210 
 

American Scientific Research Journal for Engineering, Technology,  and Sciences  (ASRJETS) 

ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 

© Global Society of Scientific Research and Researchers  

http://asrjetsjournal.org/  
 

Predictions of the Electric Field Emissions around Power 

Transmission Lines by Using Artificial Neural Network 

Methods 

  H. Feza Carlaka*, Şükrü Özenb, Süleyman Bilginc 

a,b,cDeparments of Electrical and Electronics Engineering, Akdeniz University, Antalya 07058, Turkey 

aEmail: fezacarlak@akdeniz.edu.tr 

bEmail: sukruozen@akdeniz.edu.tr 

cEmail: suleymanbilgin@akdeniz.edu.tr 

 

 

 

Abstract 

In this study, Artificial Neural Network (ANN) Algorithms are used to estimate the electric field that occurred 

around the power transmission lines as an alternative approach.  Firstly, electric field levels around the high 

voltage power transmission lines are measured, and then analytically calculated. Moreover, the field levels that 

occurred around these power lines have been predicted by using multilayer perceptron artificial neural network, 

radial basis function, and generalized regression neural network models. In the paper, 154 kV typical power 

transmission line used in Turkey are studied. Electric field levels occurred around the power transmission lines 

have been predicted with ANN models with high accuracy, particularly MLPNN algorithm predicted the electric 

field intensity with very high precision. 

Keywords: Power Transmission Lines; Electric Field Emissions; Artificial Neural Network Algorithms. 

1. Introduction  

The electrical power transmission and distributions systems induce an extremely low frequency electric and 

magnetic fields. Since 1980, power frequency electric and magnetic fields have been taking an important 

attention due to concerns that exposure of such fields might cause undesired health effects [1,2,3,4,25]. 

---------------------------------------------------------------------- 

* Corresponding author. 

http://asrjetsjournal.org/


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211 
 

Growing interest in epidemiological studies aims at establishing possible links between an exposures of 

residential or occupational to power frequency fields and the onset of a number of diseases, including cancer 

and leukemia have been witnessed in the last few years [5,6,7]. Past epidemiologic studies have been criticized 

for some methodological shortcomings, especially regarding the way such exposure were evaluated [8,9,26]. 

Table 1: ICNIRP Exposure Limits for Electrical Workers (at 50 Hz) [27] 

 General Public Occupational 

Electrical Field Strength (E) 5 kV/m 10 kV/m 

Magnetic Flux Density (B) 200 µT 1000 µT 

One of the recent study showed that the leukemia risk for children has been increasing and also due to 

residential exposures of ELF-EMF, the cancer risk of adult people has been observed in some of the studies. The 

leukemia risk for adult rises dramatically around the power transmission lines. The people who live in the 50 m 

vicinity of the transmission line have 33 % higher cancer risk to the people who live in the field of 50 m to 100 

m [10,11,12,13].  

In the studies of the high voltage power line, researchers have focused more on the magnetic field exposure in 

the literature. However, outdoor exposure of the electric fields around the power transmission lines can have 

harmful effects on human health and should be taken into account for the human health. In particular, the 

electric field exposure for workers of power lines and public living in the vicinity of power lines is critical. 

Furthermore, these electric field intensity values will generate an important database for studies of the human 

health researchers.  

A lower bound on neural network discrimination of 1 mV m-1 has been suggested, but based on current 

evidence, threshold values around 10–100 mV m-1 seem to be more likely. With regard to indirect effects, the 

surface electric charge induced by electric fields can be perceived, and it can result in painful micro shocks 

when touching a conductive object. Exposure to power-frequency electric fields causes well-defined biological 

responses, ranging from perception to annoyance, through surface electric charge effects [14]. These responses 

depend on the field strength, the ambient environmental conditions and individual sensitivity. The thresholds for 

direct perception by 10% of volunteers varied between 2 and 20 kV m-1, while 5% found 15–20 kV m-1 

annoying. The spark discharge from a person to ground is found to be painful by 7 % of volunteers in a field of 

5 kV m-1. Thresholds for the discharge from a charged object through a grounded person depend on the size of 

the object and therefore require specific assessment [15]. The threshold is likely to be constant over a frequency 

range between a few hertz and a few kilohertz. Furthermore, sensitivity to electrical stimulation of the CNS 

seems likely to be associated with a family history of seizure and the use of tricyclic antidepressants, neuroleptic 

agents and other drugs that lower the seizure threshold. The function of the retina, which is a part of the CNS, 

can be affected by exposure to much weaker ELF magnetic fields than those that cause direct nerve stimulation.  

