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Anal
ysiso f t
he Probl
em
3.1 G
eneral actio
n ofZig-Zag
eart
h in g)
Transforme
r
Earthing
tr ansformer i
s oil-immers
ed type suita
ble for outdo
or installatio
n. t has an
interco
nnected star
w inding whi
ch is directly
connected t
o the low vo
ltage termina
ls
of
th e
associated s
ystem transfo
rm er. Earthi
ngtransform
er is also prov
id ed with a s
ta r
con
nected auxil
ia ry winding
arranged to
give a 400
/230V, three
phase, four
wire
s
upply.
Specif
ic ations
of
th
e transforme
r are as follow
s.
33 /0.400kV,
200kVA
ONAN
No-load
voltage ratio
Rat ing
of
nterconnected star winding
n
30Sec
E
arth fault cur
rent duty lO
Sec)
Continuous
rated current
in neutral
Vector G
roup
Extern
alSecondary
lo ad
Ze
ro sequence
im pedance
4
4/0.4kV
800A
750A
50 A
Zynll
200kVA
80
hms per phase
A zigz
ag wound tra
nsformer is u
sed as the g
rounding tra
nsformer to m
ake a neutra
l
poin
t in the delta
sid e
of
he p
ower transfo
rm er in GSSs
.
Aground fa
ult condition
on wye zigz
agtransform
er is shown
in Fig. 3.1. In
order for
in-phas
e ground cu
rre nt to flow
, the current
ineach zig
zag circuit m
ust be equal
.
N
ote that the
zero sequen
ce current, Io
, in the two
windings
of thesame cor
e is in
opposite di
rections. Th
e flux cause
d b
y
the gr
ound curren
t in the
windings
cancels a
nd there is n
o flux linkag
e to the wye
winding. Th
erefore, its cu
rrent
is
zero
i.e. th
e line curren
t ofwye conn
ected auxilia
ry winding is
zero. This c
ould be used
as
a z
ig zag earthin
g transforme
r as shown in
Fig 3.2.
2
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v
j
V
all
~
(a)-
Winding Co
nnection for
a W ye-Zigz
ag Transform
er
\ b t
az
t
I e 1
t
v.
(b
) Prima
ry
P
hases
(c)
Sp
li t Secondar
y Phases
d) Seconda
ry Phases Re
connected
F i g . ~ ye-Z
igzagTransf
orm er Wind
ing Connecti
ons and Vec
tor Diagram
I c
7
__
l
~ J b l
Fig3
4
G
rounding
Zigz
ag T r 2nsforme
r Sho,,ing
G r
ou
ndC
urrent Fl ws
8/11/2019 Zig Zag Transf_1
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)-
or
0
Primaryto Seco
ndary
Phase Shifl
-*
3rf
Cf
-*
00
Posi t iv
e N egat ive S
equence
D
iagrams
\
or
or
I
Prim
ary toSeconda
ry
Pha
se Shifl
Cf
~
Cf
Zero Se
quence Diagr
am s
Positiv
e N egative andZero
e
quenceDiag
ram s for Delta-Zigzag
and
W ye-ZigzagTransformers
___
Posi t ive
N egative andZero
Se
quence Diag
ram s for Zigz
ag Groundin
g T ransform
ers
Fig 8Se
q uence Diag
ram s ofZigz
ag Transform
ers
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Genera
lly zigzag
earthing tr
ansformers
are used wh
ere high g
round curre
nts are
desi red
on solidly gr
ounded syst
ems. On 13
.8 kV and l
owervoltag
e systems w
here
th e
g round cu
rrent is limi
ted by a gr
ounding resi
stor
or
reac
tor the delt
a-grounded
w ye
transforme
r is normall
y used. Del
ta-wye trans
formers at t
he lower vo
ltages are
high volu
m e items an
d m ore com
petitively pr
iced.W i th e
ssentially o n
ly one wind
ing
the
z igzag co
nnection sh
ould cost
less than a
delta-wye
transformer
used for
groundi
ng. Howev
er because
zigzag is le
ss commo n
and the int
ernal connec
tions
s ligh tly m or
e com plex
the cost diffe
rential m ay
not be much
.
