Investigation of pollution flashover on high voltage ... - Semantic Scholar
Expert Systems with Applications 36 (2009) 7338–7345
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Review
Investigation of pollution flashover on high voltage insulators using artificial neural network M.T. Gençog˘lu *, M. Cebeci Department of Electrical and Electronics Engineering, Faculty of Engineering, Firat University, Elazig, Turkey
a r t i c l e
i n f o
Keywords: Pollution flashover Flashover voltage Artificial neural networks
a b s t r a c t High voltage insulators form an essential part of the high voltage electric power transmission systems. Any failure in the satisfactory performance of high voltage insulators will result in considerable loss of capital, as there are numerous industries that depend upon the availability of an uninterrupted power supply. The importance of the research on insulator pollution has been increased considerably with the rise of the voltage of transmission lines. In order to determine the flashover behavior of polluted high voltage insulators and to identify to physical mechanisms that govern this phenomenon, the researchers have been brought to establish a modeling. Artificial neural networks (ANN) have been used by various researches for modeling and predictions in the field of energy engineering systems. In this study, model of VC = f (H, D, L, r, n, d) based on ANN which compute flashover voltage of the insulators were performed. This model consider height (H), diameter (D), total leakage length (L), surface conductivity (r) and number of shed (d) of an insulator and number of chain (n) on the insulator. Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.
1. Introduction Outdoor insulators are being subjected to various operating conditions and environments. The surface of the insulators is covered by airborne pollutants due to natural or industrial or even mixed pollution. Contamination on the surface of the insulators enhances the chances of flashover. Under dry conditions the contaminated surfaces do not conduct, and thus contamination is of little importance in dry periods (Gorur & Olsen, 2006). As the surface becomes moist because of rain, fog or dew, the pollution layer becomes conductive because of the presence of ionic solids. The leakage current flows through the conducting surface film, generating heat which tends to increase the film temperature most rapidly at those points where the current density is greatest, i.e. at narrow sections of the insulator, such as the area around the pin. Eventually, the temperature in these areas approaches boiling point, and rapid evaporation of the moisture occurs producing dry areas. The development of the dry areas is independent of the insulator type, something that has also been verified experimentally, since the insulator’s body diameter differs very little from one type to another (Gonos, Topalis, & Stathopulos, 2002). Pollution flashover, observed on insulators used in high voltage transmission, is one of the most important problems for power * Corresponding author. Tel.: +90 424 2370000/5237; fax: +90 424 2415526. E-mail addresses: mtgencoglu@firat.edu.tr (M.T. Gençog˘lu), mcebeci@firat.edu.tr (M. Cebeci).
transmission. Pollution flashover is a very complex problem due to several reasons such as modeling difficulties of the insulator complex shape, different pollution density at different regions, non-homogenous pollution distribution on the surface of insulator and unknown effect of humidity on the pollution (Dhahbi-Megriche & Beroual, 2000). The performance of insulators under polluted environment is one of the guiding factors in the insulation coordination of high voltage transmission lines. On the other hand, the flashover of polluted insulators can cause transmission line outage of long duration and over a large area. Flashover of polluted insulators is still a serious threat to the safe operation of a power transmission system. It is generally considered that pollution flashover is becoming ever more important in the design of high voltage transmission lines (Suflis, Gonos, Topalis, & Stathopulos, 2003). Research on insulator pollution is directed primarily to understanding the physics of the growth of discharge and to develop a mathematical model, which can predict accurately the critical flashover voltage and critical current. A common feature of all the mathematical models proposed by researchers (Alston & Zoledziowski, 1963; Boeme & Obenhaus, 1966; Rizk, 1981; Wilkins, 1969) is a representation of a propagating arc consisting of a partial arc in series with the resistance of the unbridged section of the polluted layer. Alston and Zoledziowski and Wilkins proposed mathematical models for the prediction of critical flashover voltage taking into consideration the effects of different physical parameters. The flashover of polluted insulators was the motivation for the installation of a test station in order to perform laboratory tests on
0957-4174/$ - see front matter Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.11.008
M.T. Gençog˘lu, M. Cebeci / Expert Systems with Applications 36 (2009) 7338–7345
artificially polluted insulators. Although the mentioned tests are indispensable for the study of the insulator behaviour under pollution, they are of long duration. The cost of the equipment that is necessary for these experiments is very high. For the above reasons, it seems to be very useful to predict the performance of insulators under pollution conditions using analytical expressions and computer models (Dhahbi-Megriche & Beroual, 2000). 2. Modelling the pollution flashover Flashover modelling has been a topic of interest for many researchers (Alston & Zoledziowski, 1963; Boeme & Obenhaus, 1966; Rizk, 1981; Wilkins, 1969). A major problem in all those investigations is the definition (Chaurasia, 1999; Ghosh & Chatterjee, 1995) of the value of the arc constants that affect the flashover process. Unfortunately the values of the constants determined from several investigations diverge substantially. This investigation targets the precise calculation of the arc value parameters, using relevant experimental results and close simulation of the insulator’s behaviour under polluted conditions using a suitable mathematical model (Suflis et al., 2003). The flashover process over polluted insulators is described by well-known analytical equations, published by various scientists, mainly Boeme and Obenhaus and Alston and Zoledziowski. These procedures have been used for the formulation of a mathematical model that permits determination of the parameters of the flashover under pollution of the insulators. The most known model for the explanation and evaluation of the flashover process (Alston & Zoledziowski, 1963; Wilkins, 1969) of a polluted insulator consists of a partial arc spanning over a dry zone and the resistance of the pollution layer in series. Therefore, the voltage across the insulator will be
