied to

interference problems.

µr=250 relative permeability.

Fig. 3. Top view of the parallel exposure.

and MP varies along the common distribution corridor.

**2.1 Studied electromagnetic interference problem** 

**2. Magnetic vector potential evaluation using neural networks** 

Electromagnetic Interference Problems Between Power Lines and Metal Pipelines 257

network solution used to evaluate the self and mutual impedance matrix, which describe the inductive coupling between an electrical power line and an underground pipeline in the presence of a three vertical layer earth. For such a case, no analytical formula exists so far, and this means that lengthy calculations using FEM must be made. The obtained impedance matrix can be used to build and solve the equivalent electrical circuit model and thus evaluate the induce AC voltage. This equivalent electrical circuit approach permits to solve more complex problem geometries where for example the separation distance between EPL

The first attempt of the authors to use neural networks based artificial intelligence techniques in the study of electromagnetic interference problems was focused on finding an easier method to identify the optimal solution to scale the results from a set of known problem geometries to any other new problem geometries in case of specific EPL-MP

The studied electromagnetic interference problem, presented in figure 3, refers to an underground metallic gas pipeline which shares for 25 km the same distribution corridor with a 145 kV EPL at 50 Hz frequency. The power line consists of two steel reinforced aluminium conductors per phase. Sky wire conductors have a 4 mm radius and the gas pipeline has a 0.195 m inner radius, a 0.2 m outer radius and a 0.1 m coating radius. The characteristics of the materials in this configuration have the following properties: the soil is assumed to be homogeneous; MP and sky wires have an σ =7.0E+05 S/m conductivity and a

It is assumed that a phase to ground fault occurs at point B, far away outside the common EPL–MP distribution corridor. The earth current associated with this fault has a negligible action upon the buried pipeline. This fact allows us to assume only the inductive coupling caused by the flowing fault current in the section where the power lines runs parallel to the buried gas pipeline. End effects are neglected, leading to a two dimensional (2D) problem,

presented in figure 4, were the magnetic vector potential has to be evaluated.

$$Z\_{ij} = \frac{V\_i}{I\_j} = \frac{I\_{sxi} \ne \sigma\_i}{I\_j} \tag{3}$$

Following the above procedure, effectively linking electromagnetic field variables and equivalent circuit parameters, the self and mutual impedances per unit length of the problem are computed.

By using FEM to calculate the impedances of the problem instead of classic formulae, (e.g. Carson's formulae), one can deal effectively with more complex situations, such as multilayer earth or terrain irregularities.

Nevertheless, the study of electromagnetic interference between power lines and underground pipelines using FEM for different system configurations requires expensive computing time. This is because each new problem geometry taken under consideration involves a new mesh development and new calculations. To solve system equation (1) for a given problem geometry (EPL-MP separation distance, soil resistivity) with an Intel Core2 Duo T6400 (2.0 GHz/2.0 GHz) processor PC it takes from 20 to 50 minutes depending on mesh discretization. Therefore, any scaling method of the results from one configuration case to another may be of interest if it provides less computing time.

A first attempt in applying artificial intelligence techniques to scale EPL-MP interference results was made in (Satsios et al. 1999a, 1999b). A Fuzzy Logic Block (FLB) was implemented to evaluate the Magnetic Vector Potential (MVP) for an EPL-MP interference problem where phases to earth fault occurred. The input values were the geometrical parameters of the studied problem configuration (separation distance, soil resistivity) and the coordinates of the point where the MVP should be calculated. However, the implemented FLB provide relatively good results for MVP, the main disadvantage of this method consists in determination of the optimal parameters, which describes the fuzzy logic rule base. An iterative technique based on conjugate gradient has been used to optimize the fuzzy rule base parameters. Later on a Genetic Algorithm technique had been proposed in (Damousis et al. 2002) to determine the optimal parameters and rule base configuration

Another approach in using artificial intelligence techniques in the study of electromagnetic interferences between power lines and underground metal pipelines was introduced by Al-Badi (Al-Badi et al. 2005, 2007). A feed-forward Neural Network with one output layer and one hidden layer was proposed to evaluate the induced AC interference in an underground pipeline exposed to electromagnetic fields generated by an electrical power line in case of a phase to earth fault. The input values of this Neural Network were the fault current, the soil resistivity, the separation distance and a fourth parameter which indicates the presence of mitigation wires. The main advantage of this NN solution was that it provided directly the value of the induced AC voltages. However, the limitation of this model consists in the fact that the results are obtained for a specific common distribution corridor length.

