Feedforward neural network and adaptive network-based fuzzy inference system in study of power lines

Expert Systems with Applications 37 (2010) 165–170

Contents lists available at ScienceDirect

Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

Feedforward neural network and adaptive network-based fuzzy inference system in study of power lines Jasna Radulovic´ *, Vesna Rankovic´ Faculty of Mechanical Engineering, University of Kragujevac, Sestre Janjic´ 6, 34000 Kragujevac, Serbia

a r t i c l e

i n f o

Keywords: Electromagnetic fields Power lines Feedforward neural network Adaptive network-based fuzzy inference systems

a b s t r a c t Over the past several decades, concerns have been raised over the possibility that the exposure to extremely low frequency electromagnetic fields from power lines may have harmful effects on human and living organisms. This paper presents novel approach based on the use of both feedforward neural network (FNN) and adaptive network-based fuzzy inference system (ANFIS) to estimate electric and magnetic fields around an overhead power transmission lines. An FNN and ANFIS used to simulate this problem were trained using the results derived from the previous research. It is shown that proposed approach ensures satisfactory accuracy and can be a very efficient tool and useful alternative for such investigations. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction According to the contemporary epidemiological researches, there are some indications that extremely low frequency electromagnetic fields harm human health which has been proved through numerous scientific studies published in recent years (Draper, Vincent, Kroll, & Swanson, 2005; Li et al., 2007). Several credible reports which serve as summaries of these studies have been published (Cotton, Ramsing, & Cai, 1994; WHO/IARC, 2002). Related to that, general public concern about possible detrimental health effects of this kind of fields near power lines has raised. In recent years many states have taken regulatory actions to limit the intensity of electric and magnetic fields on the edge of the transmission line right-of-way (ROW). Today, most countries use the ICNIRP (1998) guidelines and Council Recommendation (1999) as the scientific basis for their recommended levels of exposure. Belgium, Italy, Estonia and Switzerland have implemented stricter legislation making reference to the precautionary principle. As in Serbia there are no such guidelines and recommendations, an extreme attention should be paid to investigation of the electromagnetic fields surrounding power lines as well as of definition of ROW corridor. Related to this, there is a necessity for calculation of electromagnetic (EM) field in the surround of an electric power transmission lines, and a number of methods are suggested (Abdel-Salam, Abdallah, El-Mohandes, & El-Kishky, 1999; Hameyer, Mertens, & Belmans, 1995). Radulovic´ (2000) supposed an analytical approach

* Corresponding author. Tel.: +381 34 335 990; fax: +381 34 333 192. E-mail address: [email protected] (J. Radulovic´). 0957-4174/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2009.05.008

for solving the problem of the current conductor above semi-conducting half-space. It is based on some transformations, which substitute Somerfeld’s integral, the solution obtained by the integral transformation method, with Henkel’s function and their asymptotic expansion. Henkel’s functions represent linear solution combinations of the Bessel’s functions of the first and of the second kind (Abramowitz & Stegun, 1972). Numerical procedure for calculation of electromagnetic field of the current conductor above semi-conducting half-space, using Charge Simulation Method, is proposed by Radulovic´ (2000) and Velicˇkovic´ and Radulovic´ (2002). Charge Simulation Method is based on the theorem of equivalence of different electromagnetic systems (Malik, 1989; Salon & Chari, 1999; Singer, Steinbigler, & Weiss, 1974). The considered model of the current conductor above semi-conducting half-space has been applied to real, significant high voltage transmission line problems (estimation of intensity of electric and magnetic fields around an overhead 400 kV and 750 kV power transmission lines), by Radulovic´ (2000). Artificial intelligence techniques, such as artificial neural networks and fuzzy logic, have been recognized as a powerful tool which is tolerant of imprecision and uncertainty, and can facilitate the effective development of models by combining information from different sources. These techniques have been used in a wide variety of applications in engineering, science, business, medicine, psychology, and other fields. One of successful fuzzy and neural network applications is to model complex nonlinear systems. Hornik (1991) showed that multilayer feedforward networks with as few as a single hidden layer and arbitrary bounded and smooth activation functions are universal approximators. Kosko (1994) proved that a fuzzy system can uniformly approximate any real continuous function on a

