Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
Vol
.
7
,
No
. 2,
J
une
2
0
1
6
,
pp
. 44
0~
44
9
I
S
SN
: 208
8-8
6
9
4
4
40
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
A New Structu
r
e for ''Sen
'' Transf
orm
e
r Using Three Winding
Linear Transformer
Chia Lailypour, Murtez
a F
a
rsadi
Departem
ent
of
Ele
c
tri
cal
and
C
o
m
puter Engin
e
ering,
Urm
i
a Un
ivers
i
t
y
,
Ir
an
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Dec 30, 2015
Rev
i
sed
May 16
, 20
16
Accepted
May 27, 2016
In this paper a
new structure fo
r "Sen" transformer (ST) is introduced,
b
y
using three wind
ing transformers with
neutral point in order to us
e negativ
e
value of
com
p
ensating volt
a
ge
.
Com
b
ination o
f
taps will be
a
d
justed b
y
a
novel algor
ith
m, to control
the requi
r
e
d activ
e and reactive powers,
separat
e
l
y
.
Th
is paper
tri
e
s to
f
o
cus on thr
e
e
p
a
rts. First
of
all
ther
e is
an
introduction on the concept of S
T
structur
e what comes next is a tr
y
to wor
k
on power flow
control b
y
using
PI c
ontrollers and an algorithm
to find the
best and eff
i
cient combination
of ta
ps, fin
a
lly
proposed idea
and algorithm
will b
e
im
plem
ent on
a
pra
c
ti
cal
s
y
st
em
. Im
plem
enta
tion of
the
s
y
st
em
consists of tw
o separated
an
d rela
ted
par
t
s. Th
e f
i
rst on
e is
abou
t
transmission line and Sen Trans
f
ormer and thein
t
eraction b
e
tween them. Th
e
second par
t
is
programing cod
e
s that ad
just
taps for r
e
quired
active and
reac
tive
powers
.
Keyword:
FAC
T
l
e
a
r
ni
ng
Po
wer flo
w
Po
wer flo
w
c
o
ntr
o
l
Sen Tra
n
sform
e
r
Tap c
h
a
nge
r t
r
ansf
o
r
m
e
r
Vo
ltag
e
regu
latin
g
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ch
ia lailyp
o
u
r,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Urm
i
a Unive
r
s
ity
, Urm
i
a, Ira
n
Em
a
il: Ch
ia.lai
lyp
o
u
r1
991
@y
mail.co
m
1.
INTRODUCTION
In t
h
e l
a
st
dec
a
des l
o
t
s
o
f
re
searche
s
an
d devel
opm
ent
s
have
been c
o
n
duct
e
d o
n
t
h
ef
l
e
xi
bl
e AC
transm
ission s
y
ste
m
s (FACT
S
) as effective
equi
pm
ent to
regu
late vo
ltage an
d
po
wer fl
o
w
i
n
tran
sm
is
sio
n
lin
es [1
]-[2
]. Desp
ite th
eir adv
a
n
t
ag
es
, in practical sys
t
e
m
s
there are too
ma
ny transformers that they
can be
use
d
asan i
n
e
xpe
nsi
v
e FAC
T
S t
ool
s,
If
w
e
just
cha
n
ge st
ruct
u
r
e o
f
t
h
e t
r
ansf
orm
e
rs of t
r
a
n
sm
i
ssi
on l
i
n
es
in
a way th
at
will b
e
p
o
s
sib
l
e to
u
tilizeth
e
m
as a FACTS d
e
v
i
ces it will b
e
tech
n
i
cal
ly an
d
Econ
omicall
y
effi
ci
ent
I
n
pra
c
t
i
cal
ranges
.
T
h
i
s
i
s
t
h
e
sem
i
nal
ad
va
nt
age of Sen Tra
n
s
f
o
r
m
e
r.Anal
y
s
es on pe
rf
orm
a
nces o
f
pha
se shi
f
t
i
ng
t
r
ans
f
o
r
m
e
r and t
a
pc
han
g
e
r
t
r
ansf
o
r
m
e
r coul
d be
use
f
ul
t
o
com
p
rehe
nd
h
o
w
ST w
o
r
k
s
[
3
]
-
[
7
]
.
Kal
y
an K. Se
n
and M
e
y
Li
n
g
Sen i
n
t
r
o
duce
ST an
d di
scu
s
s
e
d ab
out
i
t
and
com
p
are ST w
i
t
h
UPFC
i
n
[
8
]
and
[9]
.
T
h
e
r
e a
r
e
a l
o
t
s
o
f
resea
r
chs
ab
o
u
t
U
P
FC
an
d
USSC
co
nt
r
o
l
m
e
t
hods a
n
d
pe
rf
o
r
m
a
nces t
h
at
c
oul
d
be
usef
ul
i
n
Se
n
Trans
f
o
r
m
e
r cont
rol
l
e
r
desi
ng
[1
0]
-[
1
4
]
.
In [
1
5]
-[
1
6
]
,
aut
h
ors
di
scus
sed t
h
e st
r
u
ct
ure
o
f
wind
ing
s
an
d
an
algo
rith
m
to
fi
n
d
t
h
e co
m
b
in
ation
o
f
taps. So
m
e
article
h
a
s
d
i
scu
ssed
ab
ou
t co
m
b
in
atio
n
of
high-ca
p
acity ST and a
sm
all capacity UPFC has investig
ated their
pe
rform
a
nce [17]
.
