Int
ern
at
i
onal
Journ
al of
P
ower E
le
ctr
on
i
cs a
n
d
Drive
S
ystem
s
(
IJ
PEDS
)
Vo
l.
12
,
No.
1
,
M
a
r 202
1
, p
p.
170
~
18
2
IS
S
N:
20
88
-
8694
,
DOI: 10
.11
591/
ij
peds
.
v12.i
1
.
pp
170
-
18
2
170
Journ
al h
om
e
page
:
http:
//
ij
pe
ds
.i
aescore.c
om
Impact o
f the
h
ybrid re
ac
t
ive powe
r comp
ens
ator on t
he powe
r
gr
i
d use
d a fu
zzy PI
regul
ator
Ab
delk
ad
er
Rahm
ou
ni
El
e
ct
ri
ca
l
E
ng
in
ee
ring
D
epa
r
tm
e
nt,
Fa
cul
ty
of
T
e
chnol
ogy,
T
ahr
i
Mohamm
ed
Bechar
Univer
si
ty
,
Bec
har
,
Alger
i
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Feb
6
, 2
0
20
Re
vised
Dec
2
,
20
20
Accepte
d
Ja
n 9
, 20
21
The
work
p
res
ent
ed
in
thi
s
a
rti
cle
is
a
contributi
on
to
the
problem
of
cont
rolling
re
ac
t
ive
powers
and
volt
ag
es
in
an
el
e
ct
ri
ca
l
n
et
wo
rk.
Among
the
se
cont
ro
l
too
ls,
th
e
st
at
i
c
reac
ti
ve
power
com
p
ensa
tor
(SV
C)
was
chose
n
bec
ause
of
it
s
si
mpl
icity
o
f
con
t
rol
.
SV
C
is
on
e
of
th
e
al
t
ern
ati
ve
fl
exi
bl
e
cur
ren
t
tra
nsmis
sion
sys
te
m
s
(
FA
CTS)
devi
c
e
s
which
he
lp
t
o
solve
the
proble
ms
en
cou
nte
red
in
the
op
era
t
ion
of
e
le
c
tr
ic
a
l
net
works
,
e
it
her
on
the
distri
buti
on
side
or
on
th
e
t
ran
sport
side.
To
inc
re
ase
i
ts
co
mpe
nsati
on
eff
icienc
y
in
the
face
of
har
mon
ic
cur
ren
ts
whi
c
h
ca
use
voltage
distort
ion
,
we
have
in
trodu
ce
d
a
three
-
phas
e
har
moni
c
fi
lt
e
r.
Th
is
new
hyb
rid
SV
C
is
used
to
con
trol
t
he
r
ea
c
ti
v
e
pow
er,
the
vo
lt
ag
e
a
nd
in
add
it
ion
to
red
u
ce
th
e
volt
ag
e
distortio
n
and
th
e
cor
r
e
ct
ion
of
the
po
wer
factor
in
th
e
elec
tri
c
al
ene
rgy
tr
ansport
net
work.
In
or
der
to
i
mprove
it
s
eff
i
ci
en
cy,
t
wo
volt
age
reg
ulation
sys
tems
have
be
en
chose
n
in
th
e
con
trol
sys
tem
for
thi
s
com
pensa
tor, t
h
e
fuz
zy
PI
reg
ul
a
tor
and
th
e
PIP
r
egul
a
tor.
Ke
yw
o
rd
s
:
FA
CTS
Fu
zz
y
P
I
H
ar
monics
filt
ers
HSVC
TCR
TSC
This
is an
open
acc
ess arti
cl
e
un
der
the
CC
BY
-
SA
l
ic
ense
.
Corres
pond
in
g
Aut
h
or
:
Abdelka
de
r
Ra
hmouni
Ele
ct
rical
E
ng
i
neer
i
ng
D
e
par
t
ment, Fac
ult
y of
T
ech
nolo
gy
T
ahr
i M
oh
a
m
med
Be
c
har U
niv
e
rsity
Be
char
,
Al
ger
i
a
Emai
l:
rahmo
uni.a0
01@
gm
ai
l.com
1.
INTROD
U
CTION
The
i
ncr
easi
ng
us
e
of
el
ect
ric
al
energ
y
in
th
e
eco
nomic,
s
oc
ia
l
and
i
ndus
t
rial
li
fe
of
eac
h
c
ountr
y
is
causin
g
more
and
m
or
e
probl
ems
of
distu
r
ban
ce
s,
over
vo
lt
ages,
vo
lt
a
ge
dro
ps
an
d
ha
r
monics
in
el
ec
tric
al
netw
orks.
T
he
rap
id
de
velo
pm
e
nt
of
pow
er
el
ect
ron
ic
s
has
ha
d
a
co
nsi
der
a
ble
eff
ec
t
on
imp
r
ov
i
ng
th
e
op
e
rati
ng
c
ondi
ti
on
s
of
el
ect
r
ic
al
netw
orks
by
c
on
tr
olli
ng
their
pa
ramet
ers
by
int
rod
uc
ing
co
ntr
ol
de
vices
base
d
on
ad
va
nced
very
high
po
wer
el
ect
r
on
ic
c
ompone
nts
know
n
as
the
name
of
FA
CTS:
Alte
rn
at
ive
Cu
r
ren
t T
ra
nsmi
ssion S
ys
te
ms [1
]
-
[
3].
The
researc
h
r
eported
in
t
his
arti
cl
e
is
mo
ti
vated
by
the
de
sire
to
im
pro
ve
the
co
ntr
ol
of
reacti
ve
powe
rs
a
nd
vo
lt
ages
to
furth
er
re
duce
th
e
distor
ti
on
of
volt
age
a
nd
c
urren
t
i
n
a
n
el
ec
tric
al
energ
y
tr
ans
port
netw
ork
by
m
eans
of
a
F
A
CTS
de
vice,
t
he
hybr
i
d
sta
ti
c
Var
Co
mp
e
ns
at
or
S
VC.