U ¼ xAIn þ ðL xÞRp I
ð1Þ
where xAIn is the stress in the arc and (L x)RpI is the stress in the pollution layer. x is the length of the arc, L is the leakage path of the insulator, Rp is the resistance per unit length of the pollution layer, I is the leakage current and A and n are the arc constants. Their values A = 124.8, n = 0.409 have been determined using a complex optimization method (Suflis et al., 2003) based on genetic algorithms. It has been found experimentally that the value of the flashover voltage of a polluted insulator is not constant even under identical conditions. This is mainly due to random arc phenomena on the polluted surface. Such phenomena are the arc bridging between sheds or ribs, the arc drifting away from the surface of an insulator as well as the number of consecutive arcs before flashover. These random arcs will certainly affect the flashover. The measurement of the resistance Rp of the wet zone is quite complicated. Therefore it may be substituted by the conductivity rP of the pollution layer
1 F Rp
rP ¼
ð2Þ
F is the form factor of the insulator that is given as follows:
F¼
Z
L
0
l
pDðlÞ
dl
ð3Þ
where D(l) is the diameter of the insulator that varies across the leakage path. The critical condition for propagation of the discharge along the surface of the insulator to cause flashover is (Alston & Zoledziowski, 1963)
dl >0 dx
ð4Þ
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The voltage under this critical condition yields
U c ¼ xc AIn c þ ðL xc ÞKRp I c
ð5Þ
Here the coefficient K was added to validate (1) at the critical instant of the flashover. Wilkins introduced this coefficient in order to modify the resistance Rp of the pollution layer considering the current concentration at the arc foot point. A simplified formula for the calculation of K for cap-and-pin insulators is (Dhahbi-Megriche & Beroual, 2000)
0
1
B L K ¼1þ ln B 2pF ðL xC Þ @
C L rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC A
ð6Þ
1
2pF
ðpDr rP AÞnþ1 1:45p
At the critical condition the length of the arc takes the value (Suflis et al., 2003)
xc ¼
1 L nþ1
ð7Þ
Further analysis (Topalis, Gonos, & Stathopulos, 2001) of the system equations at the moment of flashover yields for the critical current 1
Ic ¼ ðpDr rP AÞnþ1
ð8Þ
and for the critical voltage
UC ¼
n A ðL þ pDr F KnÞðpDr rP AÞnþ1 nþ1
ð9Þ
where Dr is the diameter of the insulator. 3. Artificial neural network An artificial neural network (ANN) as a computing system is made up of a number of simple, and highly interconnected processing elements, which processes information by its dynamic state response to external inputs. In recent times the study of the ANN models is gaining rapid and increasing importance because of their potential to offer solutions to some of the problems which have hitherto been intractable by standard serial computers in the areas of computer science and artificial intelligence (Lee & Cha, 1992). ANN algorithm has been tried successfully on a very wide range of applications (Bressloff & Weir, 1991) including machine vision (Fukishama, 1988), speech processing (Kohonen, 1988) and radar analysis (Farhai & Bai, 1989). In electrical power systems, ANN have been used for accurate load forecasting (Hsu & Yang, 1991), alarm processing (Chan, 1989), etc. In high voltage systems, application of ANN has been reported for pattern recognition of partial discharges (Suzuki & Endoh, 1992). Another major branch of ANN application lies in function estimation. In function estimation, ANN is useful because it acts as a model of a real-world system or function. The model then stands for the system it represents, typically to predict or to control it. The useful properties of ANN, like, adaptable and non-linearity are well suited to many function estimation tasks in the real-world (Ahmad, Ghosh, Ahmed, & Aljunid, 2004; Ghosh, Chakravorti, & Chatterjee, 1995). Processing elements in an ANN are also known as neurons. These neurons are interconnected by means of information channels called interconnections. Each neuron can have multiple inputs, while there can be only one output. Inputs to a neuron could be from external stimuli or could be from output of the other neurons. Copies of the single output that comes from a neuron could be input to many other neurons in the network. It is also possible that one of the copies of the neuron’s output could be input to itself as a feedback. There is a strength connection, synapses, or weight associated with each connection. When the weighted sum of the inputs to the neuron exceeds a certain threshold, the neuron is fired
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and an output signal is produced. The network can recognize input patterns once the weights are adjusted or tuned via some kind of learning process (Lee & Cha, 1992). Multilayer feed-forward networks are trained using two different learning algorithm, back-propagation (Rumelhart, Hinton, & Williams, 1986) and resilient propagation (Riedmiller & Braun, 1993). The back-propagation learning algorithm is the most frequently used method in training the networks, and proposed as a pollution flashover methodology in this paper. The back-propagation learning algorithm is a generalization of the Widrow–Hoff error correction rule (Widrow & Hoff, 1986). The original Widrow–Hoff technique formed an error signal, which is the difference between what the output is and what it was suppose to be, i.e., the reference or target output. Synaptic strengths, or weights, were changed in proportion to the error times the input signal, which diminishes the error in the direction of the gradient. Fig. 1 shows the schematic diagram of a multilayer feed-forward network used in this paper. The neurons in the network can be divided into three layers: input layer, output layer, and hidden layers. It is important to note that the feed-forward network signals can only propagate from the input layer to the output layer through the hidden layers. Each neuron of the output layer receives a signal from all input via hidden layer neurons along connections with modifiable weights. The neural network can identify input pattern vectors, once the connection weights are adjusted by means of the learning process. The back-propagation learning algorithm (Rumelhart et al., 1986) which is a generalization of Widrow–Hoff error correction rule (Widrow & Hoff, 1986) is the most popular method in training the ANN and is employed in this work. This learning algorithm is presented here in brief. For each neuron in the input layer, the neuron outputs are given by