There
are a
u
thors
tha
t
have investigat
ed pe
rform
a
nce of ST
and UPFC econom
ic
ally and have c
o
m
p
ared them
with each ot
he
r [18]-
[1
9]
. A st
udy
h
a
s d
one t
o
ev
ol
ve t
h
e C
ont
r
o
l
l
er f
o
r St
at
i
c
Sy
nch
r
on
o
u
s Se
ri
esC
o
m
p
ensat
o
r B
a
sed
o
n
C
o
nt
r
o
l
St
rat
e
gy
o
f
Se
n Tra
n
s
f
o
r
m
e
r [2
0]
.Thi
s
pap
e
r p
r
esent
s
a
no
vel
St
r
u
ct
u
r
e fo
r seco
n
d
ar
y
wi
ndi
ngs a
n
d an
algorithm
to choos
e taps in
order t
o
achie
ve
larger a
r
ea
of c
o
m
p
ensation.
Figure 1 illust
rates Sen Trans
f
orm
e
r
p
o
s
ition
i
n
transmissio
n
lin
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
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.
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ne 20
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4
49
44
1
Fi
gu
re
1.
Locat
i
on
o
f
Se
n T
r
a
n
sf
orm
e
r i
n
t
r
a
n
sm
i
ssi
on l
i
n
e
It will b
e
i
n
stalled
righ
t after
send
ing
end
bu
s. By
ad
d
i
n
g
v
o
ltag
e
with certain
am
p
litu
d
e
and
ph
ase
an
g
l
e
we will
h
a
v
e
a
n
e
w sen
d
i
n
g
effecti
v
e v
o
ltag
e
called (
V
) with new Phase a
ngle
δ
, as
sh
own
in
Figu
re
2. It
ca
n be proved
that
active
and
reactiv
e
powers
could be
calculated from
(1) and
(2).
(1
)
1
(2
)
Whe
r
e
V
and
V
are a
m
pli
t
udes
of
s
e
ndi
ng
an
d
rec
e
i
v
i
n
g
si
des
v
o
l
t
a
ges a
n
d
δ
is th
e effective
angl
e
bet
w
ee
n
v
o
l
t
a
ges
of
b
o
t
h
si
des.
W
e
use e
ffect
i
v
e
val
u
e
o
f
al
l
param
e
t
e
rs t
o
appl
y
t
h
e
ef
fe
ct
s of
co
m
p
en
sato
r.
All of th
ese param
e
ters
h
a
v
e
effect
on
th
e
activ
e and
reactiv
e po
wers i
n
tran
sm
issio
n
lin
e so
th
at is wh
y we u
s
e th
em
to
co
n
t
ro
l co
m
p
en
sator, im
p
l
e
m
en
t a co
n
t
rol strateg
y
fo
r
p
o
wer flow an
d
an
alg
o
rith
m
to
calcu
late th
e taps. In
tap
ch
an
g
e
rs
we can
on
l
y
gi
ve
s
p
eci
fi
ed
val
u
e
t
o
t
a
ps
,
i
n
ot
her
w
o
rds
,
t
a
ps
chan
ge
di
sc
ont
i
n
u
o
u
s
l
y
an
d s
t
ep
by
step.
It
can be one of
the disadva
n
tages of
Sen Tr
ansf
or
m
e
r
co
m
p
ar
e t
o
UPFC,
whic
h can change
param
e
ters of com
p
ensato
r continually. Because of this Prope
rty of Se
n
t
r
ans
f
o
r
m
e
r we can'
t
achi
e
ve
al
l range
of c
o
m
p
ensat
i
ng a
nd
we
m
u
st
desi
gn a m
e
t
hod
whi
c
h i
s
abl
e
to t
a
ke
the com
p
ensat
o
r to t
h
e nea
r
e
s
t state of compensating t
h
at
trans
f
orm
e
r can achieve.
This
pape
r is com
p
rised of
th
ree section
s
.
First of all we in
tro
d
u
ce
Sen
Tran
sfo
r
m
e
r an
d
co
nve
nt
i
o
nal
s
t
ruct
u
r
e
of i
t
s
wi
n
d
i
n
gs a
n
d
a
ne
w
structure whic
h covers
bigger area of com
p
ensating an
d then in the
second part we im
ple
m
ent a control
st
rat
e
gy
an
d al
go
ri
t
h
m
based
on m
a
t
l
a
b co
des t
o
c
o
nt
rol
val
u
e
of t
a
ps.
At
t
h
e en
d,
w
e
sh
ow t
h
e res
u
l
t
s
of
si
m
u
latio
n
and m
a
th
e
m
atical
eq
u
a
tion
s
.
Fi
gu
re
2.
P
h
as
e di
ag
ram
2.
STRUC
TURE OF SEN
TRA
N
SFORM
E
R
In conventiona
l Sen
T
r
a
n
sformer as
de
picte
d
in Figure
3,
for c
o
m
p
ensating each phase
,
we
use
the
sum
m
at
i
on
o
f
t
h
ree vol
t
a
ges of
t
h
ree
li
near
trans
f
orm
e
rs that are se
ries
t
oget
h
er
.
