Smanjenje Udarnih Struja Uklopa Trofaznog Energetskog Transformatora

8/12/2019 Smanjenje Udarnih Struja Uklopa Trofaznog Energetskog Transformatora

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350Petrovi, G., Kili, T., Bego, O., Smanjenje udarnih struja , Energija, god. 57 (2008 ), br. 3., str. 350-367Petrovi, G., Kili, T., Bego, O.,Reduction The Inrush Currents , Energija, Vol. 57 (2008 ), No.3, pp. 350-367

SMANJENJE UDARNIHSTRUJA UKLOPA

TROFAZNOG ENERGETSKOGTRANSFORMATORAREDUCTION OF THE INRUSH

CURRENTS OF THREE-PHASEPOWER TRANSFORMERS

Goran Petrovi Tomislav Kili Ozren Bego, Split, HrvatskaUdarne struje koje se javljaju prilikom uklopa energetskog transformatora

mogu dosei vrlo velike iznose te uzrokovati mnogobrojne problemeu elektroenergetskom sustavu. Za istraivanje ove pojave razvijen je

matematiki model transformatora s uraunatim efektima zasienja,histereze i zaostalog magnetskog toka, a opisan je i algoritam za odreivanje

povoljnog trenutka uklopa s ciljem smanjenja udarnih struja. Za metodumjerenja zaostalog magnetskog toka, predloena je integracija napona

sekundara pri prethodnom isklopu. Realizirana je laboratorijska maketa

sustava za upravljani uklop trofaznog transformatora na kojoj su mjerenjempotvreni rezultati simulacija.Inrush currents that occur during the energization of a three-phase power

transformer can reach very high values and cause many problems in anpower system. A mathematical model of a transformer has been devel-

oped for the investigation of this problem, taking into account the effects ofsaturation, hysteresis and remanent magnetic ux. An algorithm has beendescribed for the determination of the optimal instant of energization, withthe goal of reducing inrush currents. As a method for measuring remanentmagnetic ux, integration of the secondary voltage during the previous de-

energization is proposed. A circuit model has been prepared of a system forthe controlled energization of a three-phase transformer in which the simu-

lation results are con rmed by measurement.Kljune rijei: petlja histereze, remanentni magnetizam, struje uklopa,

transformatorKey words: hysteresis loop, inrush current, remanent magnetism,

transformer


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Petrovi, G., Kili, T., Bego, O., Smanjenje udarnih struja , Energija, god. 57 (2008 ), br. 3., str. 350-367Petrovi, G., Kili, T., Bego, O.,Reduction The Inrush Currents , Energija, Vol. 57 (2008 ), No.3, pp. 350-367 352

1 UVOD

Neupravljani uklop transformatora praen jevelikom nesimetrijom tokova u eljeznoj jezgri.Kao posljedica takvih nesimetrinih tokova jav-ljaju se velika izoblienja valnog oblika strujemagnetiziranja, vrlo velike udarne struje uklo-pa, te vrlo velike istosmjerne komponente struje[1] i [2]. Problemi uzrokovani udarnim strujamauklopa mogu izazvati kvarove ili pogrean radosiguraa, zatitnih releja ili drugih vrsta zatitau elektroenergetskom sustavu. Udarne strujeuklopa mogu izazvati i mehanika oteenja.Maksimalni iznos udarne struje uklopa moedosei i deseterostruki iznos nazivne strujetransformatora, a mogua je pojava struja uklo-pa iznosa 90 % struje kratkog spoja [3]. Ovi naj-gori sluajevi mogu se oekivati u otprilike 10 %uklopa. Kao posljedica izoblienja valnog oblikanapona tjekom prijelazne pojave mogu nastatioteenja na osjetljivim troilima spojenim namreu.Konano, sve navedeno pridonosi bitnomsmanjenju kakvoe elektrine energije u mrei.

Navedeni problemi pri uklopu transformatoramogu se izbjei upravljanim uklopom. U ovomradu obraena je metoda odreivanja optimal-nog trenutka uklopa na osnovi trenutanog na-pona mree odnosno njegove faze i zaostalogmagnetskog toka iz prethodnog isklopa. U svr-hu istraivanja optimalnog trenutka uklopa na-pravljen je matematiki model transformatora

s uraunatim efektom zaostalog magnetizma.Takoer je izraena i laboratorijska maketa nakojoj su mjerenjem potvreni rezultati simula-cija.