Oi ¼ ni
ð10Þ
where ni is the input of neuron i and Oi the output of neuron i. Again, for each neuron in the output layer, the neuron inputs are given by
nk ¼
Nj X
wkj Oj ;
k ¼ 1; . . . ; Nk
ð11Þ
j¼1
where xkj is connection weight between neuron j and neuron k, and Nj, Nk are the number of neurons in the hidden and output layers, respectively; the neuron outputs are given by
C
Ok ¼
1 ¼ fk ðnk ; hk Þ 1 þ expððnk þ hk ÞÞ
ð12Þ
where hk is the threshold of neuron k, and the activation functions fk a sigmoidal function. For the neurons in the hidden layer, the input and the outputs are given by the relationships similar to those given in the Eqs. (11) and (12), respectively. The connection weights of the feed-forward network are derived from the input–output patterns in the training set by the application of generalization delta rule (Rumelhart et al., 1986). The algorithm is based on minimization of the error function of each pattern p by the use of the steepest descent method (Rumelhart et al., 1986). The sum of squared errors which is the error function of each pattern is given by
Ep ¼
Nk 1X ðt pk Opk Þ2 2 k¼1
ð13Þ
where tpk and Opk are target and calculated outputs for output neuron k, respectively. The overall measure of the error for all the input–output patterns is given by
E¼
Np X
Ep
ð14Þ
p¼1
where Np is the number of input–output patterns in the training set (Ahmad et al., 2004). 4. The modelling of an insulator by ANN ANN evaluates the given patterns and it can be produce new outputs for different inputs. When complexity of the pollution flashover and a large number and difference of discharge parameters takes into consideration, ANN can be used for explain the occurring complex events throughout the discharge spread and for consider the changes on the discharge parameters. However, ANN must be trained well by help of obtained dependable patterns. The values of critical current, critical voltage, pollution resistance, withstand voltage, flashover voltage, applied voltage, pollution density, surface conductivity, leakage length, critical discharge length, conductivity factor and dimensions of the insulator can be used for train an ANN. A trained ANN on the subject of discharge spread using these values is useful for understood the flashover phenomenon. In this way, desired output values can be found easily according to aim of the ANN. For example, if input values are applied voltage, pollution density, pollution conductivity and dimensions of the insulator output value may be flashover voltage of the insulator. Moreover, a trained ANN pretty comprehensive can select insulator type which will use in any region by giving detailed information of the region and electrical transmission system. 4.1. The structure of ANN model
Fig. 1. The structure of a multilayer neural network.
In this paper, a new approach using ANN as a function estimator has been developed and used to model accurately the relationship between Vc for given H, D, L, r, n and d. Input–output data are normalized before the initiation of the training of the neural network for better convergence and accuracy of the learning process. The neural network is trained with the help of data obtained from the FLASHOVER computer program (Gencoglu & Cebeci, 2008). In this study, a multilayer feed-forward ANN was used. The back-propagation learning algorithm was used for training of the ANN model. The programs in MATLAB were developed for application. There are an input layer with 6 neurons, two hidden layers with 50 neurons and an output layer with 1 neuron in the ANN model. The structure and training parameters of the ANN model have been shown in Table 1. The structure of the ANN model and training parameters were found after several different tests. The
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Table 1 The structure of the ANN model and training parameters. Structure of ANN ANN model Number of layer Number of neuron in the layers
Start weights and threshold values Activation functions Training parameters of ANN Learning rule Adaptive learning rate
Momentum constant The sum of squared error
Multilayer feed-forward 3 Input: 6 Hidden: 50 Output: 1 According to Nguyen–Widrow method Logarithmic sigmoid Back-propagation Start: 0.01 Increase coefficient: 1.05 Decrease coefficient: 0.7 0.9 0.001
number of hidden layer, the number of neuron in the hidden layer, momentum rate, learning rate and types of activation functions were selected for the best performance. The back-propagation learning algorithm is applied on multilayer feed-forward networks, also referred as multilayer perceptrons. It is based on an error correction learning rule and specifically on the minimization of the mean squared error that is a measure of the difference between the actual and the desired output. As all multilayer feed-forward networks, the multilayer perceptrons are constructed of at least three layers, each layer consisting of elementary processing artificial neurons, which incorporate a nonlinear activation function, commonly the logistic sigmoid function. The algorithm calculates the difference between the actual response and the desired output of each neuron of the output layer of the network (Adamopoulos, 2000). The data in the multilayer networks is received by the input layer. The occurring answer in the output layer and desired answer in response to input data are compared. If there is a difference between calculated answer
Fig. 3. The used insulators for test of the ANN model.
Table 2 The characteristics values of the insulators used for test. Insulator type
H (mm)
D (mm)
L (mm)
d
I II III IV V VI VII
146 146 165 180 197 197 250
254 254 320 320 320 400 420
280 432 512 545 457 686 718
4 4 5 5 5 6 6
and desired answer the weights among the layers are prepared again. The data in the input of the ANN is stable up to reach suitable point the weights. The calculated output answers are compared with desired answers and error signal is obtained. The error signal is used for change the weights from interval layers to output layer. 4.2. Normalization In this paper, using the ANN as a function estimator, a new approach was developed. The ANN was used for modelling correctly to relationship between critical flashover voltage and insulator height, insulator diameter, leakage length, surface conductivity, number of chain, number of shed. This modelling of VC critical
Fig. 2. Training process of ANN for 886 iteration.
