TERMIČKA ANALIZA UKOPANIH VISOKONAPONSKIH KABELA

8/12/2019 TERMIKA ANALIZA UKOPANIH VISOKONAPONSKIH KABELA

1/12

676Trkulja, B., tih, ., Berberovi, S., Termika analiza ukopanih visokonaponskih kabela, Energija, god.57(2008), br. 6., str. 676-687Trkulja, B., tih, ., Berberovi, S., Thermal Analysis Of Buried High-Voltage Cables, Energija, vol. 57(2008), No. 6, pp. 676-687

TERMIKA ANALIZAUKOPANIH VISOKONAPONSKIH

KABELATHERMAL ANALYSIS OFBURIED HIGH-VOLTAGE

CABLESBojan Trkulja eljko tih Sead Berberovi, Zagreb, Hrvatska

U okviru ovog rada provedena je spregnuta elektromagnetsko termika analizatrofaznog sustava sastavljenog od tri jednoilna kabela u konguraciji delta. Sustav

kabela analizira se u termiki stacionarnom i nestacionarnom stanju, uzimajui uobzir nelinearnost provoda topline u tlu u okolini kabela. Sloeni model prijenosa

topline u tlu, uzrokovan isuivanjem tla u okolini kabela izveden je primjenom dvijezone razliitih toplinskih vodljivosti.

The present work includes the coupled electromagnetic/thermal analysis of a three-phase system composed of three single-core cables in trefoil conguration. The

cable system is analyzed in thermally stationary and non-stationary state, takinginto account the non-linearity of heat conduction in the soil surrounding the cable.

The complex model of heat transfer in soil, caused by soil drying in the cablessurrounding, has been made by applying two zones of different heat conductions.

Kljune rijei: termika analiza; visokonaponski kabeliKeywords: thermal analysis; high-voltage cables


2/12


3/12


1 UVOD

Ukopani visokonaponski kabeli esto se koriste uprijenosu elektrine energije u gusto naseljenimpodrujima. Kabeli se u pogonu zagrijavaju, a to-plina se prenosi u okolno tlo, to dovodi do pora-sta temperature unutar kabela i u njihovoj okolini.Porast temperature treba zadrati unutar propi-sanih vrijednosti kako bi se osigurala pouzdanostopskrbe energijom i produio ivotni vijek izolaci-

je kabela. Imajui u vidu visoku cijenu kabelskeinfrastrukture, potrebno je odrediti maksimalnustruju optereenja kabela, to osigurava optimal-nu iskoristivost u prijenosu energije. Proraunmaksimalnog optereenja znaajan je za termikistacionarna i nestacionarna stanja.

Razliiti se pristupi primjenjuju u proraunu struj-nog optereenja kabela. Klasine procedure za

proraun termikih svojstava kabela temeljene suna konstantnim vrijednostima vodljivosti tla i rje-enju jednadbe prijenosa topline. Najjednostav-niji sluaj koji predvia HRN IEC 60287 [1] je opte-reenje kabela neprekidnom strujom konstantnevrijednosti, koja je denirana kao maksimalnadozvoljena trajna struja od strane proizvoaa. Zatakav proraun tlo se moe smatrati uniformnimi toplinska mu je vodljivost konstantna. Struja seu uvjetima preoptereenja moe izraunati premaHRN IEC 60853 [2]. Toplinska vodljivost tla je tem-peraturno ovisna. U razvoju tonijeg modela po-trebno je uzeti u obzir temperaturnu promjenjivost

toplinske vodljivosti tla.

U okviru ovog rada promjenjiva toplinska vodlji-vost modelirana je s dva temperaturna podruja.Za vlano tlo se pretpostavlja da ima jednoliku to-plinsku vodljivost. Za granicu vlanog i suhog tlauzima se izoterma za koju je temperatura 30 Cvia od temperature okoline [3]. Termike prilikeu okolini tri jednofazna 110 kV kabela raunajuse primjenom metode konanih elemenata ko-ristei simultano programske pakete MagNet iThermNet [4], pri emu je spregnut elektroma-gnetski proraun u frekvencijskoj domeni i ter-

miki proraun u vremenskoj domeni.