2 POJAVA UDARNIH STRUJA

Magnetski tok u jezgri transformatora razmje-ran je integralu napona napajanja, to znai daza njim zaostaje za 90. Ako se transformatoruklopi u trenutku prolaska napona kroz nuluonda je maksimalni magnetski tok dvostrukovei od nazivnog, a tome se pridoda i zaostalimagnetski tok. Amplituda toka uvijek je ista, alitok posjeduje istosmjernu komponentu ije tra- janje ovisi o radnom i induktivnom otporu kruga[4]. Na slici 1 prikazana je ovisnost elektrinihi magnetskih veliina u nelinearnom magnet-skom krugu i naelni prikaz formiranja unutar-nje putanje magnetiziranja(oznaeno crvenombojom). Maksimalni tok oznaen je tokom 1.Kako se u toj toki mijenja derivacija magnet-skog toka, ta toka pripada vrhu odgovarajueputanje magnetiziranja, a odgovarajua strujamagnetiziranja oznaena je tokom 1. Kao po-sljedica ekstremnog zasienja, omjer udarnestruje uklopa i nazivne struje magnetiziranja

1 INTRODUCTION

Random power transformer energization is accom-panied by high asymmetry of the ux in the iron core.Due to such ux asymmetry, signi cant distortion ofthe magnetizing current waveform, very high inrushcurrents and a very high DC component of the inrushcurrents occur [1] and [2]. Problems caused by inr-ush currents can result in unnecessary failures orthe blowing of fuses, tripping of protective relays andother types of protective devices in an power system.Inrush currents can also cause mechanical damage.Maximum inrush currents can reach ten times theamount of the rated current of a transformer as wellas 90 % of the short-circuit current [3]. These worst-case scenarios can be anticipated approximately 10% of the time. As a consequence of the distortion ofthe voltage waveform, damage may occur duringthe transient state to the sensitive loads connectedto the network. Finally, all the aforementioned con-tributes to a signi cant reduction in the quality of theelectricity in the network.

Such problems during the energization of a tran-sformer can be avoided by controlled energization.In this article, a method is discussed for determiningthe optimal instant of energization(switching on) ba -sed upon the instantaneous network voltage, i.e. itsphases, and the remanent magnetic ux from theprevious de-energization. For the investigation of theoptimal instant of energization, a mathematical mo-del of a transformer was derived, incorporating the

calculated effect of remanent magnetism. Further-more, a circuit model was developed for con rmingsimulation results by measurement.

2 THE PHENOMENON OF IN-RUSH CURRENTS

Magnetic ux in the transformer core is proportionalto the integral of the supply voltage, which meansthat it lags 90 behind the voltage. If the transfor-mer is energized at the instant when the voltagegoes through zero, the maximum magnetic ux istwo times that of the rated magnetic ux, to whichthe remanent magnetic ux is also added. The am-plitude of the ux is always the same but the uxhas a dc component, the duration of which dependson the active and inductive circuit resistance [4]. InFigure 1, the relation between the electric and ma-gnetic parameters in a nonlinear magnetic circuit ispresented as well as the principle of the formationof internal minor magnetization trajectories(indica-ted in red). The maximum ux is indicated by Point1. Since the derivation of the magnetic ux changesat Point 1, it corresponds to the peak of the corres-ponding magnetization trajectory and the corres-ponding magnetizing current is indicated by Point 1.As a consequence of extreme saturation, the ratio


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Petrovi, G., Kili, T., Bego, O., Smanjenje udarnih struja , Energija, god. 57 (2008 ), br. 3., str. 350-367Petrovi, G., Kili, T., Bego, O.,Reduction The Inrush Currents , Energija, Vol. 57 (2008 ), No.3, pp. 350-367353

Slika 1 Prikaz zavisnosti elektrinih i magnetskih veliina u nelinearnom magnetskom krugu i naelni prikaz formiranja unutarnjeputanje magnetiziranja

Figure 1 The relation between the electric and magnetic values in a nonlinear magnetic circuit and the principle of the formation ofminor magnetization trajectories

vei je nekoliko puta od omjera udarnog toka priuklopu i nazivnog magnetskog toka.

Na istoj slici ilustrirano je nekoliko ciklusa unu-tarnje putanje magnetiziranja. Ako je zaostalimagnetizam iznosa B0, putanja magnetiziranjakree iz toke 0 s pripadajuim koordinatama,H = 0, B = B0. Kako je prirast magnetske induk-cije pozitivan, putanja magnetiziranja formira se

pribliavanjem uzlaznoj grani petlje histerezepotpunog zasienja. Prije dosezanja grane pot-punog zasienja, tj. toke S, promijeni se pred-znak prirasta magnetske indukcije(toka 1), pai putanja magnetiziranja promijeni smjer. Sadase putanja poinje formirati pribliavanjem si-laznoj grani petlje histereze potpunog zasie-nja. Primjenom opisanog algoritma dolazi se utoku 2 u kojoj se ponovo mijenja predznak pri-rasta magnetske indukcije kao i smjer putanjemagnetiziranja. Ovaj proces se nastavlja te se konano, zavr-etkom prijelazne pojave, formira trajna puta-nja magnetiziranja odnosno petlja histereza zanazivni magnetski tok. Ta petlja nalazi se unutarpetlje potpunog zasienja i simetrina je s obzi-rom na ishodite koordinatnog sustava.

3 MATEMATIKI MODEL UK-LOPA TROFAZNOG TRANS-FORMATORA

Matematiki model trofaznog transformatoraizveden je za najee koriteni tip transforma-tora, trostupni(europski ) model kojem su pri-

of the peak inrush current and the rated magneti-zing current is several times greater than the ratio ofthe peak ux at the instant of energization and ratedmagnetic ux.

