**2.1 Studied electromagnetic interference problem**

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 µr=250 relative permeability.

Fig. 3. Top view of the parallel exposure.

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.

Artificial Intelligence Techniques Applied to

*j*

*j*

Block presented in (Satsios et al. 1999a, 1999b).

**2.3 MatLab implementation of prosed neural networks** 

 P – is a RxQ1 matrix of Q1 representative R-element input vectors; T – is a SNxQ2 matrix of Q2 representative SN-element target vectors; S – is a vector representing the number of neurons in each hidden layer; TF – is a vector representing the transfer function used for each layer;

A similar function can be called to create a layer recurrent neural network:

Once a neural network is created, to train it, the following *Matlab* function can be used:

train(net,P,T) (9)

BTF – is the back propagation function used to train the NN;

 BLF – is the weight/bias learning function; PF – is performance evaluation function.

FEM and respectively.

called from command line:

where:

where *dxy* ,,,

and

technique has been applied using gradient based relations like:

*P p p j p*

*P p p j p*

 and ,,, , ,,, *<sup>p</sup> <sup>p</sup> A dxy A dxy FEM* 

*J A dxy A dxy A A dxy*

In the following, in order to improve the accuracy of the obtained results and to simplify the implementation process of the applied artificial intelligence technique, the authors propose an alternative by using a Neural Network solution instead of the presented Fuzzy Logic

To identify the optimal neural network solution different feed-forward and layer recurrent architectures were evaluated. To implement these neural network architectures the *Neural Network Toolbox* of the *MatLab* software application was used. This software was chosen because it enables the creation of almost all types of NN from perceptrons (single layer networks used for classification) to more complex architectures of feed-forward or recurrent networks. To create a feed-forward neural network in *MatLab* the following function can be

*J A dxy A dxy A A dxy*

Electromagnetic Interference Problems Between Power Lines and Metal Pipelines 259

To identify the proper rule base and the optimal parameters for each rule an iterative

 <sup>2</sup> ,,, ,,, ,,, *<sup>j</sup>*

 <sup>3</sup> ,,, ,,, ,,, *<sup>j</sup>*

*<sup>j</sup> FEM <sup>j</sup>*

(6)

*j p j*

net = newff(P,T,S,TF,BTF,BLF,PF) (7)

net = newlrn(P,T,S,TF,BTF,BLF,PF) (8)

*<sup>j</sup> FEM <sup>j</sup>*

(5)

*j p j*

 

 

are the MVP values obtained with

Fig. 4. Cross section of the studied EPL-MP interference problem.