At residential life, childhood cancers and occupational cancers as breast & brain cancer and leukemia have been 

dramatically increasing due to the harmful effects of power frequency electromagnetic fields on human health. 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

212 
 

There are also other undesired detrimental effects of the electromagnetic field exposure, i.e., the increase of the 

risk of getting miscarriage [16] neurodegenerative diseases such as amyotrophic lateral sclerosis and 

Alzheimer’s disease [17]. 

This study will shed light on the comparison of traditional methods with the method of artificial neural networks 

to be able to estimate the electric fields on the power lines. For this goal, electric field variations around the 

typical power lines used in Turkey are investigated. A number of analytic and numerical methods for calculation 

of electric field around the electric power transmission and distribution lines are implemented. Artificial neural 

networks have been widely used in recent years at various research applications such as predictions, pattern 

recognitions, classifications, medical applications, automatic control and signal processing. Many interesting 

applications have been presented in power systems, such as load forecasting, fault classifications and locations 

in transmission lines, voltage stability analysis and power systems economics. The Multi-Layer Perceptron 

(MLP) which is trained by the back propagation algorithm is the most popular artificial neural networks in 

engineering problems. 

This paper presents predicted electric field levels occurred around typical power transmission lines used in 

Turkey by implementing Multilayer Perceptron Neural Networks (MLPNN) and Radial Basis Functions model 

algorithms as an alternative approach. 

2. Theoretical Calculation of Electric Fields 

The calculation of power frequency electric fields around the power transmission lines requires separate 

evaluations due to the quasi-static field approach. In this study, charge simulation methods is used for the 

electric field calculation. In this study, Charge Simulation Method (CSM) was implemented to obtain the 

electric fields around the high voltage transmission lines [18]. The electric potential Vi at any point whether in 

the insulating region or at the surface of a conductor can be calculated by the summation of the potential 

contribution of all the individual simulation charges (equation 1). 

                           (1) 

where,
 

is the potential coefficient related to the potential of the jth charge at the ith point,  is the 

simulation charges, n is the charge number. The electric field intensity is calculated using the following 

equation. 

  (V/m)          (2) 

3. Electric Field Measurement 

Residential electric fields radiated from typical high voltage power lines used in Turkey were measured by using 

CA42 LF field meter, the Chauvin Arnoux. Electric field measurements were taken at 1m height from the 





n

j

iiji qPV
1

ijP iq

VE 




American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

213 
 

ground level, physical characteristics of the 154 kV power lines is shown in Figure 1. and Table 2. Since 154 kV 

power  

lines pass through the center of population in Turkey, measurements were acquired particularly for this voltage 

level. 

y

x

(0,0)

(xr, yr) (xs, ys) (xt, yt)

1
7
.1

5
m

6.7m 6.7m

 

Figure 1: Cross-section of 154 kV energy power transmission lines. 

4. Artificial Neural Network Algorithms 

The electric fields are determined by the prediction methods and measurements. For the long term prediction of 

this field, load characteristics of the lines are considered for a year period. In the literature, there are limited 

number of studies implemented with the electric fields for exposure analysis using Multilayer artificial neural 

network algorithms. These studies present an alternative approaches. Generally, researchers focused on the 

magnetic field exposure, but electric and magnetic field components can be induced to the human body with 

together. Electric field variations around the lines are determined by using Charge Simulation Method (CSM). A 

computer program is developed to simulate electric field variation around the power transmission lines. 