J. Radulovic´, V. Rankovic´ / Expert Systems with Applications 37 (2010) 165–170

166

closed and bounded domain to any degree of accuracy. ANFIS is also universal approximator. Artificial intelligence techniques have been successfully applied to a number of power systems problems during recent years (Warwick, Aggarwal, & Ekwue, 1997). Fuzzy logic is used for magnetic field estimations at transformer substations (Kosalay, 2008). Damouis, Satsios, Labridis, and Dokopoulos (2001, 2002) used Takagi– Sugeno fuzzy system to determine the magnetic field induced by a faulted transmission line on a buried pipeline. The genetic algorithm has been developed for the adjustment of the fuzzy parameters. Artificial neural networks are addressed in order to give accurate solutions to high voltage transmission line problems by Ekonomou, Kontargyri, Kourtesi, Maris, and Stathopulos (2007). This paper presents a novel approach based on the use of FNN and ANFIS to estimate electric and magnetic fields around an overhead power transmission lines. The backpropagation is the most popular algorithm to train FNN (Rumelhart, Hinton, & Williams, 1986). Jang (1993) presented architecture and learning procedure of the fuzzy interference system implemented in the framework of adaptive networks. The paper is organized as follows. In Section 2, the basic structure of the FNN and ANFIS is presented. The results of the simulation are shown in Section 3. Two FNN and two ANFIS are trained. Finally, in Section 4 concluding remarks are presented. 2. Feedforward neural network (FNN) and adaptive neuro-fuzzy inference system (ANFIS)

where m is the number of inputs, nH is the number of hidden neuð1Þ rons, xj is the jth element of input, xij is the first layer weight beð2Þ tween the ith hidden neuron and jth input, xi1 is the second layer ð1Þ weight between the ith hidden neuron and output neuron, bi is a ð2Þ biased weight for the ith hidden neuron and b1 is a biased weight for the output neuron. The FNN and ANFIS are trained off-line using the training set P = {p1, p2, . . ., pr}. Each element of the set, pk = (xk, tzk) is defined by the input vector xk = (x1k, x2k, . . ., xmk) and the desired response tzk. The weight updating law minimizes the function:

1 2

e ¼ ðt  tz Þ2

The backpropagation update rule for the weights with a momentum term is:

DxðtÞ ¼ g



@e

ð2Þ

i¼1

1þe

1 P m



ð1Þ ð1Þ x x þbi j¼1 j ij

 þ bð2Þ 1

ð1Þ

@e ð2Þ

¼ ðt  t z Þ 

1þe

ð1Þ ð1Þ x x þbi j¼1 j ij

ð1Þ ð1Þ x x þbi j¼1 j ij



P m

1 P m j¼1



P m

P m

1þe

@b1

ð1Þ ð1Þ x x þbi j¼1 j ij



e

ð2Þ

¼ ðt  t z Þxi1 "

@e

xð2Þ i1

¼ ðt  t z Þxi1 xj "



ð1Þ

@ xi1

nH X

ð3Þ

P m

1þe

@e

2.1. Feedforward neural network (FNN)

e

ð2Þ

ð1Þ

@ xij

@bi

t¼

@e þ aDxðt  1Þ @x

where g is the update rate and a is the momentum coefficient. Specifically,

In this work two layer neural network and ANFIS are used to estimate electric and magnetic fields around an overhead power transmission lines.

The two-layer neural network with m inputs and one output is shown in Fig. 1. It is composed of an input buffer, a nonlinear hidden layer, and a linear output layer. For adapting parameters is used the backpropagation algorithm. The backpropagation is the most popular algorithm to train FNN (Rumelhart et al., 1986). ð1Þ The inputs x = (x1, x2, . . ., xm) are multiplied by weights xij and summed at each hidden node. Then the summed signal at a node activates a nonlinear function (sigmoid function). Thus, the output y at a linear output node can be calculated from its inputs as follows:

ð2Þ

ð1Þ

ð1Þ

ð4Þ



ð1Þ ð1Þ x x þbi j¼1 j ij

xj xij þbi

 #2

 #2



¼ t  tz

ð5Þ

ð6Þ

ð7Þ

2.2. Adaptive neuro-fuzzy inference system (ANFIS) The ANFIS architecture (Jang, 1993) (type-3 ANFIS) is shown in Fig. 2. Suppose that Takagi–Sugeno fuzzy system has m inputs (x1, x2, . . ., xm) and one output t. Linguistic labels xi are A1i, A2i, . . ., Ani. The rule base contains p = nm if-then rules:

R1 : if x1 is A11 and x2 is A12 . . . and xm is A1m then f 1 ¼ p11 x1 þ p12 x2 þ    þ p1m xm þ c1 R2 : ako x1 is A11 and x2 is A12 . . . and xm is A2m then f 2 ¼ p21 x1 þ p22 x2 þ    þ p2m xm þ c2 ... Rk : ako x1 is A21 and x2 is A22 . . . and xm is A2m then f k ¼ pk1 x1 þ pk2 x2 þ    þ pkm xm þ ck ... Rp : ako x1 is An1 and x2 is An2 . . . and xm is Anm then f p ¼ pp1 x1 þ pp2 x2 þ    þ ppm xm þ cp The number of linguistic rules is p = nm. Layer 1. The outputs of layer are fuzzy membership grade of inputs lAij ðxj Þ. If the bell shaped membership function is taken lAij ðxj Þ is given by:

lAij ðxj Þ ¼ 1þ Fig. 1. Feedforward neural network with one hidden layer.



1

 bij xj aij 2 cij

;

i ¼ 1; n; j ¼ 1; m

ð8Þ

J. Radulovic´, V. Rankovic´ / Expert Systems with Applications 37 (2010) 165–170

167

Fig. 2. m-input ANFIS with p rules.

where aij, bij, cij are the parameters of the membership function or premise parameters. Layer 2. Every node in this layer is a fixed node. The output of nodes can be presented as:

u1 ¼ lA11 ðx1 Þ  lA12 ðx2 Þ . . .  lA1m ðxm Þ

3. Simulation results and comparison of the two approaches

u2 ¼ lA11 ðx1 Þ  lA12 ðx2 Þ . . .  lA2m ðxm Þ . . . uk ¼ lA21 ðx1 Þ  lA22 ðx2 Þ . . .  lA2m ðxm Þ . . . up ¼ lAn1 ðx1 Þ  lAn2 ðx2 Þ . . .  lAnm ðxm Þ Q * denotes T-norm. Nodes is marked by a circle and labeled . Layer 3. The output of each fixed node label with N can be presented as:

i ¼ u

ui p P ui

ð9Þ

i¼1

Layer 4. Every node in this layer is a square. The outputs of this layer are given by:

i  i fi ¼ u u

m X

pij xj þ ci

ð10Þ

j¼1

Layer 5. Finally, the output of the ANFIS can be presented as:

t¼

p X i¼1

p m X 1 X  i fi ¼ p ui pij xj þ ci u P j¼1 ui i¼1 i¼1

Jang (1993) used the hybrid learning algorithm for updating the parameters. For adapting premise parameters aij, bij, cij gradient descent method is used. The least squares method is used for updating the consequent parameters.

! ð11Þ

FNN and ANFIS have been used to determine the electromagnetic field in transmission line system shown in Fig. 3, where y- axis represents earth surface. The values of voltage pffiffiffiand currents flowing through the conductors are: U f ¼ 400 kV= 3; Il ¼ 50 A; s ¼ 2p=3, current frequency is 50 Hz, radius of conductor is an = 15 mm and coordinate of protective ropes are: x7 = 26 m, y7 = -7 m, x8 = 26 m, y8 = 7 m. Earth parameters are relative permittivity er = 3, relative permeability lr = 1, and conductivity r = 0.01 S/m. Coordinates of the power lines are shown in Table 1. The inputs of the neural network and ANFIS are the coordinates (x1 = x, x2 = y) where we calculate intensity of electric and magnetic field. In this paper two input variables are chosen. It is possible to add more variables, such as, for example, earth conductivity, position and dimensions of the phase conductors, etc. We restricted the number of the input variables because we wanted to show, in a simple way, the effectiveness of the proposed approaches. Two neural networks are trained using BP algorithm. The output of the first neural network is intensity of electric field Ee, while the output of the second neural network is intensity of magnetic field He. Each of the two ANFIS has one output variable, Ee and He.