The
seq
uence diagr
ams for a tra
nsformer w
ith a zigzag
winding are
shown in Fig
. 3.3.
/
n
constructio
n the trans
form er is ge
nerally the
sam e as an
ordinary th
ree-phase
core-ty
pe po
wer
tr
ansformer b
ut h aving a
single wind
ing o
n
each
limb which
is split
up into t
w o parts th
e halves
of
t
he windings
on th e three
limbs being
interconnec
ted
as sh o wn i
n Fig. 3.2.
The
neutr
al point o
f the earthing
transforme
r is connect
ed to earth
either direct
or
through a
current-lim
iting imped
ance while
the termin
als
of
the
apparatus a
re
..
conn
ected
to the th ree-pha
se lines. T
he rating
of the earthin
g transform
er is
of
course
different fr
om that of
a
pow er trans
former as th
e latter is d
esigned to ca
rry its
total load co
ntinuously
w hile the f
ormer has o
nly to
be
su
pplied with
the iron los
s
w h ilst the copper loss due to the passage
of
the short-circuit fault current occurs only;
fo r a frac
tionof a m
inute.
N
eutral earth
ing transfo
rmers are n
ormally des
igned to ca
rry the max
im um fault
cur
rent for up
to thirty se
conds or a
lternatively
a time dep
ending upon
ear thing
transfor
mer . t is
more usual
to sp ecify th
e sin gle-ph
ase earth fau
lt current th
at the
earthing tr ansformer m ust carry rather than the equivalent
r e q u i r e m e n t s ~ f
3
is the
total
e
arth
fault curren
t and the
line voltage
the earthin
g transform
er sh ort tim
e
rating is e
qualto ./ 3
VI
t som
etim es happ
ens that an
LV supply i
s required a
t an
V
su b
station. A 4
15/240
V sup
ply could b
e obtained by
installing a
conventiona
l step-down
transformer
butif
8/11/2019 Zig Zag Transf_1
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'\-
I
l
~
~ ~
"
L,
\
I
'
i
z:..c...J w 4
1 2.
LV w c
.\
.
.
3.4(o .)
Side
View
o
Ground
ing Tr
o.nsforMe
r
-
Zig
Zo.g W in
ding 1
.
~
--HI f--1-I--
ZigZo.g
\J
inding 2
/
..
.
-
, \ . .
.
, .
..
'
O
J
I I II ; I
L
v
\J
inding
'
W/_y
t
_
;
.
~
H r
tt
L 1 . .
. ~
n
; .p sions
in
3.4(b) Sec
tion o G
rounding
Tro.n
sforMer
8/11/2019 Zig Zag Transf_1
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it
is
in te
nde
d to
e
mp
lo y
a
n ea
rth
in g
tra
nsf
orm
er
it i
s p
oss
ib le
to
in
co rp
ora
te
a s
tar
c
onn
ect
ed
aux
il ia
ry
win
din
g o
f,
sa y
, 1
00 to
200
kV
A
rat
ing,
a n
d h
enc
e a
su
pp
ly i
s
a
vai
la b
le f
or t
he
loca
lL
V
l
oad
.
n
op
era
tion
th
e
in te
rco
nn
ect
ed
sta
r e
arth
ing
tr
ans
for
me
r is
re
all
y t
he
acm
e
of
sim
pl
ic it
y.