4.1. Multilayer perceptron neural networks (MLPNN) 

MLPNN is used as one of the most common Neural Network Algorithms. MLPNN may include two or more 

layers as shown in Figure 3. Input layer has neurons which are equal to the number of selected specific features 

and output layer determine the desired output classes which decide the number of the neurons in the output 

layer. The hidden layers which are between input and output layers may be used for optimizing of MLPNN 

especially for nonlinear systems. It is typical using just one hidden layer with a try and-error based number of 

neurons. The most common method to find the optimal number of neurons and hidden layers is by try-and-error 

[19]. An MLPNN occurs perceptron model based on Rosenblatt model in the 1950’s [20] shown in Figure 2.For 

one perceptron, the MLPNN is shown as, 

      (5) 
1

R

i i

i

x w p b


 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

214 
 

where; R is the number of inputs and their weights, pi are the input values of a perceptron and wi are weights for 

each inputs, x is the summation of a perceptron. The summation of the perceptron is scaled with tangent sigmoid 

activation function in the hidden layers and linear transfer function in the output layer. The output y of a 

perceptron for Tangent Sigmoid function in the hidden layers is denoted as; 

    (6) 

Linear transfer function y=f(x)=x can be calculated at the once perceptron in the output layer. The structure of 

MLPNN model is shown in figure 3 {(pn, tn)} are training patterns, n is the pattern number, the R and Q are the 

dimensions of the input vector pn and desired output vector tn respectively, vector yn is the network output of the 

n-th pattern. For the I-th hidden unit, the net input netn(I) and the output activation On(I) for the n-th training 

pattern are; 

  (7) 

    (8) 

where ω(I,j) shows the weight connecting the j-th input unit to the I-th hidden unit. The k-th output for the n-th 

training pattern is ynk is given as the following equation, 

(9) 

where ωio(k,j) denotes the output weight connecting the j-th input unit to the k-th output unit and who(k,I) denotes 

the output weight connecting the I-th hidden unit to the k-th output unit. The mapping error for the n-th pattern 

is given by, 

    (10) 

where tnk  denotes the k-th element of the n-th desired output vector. Training a neural network in batch mode, 

the mapping error for the k-th output unit is formulized by, 

    (11) 

The overall performance of an MLPNN, measured as the mean square error (MSE), can be given as 

     (12) 

 
x x

x x

e e
y f x

e e






 



   
1

1

, . ( ) ,     1 
R

n n

j

net i i j p j i N




  

    n nO i f net i

       
1

0 1

, , ,      1 
R Nh

nk jo n ho n

j i

y k j p j k i O i k Q 


 

      

2

1

[  ]
Q

n nk nk

k

E t y


 

2

1

1
( ) [  ]

hN

nk nk

nh

E k t y
N 

 

 
1

Q

k

E E k






American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

215 
 

.

.

.

1w

2w

wR

1p

2p

pR

b

x
f

( )y f x

 

Figure 2: The structure of one perceptron. 

 

Nh

..
.

..
. ..
.

Hidden Layer Output LayerInput Layer

1

2

1

2

3

Q

2

1

R

w11
 (1)

w31
(1)

wN1
(1)

wQM
(2)

w21
 (1)

w11
 (2)

wNR
(1)

p1n

p2n

pRn

y1n

y2n

yQn

net1n O1n

 

Figure 3: The Structure of a general MLPNN model 

4.2. Radial basis function (RBF) 

References The RBFNN is an alternative method to MLPNN and requires less computation time than MLPNN 

for network training. RBFNN is comprised of one input layer, one kernel (hidden), and one output layer. The 

structure of the RBF model is denoted in figure 4. The input variables are assigned to the nodes within the input 

layer and connected to the hidden layer without weights. The transfer functions in the hidden nodes are RBF that 

means symmetrical function centered upon a given mean value in a space. The parameters are optimized during 

the network training in RBFNN. When the training vectors are measured up to presumed level, linear 

combinations of RBFs can be found at the training vectors. The method of fitting RBF’s to data is closely 

related to the distance weighted regression, for function approximation. 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

216 
 

P1

P2

Pn

Y

Input Layer
Hidden Layer with 

Radial Basis Function Output Layer

...

...

 

Figure 4: The Structure of a general RBFNN model 

 

The RBFNN is formulated as following expression; 

 0

1

hn

i

i

y f 


   i
X c      (13) 

Where, f are the radial basis functions, 𝜔i are the output layer weights, ω0 is the output offset, X are the inputs 

of the network as X=[x1 , … , xn]’, ci are the centers associated with the basis functions, nh  is the number of basis 

functions in the network, and   denotes the Euclidean norm. It is denoted as; 

1

2
2

1

n

i

i

x


 
  
 
X       (14) 

The nonlinear basis function can be formulated by Gaussian function; 

 

2

2

( )x c

rf x e




       (15) 

where, c is the center of the basis function which has Radius r.   

