A METHOD FOR CHARACTERIZATION OF THREE-PHASE UNBALANCED DIPS FROM RECORDED VOLTAGE WAVESHAPES

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1 A METHOD FOR CHARACTERIZATION OF THREE-PHASE UNBALANCED DIPS FROM RECORDED OLTAGE WAESHAPES M.H.J. Bollen, L.D. Zhng Dept. Eletri Power Engineering Chlmers University of Tehnology, Gothenurg, Sweden Astrt: A proposl is presented for hrteriztion of voltge dips s experiened y threephse lod. The uthors propose this method for inlusion in interntionl stndrds nd reommendtions. The method is sed on the well-proven theory of symmetril omponents. The primry result of the method is so-lled "hrteristi mgnitude" whih orresponds to the mgnitude (remining voltge) s used for the existing methods to hrterize dips experiened y single-phse lod. The proposed method my e extended y dding dditionl prmeters where further ury is needed for hrteriztion. For three-phse lned dips the proposed method orresponds to the methods urrently in use nd reommended y interntionl stndrds.. Introdution All existing stndrd douments on voltge dips (sgs) hrterize dip through one mgnitude (remining voltge or voltge drop) nd one vlue for the durtion [6,7,8]. There re ovious limittions to this method s one e.g. neglets the phse-ngle ump [] nd the post-fult dip []. For the mority of sensitive single-phse equipment, the existing hrteriztion enles predition of the ehvior of the equipment during nd fter the event. Further, the phse-ngle ump n e inorported y using omplex dip voltge; the post-fult dip n e inorported y giving the mgnitude s funtion of time. Three-phse equipment will typilly experiene three different mgnitudes, s the mority of dips re due to single-phse or phse-to-phse fults. The existing method of hrteriztion uses the lowest of the three voltges nd the longest durtion. An exmple of three-phse unlned dip is shown in Figure. oltge in pu Time in yles Figure, exmple of three-phse unlned dip. Dip hrteriztion is often prt of the voltge hrteristis / power qulity in generl. In tht se, the results should e pplile oth to single-phse nd three-phse equipment. Using the

2 lowest of the three voltges to hrterize the dip will result in erroneous results for oth singlephse nd three-phse equipment. An lterntive tehnique is proposed in this doument, whih enles hrteriztion through one omplex voltge, without signifint loss of informtion. The method is sed on the deomposition of the voltge phsors in symmetril omponents. An dditionl hrteristi is introdued to enle ext reonstrution of the three omplex voltges. The mthemtis ehind the method nd dditionl exmples re desried in [,,5,9,,].. Bkground.. Bsi Clssifition A lssifition of three-phse unlned dips ws proposed in [5]. The lssifition onsiders three- phse, single-phse nd phse-to-phse fults, str nd delt-onneted equipment nd ll types of trnsformer onnetion. It ws further ssumed tht positive nd negtive-sequene soure impednes re equl. This resulted in four types of three-phse unlned sg, shown s phsor digrm in Figure. Type A is due to three-phse fults, types B, C nd D re due to single-phse nd phse-to- phse fults. Type B ontins zero-sequene omponent whih is rrely trnsferred down to the equipment terminls. Three-phse equipment is normlly onneted in delt or in str without neutrl onnetion. Single-phse low-voltge equipment is onneted etween phse nd neutrl, ut the numer of dips originting in the low-voltge system is smll. Therefore the vst mority of three-phse unlned dips t the equipment terminls re of type C or type D, so tht distintion etween type C nd D is suffiient, together with hrteristi mgnitude nd phse-ngle ump. The definition of hrteristi mgnitude nd phse-ngle ump is suh tht these do not hnge when the sg trnsfers from one voltge level to the other. The hrteristi mgnitude nd phse-ngle ump re defined s the solute vlue nd the rgument of the omplex phsor representing the voltge in the lowest phse for type D dip, nd the voltge etween the two lowest phses for type C dip. Type A Type B Type C Type D Figure, four types of three-phse unlned voltge dips in phsor- digrm form. The omplex voltges for three-phse unlned dip of type C with hrteristi voltge re s follows:

3 () For dip of type D the omplex voltges re: ().. Generliztion A sound mthemtil sis for the ove lssifition is given in [,,], inluding generliztion tht holds when positive nd negtive-sequene soure impednes re different. This extension of the lssifition is sed on the theory of symmetril omponents. The three (omplex) phse voltges in n unlned three-phse system n e ompletely desried through three omponent voltges, known s symmetril omponents. Positive-sequene voltge, negtive-sequene voltge nd zero-sequene voltge re lulted from the omplex phse voltges, nd s follows: () where. Knowing the omplex sequene voltges, the voltges in the three phses n e lulted from: () Compring () with () nd (), shows tht the following reltions hold for dip of type C: (5) The equivlent expressions for dip of type D re: (6)

4 In the proposed hrteriztion method these reltions re used to otin the hrteristi omplex voltge. The underlying ssumption for (5) nd (6) is tht positive nd negtivesequene soure impednes re identil. As this is not extly the se in relity, seond dip hrteristi is introdued: the PN-ftor F. For dip of type C the definitions re s follows: F (7) For dip of type D the definitions re s follows: F (8) A method to otin the type of dip from the reorded voltges will e disussed elow... Symmetril Phse Expression () gives the symmetril omponents with referene to phse. Expressions () nd () re vlid for fult in phse or etween phses nd, i.e. with phse s the symmetril phse. Inluding ll three possile symmetril phses results in six (su)types of three-phse unlned dips: C, C, C nd D, D, D. Expression () desries dip of type C; expression () desries dip of type D. Expressions for the omplex voltges of the ll six types re given in Tle. It hs een ssumed tht in ll ses, the positive rel xis is long the -phse preevent voltge. For phsor digrms s shown in Figure, the seletion of the symmetril phse is strightforwrd: the lowest phse for type D, the highest phse for type C. For non-unity PNftor nd non-zero phse- ngle ump, it my eome less ovious whih phse is the symmetril phse. The method proposed in [,] trnsforms phse voltge to symmetril omponents to otin the symmetril phse. Trnsforming the 6 different three-phse unlned dips to symmetril omponents, y using (), results in the expressions for positive-sequene voltge nd negtive-sequene voltge summrized in Tle. Note tht in ll ses the positive rel xis is long the -phse pre- event voltge nd in ll ses expression () hs een used to otin the positive nd negtivesequene voltges (i.e. the symmetril omponent trnsformtion with phse s referene phse). From Tle it follows tht the positive-sequene voltge is type independent. The diretion of the positive-sequene voltge is long the referene xis (phse pre-event voltge in this se) if the rgument of the hrteristi omplex voltge is negleted. The diretion of the negtivesequene voltge depends on the type of dip. By rotting the negtive-sequene voltge over n integer multiple of 6º ll dip types n e otined from one prototype dip. Dip type C hs een hosen s prototype dip. From Tle, the following reltion etween positive nd negtive sequene voltge is otined for the prototype dip:, ref (9)

5 TABLE, COMPLEX OLTAGES FOR THREE-PHASE UNBALANCED DIPS Type C Type C Type C Type D Type C Type D TABLE, SYMMETRICAL COMPONENTS FOR THREE-PHASE UNBALANCED DIPS. Type C Type D Type C Type D Type C Type D The dip type my e otined from the ngle etween the negtive-sequene voltge of the mesured dip nd the negtive-sequene voltge of the prototype dip. Due to vrious pproximtions mde nd mesurement errors, this ngle is not extly n integer multiple of 6º so tht the following expression my e used to otin the dip type: ( ) o 6, ngle round k () k: type C k: type D k: type C k: type D k: type C k5: type D

