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PACHET DE PROGRAME MATLAB DEDICAT CALCULULUI SUPRATENSIUNILOR TRANZITORII DE COMUTAIE

DIN REELELE ELECTRICE ALE S.T. CRAIOVA

MATLAB ROUTINES SET FOR COMMUTATIONS OVERVOLTAGES CALCULUS WITHIN THE NETWORK OF S.T. CRAIOVA

Maria BROJBOIU Virginia IVANOV Mihnea LEOVEANU

Universitatea din Craiova, Facultatea de Electrotehnic, Romnia, 200440, Craiova, Bd. Decebal nr. 107, Tel.: +40-251-436447, fax: +40-251-436447,

e-mail: mbrojboiu.elth.ucv.ro, vivanov.elth.ucv.ro, msleoveanu.elth.ucv.ro

Rezumat: Articolul prezint pachetul de programe realizat n Matlab pentru calculul supratensiunilor tranzitorii de comutaie din reelele electrice ale ST Craiova. Algoritmul de proiectare se bazeaz pe particularitile de funcionare ale reelelor electrice din cadrul ST Craiova. Pachetul de programe este realizat n manier interactiv permind utilizatorului selectarea de la tastatur a tipului de supratensiuni de calcul, respectiv tipul liniei electrice. Este posibil, de asemenea, analiza influenei lungimii liniei pn la locul de defect, pe baza reprezentrilor grafice, respectiv analiza influenei fazei iniiale a tensiunii sursei.Nivelul calculat al supratensiunilor este comparat cu performanelede inere ale izolaiei echipamentelor din staii. Keywords: supratensiuni tranzitorii de comutaie, programe interactive de calcul, reele electrice ale ST Craiova

Abstract: The paper deals with the routines set developed inMatlab for the calculus of the commutations transitory overvoltageswithin the network of the S.T. Craiova. The designing algorithm is based on the operation particularities of the network within the S.T. Craiova. The set of routines is developed in an interactivemanner. It allows to the user to select from the keyboard theovervoltage type to be computed, the type of the electric line. It is also possible, based on the graphical results, to analyse the influence of the line length up to the fault and the influence of the initial phase of the sources voltage. The computed overvoltagesare compared with the holding performances of the insulations of the equipments in the stations. Keywords: commutations transitory overvoltages, interactive routines, ST Craiova.Network

1. Introducere Calculul supratensiunilor de comutaie n reelele de

nalt tensiune, care apar ca urmare a deconectrii, de exemplu, a unei linii n gol, unei sarcini inductive sau ca-pacitive, sau n cazul apariiei fenomenelor de rezonan, este dezvoltat pe larg n literatura de specialitate [1], [2], [3].

Metodele de evaluare a supratensiunilor sunt, deasemenea, bine dezvoltate, ncepnd cu metode de calcul analitic, pe baza unui model matematic, adoptat cu ajutorul unei scheme de calcul simplificate i sfrind cu metode directe de determinare a supratensiunilor prin ncercri n sistem. Dintre metodele analitice de calcul, metoda trans-formrilor integrale, respectiv utilizarea transformateiLaplace, este cea mai extins, ca utilizare. Funciile originalale tensiunilor se pot determina fie folosind teoremelecalculului operaional, pentru calculul exact, fie metode de calcul aproximativ, cum este metoda caracteristicilor de frecven.

Articolul prezint un program de calcul automat al supratensiunilor la deconectarea transformatoarelor n gol, la deconectarea/conectarea liniei lungi n gol necom-pensat i calculul supratensiunilor temporare de rezonan.

1. Introduction The calculus of the commutations overvoltages in the

high voltage network, that appear due, as example, to the disconnection of a no load line, of an inductive or capacitiveload, or when resonance appears, is deeply developed in the literature [1], [2], [3].

The evaluation methods of the overvoltages are also well developed, starting from analytical ones, based on a mathematical model of the system, obtained starting from a simplified diagram and arriving to the direct methods forthe overvoltages determination, based on direct test on the system. By the analytic methods, the integral transformationmethod, Laplace transformation respectively, is most common.

The original functions of the voltages can be determinedboth by using the operational calculus, for the exact calculusand approximation methods, as the frequency characteristicmethod.