RBFNN can be trained with the following procedure, at first, the centers ci of the hidden neuron activation 

functions can be initialized using clustering algorithm which is the unsupervised training. Then, the parameters 

in RBFNN are updated by gradient-based optimization techniques. Training data set includes Q={q1,q2,…,qn} 

and the each element of this set is defined as qk = (pk,tdk) where pk=(p1k, p2k ,…, pRk ) and tdk is the desired 

response. The aim of this technique is minimizing the E parameters in the following equation; 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

217 
 

2

0

1
( )

2

N

dk k

k

E t t


       (16) 

where tk is the output of the network related to input vector pk. 

, ,

,

( 1) ( )i j i j

i j

E
l l   




  


    (17) 

 ,

, , 2
1

1

( )( )
( 1) ( )

N
jk i jdk k

i j i j ik i ks
k iiki

pt t
l l v t

bv



   





   


 (18) 

and 

( 1) ( )i i b

i

E
b l b l

b



  


     (19)  

 
2

,

3
1

1

( )( )
( 1) ( )

N
jk i jdk k

i i b ik i kn
k iiki

pt t
b l b l v t

bv


 





   


 (20) 

and 

( 1) ( )i i

i

E
l l   




  


     (21) 

   
1

( )
1 dk k

i i iks

iki

t t
l l v

v
  




  


    (22) 

where 

 
2

,

2
1 2

R
jk i j

ij

p

b

ikv e








       (23) 

and ηω , ηb , ηϒ are the update rates for updating the parameters ωij, bi and ωi respectively. The gradient descent 

algorithm based on the (7), (9), (11) training of the RBFNN is implemented in MATLAB. 

4.3. Generalized Regression Neural Networks (GRNN) 

The GRNN comprises of four layers; input layer, pattern layer, summation layer and output layer (see Fig. 5). 

This regression tool consists of a dynamic network structure. The GRNN model has X input values vector and Y 

output values vector. Thus, x and y are measured values of X and Y respectively, and ˆ ( , )f x y is the joint 

continuous probability density function of X and Y. The joint probability density in GRNN can be expressed as; 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

218 
 

 
2

( 1)/2 2 2

( ) ( ) ( )1 1
, exp exp

(2 )
ˆ

2 2

T

i i i

d

x x x x y y
xf y

n  

      
      

     
  (24) 

Where n is the sample observations, σ is the spread parameter, xi is the i-th training vector, vector yi is the 

corresponding value. The regression of Y on x can be formulated as; 

 
. ( , )

|
( , )

Y f x Y dY
E Y x

f x Y dY













    (25) 

and, 

   

2

21

2

21

exp( )
2

ˆ |

exp( )
2

n
i

ii

n
i

i

d
y

y x E Y x
d









 
 
 

 





   (26) 

Where di is the distance between the input vector and the i-th training vector, and is denoted as, 

2 ( ) ( )T

i i id x x x x        (27) 

The estimate ˆ( )y x  is a weighted average of all observed yi values. 

x1

x2

xn

y1

yn

Y

Input 

Layer

Pattern 

Layer

Summation 

Layer
Output Layer

 

Figure 5: The structure of GRNN 

5. Results & Discussion 

In this study, three ANN method results are compared for calculating the electric field. These methods are 

Multilayer Perceptron Neural Networks (MLPNN), Radial Basis Function (RBF) and Generalized Radial Basis 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

219 
 

Neural Networks (GRNN). The MLPNN trained by the back propagation algorithm is the most popular method 

in engineering problems [19,22]. The training dataset is shown in Table 2.   

The method of MLPNN is firstly implemented for calculation. In order to obtain the Neural Network 

performance, following steps have been implemented: 

1. The normalization of input and output datasets with maximum minimum mapping ranging between -1 and 1. 

Input values are selected as horizontal and vertical distance values. The output values are selected as measured 

electric field values. So, the ANN structure has two input values and one output values.  

2. The database is divided into 60 % train, 15 % validation and 25 % test datasets randomly.    

3. The determination of target values according to maximum minimum mapping. 

4. The MLPNN structure occurs from an input layer having two neurons, three hidden layers having two, three, 

two neurons with tangent sigmoid transfer function in each hidden layers respectively and an output layer 

having one neuron with linear transfer function. 