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flashover voltage uses data obtained by using FLASHOVER program (Gencoglu & Cebeci, 2008) which uses the finite element method. Therefore, a multilayer feed-forward ANN was preferred. Input– output data was normalized while the ANN is trained for better convergence and accuracy of the learning process. To determine the connection weights between neurons, the back-propagation learning algorithm with constant learning rate and momentum constant with one hidden layer is first employed in the training process. The effect of different learning rates and moment on the
convergence property of the learning process is studied and the best combination is defined. The number of nodes in the hidden layer is also varied to see their effect on the convergence rate. An attempt has also been made to assess the effect of more than one hidden layer on the convergence characteristics. The developed ANN was trained with the computed values by help of the FLASHOVER program (Gencoglu & Cebeci, 2008) which uses dynamic arc model of an insulator. These values have been compared by theoretical and experimental results of another
Fig. 4. The set up success of ANN model of the insulator.
Fig. 5. The comparison of the results of ANN model of the insulator and experimental results.
M.T. Gençog˘lu, M. Cebeci / Expert Systems with Applications 36 (2009) 7338–7345
researchers and accuracy of the values has been proved. Once trained, the ANN model is capable of predicting VC, under any given H, D, L, r, n and d with a mean absolute error less than 1%. It is important that the threshold value of each neuron must be trained in the same method as another weight. It was thought that the threshold value of a neuron has an output value is an adaptable connection weight between the neuron and an imaginary neuron in the former layer. The input and output data are normalized in two different ways. In Eqs. (15)–(22), p = 1, . . . , Np, Np being number of patterns in the training set; i = 1, . . . , Ni and k = 1, . . . , Nk.
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In the first method, the maximum values of the input and output vector components are determined first
ni;max ¼ maxðni ðpÞÞ
ð15Þ
and
Ok;max ¼ maxðOk ðpÞÞ
ð16Þ
Normalized by these maximum values, the input and output variables are given by
ni;norðpÞ ¼ ni ðpÞ=ni;max
Fig. 6. The comparison of ANN model of the insulator and another model results.
Fig. 7. The comparison of ANN model by experimental results (Sundararajan & Gorur, 1994) for insulator I.
ð17Þ
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Fig. 8. The comparison of ANN model by experimental results (Sundararajan & Gorur, 1994) for insulator II.
and
Ok;norðpÞ ¼ Ok ðpÞ=Ok;max
ð18Þ
After the normalization, the input and output variable ranges are within (0, 1). In the second method, the maximum values of the input and output vector components are determined by using Eqs. (15) and (16), respectively and the minimum values of the input and output vector components are determined by
ni;min ðni ðpÞÞ
ð19Þ
and
Ok;min ¼ minðOk ðpÞÞ
ð20Þ
Normalized by these maximum and minimum values, the input and output variables are given by
ni ðpÞ ni;min ni;max ni;min Ok ðpÞ Ok;min ¼ Ok;max Ok;min
ni;norðpÞ ¼
ð21Þ
Ok;norðpÞ
ð22Þ
After normalization, the input and output variable ranges are within (0, 1) (Ghosh et al., 1995). Each input–output variable was normalized one by one. 4.3. ANN model based on dynamic model A dynamic model needs shape, leakage length, dimension etc. of the insulator. The computation of these parameters by computer is suitable. Because of this, coordinates of different point throughout the leakage length on the insulator are determined. Leakage length and dimension are calculated. Approximately, 80 points were taken on the leakage length for each insulator aim to obtain the sensitive results. The training set with 200 input–output data was used at the training process. Each pattern of the training set contains 6 inputs which characterizes parameters of H, D, L, r, n, d and 1 output which represents VC critical flashover voltage. All of the input–out-
put variables in the training patterns are normalized within its series before the initiation of the training and test of the neural network. First, the developed ANN was once trained using 200 training set. After, the ANN was tested using the selected patterns at random from within the series of the input set. Later, the ANN was also tested by values of 7 string insulator that the flashover voltages were determined by experimental values (Kimoto, Fujimura, & Naito, 1973). The training process of ANN which once trained by using 200 training set is shown in Fig. 2. The shape of 7 string insulator which also was studied by Sundararajan and Gorur is given in Fig. 3. The characteristics values of these insulators are given in Table 2. Using selected data from within the series of the training pattern, the results of the tested ANN were compared the computed results using the FLASHOVER program in Fig. 4. The comparison of the obtained results using ANN and experimental results (Sundararajan & Gorur, 1994) is given in Fig. 5. The comparison of the results of the ANN model and Sundararajan–Gorur model (Sundararajan & Gorur, 1994) is given in Fig. 6. The obtained results using ANN model of the insulator were compared the experimental results belong to the insulators in Fig. 3. The results of comparison are shown in Figs. 7 and 8. It is seen that the ANN results and experimental results are nearly same. 5. Conclusion VC = f (H, D, L, r, n, d) modelling has been proposed based on ANN instead of any empirical approach. In this paper multilayer feed-forward network with back-propagation learning algorithm was used for modelling. It is shown that ANN model of the insulator was prepared with a major accomplishment from Fig. 4. It is seen that ANN model is capable for predict the flashover voltages of different type of the string insulators from Figs. 5 and 6. Separately, the results of comparison for each insulator are satisfactory.