T
his
ne
w
SV
C
hybri
d
com
pensat
or
is
made
up
of
S
VC
bas
ed
on
t
he
c
on
tr
ollable
powe
r
el
ect
r
onic
s
co
pone
nts
[4],
a
nd
the
t
hr
ee
-
ph
a
se
ha
rm
on
i
c
filt
ers
us
e
d
t
o
el
imi
nate
di
f
fer
e
nt
orde
r
ha
rm
on
ic
c
u
r
ren
t
s
an
d
th
us
mai
ntain
the
sta
ble
sta
te
of
t
he
tran
sie
nt
vo
lt
age
withi
n
the
desire
d
li
mit
s.
The
S
VC
injec
ts
or
a
bsor
bs
reacti
ve
powe
r
int
o
the
bu
s
ba
r
wh
e
re
it
is
inst
al
le
d
to
meet
t
he
dema
nd
f
or
reacti
ve
powe
r
f
rom
the
loa
d.
It
al
lows
fle
xib
le
a
nd
co
ntin
uo
us
con
t
ro
l
of the
busbar te
ns
io
n [
5
]
,
[
6].
In
this
w
ork,
this
hybr
i
d
SVC
is
us
e
d
to
c
on
t
ro
l
reacti
ve
powe
r
a
nd
vo
lt
age
in
a
n
el
ect
rical
powe
r
transmissi
on
ne
twork
,
us
i
ng
two
vo
lt
age
con
t
ro
l
s
ys
te
m
s
in
the
c
on
tr
ol
sy
ste
m
of
this
com
pe
ns
a
tor
to
impro
ve
it
s
pe
rformance
t
he
first
is
the
f
uzzy
PI
re
gula
tor
an
d
the
s
econd
is
the
PI
P
r
eg
ula
tor
[7
]
-
[
9].
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Impact
o
f t
he h
ybrid
rea
ct
iv
e
po
we
r
com
pensator (
HSVC)
on the
powe
r
gri
d
.
...
(A
bdel
kad
e
r R
ahm
ouni
)
171
Harmo
nic
filt
ers
reduce
harmo
nic
c
urren
ts
by
di
ver
ti
ng
them
into
lo
w
impe
dan
ce
path
s
s
o
t
hey
re
du
ce
th
e
THD (
Harm
onic
d
ist
or
ti
on
r
at
e)
of
t
he vo
lt
a
ge
a
t t
he
sa
me ti
me.
2.
STATIC
R
E
A
CTIVE
POW
ER CO
MPEN
SA
TO
R HYB
RID (HS
VC)
The
SV
C
react
ive
po
wer
co
m
pensat
or
hy
br
i
d
is
a
de
vice
use
d
t
o
keep
th
e
transie
nt
a
nd
sta
ti
on
a
ry
vo
lt
age
w
it
hin t
he
desire
d
li
mit
s
in
t
he
prese
nce of
harm
on
i
c
cu
rr
e
nts
in
th
e
net
wor
k.
It
in
j
ect
s
reacti
ve
powe
r
into
the b
a
r
w
he
re
it
is
co
nn
ec
te
d
in o
r
der
to sati
sfy
the
de
m
and
f
or
r
eact
iv
e
powe
r
of
th
e load
.
I
n
gen
e
ra
l,
the
SV
C
hy
br
id
is
a
co
mb
i
natio
n
of
th
yr
ist
or
-
co
ntr
olled
reacto
rs
(TCR)
,
T
SC
(t
hyristor
-
s
witc
hed
ca
pacit
ors),
an
d
three
-
phase
h
ar
monic fil
te
rs.
These a
re t
hr
ee
consti
tuents
of
the
HSVC are:
2.1.
Thy
ri
s
to
r
s co
n
tr
olled re
actance
(
T
CR)
The
TCR
is
on
e
of
the
mo
st
i
mporta
nt
co
m
pone
nts
of
a
n
SV
C.
It
pr
ov
i
de
s
fast,
c
onti
nuous
c
ontr
ol
of
reacti
ve
po
wer
on
t
he
po
wer
gr
i
d.
T
he
Th
yr
ist
or
-
C
on
t
ro
ll
ed
Re
act
or
(TCR)
th
yr
ist
or
co
ntr
olled
rea
ct
or
ha
s
a
bi
directi
onal
th
yr
ist
or
valv
e
T
1
a
nd
T
2
c
onnected
in
s
eries
with
a
f
ixed
in
du
ct
a
nc
e
coil
L
,
s
ho
wn
in
Fig
ure
1.
T
he
thyrist
or
s
a
re
switc
he
d
on
w
it
h
a
certai
n
ign
it
io
n
an
gle
α
an
d
dr
i
ve
al
te
rn
at
el
y
ov
e
r
half
a
per
i
od.
T
he
i
gnit
ion
an
gle
α
var
ie
s
fro
m
90°
to
18
0°
.
I
n
f
ull
co
nductio
n
(
α
=
90
°
),
t
h
e
cu
rr
e
nt
is
esse
ntial
ly
reacti
ve
a
nd si
nu
s
oi
dal, a
nd
wh
e
n α =
18
0
°
, one
is
in n
ull cond
uction [
10
]
-
[
12
].