T
h
ese
t
h
ree
v
o
l
t
a
ges
ha
ve
p
o
s
itiv
e v
a
lu
e an
d
fo
r d
e
feren
t
β
, d
e
feren
t
co
m
b
in
atio
n
o
f
tran
sform
e
rs
will p
a
rticip
ate in
co
m
p
en
sating
each
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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8-8
6
9
4
A N
e
w
St
r
u
ct
u
r
e f
o
r
''S
en
''
Tr
ansf
o
r
m
er
Usi
n
g
T
h
ree Wi
nd
i
ng
Li
ne
ar
Tra
n
sf
or
mer
(Ch
i
a La
ilypou
r)
44
2
pha
se. F
o
r e
x
a
m
pl
e, i
n
phase
A
f
o
r
(0<
β
<12
0
) ratio
(Kaa an
d
Kac)
o
f
p
h
a
ses
A
and
C will p
a
rticip
ate in
com
p
ensating.
Fo
r
(1
20
<
β
<
2
4
0
)
rat
i
o
(
K
ac a
nd
Ka
b)
of
p
h
a
s
e C
an
d
B wil
l
p
a
rticip
ate in
co
m
p
en
satin
g.
And
finally
fo
r (
2
4
0
<
β
<3
60
)
ratio (Kab
and
Kaa) of ph
ases B
an
d
A
will p
a
rticip
ate in
co
mp
ensatin
g. For
o
t
h
e
r
p
h
a
ses, B an
d
C also th
e p
e
rform
a
n
ce of tap
s
will b
e
th
e
sam
e
Th
e on
ly d
i
f
f
eren
ce lies in th
e v
a
l
u
e
o
f
B
wh
ich
will
b
e
(
β
+120
) fo
r phase C and (
β
+2
40) for
p
h
a
se B. th
e ratio of co
m
p
en
sating fo
r
ph
ase C
will b
e
d
e
term
in
ate b
y
(Kca, Kcb
,
Kcc) and
for
phase B
will b
e
d
e
term
in
ate b
y
(Kb
a
,
Kb
b,
Kb
c).
It m
u
st b
e
no
ted
that (Kaa, Kbb, Kcc
)
a
n
d
(Kab,
Kbc,
Kc
a) a
n
d
(Kac
,
Kba
,
Kc
b) are
equals i
n
order to
have
sy
mme
trical
com
p
ensating.
Fi
gu
re
3.
Sc
he
m
a
t
i
c
di
agram
of
co
n
v
ent
i
o
na
l
ST
Fig
u
re
4
.
Three wind
ing
linear tran
sform
e
r
In
th
is p
a
p
e
r we sug
g
e
st a n
e
w stru
cture, as will
b
e
se
en
at th
e n
e
x
t
p
a
g
e
,
wh
ich
is cap
ab
le of
cove
ri
n
g
bi
g
g
e
r
areas
o
f
c
o
m
p
ensat
i
ng. Fi
gu
re
4 s
h
o
w
s th
ree wind
ing
s
tran
sform
e
r
with
n
e
u
t
ral po
in
t
in
mid
d
l
e o
f
secon
d
a
ry. Th
e seco
nd
ary h
a
s m
a
d
e
up
fro
m
tw
o
po
sitiv
e and
n
e
g
a
tiv
e
p
a
rts. By slid
in
g
th
e b
l
ad
e
fro
m
D to
E in po
sitiv
e area,
th
e v
a
l
u
e of
v
o
ltag
e
d
e
creases bu
t still re
m
a
i
n
s
p
o
s
itiv
e
un
til it b
eca
m
e
ze
ro
i
n
O.
pu
shi
ng t
h
e
sl
i
d
i
ng
bl
ad
e i
n
ne
gat
i
v
e a
r
ea
, val
u
e o
f
vol
t
a
ge i
n
c
r
eases
b
u
t
ne
gat
i
v
e,
F
poi
nt
. A
n
d fi
n
a
l
l
y
at
G poi
nt
we
ca
n
ac
hi
eve
m
a
xim
u
m
negat
i
v
e val
u
e
o
f
v
o
l
t
a
g
e
.
T
h
e per
f
o
rm
ance of
pr
op
os
e
st
ru
ct
ure
i
s
si
m
i
l
a
r
to conve
n
tional ST and for each phase
we use summa
tion of three
symmetrical
voltage
s in order t
o
co
m
p
en
sate. B
u
t th
ere is on
e fund
am
ent
a
l
di
ffere
nce,
i
n
c
o
n
v
e
n
t
i
onal
S
T
com
p
ensat
i
n
g
vol
t
a
ges
o
n
l
y
coul
d
b
e
po
sitiv
e,
but in
th
is case they can
b
e
n
e
g
a
tiv
e and
b
ecause o
f
th
is ab
ilit
y ST can
ach
i
ev
e m
o
re reliab
i
lity in
or
der
t
o
re
gul
a
t
e po
we
r fl
ow
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
440
–
4
49
44
3
Dat
a
o
f
sy
st
em
st
udi
e
d
wi
t
h
S
T
Suc
h
as
resi
s
t
ance an
d i
m
pedance
o
f
t
r
a
n
s
m
i
ssi
on l
i
n
e an
d wi
ndi
ng
s
can be f
o
u
n
d
fr
om
Tabl
e 1. Figu
re 5 sh
o
w
s g
e
neral
st
r
u
ct
ur
e of t
r
ansm
i
ssion l
i
n
e an
d ST
wi
ndi
ngs c
o
n
n
ect
e
d
to
g
e
th
er and
ho
w th
e co
llectio
n stays tog
e
ther.
