I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
P
owe
r
E
lec
t
r
on
ics
an
d
Dr
ive
S
ys
t
e
m
s
(
I
JP
E
DS)
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
,
pp.
594
~
605
I
S
S
N:
2088
-
8694,
DO
I
:
10
.
11591/i
jpeds
.
v
13
.i
1
.
pp
594
-
605
594
Jou
r
n
al
h
omepage
:
ht
tp:
//
ij
pe
ds
.
iaes
c
or
e
.
c
om
Im
p
le
m
e
n
t
at
io
n
o
f
r
e
ac
t
iv
e
c
o
m
p
e
n
sat
o
r
f
or
vol
t
age
b
al
an
c
i
n
g
u
si
n
g A
I b
as
e
d
m
o
d
e
ls
a
n
d
n
o
ve
l
p
e
r
f
o
r
m
an
c
e
i
n
d
e
x
Dana
Ragab
1
,
Jas
im
Gh
ae
b
2
1
M
e
c
h
a
tr
oni
c
s
E
ngi
ne
e
r
in
g D
e
pa
r
tm
e
nt
, P
a
le
s
ti
ne
T
e
c
hni
c
a
l
U
ni
ve
r
s
it
y
-
K
a
door
ie
,
T
ul
ka
r
e
m,
P
a
le
s
ti
ne
2
E
le
c
tr
ic
a
l
E
ngi
ne
e
r
in
g D
e
pa
r
tm
e
nt
, P
hi
la
de
lp
hi
a
U
ni
ve
r
s
it
y,
A
mm
a
n,
J
or
da
n
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
Aug
16
,
2021
R
e
vis
e
d
J
a
n
24
,
2022
Ac
c
e
pted
J
a
n
31
,
2022
V
o
l
t
a
g
e
-
u
n
b
a
l
an
ce
i
s
o
n
e
o
f
t
h
e
p
o
w
er
q
u
a
l
i
t
y
d
ef
i
ci
en
ci
e
s
t
h
a
t
d
eg
ra
d
e
s
el
ect
r
i
cal
p
o
w
er
s
y
s
t
em
s
p
erfo
rma
n
ce.
In
t
h
i
s
w
o
r
k
,
v
o
l
t
ag
e
u
n
b
a
l
an
ce
p
ro
b
l
em
i
s
t
ack
l
e
d
t
h
ro
u
g
h
t
w
o
s
t
ag
e
s
;
e
v
al
u
at
i
o
n
u
s
i
n
g
a
n
o
v
el
p
erf
o
rman
ce
i
n
d
ex
an
d
mi
t
i
g
at
i
o
n
u
s
i
n
g
a
t
h
y
r
i
s
t
o
r
-
c
o
n
t
ro
l
l
e
d
react
o
r
(T
CR)
co
mp
en
s
a
t
o
r
w
i
t
h
ar
t
i
f
i
ci
a
l
i
n
t
e
l
l
i
g
e
n
t
(
A
I)
b
a
s
ed
m
o
d
e
l
s
.
U
n
l
i
k
e
s
t
an
d
ar
d
p
erf
o
rman
ce
i
n
d
i
ce
s
t
h
at
re
l
y
o
n
v
o
l
t
ag
e
s
'
ro
o
t
mea
n
s
q
u
are
(
RMS
)
v
al
u
es
,
t
h
e
p
ro
p
o
s
ed
i
n
d
ex
d
ep
e
n
d
s
o
n
t
h
e
s
p
ac
e
v
ec
t
o
r
(SV
)
s
i
g
n
a
l
a
mp
l
i
t
u
d
e
fo
r
v
o
l
t
a
g
e
u
n
b
al
a
n
ce
ev
al
u
a
t
i
o
n
.
T
h
i
s
s
i
g
n
a
l
d
e
p
en
d
s
o
n
t
h
e
i
n
s
t
an
t
an
eo
u
s
v
a
l
u
e
s
o
f
t
h
e
t
h
ree
-
p
h
a
s
e
v
o
l
t
ag
e
s
an
d
h
a
s
t
w
i
ce
t
h
e
s
y
s
t
em
freq
u
en
cy
.
T
h
eref
o
re,
t
h
e
p
ro
p
o
s
ed
i
n
d
ex
en
t
i
t
l
e
d
as
s
p
ace
v
ect
o
r
u
n
b
a
l
an
ce
fact
o
r
(SV
U
F)
refl
ec
t
s
t
h
e
amo
u
n
t
o
f
v
o
l
t
a
g
e
u
n
b
a
l
an
c
e
a
n
d
re
d
u
ces
t
h
e
t
i
me
n
ec
es
s
ar
y
fo
r
ev
al
u
at
i
o
n
b
y
h
al
f.
S
u
b
s
eq
u
en
t
l
y
,
ad
v
a
n
ce
d
mo
d
el
s
b
a
s
ed
o
n
s
e
v
eral
a
l
g
o
ri
t
h
m
s
are
p
ro
p
o
s
ed
t
o
g
en
e
rat
e
t
h
e
req
u
i
re
d
fi
ri
n
g
a
n
g
l
es
fo
r
T
CR
co
mp
en
s
at
o
r
t
o
res
t
o
re
v
o
l
t
a
g
e
b
al
a
n
ce,
i
n
c
l
u
d
i
n
g
rad
i
al
b
as
i
s
fu
n
ct
i
o
n
s
n
et
w
o
rk
s
(R
BFN
s
),
h
y
b
ri
d
-
RBFN
s
(
H
-
RBFN
s
),
p
o
l
y
n
o
mi
al
s
(PN
s
),
an
d
s
i
m
p
l
i
fi
e
d
n
eu
ra
l
n
et
w
o
r
k
s
(N
N
s
).
