A Method for Averting Saturation From Series Transformers of Dynamic Voltage Restorers

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IEEE TRANSACTIONS ON POWER DELIVERY 1

A Method for Averting Saturation From SeriesTransformers of Dynamic Voltage Restorers

Darlan A. Fernandes, Member, IEEE, Fabiano F. Costa, Member, IEEE, and Montiê A. Vitorino, Member, IEEE

Abstract—This paper proposes a technique for preventingsaturation in series transformers from dynamic voltage restorer(DVR) systems. The method consists in correcting the voltageswhich are injected through the transformers into the power systemto compensate voltage sags. It restricts the compensating voltagesduring the sag whenever it predicts that a maximum limit forthe flux linkage is about to be exceeded. The prediction is carriedout at the beginning of a stabilized voltage sag. Moreover, thetechnique allows a certain level of sag compensation even whenthe estimated flux is expected to exceed the saturation limit. Thevoltage sag level and phase are computed through an adaptiverecursive least squares (RLS). The RLS estimation incorporatesa transient period before it achieves a stable state wheneverthere is a sag event. The DVR is not supposed to operate in thisperiod. Therefore, this paper also outlines a simple procedure fordetecting the RLS estimation stable level. Simulation of differentscenarios of voltage sags and the results from the experimentalimplementation of a DVR show the effectiveness of the method.

Index Terms—Dynamic voltage restorer (DVR), flux linkage,power quality (PQ), recursive least squares, saturation, trans-former.

I. INTRODUCTION

V OLTAGE sags are the most incident disturbances in-flicting the power system. Surveys indicated that 92% of

interruptions in industrial facilities may occur due to voltagesags [1]. The economic impact to the industries and utilities issevere due to equipment damage and loss of production [2].To mitigate this problem, the utilities can invest in the powersystem design in order to reduce the faults incidence and thetime for their clearance. Also, redundant lines can be installedto feed critical loads [3]. Unfortunately, these solutions arecomplex and costly to implement. This enables local-basedalternatives where some equipment is fixed in the system-load

Manuscript received August 05, 2013; revised January 28, 2014 and March07, 2014; accepted March 09, 2014. This work was supported by the BrazilianResearch Council (CNPq) through project processes nos. 482736/2011-9,454638/2012-4, and 420442/2013-8. Paper no. TPWRD-00876-2013.D. A. Fernandes is with the Department of Electrical Engineering, Federal

University of Paraı́ba (UFPB), João Pessoa PB, 58.051-900, Brazil (e-mail:[email protected]).F. F. Costa is with the Department of Electrical Engineering, Federal Uni-

versity of Bahia (UFBA), Salvador BA, 40210–630, Brazil (e-mail: [email protected]).M. A. Vitorino is with the Department of Electrical Engineering, Center of

Electrical Engineering and Informatics, Federal University of Campina Grande(UFCG), Campina Grande- PB, 58.429-900, Brazil (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TPWRD.2014.2311577

Fig. 1. System configuration with a DVR.

interface. One example of this approach is the usage of dynamicvoltage restorers (DVRs).A DVR is one of the most effective custom power devices for

voltage sag and swell compensation and it has been attractinggrowing attention in recent years [1], [4]–[8]. A typical testsystem, incorporating a DVR, is depicted in Fig. 1. The DVRinjects compensating voltages to the power lines through athree-phase series transformer or three single-phase seriestransformers. A problem may arise when the DVR system cor-rects a severe sag. In this situation, the compensating voltagescan cause flux linkage in the core to exceed the transformernominal limit [9]. The exceeding flux is caused by a dc com-ponent whose amplitude depends on the initial phase angle ofthe compensating voltage. This, in turn, leads to overcurrentand overheating, reducing the useful life of the transformer. Toovercome this problem, one alternative is to enlarge the seriestransformers. This solution brings an increase in physical size,weight, and cost to the transformer [10]. Another approach isto apply DVR systems without transformers [11], [12]. Thisincreases the number of switches and their associated controlcircuits needed to apply the compensating voltage. Finally,there is the strategy of controlling the flux linkage by limitingthe voltage injected to compensate the sag. This approach hasa compromising nature. It deals with the necessity of reducingthe sag and the demand of not changing the transformer’s fluxlimit.In [13], the flux linkage in the DVR’s transformers is kept

under a maximum limit by shutting off the reference voltageswhile the currents are over a specified limit, or the referencevoltages are reversed. The drawback is to impose a full sag to the