5. The structure is determined as experimental and the selected structure has the highest scores of achievement.  

6. This structure is trained using Levenberg-Marquardt algorithm that determines the most optimum values 

between other back propagation training algorithms used as experimental comparison [23]. 

7. Test accuracy of Training Simulation is determined according to mse (Mean Squared Error) scores.  

8. Test accuracy of Testing Simulation is also determined by mse scores. 

9. The achievement is compared with other methods as relative errors and mse scores.  

In the RBF analysis, database is selected as 75% for training and 25% for test. So, it has an input layer with two 

neurons, one hidden layer including radial basis functions and one output having one neuron. Input data is 

directly connected to the hidden layer without having weighted in contrast to the MLPNN model [23,24]. The 

neuron in the hidden layer is delicate for data points near its center. This sensitivity is adjusted by selection of 

the spread factor, where a smaller spread factor states more precision. The spread factor is chosen as 0.6 by trial 

and error.  

In the GRNN analysis, database is selected as 75% for training and 25% for test similar to RBF structure. It has 

an input layer with two neurons, one pattern layer including radial basis functions, a summation layer and one 

output having one neuron. Spread factor that is only adjustable parameter in GRNN structure is selected as 0.5 

experimentally in this study. The spread parameter is the distance an input vector from the weight vector of a 

neuron. 

 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

220 
 

Table 2: Training Dataset 

X(m) Y(m) 

0,2 0,5 1 1,5 2 

Ecal Emeas. Ecal Emeas. Ecal Emeas. Ecal Emeas. Ecal Emeas. 

0 1,124 1,164 1,16 1,18 1,224 1,26 1,294 1,3 1,369 1,4 

3 1,101 1,13 1,136 1,1 1,198 1,22 1,265 1,255 1,338 1,37 

6 1,036 1,1 1,068 1,032 1,123 1,16 1,183 1,14 1,248 1,3 

9 0,9396 0,95 0,9659 0,93 1,012 0,98 1,062 1,1 1,115 1,119 

12 0,8261 0,798 0,8466 0,81 0,8826 0,905 0,9206 0,928 0,961 0,98 

15 0,7106 0,735 0,7259 0,75 0,7524 0,742 0,7801 0,81 0,8092 0,842 

18 0,6037 0,59 0,6148 0,59 0,6337 0,64 0,6533 0,67 0,6736 0,68 

21 0,5106 0,53 0,5185 0,535 0,5318 0,521 0,5455 0,531 0,5595 0,56 

24 0,4323 0,42 0,4379 0,45 0,4473 0,448 0,4569 0,44 0,4666 0,464 

27 0,3675 0,358 0,3716 0,35 0,3783 0,365 0,3851 0,4 0,3919 0,4 

30 0,3145 0,32 0,3174 0,3 0,3223 0,31 0,3272 0,332 0,332 0,321 

33 0,271 0,28 0,2731 0,26 0,2767 0,276 0,2803 0,283 0,2838 0,29 

36 0,2352 0,228 0,2368 0,24 0,2395 0,235 0,2421 0,246 0,2447 0,254 

39 0,2056 0,199 0,2068 0,21 0,2088 0,21 0,2108 0,21 0,2128 0,22 

42 0,1809 0,182 0,1819 0,187 0,1834 0,177 0,185 0,18 0,1865 0,19 

45 0,1602 0,163 0,161 0,155 0,1622 0,165 0,1634 0,17 0,1646 0,162 

48 0,1428 0,139 0,1434 0,139 0,1443 0,141 0,1453 0,14 0,1462 0,15 

51 0,1279 0,124 0,1284 0,131 0,1292 0,13 0,1299 0,126 0,1307 0,132 

54 0,1152 0,111 0,1156 0,112 0,112 0,117 0,1168 0,12 0,1174 0,115 

 

Table 3: Mean Squared Error values for proposed methods. 

Method MSE (Mean Square Error) 

MLPNN 2.2164E-04 

RBF 0.0068 

GRNN 5.5240E-04 

 

The relative error is calculated mathematically, 

100
)(





meas

MLPNNcalmeas

MLPNN
E

EE
e   (28) 



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

221 
 

where, Emeas is measurement value of the electric field, 𝐸𝑐𝑎𝑙(𝑀𝐿𝑃𝑁𝑁) is the value of MLPNN output. 