J. Radulovic´, V. Rankovic´ / Expert Systems with Applications 37 (2010) 165–170

168

Table 4 Parameters of the FNN for He calculation. i

ð1Þ xi1

ð1Þ xi2

bi

ð1Þ

ð2Þ xi1

1 2 3 4 5 6 7

0.5751 0.5629 19.0486 0.4698 17.8109 0.1172 0.216

0.1524 0.1488 1.2952 0.3145 4.719 0.4508 0.1112

1.4676 1.4353 28.895 7.9856 208.1719 1.2626 3.5932

17.9676 18.8584 0.0471 0.1064 0.0309 0.2351 0.4322

Fig. 3. Cross-section of the 400 kV power transmission lines.

Table 1 Coordinates of the power transmission lines. Phase I n xn (m) yn (m)

Phase II

1 21.5 11.2

2 21.5 10.8

Phase III

3 21.5 0.2

4 21.5 0.2

5 21.5 10.8

6 21.5 11.2

Table 2 Training data set. y

0 2 5 7 10 13 16 18 20 23 25 28 31 34 37 41 44 47 50

x 0

2

5

0

2

5

0.648 0.718 1.014 1.211 1.521 1.714 1.803 1.81 1.753 1.606 1.472 1.289 1.119 0.951 0.824 0.683 0.585 0.51 0.431

0.761 0.873 1.099 1.296 1.592 1.782 1.873 1.866 1.796 1.606 1.472 1.289 1.119 0.951 0.824 0.683 0.585 0.51 0.431

1.352 1.38 1.507 1.648 1.873 2.035 2.042 1.993 1.894 1.662 1.532 1.331 1.133 0.951 0.824 0.683 0.585 0.51 0.431

0.983 0.988 1.004 1 0.984 0.936 0.893 0.854 0.825 0.771 0.743 0.693 0.636 0.593 0.539 0.493 0.461 0.425 0.4

1.1 1.111 1.127 1.129 1.111 1.039 0.995 0.946 0.896 0.841 0.796 0.729 0.664 0.611 0.568 0.511 0.471 0.457 0.421

1.339 1.354 1.362 1.339 1.311 1.232 1.146 1.089 1.029 0.932 0.875 0.789 0.725 0.664 0.611 0.55 0.511 0.479 0.442

Fig. 4. The memberships functions of input variables (x and y) of the ANFIS used to determine Ee after training is performed.

Table 3 Parameters of the FNN for Ee calculation. i

ð1Þ xi1

xð1Þ i2

bi

ð1Þ

ð2Þ xi1

1 2 3 4 5 6 7 8 9 10

0.0569 3.338 0.0118 3.4648 13.3449 14.2972 0.2524 6.2536 11.5712 12.9179

0.1523 12.5898 0.0086 0.4338 0.5903 7.2844 0.6758 7.9368 0.7223 1.5739

1.0655 7.5295 0.7886 13.8505 7.9181 1.5262 15.4775 6.295 38.6532 18.5615

7.3737 0.1537 8.1564 0.2927 0.0872 0.1181 0.1453 0.1746 0.1533 0.052

The training data set is shown in Table 2. Parameters of the FNN are given in Tables 3 and 4. The number of the hidden neurons of the first neural network is 10 ð2Þ ð2Þ ðb1 ¼ 1:4047Þ and second is 7 ðb1 ¼ 19:54Þ.

Fig. 5. The memberships functions of input variables (x and y) of the ANFIS used to determine He after training is performed.

Fig. 4 shows the memberships functions of input variables (x and y) of the ANFIS used to determine Ee after training is performed. Gaussian function was used as a membership function in the ANFIS model. The number of membership functions assigned to each input of the ANFIS was set to 2, so the rule number is 4.

J. Radulovic´, V. Rankovic´ / Expert Systems with Applications 37 (2010) 165–170

169

Table 5 Ee and He for several new configuration cases of the examined EM field problem, obtained by Radulovic´ (2000) and by FNN, and proper absolute errors. x

y

Ee

He

Ee(FNN)

eE (%)

He(FNN)

eH (%)