M.T. Gençog˘lu, M. Cebeci / Expert Systems with Applications 36 (2009) 7338–7345
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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
Review
Investigation of pollution flashover on high voltage insulators using artificial neural network M.T. Gençog˘lu *, M. Cebeci Department of Electrical and Electronics Engineering, Faculty of Engineering, Firat University, Elazig, Turkey
a r t i c l e
i n f o
Keywords: Pollution flashover Flashover voltage Artificial neural networks
a b s t r a c t High voltage insulators form an essential part of the high voltage electric power transmission systems. Any failure in the satisfactory performance of high voltage insulators will result in considerable loss of capital, as there are numerous industries that depend upon the availability of an uninterrupted power supply. The importance of the research on insulator pollution has been increased considerably with the rise of the voltage of transmission lines. In order to determine the flashover behavior of polluted high voltage insulators and to identify to physical mechanisms that govern this phenomenon, the researchers have been brought to establish a modeling. Artificial neural networks (ANN) have been used by various researches for modeling and predictions in the field of energy engineering systems. In this study, model of VC = f (H, D, L, r, n, d) based on ANN which compute flashover voltage of the insulators were performed. This model consider height (H), diameter (D), total leakage length (L), surface conductivity (r) and number of shed (d) of an insulator and number of chain (n) on the insulator. Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved.
1. Introduction Outdoor insulators are being subjected to various operating conditions and environments. The surface of the insulators is covered by airborne pollutants due to natural or industrial or even mixed pollution. Contamination on the surface of the insulators enhances the chances of flashover. Under dry conditions the contaminated surfaces do not conduct, and thus contamination is of little importance in dry periods (Gorur & Olsen, 2006). As the surface becomes moist because of rain, fog or dew, the pollution layer becomes conductive because of the presence of ionic solids. The leakage current flows through the conducting surface film, generating heat which tends to increase the film temperature most rapidly at those points where the current density is greatest, i.e. at narrow sections of the insulator, such as the area around the pin. Eventually, the temperature in these areas approaches boiling point, and rapid evaporation of the moisture occurs producing dry areas. The development of the dry areas is independent of the insulator type, something that has also been verified experimentally, since the insulator’s body diameter differs very little from one type to another (Gonos, Topalis, & Stathopulos, 2002). Pollution flashover, observed on insulators used in high voltage transmission, is one of the most important problems for power * Corresponding author. Tel.: +90 424 2370000/5237; fax: +90 424 2415526. E-mail addresses: mtgencoglu@firat.edu.tr (M.T. Gençog˘lu), mcebeci@firat.edu.tr (M. Cebeci).
transmission. Pollution flashover is a very complex problem due to several reasons such as modeling difficulties of the insulator complex shape, different pollution density at different regions, non-homogenous pollution distribution on the surface of insulator and unknown effect of humidity on the pollution (Dhahbi-Megriche & Beroual, 2000). The performance of insulators under polluted environment is one of the guiding factors in the insulation coordination of high voltage transmission lines. On the other hand, the flashover of polluted insulators can cause transmission line outage of long duration and over a large area. Flashover of polluted insulators is still a serious threat to the safe operation of a power transmission system. It is generally considered that pollution flashover is becoming ever more important in the design of high voltage transmission lines (Suflis, Gonos, Topalis, & Stathopulos, 2003). Research on insulator pollution is directed primarily to understanding the physics of the growth of discharge and to develop a mathematical model, which can predict accurately the critical flashover voltage and critical current. A common feature of all the mathematical models proposed by researchers (Alston & Zoledziowski, 1963; Boeme & Obenhaus, 1966; Rizk, 1981; Wilkins, 1969) is a representation of a propagating arc consisting of a partial arc in series with the resistance of the unbridged section of the polluted layer. Alston and Zoledziowski and Wilkins proposed mathematical models for the prediction of critical flashover voltage taking into consideration the effects of different physical parameters. The flashover of polluted insulators was the motivation for the installation of a test station in order to perform laboratory tests on
0957-4174/$ - see front matter Crown Copyright Ó 2008 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2008.11.008
M.T. Gençog˘lu, M. Cebeci / Expert Systems with Applications 36 (2009) 7338–7345
artificially polluted insulators. Although the mentioned tests are indispensable for the study of the insulator behaviour under pollution, they are of long duration. The cost of the equipment that is necessary for these experiments is very high. For the above reasons, it seems to be very useful to predict the performance of insulators under pollution conditions using analytical expressions and computer models (Dhahbi-Megriche & Beroual, 2000). 2. Modelling the pollution flashover Flashover modelling has been a topic of interest for many researchers (Alston & Zoledziowski, 1963; Boeme & Obenhaus, 1966; Rizk, 1981; Wilkins, 1969). A major problem in all those investigations is the definition (Chaurasia, 1999; Ghosh & Chatterjee, 1995) of the value of the arc constants that affect the flashover process. Unfortunately the values of the constants determined from several investigations diverge substantially. This investigation targets the precise calculation of the arc value parameters, using relevant experimental results and close simulation of the insulator’s behaviour under polluted conditions using a suitable mathematical model (Suflis et al., 2003). The flashover process over polluted insulators is described by well-known analytical equations, published by various scientists, mainly Boeme and Obenhaus and Alston and Zoledziowski. These procedures have been used for the formulation of a mathematical model that permits determination of the parameters of the flashover under pollution of the insulators. The most known model for the explanation and evaluation of the flashover process (Alston & Zoledziowski, 1963; Wilkins, 1969) of a polluted insulator consists of a partial arc spanning over a dry zone and the resistance of the pollution layer in series. Therefore, the voltage across the insulator will be
