capacitance example - acsr - etc
TRANSCRIPT
Lin
e C
apa
citance E
xam
ple
•C
alcu
late
th
e p
er p
has
e ca
pac
itan
ce a
nd
susc
epta
nce
of
a b
alan
ced 3
ph
ases
, 6
0 H
z,
tran
smis
sio
n l
ine
wit
h h
ori
zon
tal
ph
ase
spac
ing o
f
10
m u
sing
th
ree
con
du
cto
r b
un
dli
ng w
ith
a
spac
ing b
etw
een
con
du
ctors
in
th
e b
und
le o
f 0.3
m.
Ass
um
e th
e li
ne
is u
nif
orm
ly t
ran
spo
sed
an
d t
he
cond
uct
ors
hav
e a
1cm
rad
ius.
Lin
e C
apa
citance E
xam
ple
, cont’d
13
13
m
12
11
c11
8
(0.0
10
.30
.3)
0.0
96
3 m
D(1
01
02
0)
12
.6 m
28
.854
10
1.1
41
10
F/m
12
.6ln
0.0
96
3
11
X2
60
1.1
41
10
F/m
2.3
31
0
-m (
no
t /m
)
c bR C
Cp wp
--
-
=´
´=
=´
´=
´´
==
´
==
´´
=´
WW
Lin
e C
ond
ucto
rs
•T
yp
ical
tra
nsm
issi
on l
ines
use
mult
i-st
rand
con
du
ctors
•A
CS
R (
alu
min
um
con
du
cto
r st
eel
rein
forc
ed)
cond
uct
ors
are
mo
st c
om
mo
n.
A t
yp
ical
Alu
min
um
to S
teel
rat
io i
s ab
out
4 t
o 1
.
Alu
min
um
stra
nd
s o
n
ou
tsid
e
Ste
el s
tran
d c
ore
Lin
e C
ond
ucto
rs, cont’d
•T
ota
l co
nd
uct
or
area
is
giv
en i
n c
ircu
lar
mil
s.
•E
xa
mp
le:
what
is t
he t
he a
rea o
f a s
oli
d, 1
” d
iam
ete
r
circ
ula
r w
ire?
An
swer
:10
00
kcm
il (
kil
o c
ircu
lar
mil
s)
•B
ecau
se c
ond
uct
ors
are
str
and
ed, th
e eq
uiv
alen
t
radiu
s m
ust
be
pro
vid
ed b
y t
he
man
ufa
ctu
rer.
In
tab
les
this
val
ue
is k
no
wn
as
the
GM
R a
nd i
s usu
ally
exp
ress
ed i
n f
eet.
Lin
e R
esis
tance
-8
-8
Lin
e re
sist
ance
per
un
it l
eng
th i
s g
iven
by
R=
w
her
e i
s th
e re
sist
ivit
yA
Res
isti
vit
y o
f C
op
per
= 1
.68
10
Ω-m
Res
isti
vit
y o
f A
lum
inu
m =
2.6
51
0 Ω
-m
Ex
amp
le:
Wh
at i
s th
e re
sist
ance
in
Ω /
mil
e o
f a
rr
´
´
-8
2
1"
dia
met
er s
oli
d a
lum
inu
m w
ire
(at
dc)
?
2.6
51
0 Ω
-m1
60
90
.084
0.0
12
7m
mR
mile
mile
p´
W=
=´
Lin
e R
esis
tance, cont’d
•B
ecau
se a
c cu
rren
t te
nd
s to
flo
w t
ow
ard
s th
e
surf
ace
of
a co
nd
uct
or,
th
e re
sist
ance
of
a li
ne
at 6
0
Hz
is s
lig
htl
y h
igh
er t
han
at
dc.
•R
esis
tiv
ity
an
d h
ence
lin
e re
sist
ance
in
crea
se a
s
con
du
cto
r te
mp
erat
ure
incr
ease
s (c
han
ges
is
abo
ut
8%
bet
wee
n 2
5º
C a
nd
50
º C
)
•B
ecau
se A
CS
R c
on
du
ctors
are
str
and
ed, ac
tual
resi
stan
ce, in
du
ctan
ce a
nd
cap
acit
ance
nee
ds
to b
e
det
erm
ined
fro
m t
able
s.
AC
SR
Table
Data
(S
imila
r to
Table
A.4
)
Ind
ucta
nce
an
d C
ap
acita
nce
assu
me a
Dm
of
1 f
t.
GM
R is e
qu
ivale
nt
to r
’
AC
SR
Data
, cont’d
7L
3 33
X2
41
0ln
160
9
/mil
e
12
.02
10
lnln
12
.02
10
ln2
.02
10
ln
m
m
m
DfL
fGMR
fD
GMR
ffD
GMR
pp
-
- --
==
´´
W
éù
=´
+ê
úë
û
=´
+´
Ter
m f
rom
tab
le a
ssu
min
g
a on
e fo
ot
spac
ing
Ter
m i
ndep
end
ent
of
cond
uct
or
wit
h
Dm
in f
eet .