0.5 1.55 2 3.025 3.55 4.065 4.87 5

10.5 18.65 5.07 22.05 15.86 32.65 29.5 48.07

1.5428 1.8015 1.1623 1.6955 1.9578 1.0751 1.2347 0.4467

1.0165 0.9354 1.1267 0.8499 1.0014 0.6389 0.7598 0.4671

1.5210 1.8355 1.1051 1.6813 1.9799 1.0211 1.2015 0.4691

1.413 1.8873 4.9213 0.8375 1.1288 5.0228 2.6889 5.0146

0.9976 0.9139 1.1255 0.8668 1.0442 0.6502 0.7444 0.4574

1.8593 2.2985 0.1065 1.9885 4.2740 1.7687 2.0268 2.0766

Table 6 Ee and He for several new configuration cases of the examined EM field problem, obtained by Radulovic´ (2000) and by ANFIS, and proper absolute errors. x

y

Ee

He

Ee(ANFIS)

eE (%)

He(ANFIS)

eH (%)

0.5 1.55 2 3.025 3.55 4.065 4.87 5

10.5 18.65 5.07 22.05 15.86 32.65 29.5 48.07

1.5428 1.8015 1.1623 1.6955 1.9578 1.0751 1.2347 0.4467

1.0165 0.9354 1.1267 0.8499 1.0014 0.6389 0.7598 0.4671

1.5548 1.7839 1.2042 1.7182 1.9437 1.0962 1.2513 0.4284

0.7778 0.9770 3.6049 1.3388 0.7202 1.9626 1.3445 4.0967

1.0151 0.95 1.1118 0.8526 0.9949 0.6291 0.7517 0.4748

0.1377 1.5608 1.3224 0.3177 0.6491 1.5339 1.0661 1.6485

Fig. 7. Magnetic field distribution in surrounding of 400 kV power transmission lines.

The absolute errors have been computed as:

      Ee  EeðFNN=ANFISÞ He  HeðFNN=ANFISÞ eE ¼  100 and eH ¼  100 E H e

e

Electric and magnetic fields distribution in surrounding of 400 kV power transmission lines obtained by the ANFIS is shown in Figs. 6 and 7, respectively. Visual presentation obtained by FNN is very similarly with presented distribution obtained by ANFIS.

4. Conclusions

Fig. 6. Electric field distribution in surrounding of 400 kV power transmission lines.

Fig. 5 shows the memberships functions of input variables (x and y) of the ANFIS used to determine He after training is performed. The rule base of the ANFIS for Ee calculation:

If x is small and y is small then f 1 ¼ 0:1051x þ 0:1378y þ 0:7088 If x is small and y is big then f 2 ¼ 0:1564x þ 0:04459y  2:144 If x is big and y is small then f 3 ¼ 0:2743x þ 0:1074y þ 0:06638 If x is big and y is big then f 4 ¼ 0:3609x þ 0:04062y  0:09911 The rule base of the ANFIS for He calculation:

If x is small and y is small then f 1 ¼ 0:191x þ 0:004974y þ 1:089 If x is small and y is big then f 2 ¼ 0:02403x  0:0009426y þ 0:4061 If x is big and y is small then f 3 ¼ 0:2574x þ 0:002872y þ 0:135 If x is big and y is big then f 4 ¼ 0:0242x þ 0:004821y þ 0:03016 Tables 5 and 6 summarize test results where Ee and He calculations by the FNN (Ee(FNN), He(FNN)), ANFIS (Ee(ANFIS), He(ANFIS)) and the method proposed by Radulovic´ (2000) have been compared.

Electromagnetic fields which originate from power transmission lines may be implicated in a number of adverse health effects. It is very important to know the intensity of the components of these electromagnetic fields. In this paper, FNN and ANFIS are addressed in order to estimate the electric and magnetic field around an overhead power transmission lines. Results of the simulations presented in this paper show that the application of the FNN and ANFIS to electromagnetic field approximation gives satisfactory results. ANFIS and FNN test results are in a very good agreement with the results obtained by Radulovic´ (2000). Maximal absolute error is less then 5% when ANFIS is used. The error is slightly bigger than that when FNN is used. The first neural network has 10 hidden neurons and second one has 7 hidden neurons. Each of the two ANFIS used here contains a total of 20 fitting parameters, of which 8 are the premise parameters and 12 are the consequent parameters. The optimal values of the premise parameters and consequent parameters are obtained by the hybrid learning algorithm. It can be concluded that relatively small number of hidden neurons, that is to say a small number of fitting parameters provides sufficient accuracy. Expert systems proposed in this paper are capable of determining the electric and magnetic fields around an overhead power transmission lines, and of providing the results of a satisfying convergence and accuracy. References Abdel-Salam, M., Abdallah, H., El-Mohandes, M. Th., & El-Kishky, H. (1999). Calculation of magnetic fields from electric power transmission lines. Electric Power Systems Research, 49, 99–105. Abramowitz, M., & Stegun, I. (1972). Handbook of the mathematical functions. New York: Dover Publications.

