05508306

IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010 2859

Parameter Identification of Arc Furnace Based onStochastic Nature of Arc Length Using Two-Step

Optimization TechniqueS. M. Mousavi Agah, Member, IEEE, S. H. Hosseinian, H. Askarian Abyaneh, Senior Member, IEEE, and

N. Moaddabi

Abstract—Recent studies on the effect of arc furnaces in a powersystem lack accurate predicting voltage waveform of an arc fur-nace. This is mainly due to the random nature of the arc length. Inthis paper, a novel two-step optimization technique is presented toidentify the arc furnace parameters considering the stochastic na-ture of the arc length. The proposed method is based on a geneticalgorithm (GA) which adopts the arc current and voltage wave-forms to estimate parameters of the nonlinear time-varying modelof an electric arc furnace. Simulation results are compared withdata obtained from two real arc furnace plants. Analyses show thatthe proposed method is profitable to identify accurate values of thearc furnace parameters which incorporate the stochastic nature ofthe arc length.

Index Terms—Arc furnace, genetic algorithm (GA), nonlineartime-varying arc model, parameter estimation, power quality(PQ).

I. INTRODUCTION

A RC FURNACES used for refining and melting metalsin the steel production procedure are some of the main

causes of power-quality (PQ) problems in electric power sys-tems. As the popularity of the arc furnaces increases, PQ prob-lems will be more severe [1]. In order to take precautions tominimize the adverse effects of arc furnaces, it is necessary todevelop an accurate and easy-to-use electric arc model. How-ever, this has so far been quite a challenging task. The reasonwas the complexity of the electric arc physical phenomena andthe randomness associated with the melting stage of arc furnaceoperation [2].

In [3] and [4], a nonlinear resistance model has been pro-posed which uses numerical analysis to solve differential equa-tions describing the arc furnace. However, this model does notconsider the time-varying nature of the arc. A time-varying re-sistance model has been recently presented in [5] which relatesthe reference resistance of the arc to power consumed by it. Theactual arc resistance can have sinusoidal or bandlimited whitenoise variation around the reference value [6].

Manuscript received July 26, 2009; revised November 24, 2009. First pub-lished July 12, 2010; current version published September 22, 2010. Paper no.TPWRD-00562-2009.

The authors are with the Department of Electrical Engineering, AmirkabirUniversity of Technology, Tehran 15914, Iran (e-mail: [email protected];[email protected]; [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2010.2044812

Cox and Mirbod in [7] have used a current-source model forarc. The source current has been represented by the Fourier se-ries where the Fourier coefficients change randomly in each pe-riod. It takes into account the stochastic behavior of the arc fur-nace in a correct way. However, it is more suited to design filtercomponents [8].

An alternative method to model the arc furnace is based onchaos theory [9]. The method has become a modeling issue, sub-sequent to recognize the chaotic responses in electric arc fur-naces [10]. A model based on chaotic dynamics is introducedin [11]. The main disadvantage of the model is that it does notgenerally have an accepted precise mathematical definition [2].Furthermore, it exhibits extreme sensitivity in the state trajec-tory with respect to the initial conditions [12].

A frequency-domain analysis method has been proposed in[13] which represents the arc voltage and current by their har-monic components. In this model, it is assumed that the arc fur-nace draws the maximum power in the fundamental frequency,which is not always true [2]. The model is simple. However, itcannot represent the stochastic nature of the arc [14].

In [2] and [15], a power balance method is proposed. Themodel is based on the energy balance equation, which is a non-linear differential equation of the arc radius and the arc current.Since this method is based on the experimental formula, whichvaries in different furnaces, any change in load requires the ap-plication of different models in the simulation process [8].

A voltage-source model is used in [16], where voltage is con-sidered as square waves with modulated amplitude. The newamplitude of voltage is generated after every zero crossing ofthe arc current during the reinitiating process [8]. In [17], a non-linear time-varying voltage-source model has been presented. Inthis model, the arc voltage is defined as a nonlinear function ofthe arc length. The time variation of the arc length is modeledby using deterministic or stochastic laws. The deterministic lawusually assumes a sinusoidal behavior for the arc length.