Mo
d
e
l
s
'
s
t
ru
c
t
u
re,
p
re
d
i
c
t
i
o
n
cap
a
b
i
l
i
t
y
,
an
d
res
p
o
n
s
e
t
i
me
are
an
al
y
zed
.
Res
u
l
t
s
s
h
o
w
t
h
at
t
h
e
t
i
me
req
u
i
red
fo
r
v
o
l
t
a
g
e
u
n
b
al
a
n
ce
mi
t
i
g
a
t
i
o
n
i
s
red
u
c
ed
.
Mo
re
o
v
er,
t
h
e
mo
d
e
l
s
u
s
ed
t
o
g
en
erat
e
t
h
e
fi
r
i
n
g
an
g
l
es
are
s
i
mp
l
i
f
i
ed
s
i
g
n
i
f
i
can
t
l
y
w
h
i
l
e
mai
n
t
ai
n
i
n
g
h
i
g
h
accu
racy
.
K
e
y
w
o
r
d
s
:
Ne
ur
a
l
ne
twor
k
P
owe
r
qua
li
ty
R
a
dial
ba
s
is
f
unc
ti
ons
ne
twor
ks
S
pa
c
e
ve
c
tor
T
hyr
is
tor
c
ont
r
oll
e
d
r
e
a
c
tor
Voltage
unba
lanc
e
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Da
na
R
a
ga
b
M
e
c
ha
tr
onics
E
nginee
r
ing
De
pa
r
tm
e
nt
,
P
a
les
ti
ne
T
e
c
hnica
l
Unive
r
s
it
y
-
Ka
door
ie
J
a
f
f
a
S
t,
T
ulkar
e
m
,
P
a
les
ti
ne
E
mail:
dm
r
a
f
a
t@gm
a
il
.
c
om
1.
I
NT
RODU
C
T
I
ON
Ge
ne
r
a
ti
on,
t
r
a
ns
mi
s
s
ion,
a
nd
uti
li
z
a
ti
on
o
f
e
lec
tr
ica
l
powe
r
a
r
e
c
r
it
ica
l
is
s
ue
s
pr
one
to
s
e
ve
r
a
l
powe
r
qua
li
ty
de
f
e
c
ts
.
Vol
tage
unba
lanc
e
is
on
e
of
thes
e
pr
oblems
whic
h
de
ter
io
r
a
tes
va
r
ious
s
e
c
tor
s
pe
r
f
or
manc
e
[
1]
.
T
he
thr
e
e
-
pha
s
e
powe
r
s
ys
tem
is
c
ons
ider
e
d
ba
lanc
e
d
i
f
the
th
r
e
e
-
pha
s
e
volt
a
ge
s
a
nd
c
ur
r
e
nts
a
r
e
s
ymm
e
tr
ica
l
with
a
pha
s
e
s
hif
t
o
f
120°
[
2
]
.
T
he
p
r
im
e
f
a
c
tor
that
lea
ds
to
volt
a
ge
unba
lanc
e
is
d
is
tr
ibut
ing
the
s
ingl
e
-
pha
s
e
loads
ir
r
e
gular
ly
ove
r
the
thr
e
e
-
pha
s
e
s
ys
tem.
M
or
e
ove
r
,
unba
lanc
e
c
ould
r
e
s
ult
f
r
o
m
the
a
s
ymm
e
tr
y
in
tr
a
ns
mi
s
s
ion
li
ne
s
'
im
pe
da
nc
e
s
a
nd
tr
a
ns
f
or
mer
windings
[
3]
.
Voltag
e
unba
lanc
e
ha
s
s
e
ve
r
e
e
f
f
e
c
ts
on
dif
f
e
r
e
nt
de
vice
s
,
s
uc
h
a
s
a
lt
e
r
na
ti
ng
c
ur
r
e
nt
(
AC
)
to
dir
e
c
t
c
u
r
r
e
nt
(
DC
)
c
onve
r
ter
s
,
a
djus
table
s
pe
e
d
dr
ives
,
a
nd
induction
mot
or
s
[4
]
−
[
7]
.
B
a
s
e
d
on
the
de
gr
e
e
of
volt
a
ge
unba
lanc
e
,
a
de
r
a
ti
ng
f
a
c
tor
mus
t
be
us
e
d
in
de
ter
mi
ning
t
he
mot
or
s
ize
;
f
or
ins
tanc
e
,
12
%
lar
ge
r
mot
or
is
de
mande
d
in
c
a
s
e
of
a
3
%
vo
lt
a
ge
unba
lanc
e
[
8]
.
T
he
r
e
f
or
e
,
qua
nti
f
ying
vol
tage
unba
lanc
e
is
e
s
s
e
nti
a
l
f
or
e
va
luating
s
ys
tem
pe
r
f
o
r
manc
e
a
nd
e
mpl
oying
a
s
uit
a
ble
c
ontr
ol.
T
o
f
ul
f
il
l
thi
s
r
e
quir
e
ment,
the
e
nginee
r
i
ng
c
omm
unit
y
de
f
ined
s
e
ve
r
a
l
indi
c
e
s
to
e
va
l
ua
t
e
volt
a
ge
unba
lanc
e
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mple
me
ntat
ion
of
r
e
ac
ti
v
e
c
ompe
ns
ator
for
v
olt
age
balancing
us
ing
…
(
Dana
M
.
R
agab
)
595
T
he
t
r
ue
r
e
pr
e
s
e
ntation
of
vol
tage
unba
lanc
e
,
wa
s
s
tate
d
by
in
ter
na
ti
ona
l
e
lec
tr
otec
hnica
l
c
omm
is
s
ion
(
I
E
C
)
a
s
the
r
a
ti
o
be
twe
e
n
the
ne
ga
ti
ve
a
nd
pos
it
ive
s
e
que
nc
e
volt
a
ge
s
.
T
h
is
index
is
k
nown
a
s
volt
a
ge
unba
lanc
e
f
a
c
tor
(
VU
F
)
[
9]
.