Analiza je za stacionarno stanje provedena za dvamodela kabela. U pojednostavljenom modelu jebakreni ekran kabela modeliran cilindrom jedna-ke povrine poprenog presjeka. U detaljnom jemodelu uzeta u obzir stvarna geometrija bakrenihica u ekranu.

U analizi kabela u termiki nestacionarnom stanjuproraunate su struje preoptereenja za tempe-raturno promjenjivi i konstantni model toplinskevodljivosti tla. Proraun je proveden za razliite

struje preoptereenja i struje prethodnog optere-enja kabela. Rezultati su usporeeni s vrijedno-

1 INTRODUCTION

The buried high-voltage cables are often used forelectricity transmission in densely populated are-as. Cables in operation warm up and heat spreadsto the surrounding soil, which leads to temperatu-re rise inside and around the cables. Temperatureincrease should be kept within certain prescribedlimits so as to ensure power supply reliability andto prolong the life-cycle of cable insulation. In viewof the costly cabling infrastructure, it is necessaryto determine maximum cable current load to en-sure optimum power transmission usability. Themaximum load calculation is important for ther-mally stationary and non-stationary states.

Different methods are applied in calculating thecable current load. Classical procedures for cal-culating the thermal properties of cables are ba-

sed on constant values of soil conductivity and theresult of the heat transfer equation. The simplestcase envisaged by HRN IEC 60287 [1] is cable lo-ading by uninterrupted current of constant value,dened as maximum constant current allowed bythe manufacturer. For such a calculation soil canbe considered uniform and its thermal conductivi-ty is constant. Under overload conditions, currentcan be calculated according to HRN IEC 60853 [2].The thermal conductivity of soil is temperature-dependent. In developing a more accurate modelit is necessary to take into account the temperatu-re variability of the thermal conductivity of soil.

In this work the variable thermal conductivity ismodeled with a two-zone model. For damp soila uniform thermal conductivity is assumed. Forthe boundary between damp and dry soil an isot-herm is taken for which temperature is by 30 Chigher than the ambient temperature [3]. Thermalconditions in an environment of three 110 kV sin-gle-phase cables are calculated by the nite ele-ment method simultaneously using the coupledMagNet and ThermNet software packages [4],where the coupled electromagnetic calculation isin the frequency domain and thermal calculation

in the time domain.

The analysis for the stationary state was made fortwo cable models. In the simplied model the co-pper screen of the cable was modeled by a cylin-der of equal cross-section surface. In the detailedmodel the real geometry of copper wires in thescreen was taken into account.

In analyzing the cable in the thermally non-stati-onary state the overload currents were calculatedfor a temperature variable and a constant modelof the thermal conductivity of soil. The calculation

was carried out for different overload currents andprior overload currents. The results were compa-


4/12

679 Trkulja, B., tih, ., Berberovi, S., Termika analiza ukopanih visokonaponskih kabela, Energija, god.57(2008), br. 6., str. 676-687Trkulja, B., tih, ., Berberovi, S., Thermal Analysis Of Buried High-Voltage Cables, Energija, vol. 57(2008), No. 6, pp. 676-687

stima dobivenima prema HRN IEC 60853 [2].

2 ANALIZA KABELA U STACIONARNOMSTANJU

Analiza termikih prilika za sustav tri jednofaznakabela 110 kV u stacionarnom stanju

provedena je za konguraciju kabela prema slici1.

red with the values obtained according to HRN IEC60853 [2].

2 ANALYZING A CABLE IN THE STATIONARYSTATE

An analysis of thermal conditions for a system of

three 110 kV single-phase cables in the stationarystate was made for a cable conguration shownin Figure 1.

Slika 1 Tri jednoilna kabela u konguraciji delta u kanaluFigure 1 Three single-core cables in a trench

Slika 2 Popreni presjek jednofaznog visokonaponskog kabelaFigure 2 Cross-section of single-core cable

Popreni presjek jednofaznog kabela ilustriran jeslikom 2.