The paper presents an automatic calculus algorithm for the overvoltages due to the no load transformers dis-connection, no load uncompensated long lines disconnectionand for the transitory resonant overvoltages.

1.1. Supratensiuni la conectarea liniilor n gol Calculul analitic al supratensiunii se realizeaz conside-

rnd dou ipoteze: liniile sunt fr pierderi i simultaneitateaconectrii celor trei faze ale ntreruptorului.

1.1. Overvoltages at no load lines connection The analytical calculus of the overvoltage is based on

two hypotheses: the looses are neglected and all the three phases of the breaker are quite simultaneously connected.

The 6th International Power Systems Conference 96

Metoda de calcul utilizat este metoda transformatei Laplace, considernd linia lung cu parametri uniform distribuii. Notnd u2(t) valoarea supratensiunii la captul n gol al liniei conectate, expresia analitic este dat de formula [2]:

The used method is the method of Laplace transfor-mation, by considering the long line with uniform distrib-uted parameters. By denoting he overvoltage at the end of the no load connected line, the analytical expression is given by [2]:

( ) ( ) n2 k kkk 1

u t B sin t B cos t arctg ctg=

= + (1)unde: where:

ms

c

EBLcos sin

Z

= i

2k

k m 2 2kk k

k

1B Ecos

sin

= +

Emvaloarea de vrf a tensiunii sursei; Ls inductivi-tatea sistemului electric conectat la bare; Zc impedana caracteristic a liniei; durata propagrii unui semnal n lungul liniei; ksoluia obinut prin metoda grafic a ecuaiei transcendente: s kk

c

Lctg

Z = .

Em the peak value of the sources voltage; Ls induc-tivity of the electric system on the bars; Zc the charac-teristic impedance of the line; the time of the propaga-tion of a signal along the line; kthe graphical solution of the transcended equation s kk

c

Lctg

Z = .

1.2. Supratensiuni la deconectarea liniilor n gol Utiliznd aceeai metod de calcul, considernd linia

lung cu parametri uniform distribuii, urmtoarele relaii pentru calculul supratensiunilor la sfritul i respectivnceputul liniei n gol sunt aplicabile.

Pentru calculul supratensiunilor de la sfritul liniei s-autilizat relaia [2]:

1.2. Overvoltages at no load lines disconnection By using the same computation method and considering

the long line with uniform distributed parameters, the follow-ing expressions are applicable for the calculus of the over-voltages at the front end and at the end of the no load line.

For the calculus of the overvoltage at the end of the line, the following expression was used [2]:

( ) 2 2n k k2 m 2 2s kk 1 k k

kc

2 2cos tcos tu t E 1L coscos sin

sinZ=

= + + (2)

respectiv, relaia pentru calculul supratensiunilor de lanceputul liniei:

and for the calculus of the overvoltages at the front end of the line respectively

( ) 2 2n k k k1 m m 2 2s kk 1 k k

kc

2 2 cos cos tcos t cosu t E EL coscos sin

sinZ=

= + (3)

1.3. Supratensiuni la deconectarea transformatoarelor n gol

La deconectarea transformatoarelor n gol sau a oricreisarcini mici inductive (cu condiia ca amplitudinea curen-tului s nu depeasc valoarea de 100A [3]), este posibil ca ntreruperea s devin efectiv la o valoare a curentului diferit de zero. Prin urmare, la deconectarea unui astfel de curent este posibil apariia unei supratensiuni, datorit smulgerii de curent. Fenomenul se ntlnete la transforma-toarele cu neutrul legat la pmnt iar analiza producerii supratensiunilor se poate face folosind o schem echivalentmonofazat, n care se neglijeaz rezistenele i decalarea momentelor ntreruperii pe cele trei faze.

Amplitudinea supratensiunilor se determin din bilanulenergetic, scris cu considerarea pierderilor, prin introducereaunui coeficient de restituire subunitar ( = 0,30,5):

1.3. Overvoltages at no load transformers disconnectionAt no load transformers disconnection, or any small

inductive load (with current no more than 100 A [3]), it is possible that the breaking to become effective at non zero current. Thus, when such current is disconnected, it is possible that overvoltages appear, due to the current cutting.This phenomenon appears when transformers with grounded neutral are disconnected. The analysis of the overvoltages generation can be performed by using an equivalent mono-phased diagram with no resistances and different breaking instants on the three phases.