Fi
gu
re
5.
Ge
ne
ral
st
r
u
ct
ure
o
f
t
r
ansm
i
ssi
on l
i
n
e a
n
d
ST
wi
n
d
i
n
gs
Th
e v
a
l
u
e o
f
wind
ing
s
ratio (Kaa, Kbb
,
Kcc, Kab,
Kb
c,
Kca, Kac, Kb
a,
Kcb) can
b
e
p
o
s
itiv
e an
d
negative
.
At a
ny
m
o
m
e
nt, summa
tion of t
w
o
volta
ge
s of
t
h
ree
wi
ndi
ng, according
t
o
value
of
β
, parti
c
ipate
in
com
p
ensating.
For e
x
am
ple, to
com
p
ensate
pha
se A
for (0<
β
<60
)
ratio
(Kaa and
Kab)
o
f
p
h
ases A and
B will
part
i
c
i
p
at
e i
n
c
o
m
p
ensat
i
n
g
.
B
u
t
i
t
shoul
d b
e
not
ed t
h
at
t
h
e rat
i
o
of
pha
s
e
B
t
h
at
part
i
c
ipat
e i
n
com
p
ensat
i
n
g
i
s
negat
i
v
e
.
F
o
r (
60<
β
<120
) ratio
(Kac
and
Kab) o
f
ph
ases
B
a
n
d
C
will p
a
rticip
ate in
co
m
p
en
satin
g
wh
ere
Kab
is
n
e
g
a
tive. By th
e same way, for (1
20
<
β
<1
80
)
ratio (Kac and
Kaa) of ph
ases A
an
d
C
will p
a
rt
icip
ate
in com
p
ensating where
Kaa adju
st
o
n
ne
gat
i
v
e si
de. F
o
r
(1
80<
β
<2
4
0
) rat
i
o (
K
aa an
d Ka
b)
of p
h
ases
A and
B
will p
a
rticip
ate in
co
m
p
en
satin
g
wh
ere Kaa
is n
e
g
a
tiv
e.
Reme
m
b
er (Kaa, Kbb
,
Kcc) and
(Kab, Kb
c,
Kca)
and
(
K
ac,
Kba
,
Kcb
)
are
eq
ua
l
s
i
n
or
de
r t
o
h
a
ve sy
m
m
e
t
r
i
c
al
com
p
ensat
i
ng, a
nd al
l
of t
h
em
can be
posi
t
i
v
e,
negative
a
n
d z
e
ro accordi
n
g t
o
value
of
β
.
Table
1.
Data
of Electrical Syste
m
and ST
Parameters Value
No
m
i
nal values of power
and voltage
160 M
VA and 168 kV
Sending end volta
ge
1< 20 pu
Receiving end volt
a
ge
1< 0 pu
T
r
ans
m
ission line im
p
e
dance and inductance
4.
5159
Ω
and 0.
20
919 H
Pr
im
ary
,
secondary
and T
e
r
tiar
y
win
d
ings im
pedances &
inductances
R= 0.
002 pu and L
=
0.
08 pu
Rating of ST
tr
ansform
e
r
30 M
V
A
3.
CO
NTR
O
L S
T
RATEG
Y
3.
1. Spl
i
tti
n
g
Com
p
ens
a
ti
n
g
Vol
t
a
g
e
i
n
to
Ph
aros
C
o
mp
onen
t
Co
n
s
i
d
eri
n
g ST transfo
r
m
e
r as wh
at was sh
own
in Figure 5
,
fo
r adju
stin
g tap
s
po
sition
s
we m
u
st
h
a
v
e
an
algorith
m
in
o
r
d
e
r to
select th
e
b
e
st
p
o
s
ition
i
n
all rang
es of
co
mp
ensatin
g.
Th
e tap
s
ch
an
g
e
in step
s
of
0.
1
pu
fr
om
zero t
o
0
.
4
p
u
di
sco
n
t
i
n
uo
usl
y
. B
u
t
I
n
o
r
de
r
t
o
ha
ve si
m
p
l
i
fi
ed si
m
u
l
a
t
i
on, we c
o
nsi
d
e
r
t
h
at
i
t
ch
ang
e
w
ithout an
y d
e
lay. Fi
g
u
r
e
6
d
e
m
o
n
s
tr
ates six
zo
n
e
s an
d
in
all o
f
th
em co
m
p
en
satin
g
vo
ltag
e
vector
can
o
n
l
y
st
ay
o
n
t
h
e c
r
ossi
n
g
poi
nt
s t
h
at
was
m
a
de up
by
d
a
shes l
i
ne.