Among the literature reviewed, it can be seen thattime-varying resistance and voltage models not only areable to perfectly simulate the stochastic nature of the arc length,but they also have some advantages to the other methodsmentioned before. The advantages are reported in [17].

Several papers have been published which aim to identifyparameters of the arc furnaces. A power balance method wasadopted in [1], together with differential evolution algorithm, toestimate the arc furnace parameters. However, the main disad-vantage of the proposed method in [1] is that the time variation

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2860 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 4, OCTOBER 2010

Fig. 1. Typical circuit diagram of an electric plant supplying an arc furnaceimplemented in PSCAD/EMTDC.

of the arc length was not addressed. A procedure is presentedin [18] for measurements of voltage flicker using genetic algo-rithm (GA). However, it represents the arc-length behavior in adeterministic manner which is different from real experiments.

Despite the importance of stochastic representation of electricarc length to achieve real and accurate model in PQ studies,less attention has been paid to it in the literature. Therefore,it remains unclear how the stochastic nature of arc length canbe addressed in the parameter identification of the arc furnace.Hence, the additional study of this phenomenon is needed.

This paper tries to fill this gap by proposing a novel two-stepoptimization technique. The proposed method is capable of in-corporating the stochastic nature of arc length in the parameteridentification procedure of an electric arc furnace. The arc isdescribed by a voltage-source model. The arc furnace modelis simulated by PSCAD/EMTDC. The GA-based two-step op-timization procedure is implemented by using MATLAB. Themethod is applied by using data adopted from [17] which areattributed to a real arc furnace plant installed in Northern Italy.The proposed method is also validated by making a comparisonbetween the simulation results and the measurements conductedon a real arc furnace plant in Tabriz, Iran. Analyses show that theproposed method is profitable to achieve precise estimation ofthe parameters describing the stochastic nature of the arc. Thispaper is organized as follows.: Section II presents a brief reviewof the nonlinear time-varying arc model. Section III denotes theobjective function, proposed method, as well as the GA appli-cation to the problem. Simulation results are presented in Sec-tion IV and finally conclusions are given in Section V.

II. NONLINEAR TIME-VARYING ARC FURNACE MODEL

A typical circuit diagram of an electric plant supplying an arcfurnace is shown in Fig. 1. The figure is presented before in [8],[17], and [19]. Parameters of the studied system shown in Fig. 1are presented in the Appendix. The nonlinear model of the arcfurnace can be described with a voltage–current characteristicas follows:

(1)

where and are the arc voltage and the arc current, respec-tively.

is the arc length,is the threshold value to which voltage tends when cur-

rent increases.and are two constants whose values are considered to

be dependent on the derivative of the current and are different

Fig. 2. Dynamic arc furnace voltage-current characteristic obtained by the pro-posed arc model in [17], implemented by PSCAD/EMTDC.

TABLE IDYNAMIC ARC FURNACE MODEL PARAMETER

VALUES IN (1) USED FOR SIMULATION

in increasing ( and ) and decreasing ( and ) parts ofcurrent in the V-I characteristic.

Fig. 2 shows the voltage-current characteristic, which is ob-tained from (1). The parameters proposed in [17], [19], and [20]were used to plot the figure. The data are presented in Table I.

Due to the intrinsic nonlinearity of the arc characteristic, thearc length variation, which is the cause of flicker, is unavoid-able. Considering these variations, it is possible by the followingequation:

(2)

where represents a constant that accounts for the voltage dropin the anode and cathode electrodes of the furnace, and is theper-unit length voltage across the arc.

The rapid variation of the arc current during the meltingprocess is highly correlated with the arc-length variations [17].Therefore, the accurate representation of the arc-length varia-tion is difficult to achieve [19]. The complicated nature of thephenomenon has led to different deterministic [20], [21] andstochastic [22] approaches to study the arc-length variation.