The cross-section of a single-core cable is shownin Figure 2.

zrak / air

kanal / trench

aluminijska jezgra / aluminium core

kabel 110 kV / cable 110 kV

X

Z

bakreni ekran /copper screen

Zatitno ue u okolini kabela modelirano je bakre-nom icom poprenog presjeka 185 mm2. Metalniekran kabela, sastavljen od koncentrinih bakre-nih ica modeliran je na dva naina:

2.1 Pojednostavljeni model

Za ovaj model metalni je ekran nadomjeten ba-krenim cilindrom jednakog poprenog presjeka.

Presjek aluminijske jezgre kabela je 1 000 mm2.

The protection line in the surrounding of the cableis modeled by a 185 mm2 cross-section copperwire. The metal screen of the cable, made up ofconcentric copper wires, is modeled in two ways:

2.1 A simplied model

For this model the metal screen is substituted by acopper cylinder of equal cross-section. The cable

core cross-section is 1 000 mm2.


5/12


Najjednostavniji sluaj koji predvia HRN IEC60287 [1] je optereenje kabela neprekidnom stru-

jom konstantne vrijednosti, koja je denirana kaomaksimalna dozvoljena trajna struja od straneproizvoaaI

n= 798 A, to je dobiveno izrazom:

The simplest case according to HRN IEC 60287[1] is cable overloading by uninterrupted currentof constant value, dened as maximum constantcurrent allowed by the manufacturer, I

n= 798 A,

obtained by the expression:

(1). ( )[ ] A798

)()1()1(

5,0

4321211

4321n =

++++++

+++=

TTnRTnRRT

TTTnTWI

d

Pri tom je:

porast temperature vodia iznadtemperature okoline 20 C,

R elektrini otpor vodia [/m],

T1, T

2iT

3 termiki otpori slojeva vodia po jedi-

nici duljine [K m/W],T

4 termiki otpor povrine kabela prema

okolini po jedinici duljine [K m/W],W

d dielektriki gubici po jedinici duljine

[W/m],n broj vodia protjecanih strujom u jed-

nom kabelu

1 omjer gubitaka u metalnom ekranu

kabela i ukupnih gubitaka u vodii-ma,

2 omjer gubitaka u metalnoj armaturi i

ukupnih gubitaka u vodiima.

Za In = 798 A stacionarna temperatura povrinealuminijskog vodia ne bi trebala prelaziti vrijed-nost 90 C prema HRN IEC 60287 [1]. Kabeli suukopani na dubini 1,2 m. Izolacijski materijal ka-bela je XLPE . Pojednostavljeni model kabela urasporedu delta prikazan je slikom 3.

where:

conductor temperature increaseabove ambient temperature 20 C,

R electrical resistance [/m],

T1, T

2iT

3 thermal resistances of conductor

layers by unit of length [K m/W],T

4 thermal resistance of cable surface

against the environment by unit oflength [K m/W],

Wd dielectric losses by unit of length

[W/m],n number of current-own conductors

in one cable

1 ratio between losses in the metal

screen and total losses in the con-ductors

2 ratio between losses in the metal ar-

mor and total losses in the conduc-

tors

For In= 798 A the stationary temperature of the

aluminium conductor surface should not exceed90 C according to HRN IEC 60287 [1]. The cablesare buried at the depth of 1,2 m. Cable insulationmaterial is XLPE. The simplied cable model intrefoil conguration is shown in Figure 3.

Slika 3 Pojednostavljeni model kabela u rasporedu deltaFigure 3 Simplied model of the cable system

bakreni ekran /copper screen

izolacija / insulation

aluminijska jezgra (vodi) /aluminium core


6/12


Proraun temperature unutar kabela i u njegovojokolini prikazan je slikom 4.

The calculation of temperature within the cableand in its surrounding is shown in Figure 4.

Slika 4 Prikaz temperaturnog polja u okolini kabelaFigure 4 Temperature eld plot for a simplied model

Slika 5 Elektrini krug metalnih ekrana i zatitnog uetaFigure 5 Electric circuit of copper screens and protection line

Metalni ekrani kabela, kao i zatitno ue uzemljenisu preko otpora uzemljenja 20 m na oba krajakabela. Elektrini krug metalnih ekrana i zatit-nog ueta prikazan je slikom 5.