Table 4: Electric field values obtained at different coordinates by implementing Theoretical calculation, 

MLPNN, RBF, GRNN methods, and measurements and corresponding relative errors for each method. 

Hor.  

Dist. 

(m) 

Ver. 

Dist. 

(m) 

Electric 

Field 

Meas. 

(V/m) 

Electric 

Field 

Theo. 

(V/m) 

MLPNN 

Calc. 

(V/m) 

RBF 

Calc. 

(V/m) 

GRNN 

Calc. 

(V/m) 

etheo 

(%) 

eMLPNN 

(%) 

eRBF 

(%) 

eGRNN 

(%) 

etheo- 

eMLPNN 

(%) 

24 0.2 0.420 0.4323 0.4339 0.2825 0.4480 2.93 3.32 32.73 6.67 0.38 

30 0.2 0.320 0.3145 0.3163 0.2289 0.3111 1.72 1.17 28.47 2.77 0.56 

42 0.2 0.182 0.1809 0.1805 0.1940 0.1869 0.60 0.84 6.58 2.70 0.23 

51 0.2 0.124 0.1279 0.1285 0.1450 0.1310 3.15 3.63 16.95 5.65 0.47 

0 0.5 1.180 1.16 1.1914 1.2836 1.2064 1.69 0.97 8.78 2.24 2.71 

24 0.5 0.450 0.4379 0.4383 0.3588 0.4480 2.69 2.61 20.27 0.44 0.09 

30 0.5 0.300 0.3174 0.3184 0.2511 0.3124 5.80 6.14 16.29 4.15 0.32 

48 0.5 0.139 0.1434 0.1428 0.1384 0.1398 3.17 2.77 0.40 0.57 0.39 

15 1 0.742 0.7524 0.7561 0.6749 0.7770 1.40 1.90 9.05 4.71 0.49 

27 1 0.365 0.3783 0.3783 0.2993 0.3561 3.64 3.64 17.99 2.43 0.00 

42 1 0.177 0.1834 0.1827 0.1811 0.1835 3.62 3.24 2.30 3.67 0.37 

51 1 0.130 0.1292 0.1296 0.1517 0.1311 0.62 0.32 16.67 0.85 0.30 

6 1.5 1.140 1.183 1.1812 1.3493 1.2173 3.77 3.62 18.36 6.78 0.15 

9 1.5 1.100 1.062 1.0621 1.1121 1.0417 3.45 3.45 1.10 5.30 0.01 

24 1.5 0.440 0.4569 0.4588 0.3588 0.4480 3.84 4.28 18.46 1.82 0.42 

27 1.5 0.400 0.3851 0.3863 0.3391 0.3939 3.73 3.43 15.23 1.54 0.31 

36 1.5 0.246 0.2421 0.2432 0.2385 0.2441 1.59 1.16 3.05 0.77 0.43 

51 1.5 0.126 0.1299 0.1305 0.1522 0.1319 3.10 3.58 20.76 4.67 0.47 

54 1.5 0.120 0.1168 0.1189 0.1126 0.1157 2.67 0.91 6.16 3.56 1.81 

24 2 0.464 0.4666 0.4741 0.2485 0.4480 0.56 2.17 46.45 3.45 1.60 

30 2 0.321 0.332 0.3358 0.2783 0.3296 3.43 4.61 13.29 2.67 1.14 

42 2 0.190 0.1865 0.1871 0.1949 0.1800 1.84 1.53 2.59 5.25 0.32 

45 2 0.162 0.1646 0.1647 0.1876 0.1694 1.60 1.68 15.81 4.56 0.07 

48 2 0.150 0.1462 0.1465 0.1734 0.1401 2.53 2.36 15.59 6.59 0.18 

Comparison of MLPNN, RBFNN and GRNN & Measurement Results with respect to Training Dataset are 

found in figure 6. As it can also be seen visually from the figure, the dataset of MLPNN Algorithm matches 

almost perfectly with the measured data. According to the mean square error analysis, and relative errors with 

respect to the measured values, the best results are obtained by MLPNN Algorithm. Numerical results are 

shown in Table 3 & Table 4. In figure 7, electric field intensity values at different heights are denoted. These 

results are obtained using 3 different neural algorithm methods. To be able to make a comparison and see the 

accuracy precision, measured values are also denoted in these graphs. Since other two methods are allowed to 



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alter just one parameter and MLPNN allows to change more parameters which are neuron numbers, layer 

numbers, activation function types etc., the most accurate result is obtained using MLPNN algorithm. 