Let
be
t
h
e
re
qui
re
d c
o
m
p
ensat
i
n
g
v
o
ltag
e
wh
ich
falls in
area
b
e
tween
4
satisfacto
r
y po
in
ts
. In
UPFC th
er
e
w
e
r
e
no
pro
b
l
e
m
s f
o
r
t
h
is vo
ltage
but
, i
n
ST
bec
a
use o
f
di
sco
n
t
i
nu
ou
s nat
u
re
of c
o
m
p
ensat
i
ng
v
o
l
t
a
ge m
u
st
be ad
j
u
st
o
n
t
h
e nea
r
est
Po
i
n
t
.
Fo
r
A
C
A
C
A
C
A
C
A
C
A
C
Phase
A
Phase
B
Phase
C
C
C
C
B
B
B
A
A
A
Sen
d
i
n
g si
de
Receiving side
Trans
m
ission
line
(
R
,H
)
ka
c
kb
c
kc
c
ka
b
kb
b
kc
b
ka
a
kb
a
kc
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
e
w
St
r
u
ct
u
r
e f
o
r
''S
en
''
Tr
ansf
o
r
m
er
Usi
n
g
T
h
ree Wi
nd
i
ng
Li
ne
ar
Tra
n
sf
or
mer
(Ch
i
a La
ilypou
r)
44
4
this purpose we can calcu
late th
e v
a
lue of erro
r
(dista
nce
betwee
n com
p
ensating
vect
or a
n
d accepta
ble
poi
nt
) a
n
d c
h
o
o
se t
h
e
poi
nt
d
e
di
cat
ed
by
m
i
ni
m
u
m
val
u
e o
f
(
k
=1
,
2
,
3 or
4
)
.
Ap
pa
rent
l
y
, i
t
can be
di
f
f
i
c
ul
t
and Ti
m
e
-consum
i
ng t
o
cal
cul
a
t
e
fo
r eac
h p
o
int.
In t
h
is pape
r to
find
n
e
arest
p
o
in
t to
vecto
r
,
we use a
n
al
gorithm
that it can be easily
im
plement with
fortran , m
a
tlab ,
c++ …cod
es to in
terface wit
h
th
e rest
of syst
e
m
.
Fo
r ex
am
p
l
e by atten
tio
n to
Fig
u
re 6 First
o
f
all
we calcu
late v
a
l
u
e
of
an
d
kee
p
i
n
m
i
nd t
h
at
according t
o
the zone t
h
at we are in,
and
can
be
placed
in the sam
e
dir
ection with phasors
a, b,
c
a
n
d
negative
value
of these t
h
ree
phas
ors.
Ka
a*
Va
(pu
)
Ka
b
*
V
b
(pu)
Ka
c*
V
c
(pu
)
‐
Ka
b*
V
b
(pu)
‐
Ka
c*
V
c
(pu)
‐
Ka
a*
Va(
p
u)
Vd
‐
q
0.1
0.2
0.
3
0.
4
0.1
0.
2
0.
3
0.
4
0.1
0.
2
0.
3
0.
4
Vq
Vd
β
Zo
n
e
2
Zo
n
e
3
Zon
e
4
Zone
5
Zon
e
6
Zone
1
Ɛ
1
Ɛ
2
Ɛ
4
Ɛ
3
Fig
u
re 6
.
Tap p
o
s
ition
g
r
i
d
fo
r
th
e
con
s
tru
c
tio
n
o
f
Vd
-q
Here
is an exa
m
ple we try to explain the al
gorithm
,
Im
agine that t
h
e c
o
m
p
ensating
ve
ctor is i
n
z
one
1
and v
a
l
u
e
of
and
ha
ve det
e
r
m
i
n
ed 0.
2
4
p
u
and
0.
36
p
u
re
spect
i
v
el
y
.
N
o
w
i
f
we
use f
o
l
l
o
wi
n
g
c
odes
i
n
matlab
co
mma
n
d
wi
n
dows, t
h
e
resu
lt
will b
e
n
earest
po
in
t to
t
h
e co
mp
ensatin
g v
ect
o
r
and
it is the m
o
st
convinci
ng poi
n
t.
10
∗
0
.
2
4
0
.
5
10
0
.
2
10
∗
0
.36
0
.
5
10
0
.
4
Wh
ere
wo
rd
"floo
r
"
rep
r
esen
ts th
e ceilin
g
fu
n
c
tion in
Matlab
.
Th
is
alg
o
rith
m
fo
r
and
bet
w
ee
n (
0
t
o
0.
05
) , (
0
.
1
t
o
0.
15
),
(0
.2 t
o
0
.
2
5
) a
nd
(0
.3 t
o
0.
3
5
)
gi
ves
as t
a
p po
si
t
i
ons at
0,
0.
1,
0.
2, 0
.
3
and
fo
r
and
bet
w
een
( 0
.
0
5
t
o
0
.
1
)
,
(0
.1
5 t
o
0
.
2
)
, (
0
.
25 t
o
0.
3
)
an
d (
0
.
35 t
o
0.
4
)
gi
ve as t
a
p
p
o
s
ition
s
at
0.1
,
0
.
2
,
0.3 and
0
.
4
. It is
ob
v
i
ou
s t
h
at b
y
im
p
l
e
m
en
tatio
n
th
i
s
algo
rith
m
,
the n
e
arest po
i
n
t
to
th
e
co
m
p
en
sato
r vecto
r
will b
e
fi
n
d
and
t
h
ere is
n
o
n
e
ed
s to
cal
cu
late error
.