Inducirane struje u metalnim ekranima i zatit-nom uetu su temperaturno promjenjive zbogpromjenjive vrijednosti elektrine otpornosti ba-kra. Za elektrini otpor bakrenih ekrana i zatitnogueta pretpostavljeno je da je linearno promjenjivs temperaturom.

The metal screens of cables, as well as the pro-tection line, are grounded via 20 m grounding re-sistance at both cable ends. The electric circuit ofmetal screens and the protection line are shownin Figure 5.

The induced currents in the metal screens andthe protection line are temperature-variable dueto the variable resistance values of copper. Theelectrical resistance of the copper screens andthe protection line is assumed to be linearly varia-ble with temperature.

2.2 Detaljni model

U ovom je modelu primijenjena tona geometrijametalnog ekrana. Metalni je ekran modeliran s 97ica promjera 1,1 mm.

Detalj mree u metodi konanih elemenata prika-zan je slikom 6.

2.2 Detailed model

In this model the exact metal screen geometry isapplied. The metal screen is modeled with 97 wi-res, diameter 1,1 mm.

A detail of the mesh in the nite element methodis shown in Figure 6.


7/12


Kao i u jednostavnijem modelu sve su ice u me-talnim ekranima zajedno sa zatitnim uetom nakrajevima kabela kratko spojene i uzemljene pre-ko 20 m.

Termiki su rubni uvjeti ilustrirani slikom 7. Zatemperaturu tla pretpostavlja se linearni porastod 13 C na dubini 7 m do temperature okoline 20C na povrini zemlje. Linearni je porast priblienpo dijelovima stalnim iznosima prema slici 7. Napovrini zemlje je za koecijent prijenosa toplineuzeta vrijednost 11 W/(m2 K)[5].

As in a simpler model, all wires in metal screenstogether with the protection line are short-circui-ted at cable ends and grounded via 20 m.

The thermal boundary conditions are shown inFigure 7. For soil temperature a linear increasefrom 13 C at the depth of 7 m to ambient tem-perature of 20 C on the ground surface is assu-med. The linear increase is approximated by partsto constant values according to Figure 7. For theground surface, the value 11 W/(m2 K)[5] is takenfor the heat transfer coefcient.

Slika 6 Detalj mreeFigure 6 Detail of mesh

Slika 7 Termiki rubni uvjetiFigure 7 Thermal boundary conditions

Slika 8 Distribucija temperature u okolici kabela

Figure 8 Temperature eld distribution for a detailed model

Distribucija temperature u okolini kabela prikaza-na je slikom 8.

Temperature distribution in the cable surroundingis shown in Figure 8.


8/12


Temperaturni tranzijent za pojednostavljeni i de-taljni model prikazan je slikom 9.

Temperature transients for simplied and detailedmodels are shown in Figure 9.

Slika 9 Temperaturni tranzijent za pojednostavljeni model i detaljni modelFigure 9 Temperature transients for simplied and detail model

jednostavni model / simplifed model

detaljni model / detailed model

Razlika izmeu stacionarne temperature za po-jednostavljeni model i detaljni model je manje od3 C. Budui da je razlika u proraunu tempera-ture pojednostavljenog i detaljnog modela mala,pojednostavljeni model moe se primjenjivati uveini sluajeva. Prema tome, analiza u termikinestacionarnom stanju bit e provedena uz pri-mjenu pojednostavljenog modela kabela.

3 PRORAUN TERMIKIHPRILIKA PREOPTEREENOGKABELA

Preoptereenje kabela posebno je interesantno uprijenosu elektrine energije. Trajanje doputenogpreoptereenja ovisno je o prethodnom opteree-nju kabela i struji preoptereenja. U ovom se raduanalizira doputeno preoptereenje za razliitestruje prethodnog optereenja i preoptereenjabazirano na porastu temperature unutar kabela.