The deterministic approach is based on a sinusoidal repre-sentation of the arc-length variation, with the frequency beingchosen in the range typical of flicker (0.5–25 Hz). Despite thereasons reported in [17] on the suitability of the approach incomputer simulations, it does not clearly represent a normalworking condition of the arc furnace.

The stochastic approach is supported by the observation thatthe arc-length time variation can be considered as a random phe-nomenon [22]. As mentioned in [19] for more realistic calcula-tions, the stochastic model will be more precise. Therefore, inthis paper, the arc length is considered to vary stochastically.

Using this method, the time variation of the arc length is givenby

(3)

MOUSAVI AGAH et al.: PARAMETER IDENTIFICATION OF ARC FURNACE BASED ON STOCHASTIC NATURE OF ARC LENGTH 2861

where is the reference arc length and is the white noisesignal with a frequency range, in which voltage fluctuations pro-duce flicker (5 to 20 Hz). Its amplitude varies up to the max-imum arc-length deviation [17], [19], [20].

III. PARAMETER IDENTIFICATION OF THE ARC FURNACE

A. Objective Function

The subsection describes the objective function which is usedto estimate the parameters of the nonlinear time-varying arc fur-nace model introduced in Section II. The main purpose of theprocedure is to identify the set of arc furnace parameters be-longing to the solution space that minimize the global errorbetween the measured and the estimated voltagesamples.

In particular, the overall problem can be regarded as an un-constraint minimization of the estimation error as follows:

(4)

Two different objective functions (OFs) have been used in asimilar optimization process in the literature [18]. According tothe previous works [2], [18], one of them has been reported tobe more appropriate than the other for this purpose. Here, thisOF is used, which calculates the mean value for the rooted sumof squared errors, as follows:

(5)

where and are the estimated and the measured valueof the arc furnace voltage related to the th arc current sample,respectively. is the number of samples per half cycle.

It is noted that a similar OF was used in [18]. However, theproposed algorithm in [18] did not consider the stochastic natureof the arc length. The following subsection describes how thisimportant criterion is incorporated in arc furnace modeling.

B. Arc Furnace Modeling

The arc furnace model is developed in the power system sim-ulation tool, PSCAD/EMTDC, by using the PSCAD componentbuilder. Internal to the component, FORTRAN code is writtento simulate the arc furnace as a voltage-dependent source, baseon the model described in Section II. The stochastic nature ofarc length is incorporated into the model by generating a whitenoise signal representing arc-length deviations. The idea is sup-ported by findings reported in [13]and [17]. The white noisesignal is created by using a random number generator havinga uniform distribution over the interval . is refer-ence arc length and is maximum arc-length deviation. Theoutput of the random number generator is fed to a band-passfilter with lower and uppercut frequencies 4 Hz and 14 Hz, re-spectively (according to the frequency range reported in [20]).Fig. 3 depicts the stochastic variation of arc length that is simu-lated with a reference arc length of 30 cm and maximum devia-tion of 10 cm. As can be seen from Fig. 3, the arc length varies

Fig. 3. Stochastic nature of arc-length implementation using the band-passwhite noise signal.

every 10 ms. This duration of time is chosen because of the factthat although the arc length has a random value, its value willnot change at least for a half cycle, as mentioned in the literature[13], [17].

The following proposed method, which is capable of identi-fying arc furnace parameters, is presented.

C. Proposed Method

The main objective of this paper is to identify electric arcfurnace parameters. Among the parameters introduced in theprevious section, , and are deterministic variables;however, has a stochastic nature. The value of arc lengthvaries in subsequent half cycles and its variation is describedby a uniformly distributed random variable in the range whichis defined by the reference arc length , and maximum arc-length deviation .

Different optimization algorithms can be used to solve theaforementioned parameter identification problem. However, thenumber of iterations in most of these algorithms is limited. Dueto this and many other reasons (such as the heuristic nature ofmodern optimization techniques and probability of trapping intothe local optimum), implementing these techniques for varioushalf cycles may lead to obtaining different values for the modelparameters. However, as mentioned previously, among the pa-rameters, only has a stochastic nature (its value can be differentin various half cycles), and all of the other deterministic param-eters should have a unique value in all of the half cycles of theobservation window.