I
ns
ti
tut
e
of
E
lec
tr
ica
l
a
nd
E
lec
tr
onics
E
nginee
r
s
(
I
E
E
E
)
a
ppr
ov
e
d
thr
e
e
de
f
ini
ti
ons
f
or
vol
tage
unba
lanc
e
.
Ac
c
or
ding
to
I
E
E
E
S
td.
936
-
1987,
volt
a
ge
unba
lanc
e
is
e
xpr
e
s
s
e
d
a
s
"
the
dif
f
e
r
e
nc
e
be
twe
e
n
the
highes
t
a
nd
the
lowe
s
t
R
M
S
pha
s
e
volt
a
ge
,
r
e
f
e
r
r
e
d
to
the
a
ve
r
a
ge
of
the
thr
e
e
volt
a
ge
s
"
[
10]
.
Additi
ona
ll
y
,
I
E
E
E
S
td
.
112
-
1991,
int
r
oduc
e
d
pha
s
e
volt
a
ge
unba
lanc
e
r
a
te
(
P
VU
R
)
,
whic
h
is
de
f
ined
a
s
the
maximum
de
viation
f
r
om
the
a
ve
r
a
ge
of
pha
s
e
volt
a
ge
s
divi
de
d
by
thi
s
a
ve
r
a
ge
[
11
]
.
F
inally
,
I
E
E
E
S
td
.
1159
c
on
f
ir
med
the
de
f
ini
t
ion
pr
e
s
e
nted
by
I
E
C
in
a
ddit
ion
to
I
E
E
E
S
td.
112
[
12]
.
F
u
r
th
e
r
mor
e
,
na
ti
ona
l
e
lec
tr
ica
l
manuf
a
c
tur
e
r
s
a
s
s
oc
iation
(
NE
M
A
)
a
uthentica
ted
a
nother
s
tanda
r
d
index
know
n
a
s
li
ne
volt
a
ge
unba
lanc
e
r
a
ti
o
(
L
VU
R
)
.
I
t
is
de
f
ined
a
s
t
he
r
a
ti
o
be
twe
e
n
the
maximum
de
viation
f
r
om
the
a
ve
r
a
ge
of
li
ne
volt
a
ge
s
a
nd
thi
s
a
ve
r
a
ge
[
13]
.
All
thes
e
indi
c
e
s
r
e
ly
on
the
c
a
lcula
ti
on
of
the
R
M
S
volt
a
ge
s
ther
e
f
or
e
20
ms
is
r
e
quir
e
d
a
t
lea
s
t
to
c
a
lcula
te
them.
M
or
e
ove
r
,
s
e
ve
r
a
l
publi
c
a
ti
ons
int
r
oduc
e
d
other
f
a
c
tor
s
to
e
va
luate
or
a
s
s
e
s
s
the
e
f
f
e
c
t
o
f
volt
a
ge
unba
lanc
e
on
the
s
ys
tem.
T
hr
e
e
indi
c
e
s
,
na
mely
,
maximum
c
ur
r
e
nt
de
viation
(
M
C
D)
,
c
ombi
ne
d
c
ur
r
e
nt
de
viatio
n
(
C
M
C
D)
,
a
nd
e
f
f
e
c
ti
ve
c
ur
r
e
nt
de
viatio
n
(
E
C
D)
,
we
r
e
pr
opos
e
d
in
[
14]
.
He
nr
iques
a
nd
C
or
mane
i
n
[
15]
,
volt
a
g
e
unba
lanc
e
wa
s
e
va
luate
d
in
the
ti
me
domain,
a
nd
volt
a
ge
unba
lanc
e
leve
l
(
VU
L
)
pe
r
f
or
manc
e
index
wa
s
pr
opos
e
d.
T
his
index
r
e
quir
e
s
many
s
teps
f
or
c
a
lcula
ti
on
ba
s
e
d
on
the
s
e
c
ond
-
or
de
r
volt
a
ge
tens
or
theor
y.
T
he
s
ubs
e
que
nt
s
tep
whe
n
unba
lanc
e
e
xc
e
e
d
s
the
a
ll
owa
ble
li
mi
t
whic
h
is
3
%
a
c
c
or
ding
to
Ame
r
ica
n
Na
ti
ona
l
S
tanda
r
ds
I
ns
ti
tut
e
(
AN
S
I
)
s
tanda
r
d
is
volt
a
ge
unba
lanc
e
mi
t
igation
[
16
]
.
M
a
ny
tec
hniques
we
r
e
pr
opos
e
d
in
the
li
ter
a
tur
e
f
or
th
is
pur
pos
e
,
in
[
17
]
dyna
mi
c
r
e
c
onf
igur
a
ti
on
wa
s
us
e
d
to
ba
lanc
e
the
d
is
tr
ibut
ion
s
ys
tem
by
c
ha
nging
the
di
s
tr
ibut
ion
ne
twor
k
s
tr
uc
tur
e
.
Othe
r
tec
hniques
that
e
mpl
oy
dyna
mi
c
volt
a
ge
r
e
s
tor
e
r
or
a
un
if
ied
powe
r
c
ondit
ioner
to
r
e
s
tor
e
volt
a
ge
we
r
e
pr
opos
e
d
in
[
18
]
a
nd
[
19
]
.
Anothe
r
e
f
f
icie
nt
tec
hnique
is
the
us
e
of
f
lexi
ble
AC
tr
a
ns
mi
s
s
ion
s
y
s
tem
(
F
AC
T
S
)
de
vice
s
.
T
he
s
e
de
vice
s
include
s
ta
ti
c
VA
R
c
om
pe
ns
a
tor
s
(
S
VC
)
a
nd
s
tatic
s
ync
hr
onous
c
ompens
a
tor
s
(
S
T
AT
C
OM
)
,
w
hich
a
r
e
wide
ly
us
e
d
in
volt
a
ge
ba
lanc
ing
[
20
]
−
[
22
]
.