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2 IEEE TRANSACTIONS ON POWER DELIVERY

load during a certain period. In [14], the controller uses the mag-nitude of the positive-sequence component of the line voltagesto identify voltage sags. The flux is estimated by means of theintegral of the voltage and whenever it reaches a given limit, thevoltage is set to zero. The method proposed in [15] also makesuse of the flux estimation in order to limit the compensating volt-ages. The voltage injection action is divided into three intervals.Between the sag detection instant and one-sixth of the funda-mental period , after the sag detection, the injected compen-sating voltage is fully applied to compensate the sag. Between

and , the injected voltage is adjusted to zero. From theinstant on, after the detection, again the full compensatingvoltage is applied. In [16], two methods for flux-linkage con-trol are presented. In the first one, the compensating voltage bemultiplied by half during the first half fundamental cycle afterthe sag detection instant and, after this period, the full compen-sating voltage is used. This ensures that the dc flux is wiped off.The second method predicts, at the detection instant, whetherthe flux will surpass the maximum limit within half a cycle pastthe zero cross. If the flux is exceeded, then it is introduced a formfactor to limit the compensating voltage. This method has theadvantage of allowing a level of voltage to be injected throughthe transformers during all periods of the sag.The inrush control systems for all of the aforementioned

works rely on the estimation of the load voltage phasors tocompute the compensating voltages. Some works employ thestandard least-squares error to estimate these phasors [17],[18], notwithstanding, in general, that the techniques for es-timating them are not exploited or discussed by the authors.This paper expands the ideas developed in [16] by dealing withthe possibility of more restrictive limits for the saturation inthe transformer’s core. In addition, it proposes the use of anadaptive RLS-based technique for the estimation of phasors,suitable to be incorporated to the compensation voltage controlas well as the inrush control. The voltage phasor amplitudes areemployed to verify whether the flux surpasses the transformer’sflux limit. The RLS algorithm necessarily includes a transitiontime before its estimation achieves a constant level. In theproposed method, it is assumed that the DVR system shouldnot operate before it has a stabilized reference for the sag.Therefore, this paper also proposes a simple procedure to detectwhether the RLS estimation reaches a constant value for theestimation of phasors.

II. METHOD FOR CONTROLLING SATURATION

This section devises the method of controlling saturation pro-posed in this paper. The fundamental idea is to constrain thecompensating voltage by multiplying it by a form factor .In order to accomplish such a goal, one must predict, at the mo-ment of the sag detection, the value for the form factor to beapplied up to the end of the next half cycle (or the next wholecycle) of the compensating voltage after the sag detection andkeep the flux at its limit value. In general, can be described as

(1)

where and are, respectively, the fundamental frequency andthe initial phase of the compensating voltage. By Faraday’s law,

the linked flux in the transformer’s core at a given instantcan be expressed by

(2)

Solving (2) and assuming that the transformer is demagnetized,that is, 0 at the 0, the following expression for the fluxis obtained:

(3)

The first part of (3) represents the ac component of the flux,while the second one is its dc component.Whenever the injectedvoltage started at a zero cross, that is, , the peak ofthe flux reaches its maximum value. For instance, if ,the expression for the flux is given by

(4)

The technique proposed in this paper is inspired by the onedescribed in [16]. Consider Fig. 2, where the injected voltagestarts at angle . It is possible to predict the maximum excursionfor the flux linkage through the following integration:

(5)

where is a form factor which is first set to unity. Note that be-tween and , the injected voltage contributes positively tothe flux. Between and , the voltage contributes nega-tively to the flux. Therefore, in the situation depicted in Fig. 2,at the angle , the flux reaches its minimum value. If themodule of the prediction provides a value higher than the al-lowed limit for the transformer, then the parameter must beadjusted to a value which restricts the amplitude to be equal tothe lower limit. Thus, if , make in (5)and find as

(6)

Applying the factor , computed through (6), to the compen-sating voltage during its negative semicycle, ensures that theflux will not surpass the minimum limit. When the injectedvoltage starts within a negative semicycle, at the point ,is predicted through

(7)

If , the injected voltage is required to be scaled bythe form factor computed by

(8)


FERNANDES et al.: METHOD FOR AVERTING SATURATION FROM SERIES TRANSFORMERS 3

Fig. 2. Compensating voltage for one of the phases.