In this chapter two artificial intelligence techniques are presented. These were applied by the authors in some EPL-MP electromagnetic interferences studies (Micu et al. 2009, 2011). The first one is a neural network alternative to the EPL-MP interference problem presented in (Satsios et al. 1999a, 1999b). The advantage of the proposed alternative consists in the accuracy of the obtained results and in the shorter training time. The second is a neural

*V J <sup>Z</sup> ij n I I* 

Following the above procedure, effectively linking electromagnetic field variables and equivalent circuit parameters, the self and mutual impedances per unit length of the

By using FEM to calculate the impedances of the problem instead of classic formulae, (e.g. Carson's formulae), one can deal effectively with more complex situations, such as

Nevertheless, the study of electromagnetic interference between power lines and underground pipelines using FEM for different system configurations requires expensive computing time. This is because each new problem geometry taken under consideration involves a new mesh development and new calculations. To solve system equation (1) for a given problem geometry (EPL-MP separation distance, soil resistivity) with an Intel Core2 Duo T6400 (2.0 GHz/2.0 GHz) processor PC it takes from 20 to 50 minutes depending on mesh discretization. Therefore, any scaling method of the results from one configuration

A first attempt in applying artificial intelligence techniques to scale EPL-MP interference results was made in (Satsios et al. 1999a, 1999b). A Fuzzy Logic Block (FLB) was implemented to evaluate the Magnetic Vector Potential (MVP) for an EPL-MP interference problem where phases to earth fault occurred. The input values were the geometrical parameters of the studied problem configuration (separation distance, soil resistivity) and the coordinates of the point where the MVP should be calculated. However, the implemented FLB provide relatively good results for MVP, the main disadvantage of this method consists in determination of the optimal parameters, which describes the fuzzy logic rule base. An iterative technique based on conjugate gradient has been used to optimize the fuzzy rule base parameters. Later on a Genetic Algorithm technique had been proposed in (Damousis et al. 2002) to determine the optimal parameters and rule base configuration

Another approach in using artificial intelligence techniques in the study of electromagnetic interferences between power lines and underground metal pipelines was introduced by Al-Badi (Al-Badi et al. 2005, 2007). A feed-forward Neural Network with one output layer and one hidden layer was proposed to evaluate the induced AC interference in an underground pipeline exposed to electromagnetic fields generated by an electrical power line in case of a phase to earth fault. The input values of this Neural Network were the fault current, the soil resistivity, the separation distance and a fourth parameter which indicates the presence of mitigation wires. The main advantage of this NN solution was that it provided directly the value of the induced AC voltages. However, the limitation of this model consists in the fact that the results are obtained for a specific common distribution

In this chapter two artificial intelligence techniques are presented. These were applied by the authors in some EPL-MP electromagnetic interferences studies (Micu et al. 2009, 2011). The first one is a neural network alternative to the EPL-MP interference problem presented in (Satsios et al. 1999a, 1999b). The advantage of the proposed alternative consists in the accuracy of the obtained results and in the shorter training time. The second is a neural

*ij*

case to another may be of interest if it provides less computing time.

problem are computed.

corridor length.

multilayer earth or terrain irregularities.

*j j*

/ , 1,2, , *i szi i*

(3)

network solution used to evaluate the self and mutual impedance matrix, which describe the inductive coupling between an electrical power line and an underground pipeline in the presence of a three vertical layer earth. For such a case, no analytical formula exists so far, and this means that lengthy calculations using FEM must be made. The obtained impedance matrix can be used to build and solve the equivalent electrical circuit model and thus evaluate the induce AC voltage. This equivalent electrical circuit approach permits to solve more complex problem geometries where for example the separation distance between EPL and MP varies along the common distribution corridor.