Figure
1. Sin
gl
e
-
phase ci
rcu
it
of a TCR
Re
la
ti
on
sh
i
p b
et
ween
t
he
i
gn
i
ti
on
a
ng
le
α
and
B
max
the
s
us
c
eptance
B
TVR
of in
duct
ance
L:
Let
the s
ourc
e
vo
lt
age
v
s
gi
ve
n by the
f
ollowi
ng
relat
ion
:
(
)
=
sin
(
)
(
1)
Fr
om
F
i
gure
1 t
he
eq
uatio
n of t
he vo
lt
ag
e
of
the circ
uit i
s:
(
)
−
(
)
(2)
With the
init
ia
l co
nd
it
io
n (ωt0
= α),
the s
olu
ti
on of t
his equa
ti
on
is
giv
e
n b
y:
(
)
=
1
∫
(
)
/
(3)
We th
e
n get:
(
)
=
−
(
−
)
(4)
Accor
ding to
the Fo
ur
ie
r
an
al
ys
is, t
he fu
nda
mental
c
omponent i
TCR
(t)
of
the curre
nt is
gi
ven
by
:
1
(
)
=
1
+
1
(5)
Fr
om
(4
), t
he
c
urren
t i
s
a fu
nc
ti
on
pair
i
TCR
(t
)
= i
TCR
(
-
t), t
ha
t i
s to
sa
y b
1
=
0
.
T
he
c
oeffici
ent a
1
is
:
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
170
–
18
2
172
1
=
4
∫
−
(
−
)
.
.
/
/
(6)
The ma
gnit
ude
of the
fundam
ental
curre
nt is
the
resu
lt
of (6
):
1
(
)
=
1
(
)
=
(
2
−
2
+
2
)
(
7)
1
(
)
=
(
)
(8)
This
relat
ion
s
hi
p
can
b
e
writ
te
n
as:
(
)
=
(
2
−
2
+
2
)
(9)
=
1
=
1
(
1
0
)
2.2.
Thy
ri
s
to
r
switche
d c
apa
ci
to
r
(
TS
C
)
The
th
yr
ist
or
-
switc
he
d
ca
pa
ci
tor
TSC
is
com
posed
of
a
fi
xed
ca
paci
tor
C
plu
s
a
n
at
te
nuat
ion
inducta
nce
coil
L
c
onnecte
d
i
n
se
ries
with
a
bid
irect
io
nal
t
hyristo
r
valve
F
ig
ure
2.
The
f
unct
ion
of
t
he
s
witc
h
is
to
t
urn
on
a
nd
off
t
he
ca
pac
it
or
for
a
n
i
nteger
n
umbe
r
of
half
c
ycles
of
t
he
a
ppli
ed
vo
lt
age.
The
ca
pac
it
or
is
thu
s
not
co
ntr
olled
in
phase,
bu
t
sim
ply
sw
it
ched
on
a
nd
off.
T
he
at
te
nu
at
ion
in
duct
an
ce
serv
e
s
to
li
mit
the
current
in
ca
se
of
a
bnormal
operati
on
a
nd
t
o
a
vo
i
d
res
on
a
nce
with
t
he
gr
at
ing
at
par
t
ic
ular
fr
e
quencie
s
.
T
o
hav
e
a
mi
nim
um
of
tra
ns
ie
nt
distu
r
ban
ces
,
the
s
witc
hing
ti
mes
are
c
hosen
so
t
hat
th
e
volt
age
ac
ross
the
thyrist
or
s
is
minimal
.
I
nterloc
king
is
the
refo
re
performe
d
wh
e
n
the
resi
dual
vo
lt
age
of
the
ca
pacit
or
i
s
eq
ual
to the i
ns
ta
nta
ne
o
us
netw
ork v
oltage
[1
3]
-
[
1
6
].
The
ca
pacit
or
can
be
s
witc
he
d
with
a
mini
mu
m
of
tran
sie
nt
if
the
th
yr
i
stor
is
on
(stat
e
on),
at
the
instant
w
hen
t
he
volt
age
v
C
of
t
he
capaci
to
r
and
t
he
volt
ag
e
v
s
of
t
he
net
work
ha
ve
the
same
value
.
Si
nce
the
su
sce
ptance
is
f
ixe
d,
t
he
c
urren
t
i
n
the
TS
C
var
ie
s
li
nearl
y
with
volt
ag
e
V
(which
ex
plains
t
he
a
bs
e
nce
of
harmo
nics
on
the
TSC)
.
T
ypic
al
ly,
TSC
t
yp
e
SV
C
c
onta
ins
n
be
nch
of
T
SCs
m
ounted
in
pa
rall
el
.
Th
e
su
sce
ptance
is
adjuste
d
by
co
ntr
olli
ng
the
num
ber
of
par
al
le
l
capaci
tors
in
co
nductio
n.
Each
ca
pacit
or
al
ways
dr
i
ves for a
n
in
te
gr
al
numb
e
r of half
cy
cl
es
.
Figure
2. Sin
gl
e
-
phase ci
rcu
it
of a TSC
w
it
h
series in
duct
an
ce
2.
3
.
Th
ree
-
p
h
as
e h
arm
on
ic
filters
(
HF
)
Thr
ee
-
ph
ase
ha
rm
on
ic
filt
ers
(
bu
il
t
of
RLC
el
ements
)
Fig
ur
e
3
a
re
s
hunt
el
ements
that
are
use
d
in
powe
r
s
ys
te
ms
for
decr
ea
sin
g
volt
age
distor
t
ion
a
nd
f
or
power
facto
r
c
orr
ect
ion
.
N
on
li
ne
ar
el
eme
nts
s
uch
as
powe
r
el
ect
ron
ic
conve
rters
ge
ner
at
e
harm
onic
cu
rr
e
nts
or
ha
rm
on
ic
volt
ages,
w
h
ic
h
ar
e
injec
te
d
i
nto
powe
r
sy
ste
m.