Prema [2] maksimalna struja preoptereenjamoe se raunati prema jednadbi:

The stationary temperature difference betweenthe simplied and the detail model is less than3 C. Considering such a small difference in tem-perature calculation between the simplied andthe detail model, the simplied model can beapplied in most cases. Therefore, the analysis inthe thermally non-stationary state will be made byusing the simplied cable model.

3 CALCULATION OF THERMALCONDITIONS OF AN OVER-

LOADED CABLE

Cable overload is particularly interesting whenit comes to power transmission. The duration ofoverload depends on the prior load and the overlo-ad current. The present work analyzes the allowedoverload for different currents of prior load andoverload based on temperature increase withinthe cable.

According to [2], maximum overload current canbe calculated by means of the following equation:

(2)

( )( )

,

R

R

R

12

1

max

R

max

1

2

1n2

+

=t

R

Rhr

R

R

R

RhII


9/12


gdje su:

In maksimalna doputena konstantna struja,

I1 struja koja prethodi preoptereenju,

I2 struja preoptereenja,

R1 otpor vodia prije preoptereenja [/m],

RR otpor vodia pri maksimalnoj doputenoj

konstantnoj struji [/m],Rmax

otpor vodia na kraju perioda preopteree-nja [/m].

h1 omjer struje koja prethodi preoptereenju i

maksimalne doputene konstantne struje

Rezultati prorauna za struje prethodnog optere-enja od 40 %I

n, 60 %I

ni 80 %I

nprikazani su u

tablici 1. Doputena su preoptereenja pri kojimatemperatura ne smije prelaziti 105 C, na emu subazirani dobiveni rezultati.

Proraun dopustivih struja preoptereenja bit e

proveden za konstantne i promjenjive vrijednostitoplinske vodljivosti tla.

3.1 Proraun baziran na konstantnim vrijed-nostima toplinske vodljivosti tla

U ovom se proraunu pretpostavlja temperaturnonepromjenjiva vrijednost toplinske vodljivosti tla.Za toplinsku je vodljivost tla pretpostavljen iznos1 W/(K m).Rezultati za razliite prethodne struje optereenjaprikazani su slikama 10, 11 i 12.

where:

In maximum allowed constant current,

I1 current prior to overload,

I2 overload current,

R1 conductor resistance prior to overload

[/m],

RR conductor resistance at maximum allowedconstant current [/m],R

max conductor resistance at the end of the

overload period [/m],h

1 ratio between current prior to overload and

maximum allowed constant current.

Calculation results for prior load currents 40 %In,

60 %Inand 80 %I

nare shown in Table 1. Overloads

are allowed where temperature may not exceed105 C, on which the obtained results are based.

The calculation of permissible overload currents

will be carried out for constant and variable valuesof the thermal conductivity of soil.

3.1 Calculation based on constant values ofthe thermal conductivity of soil

In this calculation a constant temperature valueof the thermal conductivity of soil is assumed. Theamount assumed for the thermal conductivity ofsoil is 1 W/(K m).The results for different prior overload currentsare shown in Figures 10, 11 and 12.

Slika 10 Temperaturni tranzijent za prethodno optereenje 40 %I

n

Figure 10 Temperature transient for prior load 40 %In

Slika 11 Temperaturni tranzijent za prethodno optereenje 60 %InFigure 11 Temperature transient for prior load 60 %I

n


10/12


3.2 Proraun baziran na promjenjivoj toplin-

skoj vodljivosti tla

Toplinska vodljivost tla modelirana je s dvije zone.Za temperature ispod kritine izoterme na 50 Cza toplinsku vodljivost tla se pretpostavlja vrijed-nost 1 W/(K m). Za temperature iznad 50 C pret-postavlja se toplinska vodljivost 0,33 W/(K m)[3].Rezultati prorauna prikazani su na slikama 13,14 i 15.

