steady state and transient ampacities of gas-insulated transmission lines

8/11/2019 Steady State and Transient Ampacities of Gas-Insulated Transmission Lines

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I MELECON

2002,

May 7-9,2002, Cab,EGYPT.

Steady State and Transient Ampacities of

Gas-Insulated Transmission

Lines

M.

B.Eteiba

ElectricalEngineeringDepartment

Cairo

University,

Fayoum, Egypt

Tel: 02)0101

500885

Email [email protected]

Abstract

This

paper presents

a t h d

model

for

predicting the

steady state and transient ampacities

of gas--

transmissionlines (GILs).

Using the

t h d

odel, a

computerprogram

hasbeen formulated such

th t it caa

estimate he ampacity of a GIL for any time-varyingor

collstant QllTent loading and any variation

m

e n v i r o d

conditions

Relations

for

the oonve tion

and

radiation

heat

trander d u e a h

ar a GIL

tilled

mixture

of

both

gases

arepresente&

The

validity

and a c ~ u ~ c yf

the

ampacity

model were

vaified

by

comparing

the predicted tempersture of

core, gas,

and

enclosure

of

the GIL wiib

measured

temperatures

reported

m

the l i t e under the 58me

conditions. Analytically predicted and -tally

values both show close agreement to each

nitrogen resulted

in

a

CoadudOT temperatwe of only

lessthan1chotteal3lailsF6alone.

Keywords transmission

lines,

t hermal rating,

m w as cables, trans iatcableamPScity.

with sutfiuHeaxfluoride

( S F s ) ,

& &

OT a gas

O k . bkeOVer, using

a 50 -50

R l h l l l ?Of

SF6

and

1. INTRODUCTION

Convdonal solid insulation power t r d o n

cables are gtmerally limited to working below about

2000

A. Superconducting cables

can

of course,

transnit a considerably higher ament, but

the

method

at

present in

an

early state of

development and much

would

seea

to

depend

on the economic

ma f

.

the ceramic

conductor [l]. Gas-hsdated transmssi on

Lines (GILs), on the other hand,

are

promising

alternatives as

the

basic technology has a proven

pedigree because

it is well established in the form of

not require

supplementay

cooling

and can

be run over

di stances of more than

25-30

km

without additional

power

faEtor

c o d o n

[4].

Typical

i nstal l ati ons

of

GIL systems

have

been in buried and abovegrouud

getaways,

links

iuside substations, and far systems

SFs s w i t c h g ~nd bus ducts [2,3].Moreover,

they

Q

. .

inside unnels, vertical shafts, and n

owers

A few papers

have

been written that discuss the

calculation of

steady state ampacity

of

GILs [5,6].

Little

effort

has

been put mto

the

subject of transient

q a c i t y models for GILs

p].

i r e ratingsbetter

refled the

thermal

performance

of

a d u c t o r than

steady

state

values,

because

H

d u c t o r

will

not

mstantaneouslyjump nnn

one

itemperatueto another

when the

current or environmeartal

conditionschauge.

The

conductor

h ever ,

changes tern-

graduauy as the

metal

s t o r e s e l u ~ d u e t otsthemal

capacitance.

The object of the present p i w is to present a

ahl

hermal

model which enables the

prediction

of the

heat transfix characteristicsof

a single

[5-lo].

abovegrwnd

GIL

systan

nlsulated

wth

p m

F6

OT sF6 m g e n gas

The factors f i m c h g

such charaG-9 are

s y s t s ~

tudied and

compared

with

the

available

reported a p e r i m e d

data

m

the

iteratwe.

After thisbriefintroduction,afull

descnption of

the

Gal model

is

pmealted.

The

result

of

testing

the

model

on

a

real experimental

data is followed togethea with fi nal u m d d and

l-ehmxx.

2. THERMAL,MODEL DEVELOPMENT

The CUrrentGarrying capacity, or ampacity,

of al l

elements

in

he

current path of

a

power delivery system

is

limited by a

maximum

openlting

temperature.