U ¼ xAIn þ ðL xÞRp I
ð1Þ
where xAIn is the stress in the arc and (L x)RpI is the stress in the pollution layer. x is the length of the arc, L is the leakage path of the insulator, Rp is the resistance per unit length of the pollution layer, I is the leakage current and A and n are the arc constants. Their values A = 124.8, n = 0.409 have been determined using a complex optimization method (Suflis et al., 2003) based on genetic algorithms. It has been found experimentally that the value of the flashover voltage of a polluted insulator is not constant even under identical conditions. This is mainly due to random arc phenomena on the polluted surface. Such phenomena are the arc bridging between sheds or ribs, the arc drifting away from the surface of an insulator as well as the number of consecutive arcs before flashover. These random arcs will certainly affect the flashover. The measurement of the resistance Rp of the wet zone is quite complicated. Therefore it may be substituted by the conductivity rP of the pollution layer
1 F Rp
rP ¼
ð2Þ
F is the form factor of the insulator that is given as follows:
F¼
Z
L
0
l
pDðlÞ
dl
ð3Þ
where D(l) is the diameter of the insulator that varies across the leakage path. The critical condition for propagation of the discharge along the surface of the insulator to cause flashover is (Alston & Zoledziowski, 1963)
dl >0 dx
ð4Þ
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The voltage under this critical condition yields
U c ¼ xc AIn c þ ðL xc ÞKRp I c
ð5Þ
Here the coefficient K was added to validate (1) at the critical instant of the flashover. Wilkins introduced this coefficient in order to modify the resistance Rp of the pollution layer considering the current concentration at the arc foot point. A simplified formula for the calculation of K for cap-and-pin insulators is (Dhahbi-Megriche & Beroual, 2000)
0
1
B L K ¼1þ ln B 2pF ðL xC Þ @
C L rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiC A
ð6Þ
1
2pF
ðpDr rP AÞnþ1 1:45p
At the critical condition the length of the arc takes the value (Suflis et al., 2003)
xc ¼
1 L nþ1
ð7Þ
Further analysis (Topalis, Gonos, & Stathopulos, 2001) of the system equations at the moment of flashover yields for the critical current 1
Ic ¼ ðpDr rP AÞnþ1
ð8Þ
and for the critical voltage
UC ¼
n A ðL þ pDr F KnÞðpDr rP AÞnþ1 nþ1
ð9Þ
where Dr is the diameter of the insulator. 3. Artificial neural network An artificial neural network (ANN) as a computing system is made up of a number of simple, and highly interconnected processing elements, which processes information by its dynamic state response to external inputs. In recent times the study of the ANN models is gaining rapid and increasing importance because of their potential to offer solutions to some of the problems which have hitherto been intractable by standard serial computers in the areas of computer science and artificial intelligence (Lee & Cha, 1992). ANN algorithm has been tried successfully on a very wide range of applications (Bressloff & Weir, 1991) including machine vision (Fukishama, 1988), speech processing (Kohonen, 1988) and radar analysis (Farhai & Bai, 1989). In electrical power systems, ANN have been used for accurate load forecasting (Hsu & Yang, 1991), alarm processing (Chan, 1989), etc. In high voltage systems, application of ANN has been reported for pattern recognition of partial discharges (Suzuki & Endoh, 1992). Another major branch of ANN application lies in function estimation. In function estimation, ANN is useful because it acts as a model of a real-world system or function. The model then stands for the system it represents, typically to predict or to control it. The useful properties of ANN, like, adaptable and non-linearity are well suited to many function estimation tasks in the real-world (Ahmad, Ghosh, Ahmed, & Aljunid, 2004; Ghosh, Chakravorti, & Chatterjee, 1995). Processing elements in an ANN are also known as neurons. These neurons are interconnected by means of information channels called interconnections. Each neuron can have multiple inputs, while there can be only one output. Inputs to a neuron could be from external stimuli or could be from output of the other neurons. Copies of the single output that comes from a neuron could be input to many other neurons in the network. It is also possible that one of the copies of the neuron’s output could be input to itself as a feedback. There is a strength connection, synapses, or weight associated with each connection. When the weighted sum of the inputs to the neuron exceeds a certain threshold, the neuron is fired
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and an output signal is produced. The network can recognize input patterns once the weights are adjusted or tuned via some kind of learning process (Lee & Cha, 1992). Multilayer feed-forward networks are trained using two different learning algorithm, back-propagation (Rumelhart, Hinton, & Williams, 1986) and resilient propagation (Riedmiller & Braun, 1993). The back-propagation learning algorithm is the most frequently used method in training the networks, and proposed as a pollution flashover methodology in this paper. The back-propagation learning algorithm is a generalization of the Widrow–Hoff error correction rule (Widrow & Hoff, 1986). The original Widrow–Hoff technique formed an error signal, which is the difference between what the output is and what it was suppose to be, i.e., the reference or target output. Synaptic strengths, or weights, were changed in proportion to the error times the input signal, which diminishes the error in the direction of the gradient. Fig. 1 shows the schematic diagram of a multilayer feed-forward network used in this paper. The neurons in the network can be divided into three layers: input layer, output layer, and hidden layers. It is important to note that the feed-forward network signals can only propagate from the input layer to the output layer through the hidden layers. Each neuron of the output layer receives a signal from all input via hidden layer neurons along connections with modifiable weights. The neural network can identify input pattern vectors, once the connection weights are adjusted by means of the learning process. The back-propagation learning algorithm (Rumelhart et al., 1986) which is a generalization of Widrow–Hoff error correction rule (Widrow & Hoff, 1986) is the most popular method in training the ANN and is employed in this work. This learning algorithm is presented here in brief. For each neuron in the input layer, the neuron outputs are given by