170

J. Radulovic´, V. Rankovic´ / Expert Systems with Applications 37 (2010) 165–170

Cotton, G. W. L., Ramsing, K. C. K., & Cai, C. (1994). Design guidelines for reducing electromagnetic field effects from 60 Hz electrical power systems. IEEE Transactions on Industry Applications, 30(6), 1462–1471. Council Recommendation of 12 July 1999 on the limitation of exposure of the general public to electromagnetic fields (0 Hz to 300 GHz) (1999). Official Journal of European Communities, L 199, 59–71. Damouis, I. G., Satsios, K. J., Labridis, D. P., & Dokopoulos, P. S. (2001). A fuzzy logic system for calculation of the interference of overhead transmission lines on buried pipelines. Electric Power Systems Research, 57, 105–113. Damouis, I. G., Satsios, K. J., Labridis, D. P., & Dokopoulos, P. S. (2002). Combined fuzzy logic and genetic algorithm techniques – Application to an electromagnetic field problem. Fuzzy Sets and Systems, 129, 371–386. Draper, G., Vincent, T., Kroll, M. E., & Swanson, J. (2005). Childhood cancer in relation to distance from high voltage power lines in England and Wales: A case-control study. British Medical Journal, 330(7503), 1290–1292. Ekonomou, L., Kontargyri, V. T., Kourtesi, St., Maris, T. I., & Stathopulos, I. A. (2007). Artificial neural networks in high voltage transmission line problems. Measurement Science and Technology, 18, 2239–2244. Hameyer, K., Mertens, R., & Belmans, R. (1995). Numerical methods to evaluate the electromagnetic fields belowoverhead transmission lines and their measurement. In Proceedings of 1st IEEE international caracas conference on devices, circuits and systems (ICCDCS), Venezuela (pp. 32–36). Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural network, 4(2), 251–257. International Commission on Non-Ionizing Radiation Protection (ICNIRP) (1998). Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz). Health Physics, 74(4), 494–522. Jang, J.-S. R. (1993). ANFIS: Adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685.

Kosalay, I. (2008). Fuzzy logic based ELF magnetic field estimation in substations. Radiation Protection Dosimetry, Advance Access published online on April 24, 1– 11. Kosko, B. (1994). Fuzzy systems as universal approximators. IEEE Transactions on Computers, 43(11), 1329–1333. Li, C.-Y., Mezei, G., Sung, F.-C., Silva, M., Chen, P.-C., Lee, P.-C., et al. (2007). Survey of residential extremely-low-frequency magnetic field exposure among children in Taiwan. Environment International, 33, 233–238. Malik, N. H. (1989). A review of the charge simulation method and its applications. IEEE Transactions on Electrical Insulation, 24(1), 3–20. Radulovic´, J. (2000). A new approach for EM field calculation of linear conductor placed ˇ acˇak, Serbia above semi-conducting half-space. PhD Thesis, Technical Faculty, C (in Serbian). Rumelhart, D. E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature, 323, 533–536. Salon, S. J., & Chari, M. V. (1999). Numerical methods in electromagnetism. Elsevier Science and Technology Books. Singer, H., Steinbigler, H., & Weiss, P. (1974). A charge simulation method for the calculation of high voltage fields. IEEE Transactions on Power Apparatus Systems, 93(5), 1660–1668. Velicˇkovic´, D., & Radulovic´, J. (2002). Electromagnetic field of current conductor above semi-conducting half-space. Facta Universitatis, Ser.: Electronics and Energetics, 15, 217–225. Warwick, K., Aggarwal, R., & Ekwue, A. (1997). Artificial intelligence techniques in power systems. Institution of Engineering and Technology (IET). World Health Organization International Agency for Research on Cancer (WHO/ IARC) (2002). Non-ionizing radiation, Part 1: Static and extremely lowfrequency (ELF) electric and magnetic fields. IARC monographs on the evaluation of carcinogenic risks to humans (Vol. 80). .