The

equation relating

the

c u t

to temperatue is

suggested, m

the

present inv&ation,

to be

duived

by

applymg the comation ofenergy approach.A cross

Section of a typical GIL system can be considered as

comprised of three major

components:

1 the core;

2

the

insulating gas; and 3 the externd she h or

enclosure.

An tmexgy

balance

is performed on

each of

these

components

ielding

a

set

of

hree,

ordinary,

first

order, Mkent i a l

equations.

Aftea calculating

the

iuitial compolrent tempatures,

the transient

temperaaues

are

obtained by :knultawously solving

the

three equations,

0-7803-7527-0/02/S17.00 02002 IEEE. 424


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2 1

Energy B alance Equations

A n energy balance on the core may be expressed

as:

cl--W,Tc

-

-h,A,(T, -Tg)-aA,FW(T: -TY)

2.1

dt

An energy balance on the insulating gas yields:

2.2

2$=h,A,bc-Tg)-h,A,(TgT -T8)

An energy balance on the outer sheath

or

enclosure

results in

the foilowing equation:

C3--=Wz+W3+aTs AcF,(Tz4-T,'4)

dt

+h, A, (Tg -

T,

- h, A,

T,

T, )

-

a Am,

(T8.4

-Ti4)

2.3

Where: To, T T,, and

T,

are

conductor,

gas

enclosure,

and ambient temperature> in

'C,

espectively. A n

asterisk denotes the absolute temperature in

K.

C,, C2

and

CJ

are conductor,

gas,

and enclosure

heat capacityin J/'K.m, respectively.

W1,

W2,

nd

W3

re conductor, enclosurepower

loss,

and the

heat increase

of enclosure by

solar

radiation,

in

Whn, respectively.

EG E L

emissivity coelficient of conductor

surface, enclosure inner surface, and enclosure

outersurface espectively.

= A Dc, = A D , , ,

= A

D,. D,, D, and D,

m) re the conductor outside

metex

and the

enclosure

inside and outside diameters,

respectively.

2.2 Heat TransferCoefficients

There are several convective heat

transfer

coefficients

in

the

energy

balance equations that must be evaluated

to

determine the average temperature of the cable

components. The convective heat trandkr weficient

between the cable core and the surrounding gas, h,

,

s

given

by

classical

Nusselt number correlation's

as

[11,12]:

where

2.4

2

N, = 9 ?

In[1+_4_]

Nui

(0.649

R ~ c [ l + ( ~ ) ' ] - X ) 1 5 + ( 0 . 1 2 R $ c ) ' 5

Pr

The convective heat transfer coefficient between the

insulating

gas

and the inside of the outer

sheath,

hp

canbe

evaluated using a similar

procedw

as:

2.5

- 2

N =

2

N

ud

usi

f

In

El--]

To

evaluate the convective heat transfer coefficient on

the outer surface of the sheath, the sheath is modeled

as a long horizontal cylinder in a r If the a r velocity

over the

sheath is

zero

(no

wind effect is considered),

the heat transfer coefficient

from

the sheath

is

by

fiee

convection. The fiee convection heat transfer Nusselt

number can be approximated by the equation

[

131:

where

gpp2(Ts-Ta)D' P, and the convective heat

w

a m

transier coefficient for

fiee

convection between the

outside

of

the sheath and the

air

is given by

425


3/5

the cmlmure

inside

surfrrce

a d

also

from

the

OIL

outer

X to

the ambient air The pr0pamon of heat

removed by radiation

is

considerable

and must be

account

for in

calculations.The

8mount of

heat

trmder

by radiation depends upon a

number of

faders

including surface temp- and

anissivitieS.

The

shapefactorF, isexpressedas:

2.7

2.4

ThermophysicalProperties

several fhamophysical properties

of

the

three

cable

components

and the mundjng

air

must

be

determined

bef ore the energy

balance

equations c ~ n

e

solved. Gas viscoSity

@),

thermal amductivity (k),

density

@It and

@heat GI be expressed as

function

of

GIL component temperatureand ev lu ted

ollce the tt-m-

has been

specified

E x p

for the

hermopbysical

PrOPeXtk Of

sF6,

OgeIl, a;,

and GIL condu~tox~material as

f uncti on

of

tempaatureare . A in[l]. Expressions for

specificheatsofthe

GIL

mrrterialsare

also

included.