The amplitude of the overvoltages can be determined by using an energetic balance, with the looses taken into account by the way of a subunit restitution coefficient (=0,30,5):

2

2 2 2T2max 2 2

T T

L UU U cos sinC L

= + (4)

22 2 2T

2max 2 2T T

L UU U cos sinC L

= + (4)

03-04.11.2005, Timioara, Romania 97

unde: LT, CT reprezint inductivitatea de magnetizare, res-pectiv capacitatea fa de pmnt a transformatorului, U este tensiunea sursei iar este faza curentului de mag-netizare n momentul producerii deconectrii.

Factorul de supratensiune () rezult:

2

2 22max TU fcos sin fU = = + (5)

Dac smulgerea de curent se produce la curent maxim (cazul cel mai defavorabil), deci / 2 = , se obine factorulde oscilaie:

Tff

= (6)Se observ n acest caz c factorul de oscilaie depinde

de raportul dintre frecvena de oscilaie a supratensiunii care apare la bornele transformatorului i frecvena reelei.Teoretic, acest raport poate ajunge la valori mari (4 sau 5, chiar mai mari). n realitate factorul este redus substanial de apariia reaprinderilor ntre contactele ntreruptorului.

where: LT, CT is the magnetising inductance and the transformer to ground capacitance respectively, U the sources voltage and - the phase of the magnetisingcurrent in the breaking instant.

The overvoltage factor () results:

2

2 22max TU fcos sin fU = = + (5)

If the current cutting arrives when the current ismaximum (the worst case), results that / 2 = and the oscillation factor is

Tff

= (6)We notice in this case that the oscillation factor depends

by the oscillation frequency of the overvoltage that appears at the transformers terminals and by the network frequency. Theoretically, this ratio can reach high values (4 or 5, or even greater). Practically, this factor is much smaller due to the re-ignition between the breakers contacts.

1.4. Supratensiuni temporare de rezonan Aa cum se cunoate, fenomenele de rezonan la

frecvena de funcionare a reelei conduc la apariia unor supratensiuni dac lungimea liniei, considerat fr pierderi,are o valoare important. Fenomenul are loc pe liniaalimentat de la un capt, avnd cellalt capt n gol. Din literatura de specialitate [3] creterea tensiunii la captul n gol a unei linii lungi, care este o supratensiune temporar, poate fi apreciat cu formula:

2si

c

1U Excos l sin lZ

=

, (7)

unde: 0 0L C = ; l este lungimea liniei; xsi este re-actana sursei.

Condiia de apariie a unui regim de supratensiuni foarte periculoase este: si cctg l x / Z = . Pentru o lungime dat regimul este cu att mai periculos cu ct puterea sistemului de alimentare este mai mic. La surs de putere dat, linia este mai aproape de rezonan cu ct lungimea este mai mare. Pen-tru un sistem de putere infinit rezonana are loc la 1500 km.

1.4. Transient resonance overvoltages As known, the resonance phenomenon at operating

frequency of the network determine overvoltages, if the line length is important and the line has no looses. The phenomenon is present on the lines that are supplied at one end and with no load at the other end. The literature [3] gives a relation for the overvoltage at the no load end of the line, that is a transient overvoltage:

2si

c

1U Excos l sin lZ

=

, (7)

where: 0 0L C = ; l the length of the line; xsi the sources reactance.

A quite dangerous overvoltage can appear if ctg l =si cx / Z . For a given length, the phenomenon is as dan-

gerous as the power of the supplying system is smaller. At a given power source, the line is closer to the reso-nance if the length of the line is greater. For an infinite power system, the resonance appears at 1500 km.

2. Descrierea pachetului de programe Pentru calculul automat al regimurilor tranzitorii din

reelele electrice ale ST Craiova, a fost conceput un programde calcul general, folosind Matlab. Programul este conceputntr-o manier interactiv, ceea ce permite utilizatorului selectarea automat a regimului de defect pentru care se calculeaz parametrii.