It must be noted that the procedure described before onlyshifts the flux curve so that, up to end of the semicycle, sub-sequently after the start of the voltage injection, its value is nothigher than the transformer’s flux limit. It still remains a dc com-ponent which can cause the flux value to surpass the allowedlimit within the subsequent opposite semicycle. Therefore, inthe proposed method, the condition

(9)

must be verified. Note that is the peak value for the compen-sating voltage. If the condition (9) is not observed, the compen-sating voltage must be computed as

(10)

where .The method implementation is carried out in such a manner

that, whenever the initial phase is detected within the intervalfrom up to , it must be subtracted by . This is neces-sary because the RLS algorithm computes ranging from 0 upand leaves out the interval up to 0.In the proposed method, there is a need to compute the ampli-

tude and phase of the compensating voltage. This task is carriedout by a recursive least squares method [19] which, for eachinstant, updates the amplitude and phase estimation. This is dis-cussed in the next section. Furthermore, the DVR voltage cor-rection only takes place in the moment where the estimation forthe parameters is stabilized, that is, during the estimation tran-sient when there is no compensating voltage injected into thegrid. The proposed method is applied for each one of the threephases, accordingly to the flowchart depicted in Fig. 3.

III. COMPENSATING VOLTAGE CONSTRUCTION

The compensating voltage construction applied in this papermakes use of an RLS algorithm which computes the amplitudeand the phase for each sample of the grid voltage . TheRLS algorithm is applied for each one of the three grid phases.It is worth emphasizing that the DVR is not meant to compen-sate the voltage while the RLS estimation is in its transient pe-riod. Therefore, in this paper, a method is proposed for flaggingwhether the RLS estimation is stable. The next subsection isdedicated to explain the RLS algorithm used in this paper. Thefollowing one outlines the procedure in which the compensatingvoltage is only injected when the RLS estimation is constant.

A. RLS Estimator

To model voltages acquired from power systems, it is usualto describe them as a sum of sinusoids, with one being thefundamental, and the others being harmonics. If the voltage iscorrupted by harmonics, this representation ensures that the dy-namics of the harmonics do not contaminate the parameters es-timation related to the fundamental sinusoid. Hence, denotingthe data of voltages by , the model is a sum of sinusoidsprovided by

(11)

where and are, respectively, the amplitude and thephase of the sinusoid of frequency, and is the time index.The time interval is the sampling period. Its selection doesnot interfere with the RLS performance once the Nyquist crite-rion is observed [19]. The first of the sinusoids is related to thefundamental phasor. The model described by (11) is not appli-cable for the RLS algorithm. The parameters are not linearwith respect to the model . Thus, the model is rewritten as

(12)

where and are related to the model (11) through equa-tions

(13)

(14)

Equation (12) can compactly be written as

(15)

where is a vector of regressors given by

(16)

and is a vector of parameters to be determined and whoseelements are given by

(17)

It should be noted that the subscript in refers to theestimation of the parameters carried out for the instant .For instance, the element is the estimation of for theinstant .The discordance between the data signal and its model

at a given instant is the prediction error , provided by

(18)



Fig. 3. Flowchart for the proposed method.

The RLS algorithm updates the estimation for the parametersaccording to the following equation:

(19)

where is a gain given by

(20)

and is the so-called covariance matrix which is updated bythe following recursive equation:

(21)

Before the algorithm is triggered, the initial covariance ma-trix must be adjusted [20]. Usually, this initial matrix is set tobe diagonal with the elements that have high values in compar-ison with the values of the parameters to be estimated. Then,this matrix has a higher norm in a sense that it has greater ca-pability to modify a norm of a vector which is multiplied by it.During the RLS application, as the estimative converges for thetrue values of the parameters, the norm is reduced. Hence,this algorithm is not intrinsically adaptive. In order to provideadaptability for the RLS, it must be added to some mechanismwhere the covariance matrix is updated so that its norm valueis always within an adequate range. The technique selected inthis paper is designated modified random walking (MRW) [19].