3.THERMALMODEL VERIFECATION

The

capability

of

the thermal

model is

i l l ustrated by

calculating the

component

tmp

hen

the

GIL

system

is

subjected to a lypaa set of opeaafing

conditions

reported

in

171. The

tested

system

con sts

of a horizontal coaxial d g u r n with the

c o m i u c W s outea

diameter

of0.18 m and a thickness

of 0.02 IIL

The enclosure's

inner

diameter

and

thi ckness are 0.47

m

and

0.015 m,@vely. Both

the amductor and the enclosure are made of

Aluminum

alloy.

The conductor's outeh sl f ce

was

tre ted wt black Alumite EO = 0.9 , while the

enclosure's

inner surface was eft

unpainted ( ~ e 0.1).

The

enclosure's OW surface was

coatedwith

a paint

having

an emissivity

E

of 0.8. Figure 3.1 showsthe

relation

between

curretlt and temperature rises above

ambient

kmpe for

the system

under

agnxment

between

calculated and measured

values is

good

and reasonable for

both the

conductor

and

the

@ d i o n With SF6 gaS PreSnae

Of

0.45

The

enclosure.

The

slight

fdakenw

between

calculated

end ahKs Of

the

sF6 gaS

hIlpelXbSe

k

I

O4 4 5 9

5.5

6

6

7

7.5

Fig. 3.1 Calculated and measu~d

emperature

rise vs.

-*A

clmelt load

t8.1 0.2 0 3 0.A

o.rP=-=ww

Fig. 3.2 Calculated and

w . e d

tempeaature ise

vs.

The

temperature

change

with time

for

a

ament

load of

7300 A

and with

no wind

ad without direct

solar

radiation

is

shown

m

Fig.

3.3, where

conductor

heat

capacity

C1=

24 (kJfK.m), SFa

gas

heat

capacity

C2

655

(JTKm),

and enclosure 'heat capacity

C,

=

45

gaspressure

at8000A

426


4/5


5/5

Dielectrics, Knoxville, TN, March

1987,

pp.

Fukuda,

S., EHV Cables

with

Compressed SFs

Gas Insulation, IEEE Trans., vol. PAS-86,

Tanizawa,T.,

Minaguchi,

D.,

and Honaga,

Y.,

Application of Gas Insulated Transmission

Line in Japan, CIGRE,

Paris 1984,

Paper

21-

05.

Kuehn, T. H., and Goldstien,

R.

J.,

An

Experimental

Study Of Natural

Convection

Heat Ttansfea in Concentric and Eccentric

Horizontal Cylindrical Annuli, Trans.

of

the

ASME,

Journal of Heat

Transfer

vol. 100,

1978,

pp.635-640.

Kuehn,

T. H.,

and Goldden, R. J., Correlating

Equations for Natural

Convection

Heat Transfer

286-313.

Janu~yl

67,

pp.

60-66.

between

Honioatal Cicular Cylinders, Int

Journal

of Heat and Mass Transfer, vol.

19,

Inmopem, F.

P.,

and Dayid, P.D.,

Fundamentals

of

Heat andMass

Tran r, 3*

Ed.,

John

Wdey

&

Sons,

1996.

Cookson, A. H., and

Pedlersen,B.

O., Thermal

Measurements in a 1200 kV Compressed Gas

Insulated Transmission Line, Proc.

7b

IEEE

/

PES Transmission and DIistribution Conference,

1976,

pp.

1127-1

134.

April

1 9 7 9 , ~ ~ .63-167.

Acknow IedBment

The author

is

grateful to

his

txAleague Dr. I.

Awad

whose cooperative

effort

has contributed

to

the

computer resultsumtained in the paper.

428

steady state and transient ampacities of gas-insulated transmission lines

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