The
r
esulti
ng
disto
r
te
d
cu
rr
e
nts
fl
ow
i
ng
t
hro
ugh
s
ys
te
m
im
pe
dan
ce
pro
duc
e
harmo
nic
volt
age
distor
ti
on.
Harmo
nic
filt
ers
reduce
disto
rtion
by
di
ver
ti
ng
ha
rm
onic
currents
in
l
ow
im
pedance
paths
.
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Impact
o
f t
he h
ybrid
rea
ct
iv
e
po
we
r
com
pensator (
HSVC)
on the
powe
r
gri
d
.
...
(A
bdel
kad
e
r R
ahm
ouni
)
173
Harmo
nic
filt
ers
a
re
desig
n
e
d
t
o
be
ca
paci
ti
ve
at
f
unda
mental
fr
e
qu
e
ncy,
s
o
that
t
hey
are
al
so
use
d
f
or
pro
du
ci
ng r
eac
ti
ve
powe
r req
uire
d by co
nve
rters a
nd fo
r power
f
act
or c
orr
ect
ion
.
The most c
om
monly
us
e
d fil
te
r
ty
pes
a
re
[1
7
]
,
[
1
8
]:
a)
Ba
nd
-
pa
ss
filt
ers,
w
hich
a
re
use
d
to
filt
er
l
owest
orde
r
harmo
nics
s
uc
h
a
s
5th
,
7th
,
11
t
h,
13
t
h,
et
c.
Ba
nd
-
pass
filt
ers
ca
n
be
t
un
e
d
at
a
sin
gle
f
re
qu
e
ncy
(
sin
gle
-
tu
ned
filt
er)
or
a
t
two
f
reque
nc
ie
s
(
double
-
tu
ned
filt
er)
.
b)
High
-
pass
filt
ers,
wh
ic
h
a
re
use
d
to
filt
er
hig
h
-
order
ha
rm
on
ic
s
a
nd
c
o
ve
r
a
wide
range
of
fr
e
quencies
.
A
sp
eci
al
ty
pe
of
high
-
pas
s
filt
e
r,
t
he
C
-
t
yp
e
hi
gh
-
pas
s
filt
er,
is
us
e
d
t
o
pro
vid
e
reacti
ve
powe
r
a
nd
a
vo
i
d
par
al
le
l
res
ona
nces.
It
al
s
o
al
lows
filt
erin
g
l
ow
or
der
ha
rm
on
ic
s
(s
uc
h
as
3rd),
wh
il
e
ke
epin
g
ze
ro
loss
es
at
f
un
d
ame
ntal fr
e
quenc
y.
Figure
3.
S
how
s the
dif
fer
e
nt t
yp
e
s
of
t
hr
ee
-
phase RLC
ha
r
monic fil
te
r
The
F
reque
nc
y
-
D
om
ai
n
Re
spon
s
e
of
th
ree
-
phase
harmo
nic
filt
ers
HF
is
gi
ven
acc
ordin
g
to
it
s
four
com
pone
nts.
T
he
fr
e
quenc
y
of
th
e
s
i
ng
le
-
t
un
ed
filt
er
is
f
n
=
5
*
60Hz
(
f
il
te
rin
g
of
the
5th
orde
r
harm
onic
),
of
the
C
-
ty
pe
h
igh
-
pass
filt
er
is
fn
=
3
*
60
Hz
(
f
il
te
rin
g
of
th
e
3rd
order
ha
r
monic),
of
the
Dou
ble
–
t
un
e
d
filt
er
are
f
n1
=
11
*
60Hz
a
nd
f
n2
=
13
*
60Hz
(
f
il
te
ring
of
the
11r
d
an
d
13r
d
order
ha
rm
on
i
cs)
an
d
t
he
h
i
gh
-
p
ass
filt
er
is
fn
=
24
*
60Hz
(
f
il
te
rin
g
of
the
24r
d
or
der
harmo
nic).
T
his
f
re
quenc
y
domain
and
t
he
pha
se
of
t
his
filt
er ar
e s
how
n
in
F
ig
ure
4
.
Figure
4. Fr
e
quenc
y
-
d
om
ai
n
r
esp
onse
a
nd
phase
of
t
hree
-
phase
harmo
nic
filt
ers
H
F
3.
SVC
COMM
AND
The
S
VC
a
djust
s
these
val
ue
s
auto
mati
cal
ly
in
res
pons
e
t
o
changes
i
n
network
operati
ng
conditi
ons
as
it
has
possi
bi
li
t
ie
s
to
est
a
blish
ca
pacit
ive
or
in
du
ct
ive
c
urre
nts
of
this
ne
twork
.
T
he
op
erati
on
of
a
n
S
VC
is
base
d
on
t
he
main
functi
on
of
t
he
esse
ntial
el
ements
t
hat
const
it
ute
this
com
pensat
or
s
uch
as
the
mea
su
ri
ng
ci
rcu
it
s,
the
volt
age
re
gu
la
t
or,
the
co
m
par
a
tors,
a
nd
t
he
c
onduct
ion
ci
rc
uits
of
TCR
a
nd
T
SC.T
he
c
on
t
r
ol
model
of
a
n
S
VC
is
s
how
n
i
n
Fi
g
ure
5
with
a
measu
re
d
vo
lt
age
re
gula
tor
.
I
n
t
his
w
ork
I
will
co
mp
a
re
the
resu
lt
s
for
t
wo
regulat
ors, t
he PIP
a
nd t
he
P
I fu
zz
y
.