In this technique, the covariance matrix is updated according tothe following rule:

(22)

where and are arbitrarily adjusted. This algorithm’s struc-ture is suitable for the proposed flux control application. Themonitoring of the error can be used not only to provideadaptability for the RLS, but also to detect the voltage sag.The DVR action must be performed only after the transient

of the parameters estimation. Thus, the next subsection outlinesa simple manner of detecting when the transient is finished, thatis, a mean of detecting the constant level for the parametersestimation.

B. Constant Level Detection

In order to detect a constant level for the parameters estima-tion, one can average an -length moving window for the esti-mation of the amplitude through the equation

(23)

where is the last sample of the amplitude estimation. Thisaverage can be used to compute a sum given by

(24)



Fig. 4. Simulation platform of the DVR system.

This sum tends to be zero whenever the parameters estimationis a constant level. Hence, if is less or equal to a given limitimmediately after a sag detection, one can ensure that the RLSestimation for the parameters, that is, the amplitude and phaseof the sag, has passed its transition time.For each voltage sample, the RLS algorithm computes the

phase and the amplitude which is provided to the con-stant level detector. This detector sets a flag signal to 1 wheneverthe parameters estimation is stable. On the instant that the pa-rameters start changing, the RLS sets the flag signal to 0. There-fore, the flag signal can be used as an enable signal to the DVRaction. The compensating voltage is injected by the DVR as

if flagif flag

(25)

where is the difference between a reference value andthe estimated .The constant level detection procedure imposes the sampling

rate to be fast enough so that a given constant level is detectedwith no critical delay in comparison with the fundamental cycle.In the simulations and experiments, the sampling frequency hasbeen set in 10 kHz and the moving average has been carriedout with five samples.

IV. SIMULATED RESULTS

In order to test the performance of the proposed algorithm,a DVR system has been simulated by using the packages Sim-PowerSystems and Simulink from Matlab. Thus, the simulationis comprised of a three-phase load which is fed by a three-phasevoltage source and is protected by the DVR, as depicted inFig. 4. Table I shows the parameters used for the simulation.The filter parameters are computed so that the cutoff frequencyis around 890 Hz.In the figure, it can be observed that the compensating voltage

is injected by means of a four-leg voltage-source inverter (VSI)controlled by a pulsewidth-modulation (PWM) strategy. Thefour-leg VSI allows the compensating voltages to be unbalanced[21]. The VSI voltage output is passed through an LC filter. TheRLS block incorporates the procedure for detecting whether the

TABLE ISIMULATED SYSTEM PARAMETERS

RLS estimation for the amplitude and phase is stabilized. It alsoencloses the logic to enable the RLS through the flag signal.Three different scenarios of voltage sags have been simu-

lated. For the first case, consider that a three-phase grid is undera phase-to-phase sag during 58 ms, as illustrated in Fig. 5(a).Fig. 5(b) shows the least-squares amplitude estimation forphase-A. Besides the amplitude, the least-squares algorithmalso estimates the angle . Moreover, the estimation enablesdetection where the changing in the estimation starts and whereit is finished by means of a flag signal. In Fig. 5(b), theseinstants are indicated by the dashed line. We can highlight fourinstants. The first two are related to the beginning of the sag andthe last two are associated with the end of the sag. Recall thatthe compensating voltage is not triggered while the amplitudeand phase are varying. Fig. 5(c) shows the injected voltage bythe DVR for the two sagged phases. It is worth noting that theinjected voltage for phase-A is ignited at the instant where theestimation for the phase-A amplitude is stabilized. Althoughnot shown in this figure, the same is true for the other phase.Fig. 5(d) shows the flux linkage associated with each phase.The fluxes for the two phases do not exceed the limit of 0.38Wbturn, given in Table I. Fig. 5(e) shows the corrected voltagesapplied to the load.In the second case, the voltage sag is depicted by Fig. 6(a)

where it is shown that a phase-to-phase fault for an angleis different from the previous one. Fig. 6(b) shows the ampli-tude estimation carried out by the least-squares algorithm forphase-A. Again, the instants where the sag is initiated and fin-ished are highlighted by the dashed line. Fig. 6(c) shows a setof four curves of voltages injected by the DVR into the grid.



Fig. 5. Simulated results for the DVR system: Case I. (a) Voltage sags onphases A and B. (b) Amplitude estimation of phase-A. (c) Compensating volt-ages injected by the DVR. (d) Flux linkages in the transformers. (e) Correctedvoltages applied to the load.