Fi
gu
re 7 sh
o
w
s
al
l st
eps of ad
j
u
st
i
n
g t
a
ps po
s
i
t
i
on as fl
ow c
h
art
i
n
or
de
r t
o
adj
u
st
t
a
ps po
si
t
i
on i
n
t
h
e
ef
f
i
cien
t
p
l
aces. A
t
f
i
r
s
t, it gets ph
ase an
g
l
e of
v
o
ltag
e
v
e
cto
r
and
its amp
litu
d
e
as inputs w
e
adj
u
st tap
s
f
o
r
pha
se a, and t
h
en
repeat t
h
ese
steps
for
othe
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
2,
Ju
ne 20
16
:
440
–
4
49
44
5
In
p
u
t
(
lV
d
‐
ql
)
Inp
u
t
(
β
)
Fi
nd
op
e
r
a
t
i
o
n
zo
n
e
ac
c
o
r
d
i
n
g
to
β
Ca
l
c
u
l
a
t
e
im
a
g
e
of
Vd
‐
q
(V
d
&
V
q
)
on
th
e
Co
o
r
d
i
n
a
t
e
ax
i
s
of
ope
r
a
t
ion
zo
n
e
Ad
j
u
s
t
ta
p
s
pos
i
t
i
ons
wi
t
h
th
e
i
r
sign
s
for
pha
s
e
A
(
K
aa
,
K
ab
,
K
ac
)
Re
p
e
a
t
ab
o
v
e
st
e
p
s
fo
r
pha
s
e
B
an
d
pha
s
e
C
Ad
j
u
s
t
ta
p
s
pos
i
t
i
ons
wi
t
h
th
e
i
r
si
g
n
s
for
ph
a
s
e
B
(K
ba
,K
bb,
K
bc
)
Ad
j
u
s
t
ta
p
s
pos
i
t
i
ons
wi
t
h
th
e
i
r
si
gn
fo
r
pha
s
e
C
(
K
ca
,
K
cb
,
K
cc
)
en
d
Fig
u
re
7
.
Flow ch
art fo
r m
a
t
l
a
b
co
d
e
s to d
e
term
in
e tap
s
po
si
tio
n
3.
2.
Ac
ti
ve
an
d Re
ac
ti
ve P
o
w
er Co
ntr
o
l
T
echni
ques
Acco
r
d
i
n
g t
o
Fi
gu
re
2 i
t
i
s
ob
vi
o
u
s t
h
at
b
y
chan
gi
n
g
i
n
, val
u
e
of
δ
c
h
ange
s an
d
have m
o
st
i
n
fl
ue
nce o
n
δ
. Equ
a
tion
(1) sh
ows t
h
at receiv
ing
en
d, active po
wer is
prop
ortion
a
l with
δ
, s
o
we ca
n c
ont
ro
l
activ
e po
w
e
r
by
ind
i
rectly.
W
i
t
h
atten
tion
to
figu
re
2
it can
b
e
also
ex
tract th
at th
e effectiv
e a
m
p
litu
d
e
,
im
pressi
bl
e
fr
om
.
Equation (2) s
h
ows
that
reac
tive power i
n
receiving
si
de
is proportional with
. Thu
s
it is po
ssib
l
e to
cont
rol receivi
ng
end reactive
powe
r by
in
d
i
rectly.
A
b
ove c
once
p
t
s
are use
d
as
t
echni
q
u
es t
o
c
o
n
t
ro
l activ
e an
d
reactiv
e
p
o
wer in
tran
smissio
n
lin
e
separately.
As
we ca
n see i
n
Figure
8,
by
receiving
side
voltage
a
n
d curre
nt,
value
of active a
n
d re
active
p
o
wer
will b
e
measu
r
ed an
d th
ey will
b
e
com
p
ared
with
referen
ce
v
a
lu
e
o
f
th
ese po
wers. Resu
lt will be u
s
ed
as
i
n
put
s f
o
r PI
co
nt
r
o
l
l
e
rs.
O
u
t
p
ut
s
of t
h
ese co
nt
rol
l
e
rs
dedi
cat
e am
pl
i
t
ude an
d
pha
s
e
angel
of c
o
m
p
ensat
o
r.
Vo
l
t
a
ge can b
e
determ
ined and
be
used as i
n
put for m
a
tla
b inte
rface, In
order to a
d
j
u
st taps
pos
ition. The pri
n
ciple of
t
h
e
al
go
ri
t
h
m
of t
a
p sel
ect
i
n
g
w
a
s di
sc
usse
d i
n
l
a
st
c
h
apt
e
r,
as a
res
u
l
t
t
h
e o
u
t
p
ut
s
of
p
o
we
r c
o
nt
rol
d
i
agram
p
e
rform
s
as an
i
n
pu
t
for
matlab
in
terface tap
s
selecto
r
. By ch
oo
sin
g
wi
n
d
i
n
g
s
th
at
p
a
rticipate i
n
com
p
ensating for each phase,
powe
r
fl
ow in t
r
ansm
ission line can
be
c
o
ntrolled as
was
dis
c
usse
d.
Fi
gu
re
8.