In the same gure, several cycles of the minor ma-gnetization trajectories are illustrated. If the rema-nent magnetism is B0, the magnetization trajectorystarts from Point 0 with the corresponding coordina-tes, H = 0, B = B0. Since the increment in the magne-tic induction is positive, the magnetization trajectory

is formed by approaching the upward trajectory ofthe fully saturated hysteresis loop, reaching com-plete saturation, i.e. Point S. The sign of the magne-tic induction increment(Point 1) changes, so that themagnetization trajectory changes direction. Now thetrajectory starts to be formed by approaching thedownward trajectory of the fully saturated hysteresisloop. Through the application of the described algo-rithm, Point 2 is reached in which the sign of the ma-gnetic induction increment changes again, as wellas the direction of the magnetization trajectory. This process continues and nally, after the transi-ent phenomena have stopped, a magnetization cu-rve or hysteresis loop at the rated magnetic ux isobtained. This loop is located inside the fully satura-ted loop and is symmetrical regarding the center ofthe coordinate system.

3 MATHEMATICAL MODELOF THE ENERGIZATION OF ATHREE-PHASE TRANSFORMER

A mathematical model of a three-phase transformerwas developed for the most frequently used type oftransformer, the three-legged(European) model in


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Petrovi, G., Kili, T., Bego, O., Smanjenje udarnih struja , Energija, god. 57 (2008 ), br. 3., str. 350-367Petrovi, G., Kili, T., Bego, O.,Reduction The Inrush Currents , Energija, Vol. 57 (2008 ), No.3, pp. 350-367 354

marni namoti spojeni u zvijezdu s nul vodiem[5] i [6]. Sekundar nije potrebno uzimati u obzir jer se opisuje model transformatora u praznomhodu,(otvoren sekundar), to je najnepovoljnijisluaj s gledita udarnih struja uklopa.

3.1 Naponske jednadbeNa slici 2 prikazana je pojednostavljena shematrostupnog trofaznog transformatora s primar-nim namotima spojenim u zvijezdu s nul vodi-em.

Jednadbe elektrinog kruga za navedeni tran-sformator su:

gdje je: N broj zavoja primarnog namota, R djelatni otpor primarnog namota, L

rasipna reaktancija primarnog namota.

Vektoriu , i , predstavljaju napon, struju i ma-gnetski tok.

Svakom stupu magnetske jezgre odgovara je-dan tok, 1, 2, 3. Suma tokova daje tok 0 kojise zatvara kroz zrak. Magnetski krug trofaznogtrostupnog transformatora moe se prikazatinadomjesnom shemom, slika 3.

which the primary windings are star connected. Thestar point is conducted to a neutral conductor [5] and[6]. It is not necessary to take the secondary windinginto consideration because the transformer modeldescribed operates under no load(open secondary),which is the worst-case scenario from the viewpointof inrush currents.

3.1 Voltage equationsIn Figure 2, a simpli ed diagram is presented of athree-legged three-phase transformer whose pri-mary windings are star connected.

The electric circuit equations for the transformer areas follows:

where:

N the number of turns of the primary winding, R the active resistance of the primary winding, L

the leakage reactance of the primary winding.

Vectorsu , i , and represent voltage, current andmagnetic ux.

Each ux corresponds to a leg of the magnetic core, 1, 2, 3. The sum of the uxes yields the ux 0 whi-ch is closed through the air. The magnetic circuit ofthe three-legged three-phase transformer can berepresented by an equivalent diagram, Figure 3.

Slika 2 Pojednostavljena shema trofaznog transformatora u praznom hoduFigure 2 A simpli ed diagram of a three-phase transformer operating under no load

(1)

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t L

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t N R

dd

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333

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222

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111

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i i i u

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Petrovi, G., Kili, T., Bego, O., Smanjenje udarnih struja , Energija, god. 57 (2008 ), br. 3., str. 350-367Petrovi, G., Kili, T., Bego, O.,Reduction The Inrush Currents , Energija, Vol. 57 (2008 ), No.3, pp. 350-367355

Neka je presjek magnetske jezgreS konstantan.Duljinel 1, l 2, l 3 su srednje duljine magnetskogputa odgovarajueg stupa. Na temelju nado-mjesne sheme prikazane na slici 3, mogu sepostaviti jednadbe magnetskih krugova trofa-znog trostupnog transformatora. Uz usvojeneoznake:

jednadbe magnetskih krugova su:

Zbog nelinearne ovisnosti izmeu magnetskogpolja i magnetskog toka, odnosno magnetske

indukcije rjeavanje sustava jednadbi(1) i (3) mogue je samo numerikim postupcima. Po-znavajui iznos i tendenciju magnetskog toka( 0d

d>

t ili 0dd

t or 0dd

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Smanjenje Udarnih Struja Uklopa Trofaznog Energetskog Transformatora