Oi ¼ ni
ð10Þ
where ni is the input of neuron i and Oi the output of neuron i. Again, for each neuron in the output layer, the neuron inputs are given by
nk ¼
Nj X
wkj Oj ;
k ¼ 1; . . . ; Nk
ð11Þ
j¼1
where xkj is connection weight between neuron j and neuron k, and Nj, Nk are the number of neurons in the hidden and output layers, respectively; the neuron outputs are given by
C
Ok ¼
1 ¼ fk ðnk ; hk Þ 1 þ expððnk þ hk ÞÞ
ð12Þ
where hk is the threshold of neuron k, and the activation functions fk a sigmoidal function. For the neurons in the hidden layer, the input and the outputs are given by the relationships similar to those given in the Eqs. (11) and (12), respectively. The connection weights of the feed-forward network are derived from the input–output patterns in the training set by the application of generalization delta rule (Rumelhart et al., 1986). The algorithm is based on minimization of the error function of each pattern p by the use of the steepest descent method (Rumelhart et al., 1986). The sum of squared errors which is the error function of each pattern is given by
Ep ¼
Nk 1X ðt pk Opk Þ2 2 k¼1
ð13Þ
where tpk and Opk are target and calculated outputs for output neuron k, respectively. The overall measure of the error for all the input–output patterns is given by
E¼
Np X
Ep
ð14Þ
p¼1
where Np is the number of input–output patterns in the training set (Ahmad et al., 2004). 4. The modelling of an insulator by ANN ANN evaluates the given patterns and it can be produce new outputs for different inputs. When complexity of the pollution flashover and a large number and difference of discharge parameters takes into consideration, ANN can be used for explain the occurring complex events throughout the discharge spread and for consider the changes on the discharge parameters. However, ANN must be trained well by help of obtained dependable patterns. The values of critical current, critical voltage, pollution resistance, withstand voltage, flashover voltage, applied voltage, pollution density, surface conductivity, leakage length, critical discharge length, conductivity factor and dimensions of the insulator can be used for train an ANN. A trained ANN on the subject of discharge spread using these values is useful for understood the flashover phenomenon. In this way, desired output values can be found easily according to aim of the ANN. For example, if input values are applied voltage, pollution density, pollution conductivity and dimensions of the insulator output value may be flashover voltage of the insulator. Moreover, a trained ANN pretty comprehensive can select insulator type which will use in any region by giving detailed information of the region and electrical transmission system. 4.1. The structure of ANN model
Fig. 1. The structure of a multilayer neural network.
In this paper, a new approach using ANN as a function estimator has been developed and used to model accurately the relationship between Vc for given H, D, L, r, n and d. Input–output data are normalized before the initiation of the training of the neural network for better convergence and accuracy of the learning process. The neural network is trained with the help of data obtained from the FLASHOVER computer program (Gencoglu & Cebeci, 2008). In this study, a multilayer feed-forward ANN was used. The back-propagation learning algorithm was used for training of the ANN model. The programs in MATLAB were developed for application. There are an input layer with 6 neurons, two hidden layers with 50 neurons and an output layer with 1 neuron in the ANN model. The structure and training parameters of the ANN model have been shown in Table 1. The structure of the ANN model and training parameters were found after several different tests. The
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Table 1 The structure of the ANN model and training parameters. Structure of ANN ANN model Number of layer Number of neuron in the layers
Start weights and threshold values Activation functions Training parameters of ANN Learning rule Adaptive learning rate
Momentum constant The sum of squared error
Multilayer feed-forward 3 Input: 6 Hidden: 50 Output: 1 According to Nguyen–Widrow method Logarithmic sigmoid Back-propagation Start: 0.01 Increase coefficient: 1.05 Decrease coefficient: 0.7 0.9 0.001
number of hidden layer, the number of neuron in the hidden layer, momentum rate, learning rate and types of activation functions were selected for the best performance. The back-propagation learning algorithm is applied on multilayer feed-forward networks, also referred as multilayer perceptrons. It is based on an error correction learning rule and specifically on the minimization of the mean squared error that is a measure of the difference between the actual and the desired output. As all multilayer feed-forward networks, the multilayer perceptrons are constructed of at least three layers, each layer consisting of elementary processing artificial neurons, which incorporate a nonlinear activation function, commonly the logistic sigmoid function. The algorithm calculates the difference between the actual response and the desired output of each neuron of the output layer of the network (Adamopoulos, 2000). The data in the multilayer networks is received by the input layer. The occurring answer in the output layer and desired answer in response to input data are compared. If there is a difference between calculated answer
Fig. 3. The used insulators for test of the ANN model.
Table 2 The characteristics values of the insulators used for test. Insulator type
H (mm)
D (mm)
L (mm)
d
I II III IV V VI VII
146 146 165 180 197 197 250
254 254 320 320 320 400 420
280 432 512 545 457 686 718
4 4 5 5 5 6 6
and desired answer the weights among the layers are prepared again. The data in the input of the ANN is stable up to reach suitable point the weights. The calculated output answers are compared with desired answers and error signal is obtained. The error signal is used for change the weights from interval layers to output layer. 4.2. Normalization In this paper, using the ANN as a function estimator, a new approach was developed. The ANN was used for modelling correctly to relationship between critical flashover voltage and insulator height, insulator diameter, leakage length, surface conductivity, number of chain, number of shed. This modelling of VC critical
Fig. 2. Training process of ANN for 886 iteration.