Th
e t
ota
l fa
ult
c u
rre
nt to
e
art
h d
ivid
es
up
w h
en
r ea
ch
ing
the
ea
rth
ing
tr
ans
fo r
mer
ne
utr
al p
oin
t i
nto
a p
pro
xim
ate
ly
equ
al
par
ts
in e
ach
p
has
e, s
o t
hat
th e
c
urr
ent
in
th e
w in
din
gs
w i
th a
si
ngl
e li
ne e
art
hfa
ult
i s
ap p
rox
im a
tel
y o
ne-
thir
d of
th
e
to ta l fa
ult
c u
rren
t
t
o
ea
rth
. T
he
cu
rren
td
istr
ibu
tion
un
de
r fa
ult
con
dit
ion
s, a
ssu
min
g
equ
al
cur
ren
ts i
n al
l w
in d
in g
s, i
s sh
ow
ni
n F
ig. 3
1
and
it
wil
l be
se
en t
hat
the
cu
rre
nts
i
n the
h a
lve
s o
f h
e w
in d
in g
s
onth
e s
am
e li
mb
f lo
wi
n o
ppo
site
d i
nt
ion
s so
th
att
hey
i
ntr
odu
ce
no
cho
kin
g e
ff e
ct,
th u
s p
erm
itt i
ng
a f
ree
flo
w o
fc
urr
ent
fro
m t
he
ear
th in
g
t
ran
sfo
rm
er
neu
tra
l to
eac
h
line
w
ire
.
T
his,
o
f c
our
se,
is
th
e
rea
son
fo
r
in
te rc
onn
ec
ting
the
w
ind
ing
s, a
s a
sta
r co
nn
ecti
on
wo
uld
pro
duc
ea
na
ddi
tion
al s
ing
le
ph
ase
m
agn
etic
f lu
xi
n ea
ch
lim
b .
3.
2
C
ore
- fl
ux
und
er
ear
th
fau
lt
con
dit
ion
s
Acc
ord
in
g to
Am
pe
re s
la
w , i
tc
an
be
e
xp
lain
ed
tha
t ev
en
the
tw
o w
ind
ing
s ar
ef
edb
y
eq
ual
and
op
po
site
cu
rren
t; s
till
t he
re
can
be
a r
esu
ltan
tfl
ux
in t
he
co r
e be
cau
se o
f
he
t
w o
dif
fe re
nt
rad
ii of
th
e w
in d
in g
s.
.
Th
ea
ver
age
fie
ld
in te
ns
ity
in
th e
co
re d
ue
to
the
o u
te r
win
din
g i
s s
mal
ler
tha
n t
hat
du
et
o th
ei
nne
rw
ind
ing
f o
r th
e s
om
e cu
rre
nt.
Th
is
phe
nom
en
on
can
b e
e x
pla
ined
as
f
ollo
ws
.
..
.
26
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Fig 3 .6
Say
n u m b er of
urns in the
winding
n and
Current thr
ough the zigz
ag winding i
s
I
i l
d strengthin
duced in the
position P b
ecause of th e
current I flo
wn through t
he
co
nductor posit
ioned at
r
di
stance fromt
he centre wi
th n No. ofu
rns is given
by
dH
:= 4.n x
2
2rXCosa
I r
de
Sina
2 7
8/11/2019 Zig Zag Transf_1
8/24
I
I
~ X
l
l
2
XrCose)
- x
Sin 9o-
e)
=
I
I
2
;ose
X
r -
2
XrCose = I -
::imCl
r
XCose)
1
Sina := ~ r = = = = = =
= = = = = = = = = =
~
0 +
l
2XrCo
se
B:=
d
[ l rde. r- XCoseTI
;
1
l l i : =
~ = = = =
= = = = = 7
~ ~
~
T I ~ X l r
2
-
2 X r
e { ~
2XrC
ose
dH := J.t{r
- XCo
se).de)
I
3
4n {Xl
l
2X.rCose
2
2n
r- x.