AC
SR
Data
, C
ont. 0
C
6
To u
se t
he
phas
e to
neu
tral
cap
acit
ance
fro
m t
able
21
X-m
wher
e 2
ln
11.7
79
10
ln
-mil
e (t
able
is
in M
-mil
e)
11
11.7
79
ln1.7
79
ln M
-mil
e
m
m
m
CD
fC
r
D
fr
Df
rf
pep
=W
=
=´
´W
W
=´
´+
´´
W
Ter
m f
rom
tab
le a
ssu
min
g
a on
e fo
ot
spac
ing
Ter
m i
ndep
end
ent
of
cond
uct
or
wit
h
Dm
in f
eet .
Dove E
xam
ple
7
0.0
313 f
eet
Outs
ide
Dia
met
er =
0.0
7725 f
eet
(rad
ius
= 0
.03863)
Ass
um
ing a
one
foot
spac
ing a
t 60 H
z
12
60
210
1609
ln
Ω/m
ile
0.0
313
0.4
20
Ω
/mil
e, w
hic
h m
atc
hes
the t
ab
le
For
the
cap
acit
ance
a a C
GMR
X X X
p-
=
=´
´´
´
=
64
11
1.7
79
10
ln9.6
510
Ω
-mil
e
fr
=´
´=
´
Additio
nal T
ransm
issio
n T
opic
s
•M
ult
i-ci
rcu
it l
ines
: M
ult
iple
lin
es o
ften
sh
are
a
com
mo
n t
ran
smis
sion
rig
ht-
of-
way
. T
his
DO
ES
cause
mutu
al i
nd
uct
ance
and
cap
acit
ance
, b
ut
is o
ften
igno
red i
n s
yst
em a
nal
ysi
s.
•C
ab
les:
Ther
e ar
e ab
ou
t 3
00
0 m
iles
of
un
der
gro
un
d
ac c
able
s in
U.S
. C
able
s ar
e p
rim
aril
y u
sed i
n u
rban
area
s.
In a
cab
le t
he
con
duct
ors
are
tig
htl
y s
pac
ed, (<
1ft
) w
ith
oil
im
pre
gnat
ed p
aper
com
mon
ly u
sed t
o
pro
vid
e in
sula
tio
n
•in
duct
ance
is
low
er
•ca
pac
itan
ce i
s hig
her
, li
mit
ing c
able
len
gth
Additio
nal T
ransm
issio
n T
opic
s
•G
rou
nd
wir
es:
Tra
nsm
issi
on
lin
es a
re u
sual
ly
pro
tect
ed f
rom
lig
htn
ing
str
ikes
wit
h a
gro
un
d w
ire.
This
to
pm
ost
wir
e (o
r w
ires
) h
elp
s to
att
enu
ate
the
tran
sien
t vo
ltag
es/c
urr
ents
th
at a
rise
du
rin
g a
lig
hti
ng
stri
ke.
T
he
gro
un
d w
ire
is t
yp
ical
ly g
rou
nd
ed a
t ea
ch
po
le.
•C
oro
na d
isch
arg
e:D
ue
to h
igh
ele
ctri
c fi
eld
s ar
ou
nd
lin
es, th
e ai
r m
ole
cule
s b
eco
me
ion
ized
. T
his
cau
ses
a cr
ack
lin
g s
ou
nd
and
may
cau
se t
he
lin
e to
glo
w!
Additio
nal T
ransm
issio
n topic
s
•S
hu
nt
con
du
cta
nce
:U
sual
ly i
gno
red. A
sm
all
curr
ent
may
flo
w t
hro
ug
h c
on
tam
inan
ts o
n i
nsu
lato
rs.
•D
C T
ran
smis
sio
n:
Bec
ause
of
the
larg
e fi
xed
cost
nec
essa
ry t
o c
on
ver
t ac
to
dc
and
th
en b
ack t
o a
c, d
c
tran
smis
sio
n i
s o
nly
pra
ctic
al f
or
sever
al s
pec
iali
zed
app
lica
tion
s
•lo
ng d
ista
nce
over
hea
d p
ow
er t
ransf
er (
> 4
00 m
iles
)
•lo
ng c
able
pow
er t
ransf
er s
uch
as
under
wat
er
•p
rovid
ing a
n a
synch
ronous
mea
ns
of
join
ing
dif
fere
nt
pow
er s
yst
ems
(such
as
the
Eas
tern
and W
este
rn g
rids)
.
DC
Tra
nsm
issio
n L
ine
+/-
40
0 k
V H
VD
C l
atti
ce t
ow
er
Sourc
e: T
om
Ern
st, M
innes
ota
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er