Slika 13 Temperaturni tranzijent za prethodno optereenje 40 %In




Prethodno optereenje /Prior load

Trajanje preoptereenja /Duration of overload[h]

1,1 %In

1,2 %In

1,25 %In

1,3 %In

1,4 %In

1,5 %In

40 %In

536 136 79 50 22 12

60 %In

517 109 60 36 16 8

80 %In

458 62 31 18 7 4

Tablica 1 Vrijeme potrebno da temperatura vodia dosegne 105 CTable 1 Time required for temperature to reach 105 C

3.2 Calculation based on variable thermal

conductivity of soil

The thermal conductivity of soil is modeled withtwo zones. For temperatures below the criticalisotherm at 50 C, the value 1 W/(K m)is assu-med for the thermal conductivity of soil. For tem-peratures above 50 C the thermal conductivity of0,33 W/( K m) [3] is assumed. The calculationresults are shown in Figures 13, 14 and 15.


11/12


4 ZAKLJUAK

Zbog visoke cijene ukopanih visokonaponskihkabela iznimno je vano tono proraunati mak-simalno doputene vrijednosti konstantne strujeoptereenja u stacionarnim uvjetima, kao i strujepreoptereenja u termiki nestacionarnim uvjeti-ma.

Analizirani su pojednostavljeni i detaljni modelkabela, a odreene su vrijednosti maksimalnodoputene stacionarne struje, kao i struje preop-tereenja za razliite vrijednosti struja prethodnogoptereenja, temeljene na porastu temperatureunutar kabela.

Razlike u dozvoljenoj temperaturi za pojednostav-ljeni i detaljni model kabela nisu znaajne, takoda pojednostavljeni model moe biti primijenjenu veini inenjerskih zadaa. Za tonije proraunedetaljni model bi trebao biti primijenjen.

Proraun baziran na konstantnim vrijednostimatoplinske vodljivosti tla pokazuje dobro slaganje svrijednostima dobivenim prema IEC standardima.

4 CONCLUSION

Due to the high prices of buried high-voltage ca-bles it is very important to exactly calculate maxi-mum allowed values of constant load current instationary conditions, as well as overload currentin thermally non-stationary conditions.

The simplied and detailed cable models wereanalyzed and the values of maximum allowed sta-tionary current determined, and so were overloadcurrents for different values of prior load currents,based on temperature increase inside the cable.

The differences in allowed temperature for both

the simplied and the detailed cable model arenot signicant, so that the simplied model canbe applied in dealing with most engineering tasks.For a more accurate calculation the detailed mo-del should be applied.

The calculation based on constant values of thethermal conductivity of soil matches well with thevalues obtained according to IEC standards.






12/12


LITERATURA /REFERENCESHRN IEC 60287,Elektrini kabeli : Proraun strujne opteretivosti[1]HRN IEC 60853, Proraun ciklike vrijednosti struje kable i struje preoptereenja[2]FREITAS, D.S., PRATA, A.T., DE LIMA, A.J., Thermal Performance of Underground Power Cables with[3]Constant and Cyclic Currents in Presence of Moisture Migration in the Surrounding Soil, IEEE Transac-tions on Power Delivery, Vol.11, No.3, July 1996Infolytica MagNet Tutorial, www.infolytica.com[4]GARRIDO, C., OTERO, A., CIDRAS, J., Theoretical Model to Calculate Steady-State and Transient Ampac-[5]ity and Temperature in Buried Cables, IEEE Transactions on Power Delivery, Vol..18, No.3, July 2003

Authors Adresses:

Bojan Trkulja, [email protected] eljko tih, [email protected] Sead Baerberovi, [email protected]

University of ZagrebFaculty of Electrical Engineering and ComputingUnska 310000 ZagrebCroatia

Manuscript received on:2008-12-23

Accepted on:2009-01-30

Adrese autora:

Dr. sc. Bojan [email protected]

Prof. dr. sc. eljko [email protected]

Prof. dr. sc. Sead [email protected]

Sveuilite u ZagrebuFakultet elektrotehnike i raunarstva

Unska 310000 Zagreb

Hrvatska

Urednitvo primilo rukopis:2008-12-23

Prihvaeno:2009-01-30

TERMIČKA ANALIZA UKOPANIH VISOKONAPONSKIH KABELA

Documents

Transcript of TERMIČKA ANALIZA UKOPANIH VISOKONAPONSKIH KABELA