eose)
~ = =
de
[{ +
2
-2
X
o ~ H
0
X:=
0 O.oi 0.02
0.03 0.04 0
.05 0.06 0.0
7 0.08 0.09
n
-
2
2
7
say r =
0.090
n
2
r - Xc
os o))
de
[
0 ? 2
x,.,..e));l
~ X ) : =
0
~ 0 ) =
194.004
~ 0 . 0
=2
23.37
~ 0 . 0 =
257.402
0 . 0 3 ) =
298.181
~ 0 . 0 4 =
349
.822
. 0 5 ) =
420.823
~ 0 . 0 6 )
=530.9
95
~ 0 . 0 7
=738
.936
~ 0 . 0
=
1.332 X
10
3
0 . 0 9 ) =
1.139X
10
3
_
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r:= f.lo l r
l.. :.fr ~ X ) d X
2 0
J
.08
:=
2r (3000
0 X
4
88 00 :>2
3 ~
194.004X)d
X
= 0.22
4 f.lo l r
-
1
for
a Unit C
urrent
X:= (0 0
.02 0 .04 0.06
0.08 0.10
0 .12 0. 14 0.
16 0.18)
0
:= 22
7
say r :=
0.
135
~ X )
: =
n
2
r-
Xcos e
)) de
[{x>
2Xr :=
1-lof.lrl..
:.fr
4 X
d
2 0
1
=2{(
370o-x
4
3700-x 100
0-X' 86.224X}d
X] _
I> =
0.
131
1-lo J.lr
- - - - -
- - - - - - -
2
for a U
nit Current
29
8/11/2019 Zig Zag Transf_1
10/24
X:=
0 0.02 0.0
4 0.06 0.08
0.10 0.12 0.
14 0.16 0.18)
n
:= 22
7
say r:=
0.180
n
~
~ X ) . = \
(r
- xcoJ.
..e ))
~
l{x 2 x,,
{ e ~
0
~ 0 )
=
48.501
=
105.206
. 0 2 ) =
55.842
0 . 1 2 ) =
132 749
=
64.351
~ 0 . 1 4 )
=
18
4.734
0 . 0 6 )
=
74.54
5
~ 0 . 1 6
= 3
33.072
0 . 0 8 )
=
87.45
5
=
284.729
r
:=
J o J l r . Z . . ~
f r 4X.f3(X
) dX
2 0
[
08
]
'
z.. J
{
400x
4
1400 3
00 :0 48.50
x)
dX
I
=0.0
8 Jo
J r---
3
for
a Unit Curren
t
X:= 0 0.0
3 0.06 0.09
0.12 0.15 0
.18 0.21 0 .2 4
0.27)
==
22
7
~
X ) : =
rr
2
0
say r
:=
0.225
(r-
x
cos{a
de
[ :0
,
2
-
2 x , , . . e )
) ~ ]
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11/24
~ 0 )
= 31.041
. 0 3 ) =
36.761
~ 0 . 0 6 ) =
43.638
~ 0 . 0 9 ) =
52.394
13(0.12
) =
64.703
0 . 1 5 =
84.959
~ 0 . 1 =
129.027
0 . 2 1 )
= 336.22
3
r
:=
~ r J : J
X ~ X ) dX
2
0
[
.08
1
' '
h o
(uoo.x
4
soo.x so
.x 31.041 X
)dXJ
=
0.059 ~ o f l
--4>4
for a Unit Cu
rrent
X:
= 0
O
.o3
0.06 0.09
0.12 0.15 0.1
8
0.21
0.24
0.27
n
-
2
2
7
say r
:= 0.270
.
..
n
~ X ) : =
2
r- Xcos(e))
de
[(x /
-2 x ,, .
.{ i ]
0
=2
1.556
=
46.758
0 3 ) =
24.819
~ 0 . 1 8 )
= 58.99
9
~ 0 . 0 6 )
= 28.6
~ 0 . 2 1 )
= 82.10
4
~ 0 . 0
=
33.131
2 4 ) =148.0
32
. 1 2 ) =
38.869
13(0.27) = 129 1
8
r :=
J.loJ.lrI.:..J r
4Xl3 X) dX
2 0
8/11/2019 Zig Zag Transf_1
12/24
' ,. 2
08
(,s5-
X
4
+ 5oo-x
+
110-x
+
21
.556-xd>:J
0.05 ll o
llr
- < >5
for a U nit C
urrent
X:
=
0
0.03
0 .