The dashed curves are the compensating voltages that would beinjected without any control for the saturation. The solid linesrepresent the compensating voltages restrained by the control ofsaturation proposed in this paper. Fig. 6(d) shows four curvesfor the fluxes within the transformers. The dashed curves arethe ones obtained without control of flux saturation. The solidones are obtained through the usage of the proposed algorithm.One verifies in this case that the solid lines do not surpass the ex-ceeding limits opposed to the situation depicted with the dashedlines. Nevertheless, they still include a dc component. Fig. 6(e)show the voltages applied to the load.The third case simulates a sag for single phase, as depicted in

Fig. 7(a). Similar to the other cases, Fig. 7(b) shows the RLS am-plitude estimation for the sagged phase voltage. Fig. 7(c) showsthe dashed curve for the voltage without any constraint with thecontrol of saturation, and the solid line represents the compen-sating voltage constrained by the proposed control of satura-tion. We verify that the difference between the curves is con-fined to the first quarter of the cycle. The flux curves associatedwith these voltages are shown in Fig. 7(d). One can note thatthe flux associated with the constrained voltage and representedby the solid line does not include any dc component. This hap-pens because unlike the second case, the condition described in

Fig. 6. Simulated results for the DVR system: Case II. (a) Voltage sags onphases A and B. (b) Amplitude estimation of phase-A. (c) Compensating volt-ages injected by the DVR. (d) Flux linkages in the transformers. (e) Correctedvoltages applied to the load.

(9) is not verified and the compensating voltage must be givenaccording to (10). This ensures that the dc component is com-pletely removed. The voltages applied to the load are sketchedin Fig. 7(e).

V. EXPERIMENTAL RESULTS

In order to test the performance of the proposed method inpractice, a DVR system has been set up in the laboratory. Fig. 8shows the photographs of the system. The experimental appa-ratus is composed of a stage of power and the other stage ofsignal and data acquisition (DAQ) is shown, respectively, inFigs. 8(a) and (b). With regards to the stage of power, the maincomponent is the voltage-source inverter (VSI), composed offour legs. The dc link is made out of four capacitors of 2200F/450 V equivalent to 2200 F/900 V. The modulated volt-ages are filtered by an LC filter for each phase. The values for thecomponents are the same as those presented in Table I. The loadsare made of power resistors. The DAQ system is formed of Hallsensors for voltages and currents. The signal processing is car-ried out by a Texas Instruments digital signal controller (DSC)TMS320F28335. The core of the series transformers used by theDVR system is made of ferromagnetic grain-oriented material



Fig. 7. Simulated results for the DVR system: Case III. (a) Voltage sag onphase-A. (b) Amplitude estimation of phase-A. (c) Compensating voltage in-jected by the DVR. (d) Flux linkage in the transformer. (e) Corrected voltagesapplied to the load.

in toroidal shape. These characteristics minimize the leakage in-ductance. The transformer is rated 1 kVA and the ratio of turnsof the secondary to the primary circuit is 1:1.The first result shown in this section is in regards to the de-

termination of the saturation value for the DVR’s transformers.Toward this purpose, it has been set a measurement circuit withcapacitors and resistors. Fig. 9 shows the experimental resultfor the hysteresis curve for the transformer. The extreme pointsof this curve represent the beginning of saturation. To the rightof this curve, the extreme point is (5.94;37.90) V. The secondcoordinate is relative to the maximum value of the flux ,which is 0.38 Wbturn.Fig. 10 summarizes three different cases of voltage sags cor-

rected by the DVR system. In the first case, the compensatingvoltages constrained (solid) and nonconstrained (dashed) startat 15 ms as shown in Fig. 10(a). The associated flux curvesare shown in Fig. 10(d). It can be noticed that the dashed fluxcurve exceeds theminimum limit. Bymeans of (5), the proposedmethod predicts, at 15 ms, whether the flux will exceed the im-posed limit. Thus, through (6), a form factor to restrain thecompensating voltage is computed and its related flux linkageis shown by the solid line.

Fig. 8. Experimental dynamic voltage restorer. (a) Power stage. (b) Controland acquisition system.

Fig. 9. Experimental hysteresis curve of the transformer (H. ch. 5 V/div, V.ch. 20 V/div).

