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Available online at www.sciencedirect.com

Electric Power Systems Research 78 (2008) 1204–1209

Parameter identification of ZnO surge arrester modelsbased on genetic algorithms

Bayadi Abdelhafid ∗Laboratoire d’Automatique de Setif, Departement d’Electrotechnique, Faculte des Sciences de l’Ingenieur,

Universite Ferhat ABBAS de Setif, Route de Bejaia Setif 19000, Algeria

Received 28 August 2006; received in revised form 6 June 2007; accepted 12 October 2007Available online 3 December 2007

bstract

The correct and adequate modelling of ZnO surge arresters characteristics is very important for insulation coordination studies and systemseliability. In this context many researchers addressed considerable efforts to the development of surge arresters models to reproduce the dynamicharacteristics observed in their behaviour when subjected to fast front impulse currents. The difficulties with these models reside essentially inhe calculation and the adjustment of their parameters.

This paper proposes a new technique based on genetic algorithm to obtain the best possible series of parameter values of ZnO surge arrestersodels. The validity of the predicted parameters is then checked by comparing the predicted results with the experimental results available in the

iterature. Using the ATP-EMTP package, an application of the arrester model on network system studies is presented and discussed.2007 Elsevier B.V. All rights reserved.

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eywords: ATP-EMTP; Genetic algorithms; Optimization; Surge arrester; Mod

. Introduction

The correct and adequate modelling of ZnO surge arrestersharacteristics is very important for insulation coordination stud-es and systems reliability. In the case of switching surge studies,he surge arresters can be represented with their non-linear V–Iharacteristic [1–3]. However, such a practice would not be suit-ble for lightning surge studies with fast front waves. This isue to the fact that the surge arresters behave differently in theresence of a fast disturbance. Typically, the residual voltage pre-icted for an impulse current having a front time equal to 1 �s is–10% higher than that predicted for an impulse current havingfront time equal to 8 �s. For longer times to crests between 45nd 60 �s, the voltage is 2–4% lower than that due to an impulseurrent having a time to crests of 8 �s [1–10]. With an aim ofeproducing the dynamic characteristics of ZnO surge arresters

entioned previously, many researchers [1–8] addressed con-

iderable efforts to the development of models of surge arresters.he authors in reference [1] recommend a model based on their

∗ Tel.: +213 73 529 283; fax: +213 36 928 418.E-mail address: a bayadi@yahoo.fr.

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378-7796/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2007.10.001

atabase for fast transient currents (Tf = 0.5–45 �s). To deter-ine model parameters, an iterative procedure try and error was

roposed to reasonably reproduce the amplitude of the voltagebtained for a current wave 8/20 �s. To determine the values ofhe starting parameters, expressions utilizing the height and theolumn number of the surge arresters, for linear elements andwo tables for the non-linear elements were proposed. The IEEE

odel was then simplified by the authors of reference [2]. Itsarameters are reported to the tests of currents 1/5 and 8/20 �s.

A comparative study of the various models suggested in theiterature was made [9]. It was concluded that the difficultiesith these models reside essentially in the calculation and the

djustment of their parameters.Recently an alternative having for objective the identifica-

ion of the parameters of the models suggested in the references1,2,5] by using a traditional optimization method was proposedn reference [10]. The authors had represented the non-linearesistances by piecewise functions and consequently a lineariza-ion was adopted. The problem of optimization was solved in two

tages with an aim of avoiding possible numerical oscillationsf the predicted voltage.

The present paper proposes to provide a new solution basedn genetic algorithms to obtain the best possible series of

A. Bayadi / Electric Power Systems R

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The algorithm also uses the mutation depending on thedistance (MDD) suggested in [14]. This technique increasesthe probability of mutation of the children when the distancebetween the parents is small to avoid a premature convergence.

Fig. 1. Typical measuring setup for ZnO arresters.

arameter values of ZnO surge arresters models. Interfacing theenetic algorithm with the ATP-EMTP was done to facilitate thealculation of the predicted voltage waveforms.

The validity of the predicted parameters is then verified byomparing the predicted results with the experimental resultsvailable in the literature.

. Formulation of the problem

A typical simplified circuit of the measurement setup to testnO surge arresters is shown in Fig. 1. In this figure V(t) is theoltage recorded at ZnO surge arresters terminals for an injectedurrent I(t) [11]. The response of a model can be correctly pre-icted if an adequate choice of its parameters x = (x1, x2, . . ., xn)T

s done. These parameters can be determined by minimizing theollowing objective function:

=∫ T

0[V (t, x) − Vm(t)]2 dt (1)

here ε is the sum of quadratic errors, T the duration of thempulse current injected, V(t, x) the predicted residual voltagend Vm(t) is the measured residual voltage.