06
0 09 0 12
0.15 0 18 0.21
24 0
.2 7
n -
22
.- -
7
say
r := 0 .
315
~ X ) : =
n
2
r
-
Xcos
(a))
de
[(x'
+ ,
2
- 2-x
'.{e)
)+]
0
=
15
.
837
=
30 006
0 . 0 3 )
= 17 .
8
71
0 . 1 8 )
35 .383
0 6 ) =2017
2 2 1 )
= 43 346
..
0 . 0 9 ) =
22 .831
0 2 4 ) 56.9
88
-
26 .
011
0 2 7 )
87.481
r := ll
O Ilr.J .-:..Jr
4 - X . ~ X dX
2
0
' ,. 2{(
8
{185-x
4
9o-x + 68-x
15.837
-x) dX]
=
0.04
llO Ilr
-
6 for c?onitCurrent
Variati
on
of
Flux, a
gainst distan
ce
to
the core
isplotted in G
ra ph A 1
3
8/11/2019 Zig Zag Transf_1
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The
results can b
e presented
graphically a
s in Fig 3.5,
variation
of flux in the c
ore
w i
th the dista
nce of the
winding from
the core.
Therefore e
ven when th
e tw
o
win dings
of hezigzag c
onnection in
oneleg are fe
d with equal
andopposite
currents,
there i
s a resultant
flux.
3.3
Sim ulated
flux phase vo
ltages unde
r fa ult
o
ndi
tio n
o
model th
e substation
setup, MatLa
b version 6.0
was used in
theprelimin
ary stages
of
the project. No in -b uild models are available for zigzag transformer. A zigzag
transf
ormer mode
l was tried
to build b
y combining
windi lgs
of single-pha
se
tran
sformers. T
his model w
as simulated
when there
is a singfe-p
hase earth fa
ult is
pre sent. Unf
ortunately th
e desired res
ultscould no
t obtain as t
he simulator
assumes
that all th
e equipment
b ehave in id
le manner. M
odeling
of
th
e earthing a
nd auxiliary
transfo
rm er with zig
zagwinding
arrangemen
t made the sim
ula tion mor
e complex.
S i
ncethe mod
eling
of
the G
SSusing M
atlab failed
in the prelim
inary stages,
it was
decided to w
ound a prot
oty pe
of
a gr
ounding tran
sformer and
simulate an e
arthfault
in the la
boratory. Th
e earthing tra
nsformer wit
h the auxiliar
y winding us
e inGSSs ha
s
th e
fo llowing s
pec ifications
.
Prim
ary
w
inding:
33 kV zigza
g connected
Aux
iliary windin
g: 415 V s
tar connected
Impedan
ce :
70 -80 Ohm
s
The
transformer
has a voltage
ratio of 156
:156:10 amon
g the section
s of the zigz
ag
wi
ndings and
auxiliary w
inding. Th
e prototype
transformer
w
~ woun
d by
maintaining
the above
ra tio amon
g the windin
gs. But the
re were diff
iculties to
maintain
im pedance
of 70-80 O
hms in the p
rototype tra
nsformer. Th
e small size
tr a
nsformer ma
nufacturers
do not hav
e the contro
l over the
im pedance
of the
tr
ansformer. T
heyjus t use
the insulating
materials av
ailable with
themwithout
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F
g
3
5
V
a
o
o
F
u
n
t
h
c
o
e
w
i
t
h
t
h
D
i
s
a
n
o
t
h
w
i
n
n
0
2
.
'
C
'
.
s
1 :
C
c
1
Q
.
-
=
-
\
'
'
0
2
\
.
\
I
0
1
I
H
Q
~
. .
: 1
~
c
: .
.