Programul principal apeleaz la subprograme carepermit: calculul parametrilor supratensiunilor tranzitorii pentru staia i linia selectate (nivelul supratensiunii, factorulde oscilaie i pulsaia); analiza grafic a influenei fazei iniiale a tensiunii sursei asupra supratensiunii tranzitorii; analiza grafic a influenei lungimii liniei asupra supra-tensiunii tranzitorii; analiza grafic a influenei puterii i tensiunii sursei. Subprogramele pot lucra independent sau n cadrul programului general.

2. Programmes set description For the automatic calculus of the transients within the

network of the ST Cariova, a general computing program was developed in Matlab. The program was conceived in an interactive manner, allowing to the user to select the fault regime for which the parameters has to be determined.

The main program runs routines that allow: the calculusof the parameters of the transient overvoltage for theselected station and line (the level of the overvoltage, the oscillation factor and the frequency); the graphical analysison the influence of the voltage initial phase on the transientovervoltage; graphical analysis on the influence of thesources power and voltage. The routines can run within the main program or independently.

Both the main program, TRANZCOMP, and the routines use operational values, classified on the types of generation:


Programul principal TRANZCOMP i subprogramele dezvoltate opereaz cu mrimi operaionale clasificate n funcie de modalitile de obinere: intrare manual mrime operaional de intrare introdus de ctre operator de la tastatur; intrare automat mrime operaional de intrare obinut n timpul rulrii programului; F.C. mrimeoperaional de intrare automat obinut pe baza uneiformule de calcul; T.B. mrime operaional de intrare automat coninut ntr-un tabel stocat n baza de date; intrare flexibil mrime operaional de intrare flexibil a crei valoare variaz n timpul rulrii programului; I.G. mrime de ieire general rezultat n urma rulriipachetelor de programe; I.L. mrime de ieire local rezultat n urma rulrii unui subprogram. Meniul principalal programului este prezentat n figura 1.

manual input operational input value supplied by the user from the keyboard; automat input operational input value obtained during the running of the program; F.C. operational input value obtained based on a calculusformula; T.B. operational input value contained within a table stored in the data base; flexible input operational flexible input value, whose value changes during therunning of the program; ; I.G. general output value, as a result of the running of the programs set; I.L. local outputvalue, as a result of the running of one routine. Figure 1 depicts the main menu of the program.

Fig. 1. Meniul principal al programului Fig. 1. The main menu of the program

Selectarea unui subprogram deschide un submeniu carepermite selectarea liniei sau o analiza grafic.

Pentru cazul n care utilizatorul dorete calculul pentrualt staie sau linie dect cele specificate n cadrul aplica-iilor dezvoltate, au fost elaborate subprograme flexibile ....._MAN.m, care permit introducerea de la tastatur a caracteristicilor staiei, respectiv liniei dorite. Mrimile de intrare manuale introduse de la tastatur sunt: Sn (valoareaputerii de scurtcircuit a sursei [VA]); St (valoarea puterii aparente a transformatorului [VA]); u2n (valoarea tensiunii nominale secundare [V]); u1n (valoarea tensiunii nominale primare [V]); usc (valoarea tensiunii nominale de scurtcircuit[%]); io (curentul de mers n gol al transformatorului [%]);C1 (capacitatea echivalent a transformatorului [F]); second(seciunea conductorului liniei [mm2]); dcond (diametruconductor [mm]); l (lungimea liniei [km]); d12 (distana ntreconductoarele 1 i 2 [m]); d23 (distana ntre conduc-toarele2 i 3 [m]); d31 (distana ntre conductoarele 3 i 1 [m]);rl (rezistena liniei de lungime l []); xc (impedana capa-citiv a liniei de lungime l []); xl (impedana inductiv a linieide lungime l []); R0 (rezistena lineic [/km]); C0 (capa-citatea lineic [F/km]); L0 (inductivitatea lineic [H/km]).

Mrimile de intrare automate sunt obinute pe baza unorformule de calcul: reactana sursei; reactana transforma-torului; rezistena sursei; rezistena transformatorului; pulsa-ia tensiunii de alimentare; factorul de amortizare; impedanacaracteristic; viteza de propagare; constanta de faz.

Mrimile de intrare flexibile sunt coninute n tabele de date sau grafice.

Mrimile de ieire sunt: valoarea supratensiunii; factorulde supratensiune; timpul dup care se obine valoarea maxim; pulsaia (frecvena) supratensiunii tranzitorii.