It is noted that a similar objective function was proposed in10]. It contains an additional term (the weight function) used toccelerate the convergence of the traditional optimization algo-ithm suggested in this reference. Its determination required aertain experiment of numerical calculation. This weight func-ion is not necessary in the objective equation for the proposedenetic algorithm.

In its discrete form, the objective function (1) can be rewrittenn the following way:

=N∑

j=1

[V (j�t, x) − Vm(j�t)]2�t (2)

here N indicates the total number of discrete points; �t = T/Nepresents the computing time step. Moreover, xj must be posi-ive, i.e., xj ≥ 0 for all j.

. Procedure of optimization

The goal of the genetic algorithms (GA) is to optimize an

bjective function on a research space. For that, a population ofndividuals evolves according to an artificial Darwinism (eval-ation, selection, reproduction) based on the fitness F of eachndividual [12–15]. The fitness is directly related to the value

esearch 78 (2008) 1204–1209 1205

f the objective function of this individual. Evolution opera-ors applied to the population allow to create new individualscrossover and mutation) and to select the individuals of theopulation who will survive (selection and replacement). Forarameters identification of a model whose structure is known,he individual is the set of the unknown parameters and conse-uently each gene coincides with a parameter.

The loop of the algorithm follows the following stages:After a random initialization of the population the algorithm

valuates the function of adaptation of each individual.

Stop criterion: It is a criterion that allows stopping the process.One of the simple criteria often used is when the maximumnumber of generations is reached.Selection: This operator selects among the parents those whowill generate children.Creation of new individuals: The creation of new individualsis done primarily using the operators of crossing and mutation.The crossover operator is an operator who combines parentsto create one or more children. The mutation operator is anoperator who modifies an individual to create another who isgenerally close to him.

The program used (Fig. 2) is an implementation of a geneticlgorithm with real coding. An interfacing of this algorithm withhe EMTP is carried out. In this program we use roulette wheelelection. The available crossovers are the multipoint and thearycentric crossover. Two mutation types are possible. The firsts the Gaussian mutation with a constant variance or a decreasingariance during iterations. The second is a non-uniform mutation13,14].

Fig. 2. Stages of the genetic algorithm.

1206 A. Bayadi / Electric Power Systems Research 78 (2008) 1204–1209

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Table 1Identified parameters (case of Model 1)

Parameter [4] [5] [17] [18]

R0 (�) 0.453 0.781 0.634 0.892R1 (�) 0.655 1.10 0.924 0.181L0 (�H) 0.161 0.152 0.167 0.413L1 (�H) 0.091 3.854 4.850 0.437C (nF) 1.040 1.031 1.245 0.959p0 1.381 3.581 2.926 2.110p1 4.710 3.651 3.673 2.313q0 13.91 14.49 12.73 12.53q1 8.080 9.104 8.609 7.033VV

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in references [1,2,7,8]. In this paper, they are denoted Model 1,

ig. 3. Comparison with EMTP and manufacturer’s data for a 108 kV surgerrester.

Technique of niching which consists in supporting the indi-iduals who are far away from the other individuals, wasntroduced by increasing their fitness avoiding that all theopulation concentrates on a region of the search space. Thelitism was also introduced by the algorithm. It ensures theecrease of the best value found during generations. Anotherechnique, important for the correct operation of the algo-ithm, is the scaling. Several strategies of the scaling wereested among which we quote the scaling by the truncatedigma.

All these techniques increase the performances of the algo-ithm.

. Static model of ZnO surge arrester

The developed genetic algorithm was subjected to a test topproximate the experimental data coming from manufacturers

f surge arresters and compared with the least squares methodsed by the ATP-EMTP. Experimental V–I characteristics of theurge arresters are generally modelled by a non-linear resistance

Mma

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ref0 (kV) 8.190 7.334 7.027 8.822

ref1 (kV) 7.501 7.135 7.286 7.353

hose variation is exponential [16].

= p

(v

Vref

)q

(3)

here i, v are the arrester current and voltage, respectively, p, qonstants of the device and are unique parameters and Vref is anrbitrary reference voltage.

By examining the results obtained and shown in Fig. 3 weonclude that the genetic algorithm presents a good approxi-ation of the experimental data of the manufacturers comparedith those obtained by the ATP-EMTP.

. Dynamic models of the ZnO surge arresters

In this section, the numerical method is applied to identify thearameters of the dynamic models of ZnO surge arresters. Theelected examples come from the references [4,5,17,18]. Theptimization is performed using the 8/20 �s current waveforms.