E
s
f
a
ha
ni
a
nd
Va
hidi
i
n
[
23]
,
a
c
ombi
na
ti
on
of
t
hyr
is
tor
-
c
ontr
oll
e
d
r
e
a
c
tor
(
T
C
R
)
a
nd
S
T
A
T
C
OM
wa
s
im
pleme
nted
to
r
e
s
tor
e
volt
a
ge
ba
lanc
ing
a
nd
r
e
duc
e
c
ur
r
e
nt
ha
r
moni
c
s
.
S
e
ve
r
a
l
c
ontr
ol
a
lgor
it
hms
we
r
e
p
r
opos
e
d
f
or
S
VC
c
ontr
ol
[
24]
.
T
he
us
e
of
a
P
I
c
ont
r
oll
e
r
with
S
VC
f
or
volt
a
ge
r
e
gulation
pur
pos
e
s
wa
s
dis
c
us
s
e
d
in
[
25]
.
H
ybr
id
a
lgo
r
it
hms
that
us
e
ne
ur
a
l
ne
twor
k
s
(
NN
s
)
dur
ing
onli
ne
mode
f
o
r
volt
a
ge
ba
lanc
ing
a
nd
other
a
lgor
it
hms
to
ge
ne
r
a
te
the
f
i
r
ing
a
ngles
of
t
he
T
C
R
c
ompens
a
tor
dur
ing
of
f
li
ne
mode
we
r
e
c
ons
ider
e
d
[
26]
−
[
28]
.
A
f
uz
z
y
r
a
nking
s
ys
tem
wa
s
us
e
d
i
n
[
26]
to
pr
ovide
the
opti
mum
s
e
t
of
f
ir
ing
a
ngles
ba
s
e
d
on
ha
r
moni
c
mi
nim
iza
ti
on
.
R
uba
iey
a
nd
R
uba
yi
[
27]
,
a
gr
a
vit
a
ti
ona
l
s
e
a
r
c
h
a
lgor
it
hm
(
GSA)
r
e
plac
e
d
the
f
uz
z
y
logi
c
with
the
s
a
me
objec
ti
ve
s
of
r
e
duc
ing
ha
r
moni
c
s
a
nd
r
e
s
tor
ing
vo
lt
a
ge
ba
lanc
ing.
P
a
r
ti
c
l
e
s
wa
r
m
opti
mi
z
a
ti
on
(
PSO
)
a
lgo
r
it
hm
with
the
o
bjec
ti
ve
f
unc
ti
on
o
f
r
e
duc
ing
VU
F
wa
s
pr
opos
e
d
in
[
28]
.
R
a
ga
b
e
t
al
.
[
29
]
,
p
r
opos
e
d
the
NN
wa
s
im
pleme
nte
d
dur
ing
the
onli
ne
mode
to
r
e
t
r
ieve
volt
a
ge
ba
lanc
e
,
whi
le
da
ta
r
e
qui
r
e
d
f
or
NN
t
r
a
ini
ng
we
r
e
obtaine
d
us
ing
a
n
e
xpe
r
im
e
ntally.
R
a
dial
ba
s
is
f
unc
ti
ons
ne
twor
ks
(
R
B
F
N
s
)
we
r
e
us
e
d
in
[
30]
a
nd
[
31]
f
or
S
VC
c
ontr
ol,
to
im
pr
ove
the
s
tabili
ty
of
the
e
lec
tr
ica
l
powe
r
s
ys
tem.
Guo
e
t
al
.
[
32]
,
us
e
d
a
model
ba
s
e
d
on
R
B
F
NN
s
a
nd
pr
incipa
l
c
omponent
a
na
lys
is
(
P
C
A)
method
wa
s
p
r
opos
e
d
t
o
moni
tor
the
powe
r
s
ys
tem.
T
he
R
R
B
F
NN
wa
s
s
ugge
s
ted
to
de
a
l
with
non
li
ne
a
r
da
ta
then
the
P
C
A
wa
s
e
mpl
oye
d
to
pe
r
f
or
m
is
landing
de
tec
ti
on.
B
oth
NN
s
a
nd
R
B
F
Ns
a
r
e
good
c
a
ndi
da
tes
to
model
c
ompl
e
x
e
nginee
r
ing
s
ys
tems
.
T
he
c
ontr
ibu
ti
on
to
knowle
d
ge
in
thi
s
wor
k
c
a
n
be
s
umm
a
r
ize
d
i
s
be
ing
a
s
:
−
P
r
opos
ing
a
nove
l
index
f
o
r
volt
a
ge
-
unba
lanc
e
e
va
luation.
T
h
is
index
de
pe
nds
on
the
S
V
magnit
ude
to
c
a
lcula
te
volt
a
ge
unba
lanc
e
pe
r
c
e
ntage
,
r
e
duc
ing
t
he
ti
me
r
e
qui
r
e
d
f
o
r
unba
lanc
e
e
va
luation
by
ha
lf
.
−
P
r
opos
ing
s
e
ve
r
a
l
models
to
ge
ne
r
a
te
the
r
e
quir
e
d
f
i
r
ing
a
ngles
of
T
C
R
to
r
e
s
tor
e
volt
a
ge
ba
la
nc
e
.
M
ode
ls
ba
s
e
d
on
R
B
F
Ns
,
hybr
id
-
R
B
F
N
s
(
H
-
R
B
F
Ns
)
,
polynom
ials
(
P
Ns
)
,
a
nd
NN
a
r
e
p
r
opos
e
d
wit
h
the
unba
lanc
e
d
thr
e
e
load
vo
lt
a
ge
s
only
a
s
input
da
ta
a
nd
the
th
r
e
e
f
i
r
ing
a
ngles
of
T
C
R
a
s
output
da
ta.