The previously mentioned shortcomings in the existing opti-mization algorithms were the main motivation for the authorsto propose a two-step optimization technique. The proposedmethod divides the observation window into several half cycles,each having the same duration of 10 ms. Then, the parameteridentification procedure is performed based on the data comingfrom the measured voltage waveform in each period of 10 ms,separately. It does not mean that the procedure should be com-pleted during 10 ms. Rather, the procedure may take some sec-onds to complete parameter identification in each half cycle. Itmay also take several minutes for the whole half cycles of theobservation window. However, these are not constraining prob-lems since the proposed method is based on offline calculations.

The steps of the proposed method are described as follows:Step 1) First, an observation window is considered on the

arc furnace voltage waveform available from direct


measurement. The observation window consists ofseveral consecutive half cycles. Then, the optimiza-tion procedure is performed by using the previouslymentioned OF, in consecutive half cycles separately.The output of the performed optimization proce-dure in each half cycle is a set of estimated arc fur-nace parameters. The average of all the estimatedparameters over various half cycles of the observa-tion window is assumed to be the identified value forthe deterministic variables (i.e., , and . Inthis manner, a unique value is obtained for the deter-ministic variables, as it is coherent to the nature ofthese parameters.

Step 2) The optimization procedure is performed againin each half cycle, using the voltage waveformobtained from direct measurement and the deter-ministic parameters of arc furnace identified fromthe previous step, as its inputs. The output of theoptimization procedure is an identified value forthe arc length over consecutive half cycles. Basedon the identified arc lengths in various half cycles,the reference value and the maximum deviation ofthe arc length are determined along the observationwindow.

For the mentioned optimization problem, GA seems to be par-ticularly suitable. Compared with the conventional optimizationmethods, such as calculus-based and enumerative strategies, GAis robust, global, and may be generally applied without recourseto domain-specific heuristics.

D. GA Application to the Problem

This section is devoted to review the notation and concept ofGA to give a better understanding and coherency of this paper.Fig. 4 shows an overall view of the step-by-step process to im-plement a real-code GA to the problem. In this figure, steps ofGA optimization are shown as a group using dashed lines. Thisis also applied for the arc furnace model. These two groups areshown again in the same figure with no more details for sim-plicity.

The goal of GA is to optimize the proposed OF on searchspace. The search space consists of predefined intervals forvalues of arc furnace parameters.

GA is started by creating the first “Parent” chromosomepool. The pool contains several sets of arc furnace parame-ters which are created randomly. Each set of parameters ispacked into a chromosome which is the key variable in GA.Each chromosome consists of the arc furnace parameters (i.e.,

). The number of arc furnace parametersets (chromosomes) is referred to as the population size. Toevaluate goodness of each parameter set in the populationregarding the accuracy of estimated parameters, the previouslydescribed OF value is calculated. Based on the calculated OFvalues, those parents who have more optimal (minimum) OFvalues are granted more opportunities to survive (i.e., theycan generate more “children”). Thus, the new arc furnace pa-rameters (i.e., ) are generated by usingthe operators of crossover and mutation, and are packed into“children” chromosomes. The evaluation of each new offspring

Fig. 4. GA application flowchart to the proposed method.

satisfaction is required in order to form the “Children” chro-mosome pool. The described procedure is then repeated untilthe stop criterion is reached. In this paper, simple criterion isused which is met when the maximum number of generationsis reached.

IV. SIMULATION RESULTS

To check the validity of the proposed method, the results ofsimulations, which are implemented in PSCAD/EMTDC, arecompared with actual data in two case studies. First, the avail-able data in [17], which are attributed to a real arc furnace plantinstalled in Northern Italy, are compared with the results ofthe proposed two-step parameter identification method (Case I).Then, the proposed method is validated by using the data ob-tained from measurement on a real arc furnace plant in Tabriz,Iran (Case II).