P
o
we
r fl
ow
co
nt
r
o
l
s
bl
oc
k
di
ag
ram
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
A N
e
w
St
r
u
ct
u
r
e f
o
r
''S
en
''
Tr
ansf
o
r
m
er
Usi
n
g
T
h
ree Wi
nd
i
ng
Li
ne
ar
Tra
n
sf
or
mer
(Ch
i
a La
ilypou
r)
44
6
4.
POWER EQU
A
T
IONS
AN
D SIM
U
LATION
R
E
SU
LTS
4.
1. Pow
er
E
q
uati
ons
In power syste
m
s,
active and reactive powe
r assi
m
ilated by receiving e
n
d bus will be calculated
fr
om
(1) a
n
d
(2
).
Acc
o
r
d
i
n
g t
o
t
h
ese e
q
uat
i
o
n
s
we
ha
ve:
(3
)
∶
1
&
1
1
1
(4
)
Equation
(4) denote that cha
nge
s in active and
reac
tive powe
r agai
nst each ot
her will be on a circl
e
in
th
e
P-Q coo
r
d
i
n
a
te
p
l
an
e wi
th
(0
,-1) as center of circle and
1
(
) as ra
diu
s
.
No
w
by
usi
n
g
ST o
r
UPFC
(b
ot
h
of
t
h
em
are si
m
i
lar but ST
has less
spee
d and ac
curacy) as
a
co
m
p
en
sato
r i
n
send
ing
end
an
d
acco
r
d
i
ng
to
[1
] , th
ere will b
e
so
m
e
ch
an
g
e
s in
p
o
wers, p
r
op
ortio
nal with
a
m
p
litu
d
e
an
d
p
h
a
se an
g
l
e
o
f
co
m
p
en
satin
g
as it is calcu
late b
e
low.
I
(5
)
1
(6
)
∶
1
&
1
(7
)
(8
)
(9
)
Equ
a
tio
n (9
) tells as, in th
e presen
ce
of
UPFC (o
r
ST sim
i
larly) active a
n
d
reactive
power c
h
anges
ag
ain
s
t each
o
t
h
e
r
will b
e
on
a circle with (
,
) as cente
r
of t
h
e circle and
as
radi
us.
dedicate t
o
value
of active a
n
d
reactive
power in the a
b
se
nce of c
o
m
p
ensator.
Figure 9 illustrates the relati
onship bet
w
een active and reactiv
e powers acc
ording to above
equat
i
o
ns
(
3
t
o
9
)
.
As i
t
ca
n b
e
see
n
, S
T
can
not
per
f
orm
co
m
p
lete
ly
si
m
ilar to
UPFC and
th
ere i
s
erro
rs
betwee
n
UPFC
and ST acce
pt on s
o
m
e
Particular a
n
gels for
β
.
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.
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ne 20
16
:
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–
4
49
44
7
Fi
gu
re
9.
R
e
l
a
t
i
ons
hi
p
bet
w
ee
n P
r
a
n
d Q
r
I
n
t
h
e p
r
ese
n
ce
of
UP
FC
, c
o
n
v
e
n
t
i
onal
ST
an
d
n
e
w e
x
p
r
esse
d
ST
In c
o
nve
nt
i
o
na
l
ST f
o
r
β
eq
ual to
0, 60
, 120
,
18
0, 240
,
30
0 and
3
6
0
d
e
g
r
ee
p
e
r
f
o
r
m
a
n
ce is ex
actly
sam
e
wi
t
h
UP
FC
but
f
o
r ot
her a
ngel
s
e
r
r
o
r i
s
eq
ua
l
t
o
defe
rence
bet
w
een ci
rcl
e
a
n
d oct
a
go
nal
(
v
acuum
corners). It is
obvious
that
new
pro
pose
d
ST could pe
rform
faster and mo
re
accurate a
n
d
vacuum
corner
will
be m
o
stly e
l
iminated. In this
case, pe
rform
a
nce of ST
ap
pro
x
i
m
a
tely
slid
e o
n
UPFC and
is ex
actly same fo
r
an
g
e
ls
0, 3
0
, 60
, 90
, 12
0, 1
50,
180
, 21
0, 2
40,
270
, 30
0, 3
30
and
3
6
0
d
e
g
r
ee.
4.
2. Si
mul
a
ti
o
n
Res
u
l
t
s
In
o
r
d
e
r t
o
in
vestig
ate th
e p
r
o
p
e
r p
e
rform
a
n
ce of
propo
sed
ST an
d
techn
i
qu
es, system illu
strated
in
Fig
u
re
5
is im
p
l
e
m
en
ted
in
Si
m
u
l
i
n
k
o
f
m
a
tl
ab
2
014
and
t
o
sp
ecify
p
o
sitio
n
of tap
s
, t
h
e co
d
e
s are
written
in
a
bloc
k
nam
e
d sfunction t
h
at pr
ovi
de situation to inte
rface c
o
des
with Si
m
u
link. And re
sult
illustrated in Figure
1
0
to Fi
g
u
r
e
12
. Figur
e
10
,
sh
ow
s ch
ang
e
s in activ
e and r
eactiv
e
p
o
w
e
r
.
co
ul
d
be
s
een i
n
Fi
g
u
re
11
,
current receive
d by
recei
ving
end is s
h
own i
n
Fi
gure
12.
Prim
aril
y, syste
m
was cond
ucted
withou
t an
y co
m
p
en
sati
n
g
un
til ti
m
e
e
q
u
a
l
5
s, th
en
= 0.