T
he
s
ugge
s
ted
NN
ha
s
a
ve
r
y
s
im
ple
s
tr
uc
tur
e
c
ons
is
ti
ng
of
one
hidden
laye
r
with
ten
ne
ur
ons
.
Als
o,
the
pr
opos
e
d
R
B
F
Ns
a
nd
NN
s
hows
a
high
pe
r
f
or
manc
e
in
pr
e
diction
c
a
pa
bil
it
ies
.
−
E
nha
nc
ing
the
r
e
s
pons
e
ti
me
r
e
qui
r
e
d
f
or
volt
a
ge
unba
lanc
e
mi
ti
ga
ti
on
thr
ough
im
pr
ove
ments
in
bo
t
h
the
e
va
luation
a
nd
c
ontr
ol
p
r
oc
e
s
s
.
T
h
e
pa
pe
r
is
o
r
ga
ni
z
e
d
is
be
in
g
a
s
:
th
e
un
ba
lan
c
e
d
th
r
e
e
p
ha
s
e
pow
e
r
s
ys
t
e
m
is
in
t
r
o
du
c
e
d
in
s
ec
t
io
n
2
.
T
h
e
n
s
pa
c
e
ve
c
t
o
r
un
ba
la
nc
e
f
a
c
t
o
r
(
S
V
UF
)
is
p
r
opo
s
e
d
f
or
vo
l
tag
e
u
nba
la
nc
e
e
va
lu
a
t
io
n
i
n
s
e
c
t
io
n
3
.
A
f
te
r
t
ha
t
s
e
c
t
io
n
4
d
is
c
us
s
e
s
t
he
s
ug
ge
s
te
d
m
od
e
ls
f
o
r
vol
t
a
ge
u
nba
la
nc
e
c
o
n
tr
o
l
.
I
n
s
e
c
ti
on
5
th
e
c
on
t
r
i
bu
t
io
n
to
k
n
ow
led
ge
in
th
is
w
o
r
k
is
e
la
bo
r
a
te
d
.
F
in
a
l
l
y
,
t
he
c
on
c
l
us
io
n
is
gi
ve
n
i
n
s
e
c
t
io
n
6
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
594
-
605
596
2.
UN
B
AL
AN
C
E
D
T
HRE
E
P
HAS
E
P
OWE
R
S
Y
S
T
E
M
T
hr
e
e
-
pha
s
e
powe
r
s
ys
tems
ope
r
a
te
e
f
f
icie
ntl
y
unde
r
ba
lanc
e
d
c
ondit
ions
.
How
e
ve
r
,
volt
a
ge
-
unba
lanc
e
a
r
is
e
s
in
s
e
ve
r
a
l
s
it
ua
ti
ons
a
nd
de
gr
a
de
s
s
ys
tem
pe
r
f
or
manc
e
.
I
n
thi
s
wor
k
,
Aqa
ba
Qa
tr
a
na
S
outh
Amman
(
AQ
S
A)
e
lec
tr
ica
l
powe
r
s
ys
tem
is
mo
de
led
a
nd
s
im
ulate
d
in
M
AT
L
AB
/S
im
uli
nk,
a
s
s
hown
in
F
igur
e
1.
T
he
s
ys
tem's
tot
a
l
length
is
328
km
,
s
tar
t
ing
a
t
Aqa
ba
s
tation,
whic
h
ope
r
a
tes
a
t
14
kV
.
T
hi
s
volt
a
ge
is
s
teppe
d
up
to
400
kV
a
nd
c
onne
c
ted
to
the
p
owe
r
s
ys
tem
li
ne
.
T
wo
s
ubs
tations
s
pli
t
the
li
ne
;
Qa
tr
a
na
s
ubs
ta
ti
on
(
bus
2)
a
t
245
km
a
nd
Amman
S
out
h
s
ubs
tation
(
bus
3
)
a
t
328
km,
r
e
s
pe
c
ti
ve
ly.
I
n
or
de
r
to
r
e
pr
e
s
e
nt
thes
e
tr
a
ns
mi
s
s
ion
li
ne
s
,
thr
e
e
pi
-
s
e
c
ti
on
s
a
r
e
us
e
d;
e
a
c
h
c
ons
is
t
s
of
two
s
hunt
c
a
pa
c
it
or
s
a
nd
s
e
r
ies
inductor
a
nd
r
e
s
is
tor
[
29]
.
At
S
outh
Amman
s
ubs
tation,
the
volt
a
ge
is
s
teppe
d
down
to
132
,
33
,
11
,
a
nd
0.
38
kV
a
t
whic
h
the
thr
e
e
-
pha
s
e
loads
a
r
e
c
onne
c
ted.
As
the
powe
r
c
ons
umpt
ion
by
the
loads
is
a
s
ymm
e
tr
ica
l
ove
r
t
he
thr
e
e
pha
s
e
s
,
volt
a
ge
unba
lanc
e
a
r
is
e
s
.
I
n
thi
s
c
a
s
e
,
the
c
ur
r
e
nts
dr
a
wn
by
the
loa
ds
a
r
e
not
identica
l,
pr
oduc
ing
a
s
ymm
e
tr
ica
l
volt
a
ge
dr
op
a
c
r
os
s
the
tr
a
ns
mi
s
s
ion
li
ne
a
nd
c
ons
e
que
nti
a
ll
y
unba
lanc
e
d
load
vol
tage
s
.
I
n
or
de
r
to
r
e
s
tor
e
volt
a
ge
ba
lanc
e
,
a
T
C
R
c
ompe
ns
a
tor
is
ins
talled
a
t
bus
3.
T
his
type
o
f
r
e
a
c
ti
ve
powe
r
c
ompens
a
tor
pr
ovi
de
s
a
good
c
a
pa
bil
it
y
f
or
ind
ivi
dua
l
pha
s
e
c
ontr
ol
a
nd
f
a
s
t
r
e
s
pons
e
.