The measurements used in the proposed method are only thephase voltage and current of the arc. Sampling is performedwith a certain number of samples per half cycle. At each sam-pling time, the instantaneous values of the arc current and the arcvoltage are extracted from the waveforms. The arc current sam-pled point is also fed into the model implemented in PSCAD/EMTDC. Obtaining the output voltage, the objective function isformed in each half cycle. Then using GA, an estimation of themodel parameters is achieved separately for each half cycle.

In this paper, GA is used with following parameters whichresult in the most accurate estimation. These values are obtained


TABLE IITOLERANCE LIMITS FOR THE PARAMETERS OF THE ARC

FURNACE MODEL USED IN SIMULATION

TABLE IIIVARIATION OF THE ESTIMATED PARAMETERS OF THE ARC

FURNACE MODEL USING THE PROPOSED METHOD

subsequently to a trial-and-error procedure.Population size: 30Maximum number of generations: 100Crossover probability: 0.5Mutation probability: 0.08.

For better functionality of the algorithm, the tolerance limit ofeach parameter should be determined. It is noted that the upperand lower tolerance limits for the parameters were determinedbased on data available in the literature [17], [19], and [20]. Insome cases, when little data were available, the tolerance limitwas chosen heuristically large enough. Table II provides the tol-erance limits for the parameters used in this study.

A. Case I: Arc Furnace Plant Installed in Northern Italy

The summary of results obtained in this case is depicted inTable III. The simulation is carried out by using the data pre-sented in Appendix A.

In this study, sample rate is selected to be five samples per halfcycle. The observation window contains 100 half cycles. There-fore, step 1 of the proposed method is carried out for each halfcycle, resulting in 100 runs for the whole observation window.

Half-cycle intervals are arranged in such a way that the deriva-tive of the arc current is positive in odd half cycles, and reverselyits value is negative in even half cycles. In Table III, the dash signcorresponds to parameters which cannot be estimated in somehalf cycles. For example, the estimated value for is markedby a dash in even half cycles. This is because the derivative ofarc current is negative in these half cycles. In the first columnof Table III, a list of arc furnace parameters is presented. In thistable, only some half cycles of the observation window (100 halfcycles) have been selected for more accurate investigation. Theestimated value of each parameter is shown in each half cycle(columns 2 to 7). Based on the reported data in Table III, thereare some differences between the estimated values of the deter-ministic variables in different half cycles.

The average value of the estimated parameters in all half cy-cles of the observation window is shown in the eighth column.

Fig. 5 shows how the values of the estimated parameters varyduring half cycles of the observation window. The average valueis depicted by bolted horizontal line in the figure.

As mentioned previously, the variation of the estimatedvalues for the deterministic parameters is related to the max-imum generation numbers in GA. The data needed to investigatethe relationship between the generation size and the variancesof the deterministic variables are presented in Table IV. As isshown in Table IV, variances of all parameters decrease moreor less, as the number of generations increases. Since the resultsobtained with the maximum generation number of 100 are ingood agreement with the data presented in [17], it is assumed tobe the base case in the study. Fig. 6 shows the stochastic natureof the arc length. It can be seen that the reference value of thearc length is estimated at 30.35 cm and the maximum deviationto 9.70 cm, which are in agreement with the data mentioned in[17].

To summarize, Table V provides a comparison between theresults of the proposed method and the actual values of the pa-rameters which are reported in [17]. The proposed method isperformed 1000 times to check validity of the obtained results.The fourth column in Table V presents the average value of therelative error between the data obtained from proposed methodover 1000 runs, and actual values. For further investigation, themaximum and minimum relative errors for various parametersare shown in columns 5 and 6 of Table V. From the reporteddata, it can be seen that the proposed method will result in amaximum relative error of about 5% in the worst case (max-imum variation of arc length). As mentioned before, the accu-racy of the proposed method depends on the sampling rate. Thisis because of the evolutionary nature of the algorithm which isused in this paper. Assuming the observation window size of 100cycles, different numbers of samples are considered. The sam-pling rate changes between 2, 3, and 5 samples per half cycle.The results show that the relative errors of the different param-eters decrease, as the sample rate increases. It is noted that incase of and , the relative error decreases more, with theincrease of sampling rate. It is due to the relatively large tol-erance limit considered for these parameters. Investigating theresults shows that five samples per half cycle provide a compro-mise between the estimation accuracy and running time of the


Fig. 5. Variation of deterministic parameters of arc furnace model in half cycles of the observation window: (a) � (in kikowatts).. (b) � (in kilowatts). (c) �(in kiloamperes). (d) � (in kiloamperes). (e) A(V). (f) B(V/cm).