E
-:
J
0
:
J
>
0
5
1o
I
15
15
10
5
>
5
10
15
R Phase
Time
I
y phas
e
T im
e
BPhase
Time
Fig:3.1 0 Observa
tionsof
Exp
eriment 03
4
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22/24
3.4.3
Experiment
setup 3 resu
lts
T
he o
served
waveforms a
re indicated
in
fi
g 10
3.5 An
alysis ofExp
erim ent Re
sults
o
observ
e the effect of
fault curr
ent o
n
the a
uxiliary w in
ding
at
an e rth
fault, a
prototy
pe
o
f a groun
ding transfo
rmer with tw
o auxil iary w
indings with
same num b
er
o
f turns)
was used.
h
e in
duced voltag
es in the aux
iliary w indin
g 1 and 2 we
re measured
in experimen
tal
se
tup 1 and e
xperimental
setup 2 . he
results are
tabulated i
n table 1
The
s uperim pose
d results are
tabulated in t
able 3.2 .
F i
g. 3 .11 show
s the variat
ion
o
f induc
ed voltages i
n two auxili
ary windings
, when
different v
oltagesare a
pplied to the
pr imary zig
zag) winding
. Curves 1 a
nd 2 in Fig .
3.1 1
are almost
identical. Th
is implies th
at the voltag
e induced in
the two auxi
liary
windings in experimental setup-1 are equal. C urves 3 and 4 show some deviation
between
them with t
he increase of
supplyvolta
ge. This imp
lies that som
e additional
vol
tage is induc
ed in auxiliar
y windings in
exper imenta
l setup 2
F ig 3.
12 shows the
induced vol
tage revel in
two auxiliar
y windings a
s a percentag
e
of nd
uced voltage
s
at
th erespe
ctive auxilia
ry windings i
n experiment
setup 1.
.
43
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0.700
0
.600 - 1 - - -
r - -
~ 0 .500
do
~ ~ ~ . ~
-
'
0.400
-
1:
i
~ ~ ~ ~
~
i
~ ~ ~ ~ ~ ~
2
,
0 0 I
::
.
0000
1
1 I
I
I I
I
I
I
I-
RYB1
-
RYB2
RYB3
R Y B 4
F ig 3.11
Graph
: V
oltage induc
ed inAux.
Wind ing ag
ainstthe in
jectedcurrent
to
theneutral
25.00
2000
.
15 00
.
s 1 00
. _
5 00
.
-
- - - - - - - - - - -
- - . - - - - - - - . -
- - - - - - - - - -
- - - - r - - - - -
- - ~ - - - - - -
- - - - - - - - - - -
-
1A
6 2V
Curr t
iVoltall
R Y B 1 1 R Y B 2
RYB2JRYB4
a .g1
ayg
2
J
F ig 3.1
2 Grap
h
:
Voltage in
creased in A
ux. W indin
g dueto the
injected
current
tothe neutr
al
44
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24/24
Theore
tically two
conditions n
eed to
e
sa t
isfied to ope
rate the grou
nding trans
former
at an earth
fault
1
The zero sequence current flow through ea ch winding should
e
equal
in
each phase
2 T he
net
flux ind
uced
in
th e
limb
y
th e
zero sequen
ce compone
nt
of
the cur
rent
flownt h
rough the w
indings sho
uld
e
zero
Base
on
the experim ent results
on
the prototy pe transform er there are two
conclusi
ons
1 There
is
a resultan
t voltage in d
uced in aux
iliary w indi
ngs wound
on
each limb
To induce
a voltage the
re should
e
a net flux
in
the limb
Therefore th
e flow
of
curr
ent through
t
he
pr imary
windings
n opposite dir
ection
is
sti l
l creating a f
lux
in the limb
2 T h ei
nduced volt
age
in
the
auxiliary w i
nding is dif f
erent for tw
o locations
i e
fo rlo
cation
o
f
au
xiliary wind
ing 1 and lo
cation
o
f
aux
iliary windin
g 2