0
1000
2000
3000
4000
5000
0
1000
2000
3000
I
m
p
e
d
a
n
c
e
I
m
p
e
d
a
n
ce
(
o
h
m
s)
0
1000
2000
3000
4000
5000
-
1
0
0
-
5
0
0
50
100
P
h
a
s
e
P
h
a
se
(
d
e
g
)
F
r
e
q
u
e
n
cy
(
H
z)
High
-
pass
Dou
ble
-
tu
ne
d
C
-
typ
e
H
i
gh
-
pa
ss
Sing
le
-
tu
ned
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
170
–
18
2
174
Figure
5
.
Sim
pl
ifie
d
bl
ock
d
ia
gr
a
m fo
r
c
on
tr
olli
ng
a
n SVC
3.1.
PIP
re
gu
l
ator
The
pro
pose
d
PI
P
re
gula
tor
i
s
a
n
IP
re
gula
tor
ass
ociat
ed
in
pa
rall
el
with
a
pro
portio
nal
re
gula
tor
P
[
19
]
,
[
2
0
].
Th
e
blo
c
k
dia
gr
a
m
of
the
c
on
t
ro
l
vo
lt
age
V
mes
including
t
he
P
IP
c
on
tr
ol
le
r
is
il
lustrate
d
in
Fig
ure
6
.
Figure
6
.
PIP
r
egu
la
to
r
sc
he
m
e f
or
t
he rms
va
lue (V
mes
) of t
he netw
ork v
oltage
w
he
re
K
i
is a
n
integral
gain
, a
nd K
p
a
pro
port
ion
al
gain.
X
s
is a
reacta
nc
e obtai
ne
d
f
r
om t
he f
ollow
i
ng
relat
ion
:
V
mes
= V
ref
-
X
s
.I
SVC
3.2.
Fuzzy
PI
regula
t
or
The
f
uzz
y
PI
r
egu
la
to
r
is
give
n
i
n
Fig
ure
7.
T
he
basic
dia
gr
a
m
of
t
he
PI
-
f
uzzy
regulat
or
rests
on
t
he
structu
re
of
a
t
rad
it
io
nal
re
gu
la
tor
P
I
[2
1
]
-
[
2
4
].
O
n
fou
nd
in
in
put
a
nd
ou
t
pu
t
of
the
c
on
t
ro
ll
er
f
uzzy
gain
s
known
as
"f
act
or
s
of
"scal
e"
wh
ic
h
al
l
ow
s
t
o
c
ha
nge
t
he
s
ensiti
vity
of
t
he
f
uzz
y
c
ontr
oller
without
cha
ng
i
ng
the str
uctu
re,
t
he
in
put an
d
outp
ut v
a
riables
b
ei
ng
nor
mali
zed.
Q
mes
V
r
e
f
V
mes
Q
S
VC
me
sure
Circ
uit
K
Control
of
rea
c
ti
ve
Ʃ
Regul
at
o
r
_
+
+
_
Q
ref
I
SVC
+
_
_
1
1+p
T
s
Ʃ
TCR
TSC
Ʃ
_
+
V
ref
X
s
V
mes
+
_
B
max
B
min
_
+
B
SVC
_
_
_
+
+
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Impact
o
f t
he h
ybrid
rea
ct
iv
e
po
we
r
com
pensator (
HSVC)
on the
powe
r
gri
d
.
...
(A
bdel
kad
e
r R
ahm
ouni
)
175
Figure
7. Re
gu
la
tor
sc
heme
of the
r
m
s
value
(
V
mes
)
of t
he
i
nter
-
phase
net
work volt
age
The
e
rror :
E
= (V
ref
–
V
mes
)
-
X
s
.I
SVC
Ė: t
he deri
vative
of the e
rror.
We
fin
d
in
the
in
put
a
nd
outpu
t
of
the
fu
zz
y
c
ontr
oller
ga
ins
cal
le
d
"sca
le
facto
rs"
that
ca
n
c
ha
nge
the
se
ns
it
ivit
y
of
the
fu
zz
y
c
on
t
ro
ll
er
without
c
ha
ng
i
ng
th
e
str
uctu
re.
Ea
ch
li
nguisti
c
va
riable
(
E
,
Ė,
u)
is
char
act
e
rized
by
se
ven
te
rm
s
of
fu
zz
y
sub
set
s:
NG
:
ne
ga
ti
v
e
gran
d;
N
M
:
neg
at
ive
M
e
diu
m
;
NP
:
neg
at
ive
Small
;
EZ
:
a
bout
zer
o;
P
G:
Po
sit
ive
gran
d;
P
M
:
P
os
it
ive
M
e
diu
m;
PP:
po
sit
ive
Sm
al
l.
The
r
ule
base
for
t
he
fu
zz
y
l
og
ic
c
ontr
oller
ca
n
be
fr
a
med
by
ta
ki
ng
possible
c
ombinati
ons
of
the
in
put
var
i
ables
as
prese
nted
i
n
Table
1.
Tab
le
1.
Infere
nce
ru
le
of the
PI
fu
zz
y re
gu
la
tor mana
ging t
he ou
t
pu
t
E
Ė
NG
NM
NP
EZ
PP
PM
PG
NG
NG
NG
NG
NG
NM
N
P
EZ
NM
NG
NG
NG
NM
NP
EZ
PP
NP
NG
NG
NM
NP
E
Z
PP
PM
EZ
NG
NM
NP
EZ
PP
PM
PG
PP
NM
NP
EZ
PP
PM
PG
PG
PM
NP
EZ
PP
PM
PG
PG
PG
PG
EZ
PP
PM
PG
PG
PG
PG
4.
SIMULA
TI
ONS A
ND D
ISCUSSI
ON
OF RESU
L
TS
The
dif
fer
e
nt
par
ts
of
the
H
SV
C
st
ud
ie
d
previ
ou
sl
y,
t
he
el
ect
rical
netw
ork
a
nd
a
non
-
li
near
l
oad
(h
i
gh
volt
age
AC
/
DC
c
onve
r
te
rs
HVDC
with
12
-
pu
lse
th
yri
stors
)
are
sim
ulate
d
on
MA
TLAB/Si
m
ulin
k
.