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flashover voltage uses data obtained by using FLASHOVER program (Gencoglu & Cebeci, 2008) which uses the finite element method. Therefore, a multilayer feed-forward ANN was preferred. Input– output data was normalized while the ANN is trained for better convergence and accuracy of the learning process. To determine the connection weights between neurons, the back-propagation learning algorithm with constant learning rate and momentum constant with one hidden layer is first employed in the training process. The effect of different learning rates and moment on the
convergence property of the learning process is studied and the best combination is defined. The number of nodes in the hidden layer is also varied to see their effect on the convergence rate. An attempt has also been made to assess the effect of more than one hidden layer on the convergence characteristics. The developed ANN was trained with the computed values by help of the FLASHOVER program (Gencoglu & Cebeci, 2008) which uses dynamic arc model of an insulator. These values have been compared by theoretical and experimental results of another
Fig. 4. The set up success of ANN model of the insulator.
Fig. 5. The comparison of the results of ANN model of the insulator and experimental results.
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researchers and accuracy of the values has been proved. Once trained, the ANN model is capable of predicting VC, under any given H, D, L, r, n and d with a mean absolute error less than 1%. It is important that the threshold value of each neuron must be trained in the same method as another weight. It was thought that the threshold value of a neuron has an output value is an adaptable connection weight between the neuron and an imaginary neuron in the former layer. The input and output data are normalized in two different ways. In Eqs. (15)–(22), p = 1, . . . , Np, Np being number of patterns in the training set; i = 1, . . . , Ni and k = 1, . . . , Nk.
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In the first method, the maximum values of the input and output vector components are determined first
ni;max ¼ maxðni ðpÞÞ
ð15Þ
and
Ok;max ¼ maxðOk ðpÞÞ
ð16Þ
Normalized by these maximum values, the input and output variables are given by
ni;norðpÞ ¼ ni ðpÞ=ni;max
Fig. 6. The comparison of ANN model of the insulator and another model results.
Fig. 7. The comparison of ANN model by experimental results (Sundararajan & Gorur, 1994) for insulator I.
ð17Þ
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Fig. 8. The comparison of ANN model by experimental results (Sundararajan & Gorur, 1994) for insulator II.
and
Ok;norðpÞ ¼ Ok ðpÞ=Ok;max
ð18Þ
After the normalization, the input and output variable ranges are within (0, 1). In the second method, the maximum values of the input and output vector components are determined by using Eqs. (15) and (16), respectively and the minimum values of the input and output vector components are determined by
ni;min ðni ðpÞÞ
ð19Þ
and
Ok;min ¼ minðOk ðpÞÞ
ð20Þ
Normalized by these maximum and minimum values, the input and output variables are given by
ni ðpÞ ni;min ni;max ni;min Ok ðpÞ Ok;min ¼ Ok;max Ok;min
ni;norðpÞ ¼
ð21Þ
Ok;norðpÞ
ð22Þ
After normalization, the input and output variable ranges are within (0, 1) (Ghosh et al., 1995). Each input–output variable was normalized one by one. 4.3. ANN model based on dynamic model A dynamic model needs shape, leakage length, dimension etc. of the insulator. The computation of these parameters by computer is suitable. Because of this, coordinates of different point throughout the leakage length on the insulator are determined. Leakage length and dimension are calculated. Approximately, 80 points were taken on the leakage length for each insulator aim to obtain the sensitive results. The training set with 200 input–output data was used at the training process. Each pattern of the training set contains 6 inputs which characterizes parameters of H, D, L, r, n, d and 1 output which represents VC critical flashover voltage. All of the input–out-
put variables in the training patterns are normalized within its series before the initiation of the training and test of the neural network. First, the developed ANN was once trained using 200 training set. After, the ANN was tested using the selected patterns at random from within the series of the input set. Later, the ANN was also tested by values of 7 string insulator that the flashover voltages were determined by experimental values (Kimoto, Fujimura, & Naito, 1973). The training process of ANN which once trained by using 200 training set is shown in Fig. 2. The shape of 7 string insulator which also was studied by Sundararajan and Gorur is given in Fig. 3. The characteristics values of these insulators are given in Table 2. Using selected data from within the series of the training pattern, the results of the tested ANN were compared the computed results using the FLASHOVER program in Fig. 4. The comparison of the obtained results using ANN and experimental results (Sundararajan & Gorur, 1994) is given in Fig. 5. The comparison of the results of the ANN model and Sundararajan–Gorur model (Sundararajan & Gorur, 1994) is given in Fig. 6. The obtained results using ANN model of the insulator were compared the experimental results belong to the insulators in Fig. 3. The results of comparison are shown in Figs. 7 and 8. It is seen that the ANN results and experimental results are nearly same. 5. Conclusion VC = f (H, D, L, r, n, d) modelling has been proposed based on ANN instead of any empirical approach. In this paper multilayer feed-forward network with back-propagation learning algorithm was used for modelling. It is shown that ANN model of the insulator was prepared with a major accomplishment from Fig. 4. It is seen that ANN model is capable for predict the flashover voltages of different type of the string insulators from Figs. 5 and 6. Separately, the results of comparison for each insulator are satisfactory.
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