Fig. 6. Variation of the arc length estimated by using the proposed method.

algorithm. Therefore, in this paper, results are only shown forthis sampling rate.

B. Case II: Arc Furnace Plant in TABRIZ, IRAN

In this case, measurement is performed on a plant in Tabriz,Iran. The plant consists of four electric arc furnaces. An elec-tronic PQ meter was installed to measure the phase voltage andcurrent in one of the existing arc furnaces. The instantaneousvalues of the arc current and voltage are then used by the pro-posed method. The parameters of the studied arc furnace arepresented in Appendix B.

TABLE IVVARIANCE OF ESTIMATED VALUES FOR DETERMINISTIC VARIABLES IN HALF

CYCLES OF THE OBSERVATION WINDOW

Similar to Case I, simulation is performed for an observa-tion window of 100 half cycles, with 5 samples per half cycle.The summary of the obtained results is presented in Table VI.This table provides the estimated parameters of the electric arcfurnace, based on the model presented in Section II. The pro-posed method is performed 1000 times. The values reportedin Table VI for identified parameters correspond to an averagevalue among 1000 runs of the proposed method. To verify theaccuracy of the obtained results, it is important to make surethat the identified values result in arc current and voltage wave-form similar to those obtained from the measurement. The val-


TABLE VCOMPARISON BETWEEN THE ESTIMATED PARAMETERS OF THE ARC FURNACE

MODEL USING THE PROPOSED METHOD AND REAL DATA PRESENTED IN [17]

Fig. 7. Electric arc furnace current waveform over the entire observationwindow obtained from (a) measurement and (b) the proposed method.

idation process is performed by applying the identified param-eters to the arc furnace model. Figs. 7 and 8 show the arc cur-rent and voltage waveform derived from the proposed method,respectively. The figures are illustrated over the entire observa-tion window. With these figures, it is found that the arc currentand voltage waveform derived by the proposed method are con-sistent with the actual system waveforms.

In order to prove the results of the proposed method, theshort-term flicker severity index associated with thevoltage waveforms obtained from measurement and simulationare computed, and the results are given in Table VII. As can be

Fig. 8. Electric arc furnace voltage waveform over the entire observationwindow obtained from the (a) measurement and (b) proposed method.

TABLE VIIDENTIFIED PARAMETER VALUES FOR A REAL ARC FURNACE IN TABRIZ, IRAN

TABLE VIIFLICKER SEVERITY INDEX FOR THE SIMULATED

AND MEASURED VOLTAGE WAVEFORMS

seen, the short-term flicker severity indices of both waveformsare approximately the same. Therefore, Table VII implies thatthe proposed method based on the two-stage optimizationtechnique can effectively incorporate the stochastic nature ofarc length in parameter identification of electric arc furnaces.

V. CONCLUSION

In this paper, a two-step optimization method has beenproposed to identify parameters of the nonlinear time-varyingmodel of the arc furnace. The performance of the proposedmethod was quite satisfactory in the computational experi-ments. Its capability to consider the stochastic nature of thearc has made it a powerful method for modeling arc furnacesin real applications. The results of the simulations have shownrobustness of the GA in the field of parameter estimation for an


electric arc furnace. The proposed method has been suggestedto be applied in modeling other electric systems in which thedeterministic and stochastic variables exist together.

APPENDIX

A. Arc Furnace Plant Installed in Northern Italy

Parameters of an electric arc furnace plant installed innorthern Italy are presented here. The parameters are used inthe first case study in this paper.

Source: An upstream network is modeled by using an idealsinusoidal ac voltage source with an amplitude of 220 kV andThevenin inductance of .