The
structu
re
stu
died
i
n
Fig
ur
e
8
is
c
omp
os
ed
of
the
H
ybri
d
SV
C
(
HSVC)
with
t
hese
tw
o
po
wer
an
d
co
ntr
ol
par
ts, u
se
d
to
c
ompen
sat
e
the r
eact
ive
po
wer
and
there
f
or
e regulat
es
the volt
age
at
the busbar o
f
t
he
el
ect
rical
netw
ork
a
nd r
e
du
ce
the
disto
r
ti
on
of cu
rr
e
nt
and volt
age.
The
nomin
al
s
ource
volt
age
i
s
init
ia
ll
y
set
at
1.0
04
pu.
In
a
dd
it
io
n,
the
re
f
eren
ce
volt
age
V
ref
is
fixe
d
at
1.0 p
u,
the
S
VC
is
init
ia
ll
y
floati
ng
(z
er
o
c
urren
t
).
T
his oper
at
in
g
point
i
s
obta
ine
d
with
a
TSC
i
n
op
e
r
at
ion
and
the
TCR
al
mo
st
i
n
fu
ll
c
onduct
io
n.
The
so
urce
volt
age
is
pro
gr
a
mme
d
with
t
wo
var
ia
ti
on
s
(
Fig
ure
9)
,
t
he
first
a
n
ove
rvolta
ge
of
1.0
125
pu,
t
he
sec
ond
a
volt
age
dr
op
o
f
0.93
pu
ca
rr
ie
d
out
res
pecti
vel
y
i
n
ti
me
intervals i
n
sec
onds
[
0,1 0.
4]
and [
0.4 0.
7
].
The
t
hr
ee
-
phas
e
ha
rm
on
ic
fil
te
rs
are:
Sin
gl
e
-
Tu
ne
d,
Hi
gh
-
Pass
filt
er,
D
ouble
–
t
un
e
d
fi
lt
er,
C
-
ty
pe
High
-
pass
filt
er
al
rea
dy
desc
r
ibed
a
bove
.
T
o
op
ti
mize
the
e
ff
ic
ie
nc
y
of
t
he
HSVC,
I
us
e
d
tow
re
gula
ti
on
of
the
ef
fecti
ve
va
lue
(
V
mes
)
of
t
he
net
w
ork
vol
ta
ge
bet
ween
phase,
t
wo
re
gu
l
at
or
s
t
he
PIP
a
nd
t
he
f
uzz
y
P
I
.
The
HSVC
co
mp
e
nsa
tor
c
on
t
ro
ls
t
he
f
unda
menta
l
vo
lt
age
a
nd
s
ends
the
a
ppr
opriat
e
pulse
s
to
the
24
th
yr
ist
ors
(
6
t
hyristors
f
or
e
ach
ph
ase
)
to
obta
in
the
su
sce
ptance
require
d
by
t
he
vo
lt
ag
e
regulat
io
n.
T
he
values
of
va
rio
us
com
pone
nts
of the s
ys
te
m t
o be sim
ulate
d
a
r
e shown i
n Fi
gure
10
.
B
SVC
_
+
V
re
f
p
E
V
mes
+
_
B
max
B
min
K
3
K
1
K
2
Ė
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
170
–
18
2
176
Figure
8. O
veral
l scheme
of t
he
s
ys
te
m t
o
si
mu
la
te
in
MA
TLAB/Si
m
ulin
k
Fig
ure
9
.
Volt
age
betwee
n phase
in prima
r
y and i
ts
a
m
plit
ud
e
pro
vid
e
d by the
pro
gr
am
m
able s
ource
Figure
10
. O
ve
rall
sch
em
e
of
the s
ys
te
m to
s
imulat
e (s
i
ng
le
-
li
ne diagr
am)
T
SC
1
9
4
Mv
a
r
T
C
R
1
0
9
Mv
a
r
T
SC
2
9
4
Mv
a
r
T
SC
3
9
4
MVa
r
Q
<
-
-
-
-
-
-
+
Vd
c
-
1
1
th
/
1
3
th
(1
5
0
Mv
a
r
)
2
4
th
H
P
1
5
0
Mv
a
r
)
3C
(1
5
0
Mv
a
r
)
C
a
p
a
c
i
to
r
(1
5
0
Mv
a
r
)
N
o
n
l
i
n
e
a
r
l
o
a
d
T
h
r
e
e
-
p
h
a
se
h
a
r
m
o
n
i
c
f
i
l
t
e
r
s
SVC
S
V
C
co
n
t
r
o
l
Vabc
_prim
Vabc
_s
ec
TCR
T
SC
1
T
SC
2
T
SC
3
r
D
i
s
c
r
e
t
e
,
T
s
=
5
e
-
0
0
5
s
.
60
f
r
e
q
1
19
a
l
p
h
a
(d
e
g
.