When a routine is selected, a submenu is opened, that allows selecting the specific line, or the graphical analysis.

If the user wishes to perform the calculus for a differentstation or line than the specified ones, flexible routines were developed ....._MAN.m, that allow to insert from the keyboard the parameters of the station or line. The input values requested to be supplied from the keyboard are: Sn(short-circuit power of the source [VA]); St (aparent powerof the transformer [VA]); u2n (secondary rated voltage [V]);u1n (primary rated voltage [V]); usc (short-circuit rated voltage [%]); io (no-load current of the transformer [%]); C1 (equivalent capacitance of the transformer [F]); second(cross section of the line conductor [mm2]); dcond (conductordiameter [mm]); l (lines length [km]); d12 (distance between the conductors 1 and 2 [m]); d23 (distance between the conductors 2 and 3 [m]); d31 (distance between theconductors 3 and 1 [m]); rl (the resistance of the l length line []); xc (capacitive impedance of the l length line []); xl (inductive impedance of the l length line []); R0(unit resistance [/km]); C0 (unit capacitance [F/km]); L0(unit inductance [H/km]).

The automatic input values are obtained based on certaincalculus formula: sources reactance; transformersreactance; sources resistance; transformers resistance; angular frequency of the voltage source; dumping factor; characteristic impedance; propagation speed; phase constant.

The flexible input values are contained within data tablesor graphics.

The output values are: overvoltage level; overvoltage factor; time of the maximum value; angular frequency of the transient overvoltage.


3. Aplicaii 3.1. Program de calcul al supratensiunilor tranzitorii

la conectarea liniei in gol Programul este aplicat pentru calculul parametrilor

supratensiunii tranzitorii la conectarea liniei n gol, utilizndrelaia (1), pentru liniile electrice Craiova Nord-Slatina 1, Craiova Nord-Turnu Mgurele, Craiova Nord-Ialnia,pentru dou valori ale fazei iniiale ale tensiunii: = 0 i = /2. Parametrii caracteristici ai liniei Craiova Nord-Slatina 1 sunt: puterea aparent a autotransformatoruluiSt = 200106 VA; tensiunea nominal Un = 220103V; lungi-mea linei l = 51 km; rezistena lineic R0 = 7.45110-2 /km;inductivitatea lineic L0 = 1.294510-3H/km; capacitatea lineic C0 = 8.800310-9F/km. Parametrii caracteristici ai liniei Craiova Nord-Turnu Mgurele sunt: rezistena lineicR0 = 6.818210-2/km; inductivitatea lineic L0 = 1.290910-3 H/km; capacitatea lineic C0 = 8.760110-9F/km. Para-metrii caracteristici ai liniei Craiova Nord-Ialnia sunt: re-zistena lineic R0 = 6.737510-2/km; inductivitatea lineicL0 = 1.27710-3H/km; capacitatea lineic C0 = 8.806610-8 F/km. n tabelul 1 sunt prezentate comparativ caracte-risticile supratensiunilor tranzitorii pentru diferite linii electrice n condiiile modificrii fazei iniiale a tensiunii sursei, sursele de alimentare avnd aceiai parametrii.

3. Applications 3.1. Program for the calculus of the transient

overvoltages at no-load line switching on The program is used for computing the parameters of

the transient overvoltage at no-load line switching on, by using the expression (1), for the following lines: Craiova Nord-Slatina 1, Craiova Nord-Turnu Mgurele and CraiovaNord-Ialnia. The calculus is performed for two values of the initial voltage phase: = 0 and = /2. The characteris-tic parameters of the Craiova Nord-Slatina 1 line are: apar-ent power of the transformer St=200106 VA; rated voltageUn = 220103V; lines length l=51km; unit resistanceR0 = 7.45110-2 /km; unit inductance L0 = 1.294510-3H/km;unit capacitance C0 = 8.800310-9 F/km. The characteristic parameters of the Craiova Nord-Turnu Mgurele line are: unit resistance R0 = 6.818210-2 /km; unit inductance L0 = 1.290910-3 H/km; unit capacitance C0 = 8.760110-9F/km. The characteristic parameters of the Craiova Nord-Ialnia line are: unit resistance R0 = 6.737510-2 /km; unit inductance L0 = 1.27710-3H/km; unit capacitance C0 = 8.806610-8 F/km. Table 1 presents the characteristics of the transient overvoltages for the specified lines, for different values of the initial phase of the voltage source. The sourceshave the same parameters.