B
y
va
r
ying
t
he
f
ir
ing
a
ngles
be
twe
e
n
90°
a
nd
180°,
the
a
bs
or
be
d
r
e
a
c
ti
ve
powe
r
va
r
ies
a
c
c
or
dingl
y.
I
n
the
c
a
s
e
of
volt
a
ge
unba
lanc
e
,
the
p
r
ovided
lagging
VA
R
s
dif
f
e
r
a
c
c
or
ding
to
e
a
c
h
ph
a
s
e
r
e
quir
e
ments
,
a
nd
thus
th
e
c
ontr
ol
a
c
ti
on
c
a
n
be
c
a
r
r
ied
out
by
f
ir
ing
e
a
c
h
pa
ir
of
th
yr
is
tor
s
with
pr
ope
r
f
ir
ing
a
ngles
[
20]
.
T
he
r
e
quir
e
d
f
ir
ing
a
ngles
a
r
e
de
ter
mi
ne
d
us
ing
s
e
ve
r
a
l
a
lgor
it
hms
,
a
s
dis
c
us
s
e
d
in
s
e
c
ti
on
4.
F
igur
e
1.
AQ
S
A
powe
r
s
ys
tem
S
im
uli
nk
model
3.
VOL
T
AGE
UN
B
A
L
AN
CE
E
VA
L
UA
T
I
ON
USI
NG
S
VU
F
I
n
th
is
s
e
c
ti
on
s
tanda
r
d
indi
c
e
s
us
e
d
f
or
volt
a
ge
unba
lanc
e
e
va
luation
a
r
e
int
r
oduc
e
d,
a
nd
the
ne
w
S
VU
F
index
is
p
r
opos
e
d
a
nd
c
ompar
e
d
to
thes
e
in
dice
s
.
3.
1
.
Volt
age
u
n
b
ala
n
c
e
f
a
c
t
or
T
he
s
ymm
e
tr
ica
l
c
omponents
theor
y
c
a
n
be
us
e
d
to
a
na
lyze
a
nd
s
tudy
the
powe
r
s
ys
tem
unde
r
unba
lanc
e
d
c
ondit
ions
[
33]
.
I
n
the
c
ontext
of
thi
s
wor
k,
it
is
us
e
d
a
s
a
pa
r
t
of
VU
F
c
a
lcula
ti
on.
Ac
c
or
ding
to
thi
s
theor
y,
the
thr
e
e
-
pha
s
e
unba
lanc
e
d
c
omponent
s
c
a
n
be
e
xpr
e
s
s
e
d
a
s
a
s
e
t
of
ba
lanc
e
d
(
i
.
e
.
,
s
ym
metr
ica
l)
one
s
.
T
he
s
e
s
ymm
e
tr
ica
l
c
omponents
a
r
e
known
a
s
pos
it
ive,
ne
ga
ti
ve
,
a
nd
z
e
r
o
s
e
que
nc
e
c
omponents
.
B
oth
the
pos
it
ive
a
nd
ne
ga
ti
ve
s
e
que
nc
e
volt
a
ge
s
ha
ve
e
qua
l
magnitudes
a
nd
a
pha
s
e
s
hif
t
of
120°.
B
ut
the
ne
ga
ti
ve
s
e
que
nc
e
volt
a
ge
s
r
otate
in
the
oppos
it
e
dir
e
c
ti
on
of
pos
it
ive
s
e
que
nc
e
volt
a
ge
s
.
T
he
z
e
r
o
-
s
e
que
nc
e
volt
a
ge
s
ha
ve
e
qua
l
magnitude
s
,
z
e
r
o
pha
s
e
s
hif
t,
a
nd
f
ixed
(
i.
e
.
,
do
not
r
otate
)
.
T
he
s
ymm
e
tr
ica
l
c
o
mponents
c
a
n
be
r
e
pr
e
s
e
nted
in
ter
ms
o
f
the
thr
e
e
-
pha
s
e
volt
a
ge
s
is
be
ing
a
s
[
33]
:
0
=
⅓
(
+
+
)
(
1)
1
=
⅓
(
+
+
2
)
(
2)
2
=
⅓
(
+
2
+
)
(
3)
W
he
r
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mple
me
ntat
ion
of
r
e
ac
ti
v
e
c
ompe
ns
ator
for
v
olt
age
balancing
us
ing
…
(
Dana
M
.
R
agab
)
597
,
:
T
hr
e
e
-
pha
s
e
unba
lanc
e
d
volt
a
ge
s
.
0
,
1
2
∶
Z
e
r
o,
pos
it
ive,
a
nd
ne
ga
ti
ve
s
e
que
nc
e
c
omponents
of
the
th
r
e
e
-
pha
s
e
volt
a
ge
s
,
r
e
s
pe
c
ti
ve
ly.
T
he
VU
F
,
whic
h
r
e
p
r
e
s
e
nts
the
tr
ue
de
f
ini
ti
on,
c
a
n
be
c
a
lcula
ted
a
c
c
or
ding
to
the
f
o
ll
owing
e
qua
ti
on:
V
U
F
=
V
2
V
1
x1
0
0
%
(
4)
3.
2
.
P
h
as
e
volt
age
u
n
b
alan
c
e
r
at
e
I
n
te
r
ms
of
I
E
E
E
s
tanda
r
ds
,
the
P
VU
R
s
a
r
e
give
n
by
(
5
)
a
nd
(
6
)
with
s
ubs
c
r
ipt
s
r
e
f
e
r
r
ing
to
the
s
tanda
r
d’
s
na
me
[
11
]
,
[
12]
.
T
he
P
VU
R
is
de
f
ined
by
I
E
E
E
-
S
td.