1<
3
0
ap
p
lied
t
o
th
e
syste
m
. Th
e valu
e of activ
e
an
d
reactiv
e
po
wer will b
e
su
stain
e
d
at 145
.5
4
M
W
and 9
7
.07
MVAR res
p
ectively,
sending end
voltage rea
c
hes
t
o
1.2
of i
t
s nom
i
nal value a
n
d cu
rre
nt reaches
to 0.25
pu.
In t
i
m
e equal
10
s, c
o
m
p
ens
a
t
i
ng
vect
o
r
c
h
ange
s t
o
a
n
ot
h
e
r val
u
e,
= 0.1< 270
and acti
v
e a
n
d
reactive power changes a
g
ain and st
ops at 58.98 M
W
and
30.67 MVAR. Voltage a
n
d c
u
rrent reachs t
o
1.1
and
0
.
1
(
p
u
)
.
I
n
t
i
m
e 15 s an
d
20
s com
p
en
sat
i
ng
vect
o
r
c
h
an
ge t
o
0
.
4<
27
0 a
n
d 0
.
4<
1
5
0
,
t
h
e
res
u
l
t
s
of t
h
i
s
chan
ges
are
sh
ow
n i
n
Fi
gu
re
10
t
o
Fi
g
u
re
1
2
.
Figure 10.
Sim
u
lin
k
resu
lts for v
a
lu
es
of
active
and
reactiv
e p
o
wer
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8-8
6
9
4
A N
e
w
St
r
u
ct
u
r
e f
o
r
''S
en
''
Tr
ansf
o
r
m
er
Usi
n
g
T
h
ree Wi
nd
i
ng
Li
ne
ar
Tra
n
sf
or
mer
(Ch
i
a La
ilypou
r)
44
8
Fi
gu
re
1
1
. C
h
a
nge
s i
n
val
u
e
o
f
se
ndi
ng
en
d
v
o
l
t
a
ge
(Vse
)
Fi
gu
re
1
2
. C
h
a
nge
s i
n
val
u
e
o
f
c
u
r
r
ent
(I
r)
5.
CO
NCL
USI
O
N
According to t
h
is pa
per it ca
n be
realized t
h
at
although using UPFC
i
n
powe
r
system
as
FACTS
eq
u
i
p
m
en
t to
reg
u
l
ate
v
o
ltag
e
and
p
o
wer fl
ow
g
i
v
e
s as
m
o
re flex
i
b
ility an
d
b
e
tter reaction
ag
ain
s
t ch
ang
e
s i
n
Dem
a
n
d
s
, ST is v
e
ry exp
e
n
s
i
v
e and
it is
M
o
re To
pu
t it
el
o
q
u
e
n
tly, tran
sform
e
rs in
g
r
id can
p
e
rform
s
i
m
i
lar
to UPFC. Although re
gulate
voltage
a
n
d power
flow is slowe
r
and m
o
re discontinuous, it takes acceptable
rate. In
th
is p
a
p
e
r we
p
r
o
p
o
s
ed
a n
e
w stru
cture an
d
algorithm fo
r ST th
at g
i
v
e
s as b
e
tter
sp
eed
an
d
flex
i
b
ility,
and
i
t
has
bee
n
p
r
o
v
e
d
t
h
at
pr
op
ose
d
st
ruct
ur
e can
be m
o
re
sim
i
l
a
r t
o
UPF
C
.
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ug
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BIOGRAP
HI
ES OF
AUTH
ORS
Chia Lail
ypour
was born
in Bo
ukan, I
r
an
in Septambr
1991. He receiv
ed B
.
Sc.
degree in
power
Ele
c
tri
cal
Engin
eering from
Univers
i
t
y
of Kurdes
tan, San
a
ndaj, Kurdestan, Iran
.
He is now a
Master studen
t
in Urmia Univer
sity
, Urmia, Ir
an
.
His main
research in
tere
sts
are about Electric
and H
y
brid veh
i
cles, vehicle to
grid and grid
to vehicle, FACTS and power Electronics in
general.
Mu
rtez
a Fars
ad
i
was born in Kho
y
, Iran
in
Septambr 1957. He received B
.
Sc. degr
ee i
n
Ele
c
tri
cal
Engin
eering
M
.
S
c
.
de
gree
in E
l
ec
tri
c
a
l
and
Electron
i
cs Engine
ering
and Ph.D. degr
ee
in El
ec
tric
al
En
gineer
ing (High
volta
ge) from
Middle
East
Techn
i
ca
l Univ
ersit
y
(ME
T
U),
Ankara, Turkey in 1982, 1984, and 1989, respectivel
y
.
He is now an associate professor in
Ele
c
tri
cal
Engin
eering
Departm
e
nt of Urm
i
a Uni
v
ers
i
t
y
,
Iran
.
Hi
s
m
a
in res
ear
ch
inter
e
s
t
s
are
in
high voltage
eng
i
neer
ing,
industr
ial power s
y
st
em studies, FUCT, HVDC trans
m
ission sy
stems,
DC/AC activ
e p
o
wer filt
ers
,
ren
e
wable
energ
y
,
h
y
brid
and electrical ve
hicles, and new control
methods.
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