Tabelul 1 Caracteristicile supratensiunilor tranzitorii

Table 1 The characteristics of the transient overvolatges Un = 220 kV St = 200 MVA

=0 =/2 Linii electrice Lines

ks uc max [kV]

f1 [Hz] ks

uc max [kV]

f1 [Hz]

Ialnia (l = 9,6 km) 1,97 275,67 550 1,091 153,07 550 Slatina 1 (l = 51 km) 1,95 273,34 668 1,06 148,18 668

Turnu Mgurele (l = 121 km) 1,91 267,90 373 1,07 150,38 373

n figurile 3 i 4 sunt prezentate variaiile grafice ale supratensiunilor tranzitorii i componentele acestora pentrulinia electric Craiova Nord-Slatina 1, pentru dou valori ale fazei iniiale ale tensiunii sursei.

Figures 3 and 4 depict the evolutions of the transient overvoltages are their components for the Craiova Nord-Slatina 1 line, for two values of the initial phase of thesources voltage.

Fig. 3. Supratensiunea tranzitorie la conectare i =0 Fig. 3. Transient overvoltage at switching on and =0

Fig. 4. Supratensiunea tranzitorie la conectare, =/2 Fig. 4. Transient overvoltage at switching on, =/2

Se constat, att din datele sintetizate n tabel, ct i din reprezentrile grafice, influena fazei iniiale a tensiunii sur-sei i a lungimii liniei asupra factorului de supratensiune i a momentului atingerii valorii primului vrf al tensiunii tranzitorii.

Both the values presented in the table and the plotted graphics highlight the influence of the initial phase of the sources voltage and of the lines length on the overvoltagefactor and on the first peak transient overvoltage instant.


3.2. Program de calcul al supratensiunilor tranzitorii la deconectarea liniilor n gol

Programul calculeaz parametrii tensiunii tranzitorii la deconectarea liniilor n gol, utiliznd relaia (2) pentrucalculul supratensiunilor de la captul liniei n gol, respectivrelaia (3) pentru calculul supratensiunilor de la nceputul liniei. Se aplic programul pentru dou linile electrice, Craiova Nord-Turnu Mgurele (l = 121km) i CraiovaNordFiliai (l=38km). Parametrii calculai ai supratensiuniitranzitorii pentru linia Craiova Nord-Turnu Mgurele sunt:supratensiunea la captul liniei n gol u2max = 2.5343105V; supratensiunea la nceputul liniei n gol u1max = 1.3446105V;factorul de supratensiune la sfritul liniei ks2 = 3.9489; factorul de supratensiune la nceputul liniei ks1 = 2.0951.Reprezentrile grafice ale supratensiunilor tranzitorii, cores-punztoare acestei linii sunt prezentate n Fig 5. Parametrii calculai ai tensiunii tranzitorii pentru linia Craiova Nord-Filiai sunt: supratensiunea la captul liniei n gol u2max = 2.5137105V; supratensiunea la nceputul liniei n gol u1max = 1.4105V; factorul de supratensiune la captul liniei ks2 = 3.9529; factorul de supratensiune la nceputul liniei ks1 = 2.2016. Reprezentrile grafice ale supratensiunilor tranzitorii, corespunztoare acestei linii sunt prezentate n Fig.6.

3.2. Program for the calculus of the transient overvoltages at no-load line switching off

The program is used for computing the parameters of the transient overvoltage at no-load line switching off, by using the expression (2) for the overvoltages at the end of the line and (3) for the overvoltages at the front end of the line. The program is applied for two lines: Craiova Nord-Turnu Mgurele (l = 121km) and Craiova NordFiliai(l = 38km). The computed parameters of the transient overvoltage for the Craiova Nord-Turnu Mgurele line are: overvoltage at the end of the no-load line u2max = 2.5343105V;overvoltage at the front end of the no-load line u1max = 1.3446105V; overvoltage factor at the end of the line ks2 = 3.9489; overvoltage factor at the front end of the line ks1 = 2.0951. The transient overvoltages for this line are plotted in Fig. 5.