112
a
s
the
maximum
de
viation
f
r
om
the
a
ve
r
a
ge
of
th
r
e
e
-
pha
s
e
volt
a
ge
s
to
the
a
ve
r
a
ge
o
f
t
hr
e
e
-
pha
s
e
volt
a
ge
s
.
T
he
I
E
E
E
-
S
td.
936
de
f
ined
P
VU
R
a
s
the
dif
f
e
r
e
nc
e
be
twe
e
n
the
highes
t
a
nd
lowe
s
t
vol
tage
to
the
a
ve
r
a
ge
of
th
r
e
e
-
pha
s
e
volt
a
ge
s
.
I
ts
c
a
lcula
ti
on
de
pe
nds
on
the
R
M
S
of
the
volt
a
ge
s
,
whic
h
r
e
quir
e
s
20
ms
of
t
im
e
.
112
=
ℎ
ℎ
100
%
(
5)
936
=
ℎ
ℎ
ℎ
1
00
%
(
6)
3.
3
.
L
in
e
vol
t
age
u
n
b
alan
c
e
r
at
io
In
(
7
)
r
e
pr
e
s
e
nts
the
NE
M
A
de
f
ini
ti
on
f
o
r
L
VU
R
[
13]
.
I
ts
c
a
lcula
ti
on
de
pe
nds
on
the
R
M
S
of
the
volt
a
ge
s
,
whic
h
r
e
quir
e
s
20
ms
of
ti
me.
=
ℎ
100
%
(
7)
3.
4
.
S
p
ac
e
ve
c
t
or
u
n
b
ala
n
c
e
f
ac
t
or
I
n
thi
s
wor
k
,
a
n
a
dva
nc
e
d
index
to
e
va
luate
vol
tage
unba
lanc
e
ba
s
e
d
on
S
V
s
ignal
is
pr
opos
e
d.
S
pa
c
e
ve
c
tor
unba
lanc
e
f
a
c
tor
(
S
VU
F
)
is
the
s
ugg
e
s
ted
na
me
f
or
the
pr
opos
e
d
index.
I
n
ge
ne
r
a
l
,
the
S
V
is
a
c
ompl
e
x
va
r
iable
us
e
d
to
r
e
pr
e
s
e
nt
the
tot
a
l
e
f
f
e
c
t
of
s
ys
tem
volt
a
ge
s
,
a
s
s
hown
by
(
8
)
[
29]
.
W
he
n
the
thr
e
e
-
pha
s
e
powe
r
s
ys
tem
is
ba
lanc
e
d,
the
S
V
ma
gnit
ude
is
c
ons
tant
a
nd
c
a
n
be
c
ons
ider
e
d
a
s
a
DC
s
ignal.
W
he
r
e
a
s
,
whe
n
the
th
r
e
e
-
pha
s
e
volt
a
ge
s
a
r
e
unba
lanc
e
d,
the
ins
tanta
ne
ous
va
lues
of
the
S
V
magnit
ude
va
r
y
c
onti
nuous
ly
pr
oduc
ing
a
s
inus
oidal
s
ignal.
T
h
e
f
r
e
que
nc
y
of
thi
s
s
ignal
is
twice
the
s
ys
tem
volt
a
ge
s
f
r
e
que
nc
y
[
29]
.
̅
=
+
1
√
3
(
−
)
(
8)
T
he
magnitude
o
f
S
V
|
̅
|
c
a
n
be
c
a
lcula
ted
by
(
9)
[
34]
.
|
̅
|
=
√
2
+
1
3
(
−
)
2
(
9)
W
he
r
e
:
v
a
,
v
b
,
a
nd
v
c
:
T
he
th
r
e
e
-
pha
s
e
load
volt
a
ge
s
.
T
he
pr
opos
e
d
S
VU
F
is
de
f
ined
a
s
the
r
a
ti
o
be
twe
e
n
the
a
mpl
it
ude
s
of
the
S
V
AC
s
ignal
a
nd
the
S
V
DC
s
ignal.
Or
"
T
he
r
a
ti
o
be
twe
e
n
the
S
V
a
mpl
it
ude
s
unde
r
unba
lanc
e
d
a
nd
ba
lanc
e
d
c
on
dit
ions
"
.
Ac
c
or
dingl
y,
S
VU
F
c
a
n
be
c
a
lcula
ted
f
r
om
(
10
)
.
%
=
(
)
(
)
∗
100
%
(
10)
W
he
r
e
:
(
)
:
S
V
a
mpl
it
ude
unde
r
ba
lanc
e
d
c
ondit
ion
.
(
)
:
S
V
a
mpl
it
ude
unde
r
unba
lanc
e
d
c
ondit
ion
.
F
igur
e
2
s
hows
the
th
r
e
e
-
pha
s
e
volt
a
ge
s
a
nd
S
V
a
mpl
it
ude
f
or
the
c
ons
ider
e
d
AQ
S
A
s
ys
tem
unde
r
ba
lanc
e
d
c
ondit
ions
.
T
he
S
V
a
mpl
it
ude
e
qua
ls
3
62
V,
whic
h
is
take
n
a
s
a
r
e
f
e
r
e
nc
e
DC
va
lue.
F
igur
e
3
s
hows
the
S
V
s
ignal
in
c
a
s
e
of
volt
a
ge
unba
lanc
e
in
whic
h
the
VU
F
is
4.
11%
.
I
n
thi
s
c
a
s
e
,
the
a
mpl
it
ude
of
S
V
is
14.
65
V,
a
nd
a
c
c
or
ding
to
(
10
)
,
the
S
VU
F
c
a
n
be
c
a
lcula
ted
is
be
ing
a
s
:
%
=
(
)
(
)
∗
100
%
=
14
.
65
3
6
2
∗
100%
=
4
.
04%
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
594
-
605
598
F
igur
e
4
s
hows
a
nother
c
a
s
e
in
whic
h
the
VU
F
e
qua
ls
1.