 

Figure 6: Comparison of MLPNN, RBFNN and GRNN & Measurement Results with respect to Training 

Dataset 

 

Figure 7: Predicted Electric Field Intensity Values at Different Heights Obtained with 3 different artificial 

neural network algorithms (MLPNN, RBFNN & GRNN Methods) and Measured Values 

Figure 7 depicts the accuracy of the neural network algorithms, particularly MLPNN algorithm. Electric Field 

Intensity values are shown with respect to horizontal and vertical locations (see Figure 8). MLPNN results are 

depicted in Figure 8. As it can be seen from the Figure 8, results are obtained very precisely by using MLPNN 

0 5 10 15 20 25
0

0.2

0.4

0.6

0.8

1

1.2

1.4

Data Number

E
le

c
tr

ic
 F

ie
ld

 (
k
V

/m
)

 

 

RBF

MLPNN

GRNN

Measured

0 5 10 15 20
0

0.5

1

1.5

E
le

c
tr

ic
 F

ie
ld

 (
k
V

/m
)

Measurement Height (0.5 m) 

 

 

MLPNN

Measured

RBFNN

GRNN

0 5 10 15 20
0

0.5

1

1.5

E
le

c
tr

ic
 F

ie
ld

 (
k
V

/m
)

Measurement Height (1 m) 

 

 

MLPNN

Measured

RBFNN

GRNN

0 5 10 15 20
0

0.5

1

1.5

Data Number

E
le

c
tr

ic
 F

ie
ld

 (
k
V

/m
)

Measurement Height (1.5 m) 

 

 

MLPNN

Measured

RBFNN

GRNN

0 5 10 15 20
0

0.5

1

1.5

Data Number

E
le

c
tr

ic
 F

ie
ld

 (
k
V

/m
)

Measurement Height (2 m) 

 

 

MLPNN

Measured

RBFNN

GRNN



American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2016) Volume 15, No  1, pp 210-226 

 

223 
 

algorithm. Measured, theoretical and predicted neural network algorithm results are obtained in consistency. 

This shows the success of neural network algorithm as MLPNN. Finally, results show that the most successful 

neural network algorithm for calculating the electric field intensity is the MLPNN method. 

 

Figure 8: Electric Field Intensity Values Obtained by Applying MLPNN Algorithms at Different Heights with 

respect to different coordinates. 

6. Conclusions 

In this study, three ANN methods are compared for determination of Electric field intensity. The MLPNN 

method has the best accuracy results relatively. The mean square error (mse) of MLPNN algorithm is obtained 

as 2.2164x10-4. On the other hand, RBFNN algorithm has 0.0068 mse and GRNN has 5.5240x10-4 mse. 

Furthermore, maximal absolute errors of neural network methods are 6.17 % for MLPNN, 46.45% for RBFNN 

and 6.78% for GRNN algorithms with respect to the measurement database. As a result, the RBFNN is not 

sufficiently good for determination of the electric field intensity. As it is seen from the results of numerical 

analysis, MLPNN algorithm is the best method for calculation of electric field intensity.  

The prediction of electric field intensity can be implemented with very low error by the Neural Network 

Algorithms, especially MLPNN method by defining the line voltage level and the physical properties of the line. 

Results of the study indicate that Neural Network Algorithms particularly MLPNN can be used as a 

complementary tool with the conventional methods for the prediction of electric field intensity around the power 

transmission lines for the study of bio-electromagnetic, occupational health and safety, and electromagnetic risk 

analysis. To be able to keep the general public and occupational exposure under control, electromagnetic 

analysis of power transmission lines should be implemented daily at existing and new electric power line project 

designs. 

 

0 10 20 30 40 50 600

1

2
0

0.5

1

1.5

Vertical Distance (m)Horizontal Distance (m)

E
le

ct
ri

c 
F

ie
ld

 (
k

V
/m

)



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Acknowledgements 

 The research is supported by the Research Project Department of Akdeniz University, Antalya, Turkey. 

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