The computed parameters of the transient overvoltage for the Craiova Nord-Filiai line are: overvoltage at the end of the no-load line u2max = 2.5137105V; overvoltage at the front end of the no-load line u1max = 1.4105V; over-voltage factor at the end of the line ks2 = 3.9529; over-voltage factor at the front end of the line ks1 = 2.2016. In Fig. 6 is plotted the transient overvoltages for this line.

Fig. 5. Supratensiunile tranzitorii - linia Turnu Mgurele

Fig. 5. Transient overvoltages - Turnu Mgurele line

Fig. 6. Supratensiunile tranzitorii pentru linia Filiai

Fig. 6. Transient overvoltages for the Filiai line

Rezultatele obinute pentru mai multe lungimi ale linieielectrice au artat c valoarea factorului de supratensiune la captul liniei n gol crete cu creterea lungimii liniei electrice deconectate.

3.3. Program de calcul al supratensiunilor tranzitorii la deconectarea transformatoarelor n gol

Programul realizeaz calculul valorilor supratensiunilorcare apar la deconectarea transformatoarelor n gol utilizndrelaia (4) i a factorului de supratensiune cu relaia (5), pentru diferite staii electrice, de exemplu staia Craiova Nord.

Parametrii transformatorului AT1 sunt: capacitatea de intrare C2 = 1010-9F; puterea nominal Sn = 200106VA; tensiunea nominal Un = 220103V; curentul de mers n golI0 = 3%.

Considernd patru momente diferite pentru deconectareatransformatorului n funcie de unghiul =[0 /6 /4 /2] se obin urmtoarele valori pentru factorul de supratensiuneks=[0.54 1.78 2.46 3.44]. Reprezentrile grafice ale supratensiunilor sunt prezentate n Fig.7.

The results for different lengths of the line highlighted that the overvoltage factor at the end of the line inflates with the length of the switched off line.

3.3. Program for the calculus of the transient overvoltages at no-load transformers switching off

The program is used for computing the parameters of the transient overvoltage at no-load transformer switching off, by using the expression (4) and of the overvoltage factor, by using the (5), for different stations, as Craiova Nord for example.

The parameters of the AT1 transformer are: inputcapacitance C2 = 1010-9F; rated power Sn = 200106VA; rated voltage Un = 220103V; no-load current I0 = 3%.

By considering four different instants for the transformerswitching off ( = [0 /6 /4 /2]), the following values of the overvoltage factor are obtained: ks = [0.54 1.78 2.46 3.44]. The overvoltages are plotted in Fig. 7.


Fig. 7. Supratensiunile tranzitorii la deconectarea transformatoarelor n gol

Fig. 7. Transient overvoltages at no-load transformer switching off

Se observ c valoarea maxim a factorului de supra-tensiune corespunde cazului cel mai defavorabil, cndcurentul de magnetizare trece prin maxim, = /2.

3.4. Program de calcul al supratensiunilor temporare de rezonan

Au fost determinate supratensiunile temporare de rezo-nan pentru mai multe linii ale Staiei Craiova Nord,respectiv staiei nreni, rezultatele obinute fiind pre-zentate n Tabelul 2, unde: 1 Linia Turnu Mgurele; 2 Linia Slatina 1; 3 Linia Ialnia; 4 Linia nreni Bradu.

We notice that the maximum value of the overvoltage factor corresponds to the worst case, when the magnetisingcurrent reaches the peak value, = /2.

3.4. Program for the calculus of the resonant transient overvoltages

The resonant transient overvoltages were computed for different lines within the Craiova Nord station and for nreni station. The results are summarised in Table 2, where: 1 Turnu Mgurele line; 2 Slatina 1 line;3 Ialnia line; 4 nreni Bradu line.