6 Knowing the dip type, the negtive-sequene voltge n e lulted k to the orresponding vlue for the prototype dip: o k 6 ' e () where k is otined ording to () nd the negtive sequene voltge of the mesured dip. Chrteristi voltge nd PN-ftor F re otined from the expressions for the prototype dip (7): ' F ' ().. Overview of Chrteriztion This method hs een pplied to reorded dips in oth trnsmission ( nd k) nd distriution ( nd k) systems. It ws shown tht the PN-ftor is very lose to unity in trnsmission systems. In distriution systems, the PN-ftor is typilly less thn unity due to the effet of indution motor lod. But even in distriution systems, the PN-ftor is rrely less thn 9% in solute vlue []. The result is tht the hrteristi mgnitude (the solute vlue of the hrteristi omplex voltge ) n e used to hrterize three-phse unlned dips without loss of essentil informtion. Using hrteristi mgnitude nd durtion for three-phse unlned dips, orresponds to the existing lssifition (through mgnitude nd durtion) for single-phse equipment. Where needed the hrteriztion for three-phse unlned dips my e extended in severl wys: the hrteristi phse-ngle ump my e defined s the rgument of the omplex hrteristi voltge in the sme wy s the phse-ngle ump my e used s n dditionl hrteristi for dips experiened y single-phse equipment. the PN-ftor my e used s n dditionl hrteristi in se positive nd negtivesequene soure impednes differ signifintly. This is the se in systems with lrge mount of indution motor lod. the zero-sequene voltge is needed s n dditionl hrteristi for speifi system onfigurtions in omintion with three-phse str-onneted lod. hrteristi mgnitude, hrteristi phse-ngle ump nd PN-ftor my ll e given s funtion of time.. The Proposed Method The proposl is to use hrteristi omplex voltge nd PN-ftor to hrterize three-phse unlned dips. The proposed lgorithm for lssifition nd hrteriztion onsists of numer of steps. It is ssumed tht time-domin smpled dt is ville for the three phses inluding t lest two yles pre-event voltges. I. Determine the voltge frequeny from the pre-event voltge smples. II. Determine voltge phsors for the three phse voltges y using DFT (Disrete Fourier Trnsform) lgorithm. The voltge frequeny is used to otin the phse shift etween the during-event nd the pre-event voltges.

7 III. Otin positive, negtive nd zero-sequene voltges y using expression (). I. Determine if the dip is lned or unlned from the mgnitude of the negtive sequene voltge ompred to the positive sequene voltge.. For lned dips the dip type is A nd the hrteristi voltge equls the positive sequene voltge. I. For unlned dips the dip type is determined from positive nd negtive-sequene voltges y using expression (), hrteristi voltge nd PN-ftor re otined y using expression (). II. A lned dip is fully hrterized through the hrteristi voltge. III. An unlned dip is fully hrterized through dip type, hrteristi voltge, PNftor nd zero-sequene voltge. IX. The hrteristi mgnitude is otined s the solute vlue of the hrteristi voltge. The phse-ngle ump is otined s the rgument of the hrteristi voltge.. Exmple of Chrteriztion The ove-proposed method hs een pplied to the three-phse unlned dip shown in Figure. The rms voltge s funtion of time, for the three voltges, is shown in Figure.. oltge in pu Time in yles Figure, rms voltge versus time for the three voltges in Figure. oltge in pu Time in yles Figure, positive-sequene voltge (solid urve) nd negtive-sequene voltge (dshed urve) for the dip in Figure.

8 Figure shows positive nd negtive-sequene voltge, otined y using expression(). Fult initition tkes ples out 5 yles fter the strt of the reording. Fult lering is.5 yles lter. Before fult initition nd fter fult lering, the negtive-sequene voltge is smll, in other words: the voltges re lned. Note tht the positive-sequene voltge does not immeditely reover upon fult lering. This is proly due to indution motor lod tking lrger urrent when their speed hs dropped elow nominl speed. Figure 5 plots the ngle in the omplex plne etween the negtive-sequene voltge nd the drop in positive-sequene voltge, s used in (). When the negtive-sequene voltge is less thn. pu, the ngle is given smll negtive vlue. This sme threshold is lso used to distinguish etween lned nd n unlned dip. Angulr differene in degrees Time in Cyles Figure 5, ngle etween (omplex) negtive-sequene voltge nd (omplex) drop in positivesequene voltge, for the dip in Figure. From the ngulr differene in Figure 5, the dip type is determined y using (). The result is shown in Figure 6. The integer vlue of the dip type is ording to the list elow (), where dip type 6 is lned dip (Type A). Note tht lso efore the fult, the event is hrterized s type A. This is due to the riterion used to detet type A dip: negtive-sequene voltge less thn. pu. Therefore the norml supply is hrterized s type A dip without voltge drop (% hrteristi mgnitude). From Figure 6 it n e onluded tht the dip shown in Figure is of type C C : drop in phses nd with no drop or minor drop in phse. This is extly s shown in Figure, ut would e hrd for n utomti lgorithm to detet. Also will it not in ll ses e strightforwrd whih is the type of three-phse unlned dip. Around fult initition nd round fult lering the lgorithm indites different dip type. This is due to the method used to otin the omplex phse voltges, whih tkes out one yle for the trnsition. During suh trnsition espeilly the ngle of the omplex voltge my otin unrelisti vlues. The prolem my e solved y inresing the negtive-sequene vlue elow whih the dip is lssified s lned. Other methods my need to e developed for this.