Fig. 10(b) depicts a situation where the compensating voltagethat is not constrained leads the flux to exceed the maximumlimit. Again, an adequate form factor is computed and appliedto the voltage during the half fundamental cycle. This procedureshifts down the flux to its allowed limit, as shown in Fig. 10(e)(solid line).Fig. 10(c) outlines two curves. The dashed curve represents a

full voltage compensation which is associated with the dashedcurve shown in Fig. 10(f). Constraining the compensatingvoltage by the form factor would result in the dashed-dottedflux curve also shown in Fig. 10(f), which is out of the al-lowed lower limit. The solid curve in Fig. 10(c) is the voltageconstraint according to (10). This voltage result in a flux isrepresented by the solid line in Fig. 10(f), which is within theallowed limits.

VI. CONCLUSION

This paper has proposed a method for controlling flux satu-ration in transformers used by a DVR system. The DVR systemmakes use of an RLS algotithm to compute the compensatingvoltage. The method relies on the correct computation of thecompensating voltage phasor which is constrained wheneverit can provoke saturation. The compensation is never rendered



Fig. 10. Experimental DVR compensations and their associated flux-linkage curves. (a)– (c) Compensating voltages with and without the control of saturation.(d)–(f) Associated flux-linkage curves.

while the RLS amplitude phasor estimation is varying. Hence,the RLS algorithm is combined with a technique for detectingwhether the estimation for the amplitude reached a constantvalue. This ensures that the compensating voltage is always ata proper level. In some cases, this is performed at a cost of notcompletely compensating the sag for a certain period of time.Yet, this is a compromise solution to be applied to loads whichcan withstand some level of sag within a limited period. Themethod has been put on test by simulations of different scenariosof voltage sags. In addition, a DVR prototype, including the pro-posed method, has been set up. For the studied cases, the resultsshow that the load voltages are properly corrected in less thanone fundamental cycle, which is a quite satisfactory time for alarge class of loads.

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Darlan A. Fernandes (S’07–M’08) received theB.S. degree in electrical engineering from the Fed-eral University of Paraı́ba, Campina Grande, Brazil,in 2002, and the M.S. and Ph.D. degrees in electricalengineering from the Federal University of CampinaGrande, Campina Grande, Brazil, in 2004 and 2008,respectively.From 2007 to 2011, he was a Professor with the In-

dustry Department in the Federal Center of Techno-logical Education, Rio Grande do Norte, Brazil. Cur-rently, he is an Assistant Professor with the Depart-

ment of Electrical Engineering, Federal University of Paraı́ba. His research in-terests are in the applications of power electronics in distribution systems, powerquality, and photovoltaic systems.

Fabiano F. Costa (M’07) received the B.S. degreein electrical engineering from the University of SãoPaulo, São Paulo, Brazil, in 1997, the M.S. degree inelectrical engineering from the Federal University ofParaı́ba (UFPB), Campina Grande, Brazil, in 2001,and the Ph.D. degree in electrical engineering fromthe Federal University of Campina Grande (UFCG),Campina Grande, Brazil, in 2005.Currently, he is an Assistant Professor with the De-

partment of Electrical Engineering, Federal Univer-sity of Bahia, Salvador, Brazil. His current research

interests include applications of digital signal processing for distributed gener-ation, islanding techniques, and real-time digital simulation of power systems.

Montiê A. Vitorino (S’11–M’13) was born inCampina Grande, Paraiba, Brazil, in 1983. Hereceived the B.Sc., M.Sc., and Ph.D. degrees inelectrical engineering from the Federal University ofCampina Grande, Campina Grande, Paraiba, Brazil,in 2007, 2008, and 2012, respectively.From 2011 to 2012, he was a Scholar with the

Center for Power Electronics Systems, VirginiaPolytechnic Institute and State University, Blacks-burg, VA, USA. From 2012 to 2013, he was with theDepartment of Electrical Engineering, Center for Re-

newable and Alternative Energies, Federal University of Paraiba (UFPB), JoaoPessoa, Brazil, where he was an Assistant Professor of Electrical Engineering.Since 2013, he has been with the Department of Electrical Engineering, Centerof Electrical Engineering and Informatics, Federal University of CampinaGrande (UFCG), Campina Grande, Brazil, where he is currently an AssistantProfessor of Electrical Engineering. His research interests include electricalmotor drives, power electronics, and renewable energy.

A Method for Averting Saturation From Series Transformers of Dynamic Voltage Restorers

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