Tabelul 2 Supratensiuni de rezonan pentru diferite linii electrice Table 2 Resonant transient overvoltages for different lines

Parametri de intrare Input parameters

Parametri de ieire Output parameters Linia

Line St [MVA]

Un [kV]

l [km]

R0 [/km]

L0 [H/km]

C0 [F/km]

U2max [kV] ks

lk [km]

1 200 220 121 0,06818 0,00129 8,710-9 129,3 1,018 121 2 200 220 51 0,07451 0,00129 8,810-9 127,7 1,005 51 3 200 220 9,6 0,00673 0,00127 8,810-9 65,55 1,007 9,6 4 400 400 196 0,0339 0,00104 1,0810-8 245,9 1,065 196

Se constat c, datorit valorilor mici ale lungimilorliniilor n raport cu lungimea tipic la care are loc fenomenulde rezonan, factorii de supratensiune sunt foarte mici. n Fig. 8 i 9 s-au reprezentat grafic supratensiunile temporarefuncie de lungime, respectiv s-a evideniat fenomenul de rezonan pentru o linie teoretic cu lungimea de 1500 km.

4. Concluzii

Articolul descrie un pachet de programe n Matlab dedi-cat calculului supratensiunilor de comutaie. Programul este aplicat pentru liniile electrice ale staiei Craiova Nord220kVlinia Slatina 1, Filiai, Turnu Mgurele, Ialnia, i staiei Tnreni 400kVlinia Bradu permind calculul supratensiunilor la deconectarea/ conectarea liniilor n gol, deconectarea transformatoarelor n gol i supratensiuniletemporare de rezonan. Algoritmul de calcul este celprezentat n literatura de specialitate, adaptat condiiilor

We notice that, due to the small lengths of the studied lines, comparing with the typical length of the line when the resonance phenomenon is present, the overvoltagefactors are quite reduced. The Fig. 8 depicts the transient overvoltages versus the length and the Fig. 9 highlight the resonance phenomenon for a theoretical 1500 km line.

4. Conclusion

The paper presents a set of Matlab programs for the calculus of the transient switching overvoltages. Theprogram was applied for the lines controlled by the CraiovaNord 220kV station: Slatina 1, Filiai, Turnu Mgurele, Ialnia lines and by the Tnreni 400kV station: Bradu line. The program allows the calculus of the overvoltages at no-load lines switching on/off, at no-load transformers switching off and of the resonant transient overvoltages. The computing algorithm is based on the literature, special


Fig .8. Maximul supratensiunii de rezonan

Fig. 8. The maximum of the resonant overvoltage

Fig. 9. Fenomenul de rezonan Fig. 9. Resonance phenomenon

concrete privind nivelul parametrilor liniilor electriceanalizate. Programul general de calcul este interactiv i poate fi aplicat, pentru oricare alt staie/linie cu parametri cunoscui.

Rezultatele programului de calcul sunt salvate n fiierede tip text, sau n reprezentri grafice adecvate n scopul evidenierii influenei anumitor parametri, cum ar filungimea liniei sau faza iniial a tensiunii sursei, asupra nivelului supratensiunilor.

Nivelul calculat al supratensiunilor poate fi comparat cu performanele de inere al echipamentelor de comutaie din staii. Din analiza efectuat [4] s-a constatat corectitu-dinea alegerii echipamentelor din staii.

Programul permite evaluarea nivelului supratensiunilorn cazul efecturii oricrei modificri n structura staiei.

adapted to the specific values of the parameters of theanalysed lines. The general computing program can interactwith the user and may be applied for any other station/line,whose parameters are known.

The outputs of the program are stored in text type files,or in proper graphical plots, in order to highlight the influence on the overvoltages level of the differentparameters, as the length of the line or the initial phase of the sources voltage.

The computed level of the overvoltages can be comparedwith the holding performances of the switching equipmentswithin the stations. The analysis [4] emphases thecorrectness of the chosen equipments of the station.

The program allows the evaluation of the overvoltages level, when any change in the station structure occurs.

Bibliografie (References) 1. Drgan, G., .a.: Supratensiuni interne n sistemele electroenergetice, Editura Tehnic, Bucureti, 1975. 2. Gu, M. D.: Regimuri tranzitorii n reelele electrice, Editura Gh. Asachi, Iai, 2002. 3. Cristescu, D., Olah, R.: Supratensiuni i izolaia reelelor electrice, Editura Didactic i Pedagogic, Bucureti, 1983. 4. ***: Solutie moderna computerizat pentru analiza regimurilor de defect n reelele electrice de nalt tensiune ale ST Craiova,

Contract de cercetare nr.18/C-19.05.2004, Beneficiar Transelectrica SA- ST Craiova.

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