)1
Vabc
I
abc
A
B
C
a
b
c
T
h
r
e
e
-
P
h
a
se
V
-
I
M
e
a
su
r
e
m
e
n
t
1
P
A
B
C
P
A
B
C
P
A
B
C
P
A
B
C
alpha_deg
A
B
C
F
req
Bloc
k
PY
PD
S
yn
ch
r
o
n
i
ze
d
1
2
-
P
u
l
se
G
e
n
e
r
a
t
o
r
1
A
B
C
a
b
c
S
e
co
n
d
a
r
y
(
1
6
kV
)
Py
Pd
Ay
By
Cy
Ad
Bd
Cd
pos
neg
R
e
ct
i
f
i
e
r
1
N
A
B
C
P
r
o
g
r
a
m
m
a
b
l
e
V
o
l
t
a
g
e
S
o
u
r
ce
3
A
B
C
a
b
c
P
r
i
m
a
r
y
(
7
3
5
kV
)
V
a
b
c_
P
r
i
m
V
a
b
c_
P
r
i
m
V
a
b
c_
S
e
c
A
B
C
F3
A
B
C
F2
A
B
C
F
1
D
e
m
u
x
A
B
C
C2
A
B
C
a
b
c
B
r
k2
A
B
C
a
b
c
B
r
k1
A
B
C
a
b
c
B
2
1
A
B
C
A
B
C
7
3
5
kV
6
0
0
0
M
V
A
A
B
C
a
b
c
7
3
5
/
1
6
kV
3
3
3
M
V
A
5
0
0
M
w
A
B
C
a2
b2
c2
a3
b3
c3
1
2
0
0
M
V
A
1
1
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-2
-1
0
1
2
v
a
b
-
s
e
c
(
p
u
)
T
e
n
s
i
o
n
e
n
t
r
e
p
h
a
s
e
s
a
u
s
e
c
o
n
d
a
i
r
e
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
.
9
0
.
9
3
1
1
.
0
2
5
1
.
1
V
m
e
s
(
p
u
)
A
m
p
l
i
t
u
d
e
m
e
s
u
r
é
e
d
e
l
a
t
e
n
s
i
o
n
a
u
p
r
i
m
a
i
r
e
e
t
s
a
r
é
f
e
r
e
n
c
e
V
r
é
f
V
m
e
s
7
35KV
60Hz
V
s
R
L
=10
Ω
L
L
=
1H
7
3
5
/1
6
KV
3
3
3
MVA
I
SVC
I
TC
R
I
TSC
L
L
=1
8
.
7
m
R
p
=9
2
.85
Ω
C
=
3
0
8
.4µ
F
R
s
=8
.52
m
V
r
e
f
V
mes
Con
tr
ol s
ys
te
m
L
s
=1
.13
m
H
I
dent
i
cal
3TSC
94MVAR
each
TCR
109MV
AR
R
=
0
.14
Ώ
Thr
ee
-
P
hase
H
arm
on
ic
Fil
te
r
7
3
5
/5
0
0
K
V
1
2
0
0
MVA
P
=
5
0
0
Mw
L
L
=
à.5H
+
-
Re
ct
ifie
r
RLC
Elements
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Impact
o
f t
he h
ybrid
rea
ct
iv
e
po
we
r
com
pensator (
HSVC)
on the
powe
r
gri
d
.
...
(A
bdel
kad
e
r R
ahm
ouni
)
177
4.1.
Simul
ati
on
resul
ts
(
hyb
ri
d S
V
C di
sco
nnecte
d)
I
n
this
first
ca
se,
we
represe
nt
the
s
hap
e
of
the
s
ource
volt
age,
it
s
am
plit
ud
e,
the
volt
age
of
t
he
nonlinea
r
loa
d,
their
zo
om,
a
nd
t
heir
total
harmo
nic
disto
rtion
T
H
D
(
Fig
ure
11
)
.
T
he
SV
C
an
d
t
he
three
-
ph
a
se
har
m
onic
f
il
te
r
are
d
isc
onnected
.
Tim
es
Tim
es
Figure
11. So
urce
vo
lt
age
,
it
s
amplit
ude
, l
oa
d vo
lt
age
and
their T
H
D
(
tota
l
harmo
nic
distor
ti
on)
I
n
th
e
sa
me
ca
se
we
represe
nt
the
sh
a
pe
of
the
c
urre
nt
s
of
t
he
source
a
nd
of
the
nonlinea
r
l
oad,
t
hei
r
zoom, a
nd th
ei
r
total
harmo
ni
c d
ist
ort
ion T
H
D
(
Fig
ur
e
1
2
)
.
Tim
es
Tim
es
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-2
-1
0
1
2
v
(p
u
)
VO
L
T
AG
E
T
H
E
L
O
AD
VO
L
T
AG
E
T
H
E
SO
U
R
C
E
VO
L
T
AG
E
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
,
8
7
0
,
9
5
1
1
,
0
2
5
Vm
e
s
(p
u
)
M
e
a
s
u
re
d
a
m
p
l
i
t
u
d
e
o
f
t
h
e
s
o
u
rc
e
v
o
l
t
a
g
e
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-2
0
2
v
(p
u
)
VO
L
T
AG
E(
Z
O
O
M
)
T
H
E
L
O
AD
VO
L
T
AG
E
T
H
E
SO
U
R
C
E
VO
L
T
AG
E
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
5
10
15
1
6
.
4
20
T
H
D
v
T
H
D
O
F
T
H
E
VO
L
T
AG
E
T
H
D
v
O
F
T
H
E
L
O
AD
T
H
D
v
O
F
T
H
E
SO
U
R
C
E
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-1
0
-5
0
5
10
i
(p
u
/
1
0
0
M
VA
C
U
R
R
EN
T
T
H
E
L
O
AD
C
U
R
R
EN
T
T
H
E
SO
U
R
C
E
C
U
R
R
EN
T
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-1
0
-5
0
5
10
i
(p
u
/
1
0
0
M
VA
C
U
R
R
EN
T
(Z
O
O
M
)
T
H
E
L
O
AD
C
U
R
R
EN
T
T
H
E
SO
U
R
C
E
C
U
R
R
EN
T
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2088
-
8
694
In
t J
P
ow
Ele
c
&
D
ri
S
ys
t,
V
ol
.
12
, N
o.
1
,
Ma
rch
20
21
:
170
–
18
2
178
Tim
es
Figure
1
2
.