9 Dip Type Time in yles Figure 6, dip type versus time, for the dip in Figure. The positive nd negtive-sequene voltges, together with the dip type, give the hrteristi voltge nd the PN-ftor for the dip. The result is shown in Figure 7. Before fult initition nd fter fult lering, hrteristi mgnitude nd PN-ftor re lmost equl euse the negtive-sequene voltge is very smll. During the fult, oth hrteristi voltge nd PNftor show deresing trend. The PN-ftor is ontinuous, i.e. it does not show ump t fult initition or t fult lering. This ehvior my e explined from the deelertion of indution motor lod during the fult nd their elertion fter the fult. The lower the motor speed, the lower their impedne nd the more the voltge in the system is redued. The PN ftor is thus n indition of the effet of the lod on the voltge dip. This reltion, nd the underlying mthemtil models, re desried in detil in []. oltge in pu Time in yles Figure 7, Chrteristi voltge (solid line) nd PN-ftor(dshed line) for the dip in Figure. 5. Conlusion A new method hs een proposed for hrteriztion of three-phse unlned voltge dips. The result of the hrteriztion is simple hrteristi mgnitude. This single vlue enles predition of the effet of the event on most single-phse nd three-phse equipment. When more detiled hrteriztion of the event is required, dditionl prmeters n e dded. For

10 three-phse lned dips, the proposed hrteriztion orresponds to the methods urrently in use nd reommended y interntionl stndrds [6,7,8]. 6. Referenes [] M.H.J.Bollen, P. Wng, N. Jenkins, Anlysis nd onsequenes of the phse ump ssoited with voltge sg, Power System Computtion Conferene, Dresden, Germny, August 996. [] M.H.J. Bollen, The influene of motor reelertion on voltge sgs, IEEE Trnstions on Industry Applitions, vol., 995, p [] L.D. Zhng, M.H.J. Bollen, A method for hrterizing unlned voltge dips (sgs) with symmetril omponents, IEEE Power Engineering Letters, July 998. [] L.D. Zhng, M.H.J. Bollen, Chrteristis of voltge dips (sgs) in power systems, IEEE Trnstions on Power Delivery, in print. [5] M.H.J. Bollen, Chrteriztion of voltge sgs experiened y three-phse dustle-speed drives, IEEE Trnstions on Power Delivery, ol., no., Otoer 997, pp [6] Eletromgneti Comptiility (EMC), Prt. Testing nd mesurement protools. Setion. oltge dips, short interruptions nd voltge vritions immunity tests. IEC doument 6--. [7] Reommended prtie for evluting eletri power system omptiility with eletroni proess equipment, IEEE Std [8] Mesurement guide for voltge hrteristis, UNIPEDE report Ren 95. [9] M.H.J. Bollen, Understnding power qulity prolems - voltge sgs nd interruptions, IEEE Press, 999. [] L. Zhng, Three-phse unlne of voltge dips, Lientite thesis, Chlmers University of Tehnology, Dept Eletri Power Engineering, Gothenurg, Sweden, Novemer 999. [] M.H.J. Bollen, L.D. Zhng, Anlysis of voltge tolerne of dustle-speed drives for three-phse lned nd unlned sgs, IEEE Trnstions on Industry Applitions, in print.