HV/MV transformer: Two windings linear single-phasetransformer. Nominal power: 95 MVA, nominal voltage ratio:220/21 kV, short-circuit voltage and losses 12.5% and 0.5%,respectively.

MV/LV transformer: Two windings linear single-phasetransformer. Nominal power: 60 MVA, nominal voltage ratio:21/0.6 kV, short-circuit voltage and losses 10% and 0.5%,respectively.

Flexible cable: resistance , inductance.

B. Arc Furnace Plant in Tabriz, Iran

Parameters of a real electric arc furnace plant installed inTabriz, Iran are presented here. The parameters are used in thesecond case study in this paper.

Source: Upstream medium-voltage (MV) network is modeledas an ideal source with an amplitude of 20 kV, which has thefollowing parameters: 0.0097 p.u., 0.0882 p.u.,

0.0124 p.u., p.u. Moreover, an existing localgenerator is modeled by using the following parameters0.005 p.u., 2.0446 p.u., 0.005 p.u., 0.200 p.u.,

0.457 s.MV cable: 21 m of XLPE cable, 3 (1 70) mm .MV/LV transformer: two windings single-phase transformer.

Nominal power: 4 MVA, nominal voltage ratio: 20/0.4 kV,impedance 7.5%.

Flexible cable: 46 m of PVC cable, 3 (3 185) mm .

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[22] M. Loggini, G. C. Montanari, L. Pitti, E. Tironi, and D. Zanmelli, “Theeffect of series inductors for flicker reduction in electric power systemssupplying arc furnaces,” presented at the IEEE/Ind. Appl. Soc. Annu.Meeting, Toronto, ON, Canada, Oct. 1993.

S. M. Mousavi Agah (M’10) was born in Rasht,Iran, on December 4, 1984. He received the B.Sc.and M.Sc. degrees (Hons.) in electrical engineeringfrom Amirkabir University of Technology (AUT),Tehran, Iran, in 2006 and 2008, respectively, andis currently pursuing the Ph.D. degree in electricalengineering at AUT.

His areas of research are power quality, powersystem protection, distributed generation systems,and probabilistic analysis of power systems. Hehas a lot of experience in protection, control, and

automation of high-voltage substations in Iran.


S. H. Hosseinian was born in Iran in 1961. He re-ceived the B.Sc. and M.Sc. degrees in electrical en-gineering from Amirkabir University of Technology(AUT), Tehran, Iran, in 1985 and 1988, respectively,and the Ph.D. degree in electrical engineering fromthe University of Newcastle, U.K., in 1995.

Currently, he is Assistant Professor in the Elec-trical Engineering Department at AUT. His specialfields of interest include transients in power systems,power quality, restructuring, and deregulation inpower systems. He is the author of four books in the

field of power systems. He is also the author and coauthor of many technicalpapers.

H. Askarian Abyaneh (SM’09) was born inAbyaneh, Isfahan, on March 20, 1953. He re-ceived the B.S. degree in electrical power systemengineering from Iran University of Science andTechnology in 1976 and the M.S. degree in electricalpower system engineering from Tehran University,Tehran, Iran, in 1982. He received a second M.S.degree and Ph.D. degree in electrical power systemengineering from the University of ManchesterInstitute of Science and Technology, Manchester,U.K., in 1985 and 1988, respectively.

Currently, he is a Professor with the Department of Electrical Engineering,Amirkabir University of Technology, Tehran, Iran, working in the area of relayprotection and power quality. He has been published in many scientific papersin international journals and conferences.

N. Moaddabi was born in Rasht, Iran, in 1984. Hereceived the B.S. and M.Sc. degrees in electricalpower engineering from Amirkabir University ofTechnology (AUT), Tehran, Iran, in 2006 and 2008,respectively, where he is currently pursuing thePh.D. degree in power electrical engineering.

His research interests include power quality, powersystem protection, power electronics, and distributedgeneration systems. He has a lot of experience in pro-tection and control design of high-voltage substationsin Iran.

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