The models used in this investigation (Fig. 4) were proposed

odel 2, Model 3 and Model 4, respectively. The non-linear ele-ents are represented by non-linear resistances whose variations

re given by Eq. (3).

odels.

A. Bayadi / Electric Power Systems Research 78 (2008) 1204–1209 1207

Table 2Identified parameters (case of Model 2)

Parameter [4] [5] [17] [18]

R0 (�) 12.76 9.020 18.21 30.34L0 (�H) 0.021 0.019 0.022 0.069L1 (�H) 0.857 0.050 0.264 0.566p0 2.616 7.137 3.535 2.240p1 2.972 3.257 3.212 3.004q0 11.30 11.70 11.53 10.25q1 11.72 11.71 8.844 12.25Vref0 (kV) 7.631 9.157 7.758 10.81Vref1 (kV) 7.832 8.437 6.878 10.46

Table 3Identified parameters (case of Model 3)

Parameter [4] [5] [17] [18]

R0 (�) 5.262 6.384 6.526 6.142L1 (�H) 0.030 0.770 0.115 0.613C (nF) 0.683 0.6533 1.065 1.829p0 3.861 6.661 4.700 2.718p1 5.775 5.068 5.147 3.923q0 8.536 11. 61 14.51 8.360q1 7.670 11.83 7.032 7.232VV

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Fig. 5. Comparison with the experimental residual stress of reference [4].

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mGA-evaluated parameter values provides high accuracy becausein one hand the models in references [2,7] are simplified versionof the IEEE one. In the first [2] the surge arrester capacitance isneglected and in the later [7] L0 inductance associated with the

ref0 (kV) 8.113 8.519 9.106 11.61

ref1 (kV) 7.930 7.976 8.566 10.72

To ensure the convergence of the algorithm, an adequatehoice of the research interval of the parameters is necessary.uring optimization the response of the model (waveforms)

s computed by the EMTP and thereafter transferred to theenetic algorithm for the evaluation of the fitness. The parame-ers optimized for the various examples and models are listed inables 1–4. A discharge current I(t) (10 kA, 8/20 �s) is applied

o the models (Model 1, Model 2, Model 3 and Model 4) withhe optimal obtained parameters. The predicted voltage V(t) isompared with the experimental curves coming from references4,5,17,18].

As it is shown in Figs. 5–8, all the models reproduce in ancceptable way the experimental characteristic.

. Response to fast front surges

The response of the various models implemented in ATP-MTP to fast front surge 10 kA, 1/2 �s is shown in Figs. 9–12.hese results show that all the models can reproduce the dynamicffects discussed before with a weak error. Among the four

able 4dentified parameters (case of Model 4)

arameter [4] [5] [17] [18]

0 (�) 0.604 0.528 0.703 0.157

0 (�H) 0.016 0.024 0.027 0.065

1 (�H) 0.067 0.205 0.130 0.403(nF) 0.860 1.197 1.388 1.117

0 3.051 5.174 4.628 3.865

0 8.047 7.536 7.216 10.03

ref0 (kV) 7.058 7.282 6.895 8.060F

ig. 6. Comparison with the experimental residual stress of reference [5].

odels studied, one can conclude that the IEEE model with

ig. 7. Comparison with the experimental residual stress of reference [17].

1208 A. Bayadi / Electric Power Systems Research 78 (2008) 1204–1209

Fig. 8. Comparison with the experimental residual stress of reference [18].

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ig. 9. Response of the various models to 10 kA, 1/2 �s for the surge arrestersf reference [4].

agnetic fields in the vicinity of the arrester is neglected; thiseads to some limitations of these models. In the other hand the

odel in reference [8] has some merits because it has approxi-ately the same structure as the IEEE one. Thus for this model

ig. 10. Response of the various models to 10 kA, 1/2 �s for the surge arrestersf reference [5].

•••

Fo

ig. 11. Response of the various models to 10 kA, 1/2 �s for the surge arrestersf reference [17].

he non-linear V–I characteristic of an arrester is representedith only one section of non-linear resistance designated A0

s shown in Fig. 4. This is why, to the author’s knowledge, inigs. 9–12, the curves predicted by these two models [1,8] haveelatively the same form and the same peak residual voltage.

. Application to a typical example of protection

Fig. 13 shows a typical protection scheme by surge arresters.lightning surge strikes at point 1. The current wave is divided

nto two parts; one part is propagated in the opposite direction ofhe line connected to the transformer. The reflection of this part

ust be avoided by considering that the line has infinite length.he other part is propagated towards the transformer.