C
urren
ts
of the
sou
rce a
nd of the
nonlinea
r
loa
d
and their
THD
4.2.
Simul
ati
on
resul
ts
(
hyb
ri
d S
V
C
c
onn
ected)
In
th
e
sec
ond
case,
we
re
pre
sent
t
he
sh
a
pe
of
the
s
ource
vo
lt
age
,
it
s
am
plit
ud
e
,
t
he
vo
lt
age
of
the
nonlinea
r
loa
d,
their
zo
om,
a
nd
t
heir
total
harmo
nic
disto
rtion
T
H
D
(
Fig
ure
1
3
)
.
T
he
SV
C
an
d
t
he
three
-
ph
a
se
har
m
onic
f
il
te
r
are
con
nected.
Figure
1
3
.
Sou
rce
vo
lt
age
,
it
s
amplit
ude
, l
oa
d vo
lt
age
and
their T
H
D
I
n
th
e
sa
me
ca
se
we
represe
nt
the
sh
a
pe
of
the
c
urre
nt
s
of
t
he
source
a
nd
of
the
nonlinea
r
l
oad,
t
hei
r
zoom,
a
nd
t
heir
total
harmo
ni
c
distor
ti
on
T
HD
al
s
o
the
r
e
act
ive
powe
r
a
bs
or
bed
or
pro
vid
e
d
by
the
S
VC
to
com
pensat
e
the
distu
rb
a
nces
of
the s
ource
volt
age
(volta
ge
drop,
over
volt
age
or d
ist
ort
io
n)
(
Fi
g
ure
1
4
)
.
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
5
10
15
20
T
H
D
i
T
H
D
O
F
T
H
E
C
U
R
R
EN
T
T
H
D
O
F
T
H
E
L
O
AD
T
H
D
O
F
T
H
E
SO
U
R
C
E
Tim
es
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-2
-1
0
1
2
v
(p
u
)
VO
L
T
AG
E
T
H
E
L
O
AD
VO
L
T
AG
E
T
H
E
SO
U
R
C
E
VO
L
T
AG
E
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
.
9
0
.
9
5
1
1
.
0
5
1
.
1
Vm
e
s
(p
u
)
M
e
a
s
u
re
d
a
m
p
l
i
t
u
d
e
o
f
t
h
e
p
ri
m
a
ry
Tim
es
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-2
-1
0
1
2
v
(p
u
)
VO
L
T
AG
E(Z
O
O
M
)
T
H
E
L
O
AD
VO
L
T
AG
E
T
H
E
SO
U
R
C
E
VO
L
T
AG
E
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
.
6
5
5
10
15
1
6
.
4
20
T
H
D
v
T
H
D
O
F
T
H
E
VO
L
T
AG
E
T
H
D
v
O
F
T
H
E
L
O
AD
T
H
D
v
O
F
T
H
E
SO
U
R
C
E
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t J
P
ow Elec
& Dri S
ys
t
IS
S
N: 20
88
-
8
694
Impact
o
f t
he h
ybrid
rea
ct
iv
e
po
we
r
com
pensator (
HSVC)
on the
powe
r
gri
d
.
...
(A
bdel
kad
e
r R
ahm
ouni
)
179
Figure
1
4
.
C
urren
ts
of the
sou
rce a
nd of the
nonlinea
r
loa
d
,
their T
H
D
a
nd
the
reacti
ve power
a
bso
rb
e
d o
r
pro
vid
e
d by
th
e SV
C
4.3.
Simul
ati
on
resul
ts
(
SVC c
on
nec
ted
and
t
he
th
ree
-
p
ha
se
filter
disconnec
ted
)
I
n
t
he
t
ir
d
cas
e,
we
re
pr
ese
nt
the
sh
a
pe
of
the
s
ource
volt
age
,
it
s
ampl
it
ud
e
,
t
he
vo
lt
age
of
t
he
nonlinea
r
loa
d,
their
z
oom,
a
nd
t
heir
t
otal
ha
rm
on
ic
distort
ion
T
HD
(
Fi
g
ur
e
1
5
)
.
T
he
S
VC
is
co
nnect
ed
a
nd
the th
ree
-
phase
h
a
rm
on
ic
filt
er
is
disco
nnect
ed
.
Tim
es
Tim
es
Figure
1
5
.
Sou
rce
vo
lt
age
,
it
s
amplit
ude
, l
oa
d vo
lt
age
and
their T
H
D
Tim
es
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-1
0
0
10
i
(p
u
/
1
0
0
M
VA)
C
U
R
R
EN
T
T
H
E
L
O
AD
C
U
R
R
EN
T
T
H
E
SO
U
R
C
E
C
U
R
R
EN
T
0
0
.
2
0
.
4
0
.
6
0
.
8
1
0
1
.
3
5
10
1
2
.
2
15
20
T
H
D
i
T
H
D
O
F
T
H
E
C
U
R
R
EN
T
T
H
D
i
O
F
T
H
E
SO
U
R
C
E
T
H
D
i
O
F
T
H
E
L
O
AD
Tim
es
0
0
.
0
2
0
.
0
4
0
.
0
6
0
.
0
8
0
.
1
-1
0
0
10
i
(p
u
/
1
0
0
M
VA)
C
U
R
R
EN
T
(Z
O
O
M
)
T
H
E
L
O
AD
C
U
R
R
EN
T
T
H
E
SO
U
R
C
E
C
U
R
R
EN
T
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-2
0
0
0
200
400
Q
(M
VAR
)
R
EAC
T
I
VE
PO
W
ER
O
F
T
H
E
SYST
EM
0
0
.
2
0
.
4
0
.
6
0
.
8
1
-2
-1
0
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