The data of the various elements are as follows:

distributed parameters line, Z = 350 � and V = 300m/�s;

c prated voltage of the surge arrester ZnO is 189 kV;the transformer capacitance is 3000 pF;surge wave (10kA, 1/2 �s).

ig. 12. Response of the various models to 10 kA, 1/2 �s for the surge arrestersf reference [18].

A. Bayadi / Electric Power Systems R

Fig. 13. Typical protection scheme by surge arresters.

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Fig. 14. Test network node’s voltages.

The surge arrester is installed at node 2. The impulse currents injected at node 1 and the voltages of the various nodes areecorded. The voltage at node 3 represents the voltage of theransformer. The results of simulation are shown in Fig. 14 byncluding the case where the surge arrester is represented by aimple non-linear resistance. It is against this part that the surgerresters installed must protect the transformer.

From this figure we can easily see that the predicted trans-ormer voltage in the case of the use of the dynamic modelModel 1 in this case) is more important than that predicted in thease of the use of the static surge arrester model. That is in perfectgreement with the experimental data of the manufacturers.

. Conclusion

In this paper, a new solution based on genetic algorithmethod to calculate the parameters of ZnO surge arresters mod-

ls is proposed. The predicted results are compared with thexperimental results available in the literature. The obtainedesults highlight well the efficiency of these algorithms in thedentification of the parameters of ZnO surge arresters models.

oreover interfacing with ATP-EMTP makes calculation of theischarge voltage waveforms more flexible. It was found that theEEE model used in conjunction with the optimized parametersrovides high accuracy.

[

esearch 78 (2008) 1204–1209 1209

The use of a model with GA-evaluated parameter values in aypical configuration of protection scheme by surge arresters isresented and discussed.

eferences

[1] IEEE Working Group 3.4.11, Modelling of metal oxide surge arresters,IEEE Trans. Power Deliv. 7 (1) (1992) 302–309.

[2] P. Pinceti, M. Giannettoni, A simplified model for zinc oxide surge arresters,IEEE Trans. Power Deliv. 14 (2) (1999) 393–398.

[3] S. Tominaga, K. Azumi, Y. Shibuya, M. Imataki, Y. Fujiwara, S. Nichida,Protective performance of metal oxide surge arrester based on thedynamic v–i characteristics, IEEE Trans. Power Syst. (1979) 1860–1871(PAS-98).

[4] W. Schmidt, J. Meppelink, B. Richter, K. Feser, L. Kehl, D. Qiu, Behaviourof MO-surge arrester blocks to fast transients, IEEE Trans. Power Deliv. 4(1) (1989) 292–300.

[5] I. Kim, T. Funabashi, H. Sasaki, T. Hagiwara, M. Kobayashi, Study of ZnOarrester model for steep front wave, IEEE Trans. Power Deliv. 11 (2) (1996)834–841.

[6] A. Haddad, P. Naylor, Dynamic impulse conduction in ZnO arresters, in:Proceedings of the 11th International Symposium on High Voltage Engi-neering, vol. 2, 1999, pp. 254–257.

[7] F. Fernandez, R. Diaz, Metal oxide surge arrester model for fast transientsimulations, in: Proceedings of the International Conference on PowerSystem Transients, 2001, paper 144.

[8] J. Ozawa, K. Ooishi, K. Shindo, S. Shirakawa, K. Nakano, A. Mizukoshi,et al., Fast transient response and its improvement of metal oxide surgearresters for GIS, in: Proceedings of the Sixth International Symposium onHigh Voltage Engineering, 1989, paper 26.03.

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11] M. Modrusan, Tests on high-voltage metal oxide surge arresters withimpulse currents, in: Proceedings of the Fourth International Symposiumon High Voltage Engineering, 1983.

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13] D.E. Goldberg, Genetic algorithms in search, in: Optimization and MachineLearning, Addison-Wesley, 1989.

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15] F. Alonge, F. D’Ipolito, G. Ferrante, F.M. Raimondi, Parameter identifica-tion of induction motor model using genetic algorithms, IEE Proc. ControlTheory Appl. 145 (6) (1998) 587–593.

16] Canadian/American EMTP User Group, Alternative Transients ProgramRule Book, 1997.

17] T. Hagiwara, T. Funabashi, H. Watanabe, N. Takeuchi, T. Ueda, A metal-

18] V. Hinrichsen, Metal oxide surge arrester fundamentals, in: Hand-book on High Voltage Metal Oxide Surge Arrester, SIEMENS AG,2001.