567%
,
a
nd
the
S
V
a
mpl
it
ude
is
5.
634
V
,
a
nd
a
c
c
or
dingl
y,
the
S
VU
F
is
1
.
556
%
.
T
he
a
bs
olut
e
e
r
r
or
be
twe
e
n
the
obtaine
d
S
VU
F
a
nd
the
r
e
a
l
VU
F
is
only
0.
07
%
a
nd
0.
011
%
,
r
e
s
pe
c
ti
ve
ly.
T
his
c
on
f
ir
ms
the
a
c
c
ur
a
c
y
o
f
the
pr
opos
e
d
S
VU
F
f
or
the
c
a
l
c
ulation
of
the
unba
lanc
e
f
a
c
to
r
in
unba
lanc
e
d
thr
e
e
pha
s
e
powe
r
s
ys
tem.
F
igur
e
2.
S
V
s
ignal
a
nd
ba
lanc
e
d
thr
e
e
-
pha
s
e
volt
a
ge
s
F
igur
e
3.
S
V
s
ignal
a
nd
unba
lanc
e
d
thr
e
e
-
pha
s
e
volt
a
ge
s
with
%
S
VU
F
o
f
4
.
04%
a
nd
%
VU
F
of
4.
11
%
F
igur
e
4.
S
V
s
ignal
with
%
S
VU
F
o
f
1
.
567%
a
nd
%
VU
F
of
1.
566
%
T
a
ble
1
s
hows
the
S
VU
F
a
nd
the
other
s
tanda
r
d
indi
c
e
s
(
L
VU
F
,
P
VU
F
112
,
a
nd
P
VU
F
936
)
in
c
ompar
is
on
with
the
t
r
ue
va
lue
whic
h
is
r
e
pr
e
s
e
nted
by
VU
F
.
I
t
c
a
n
be
s
e
e
n
that
the
va
lues
obtaine
d
u
s
ing
the
pr
opos
e
d
S
VU
F
pr
ovide
a
de
qua
te
r
e
pr
e
s
e
ntation
f
o
r
volt
a
ge
unba
lanc
e
pe
r
c
e
ntage
in
the
s
ys
tem.
F
ur
ther
mor
e
,
the
a
ve
r
a
ge
of
a
bs
olut
e
e
r
r
or
s
f
o
r
e
a
c
h
pe
r
f
or
manc
e
index
is
c
a
lcula
ted,
a
s
s
umi
ng
t
ha
t
the
%
VU
F
r
e
pr
e
s
e
nts
the
tr
ue
va
lue.
I
t
is
noti
c
e
a
ble
that
the
pr
opos
e
d
pe
r
f
o
r
manc
e
index
S
VU
F
p
r
ov
ides
the
lea
s
t
a
ve
r
a
ge
a
bs
olut
e
e
r
r
or
,
whic
h
e
qua
ls
to
0
.
48
%
.
T
he
pr
opos
e
d
index
pr
ovides
good
a
c
c
ur
a
c
y
wh
il
e
s
ur
pa
s
s
e
s
other
indi
c
e
s
in
s
e
ve
r
a
l
a
s
pe
c
ts
.
I
t
e
li
mi
na
tes
the
ne
e
d
to
e
xpr
e
s
s
the
s
y
s
tem
volt
a
ge
s
in
ter
ms
of
the
s
ymm
e
tr
ica
l
c
omponents
r
e
quir
e
d
f
or
the
VU
F
c
a
lcula
ti
on.
M
or
e
ove
r
,
the
S
V
s
ignal
ha
s
tw
ice
the
f
r
e
que
nc
y
of
the
s
ys
tem
volt
a
ge
s
s
ignal,
h
e
nc
e
thi
s
s
ignal's
a
mpl
it
ude
c
a
n
be
p
r
ovided
wi
thi
n
ha
lf
of
the
s
ys
tem
c
yc
le
(
i.
e
.
,
10
ms
f
or
50
Hz
s
ignal
f
r
e
que
nc
y)
.
W
hil
e
the
R
M
S
va
lues
of
s
ys
tem
volt
a
ge
s
r
e
quir
e
20
ms
a
t
lea
s
t
whe
n
unba
lanc
e
c
ondit
ions
a
r
e
p
r
e
s
e
nted
in
s
ys
tem.
C
ons
e
que
ntl
y,
the
p
r
opos
e
d
index
outdoe
s
the
tr
a
dit
ional
pe
r
f
or
manc
e
i
nd
ice
s
by
r
e
duc
ing
the
ti
me
ne
c
e
s
s
a
r
y
to
de
tec
t
a
nd
e
va
luate
volt
a
ge
unba
lanc
e
to
ha
lf
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mple
me
ntat
ion
of
r
e
ac
ti
v
e
c
ompe
ns
ator
for
v
olt
age
balancing
us
ing
…
(
Dana
M
.
R
agab
)
599
T
a
ble
1.
P
r
opos
e
d
S
VU
F
a
nd
s
tanda
r
d
indi
c
e
s
in
c
ompar
is
on
with
VU
F
S
V
a
mpl
it
ude
%
%
%
%
112
%
9
3
6
11.9
3.4
3.29
3.31
3.24
5.59
8.405
2.38
2.32
2.36
2.35
3.88
21.76
6.35
6.01
5.59
5.47
10.9
20.05
5.83
5.54
5.19
5.85
9.93
23.71
6.93
6.55
6.18
6.29
11.9
39.17
12
10.8
10.5
10.5
20.6
34.82
10.5
9.62
9.48
9.13
18.1
32.19
9.68
8.89
8.73
8.44
16.6
30.25
9.01
8.36
7.8
8.05
15.6
28.3
8.37
7.82
7.45
7.68
14.4
14.62
4.11
4.04
4.06
4.16
6.48
A
ve
r
a
ge
a
bs
ol
ut
e
e
r
r
or
0%
0.48%
0.72%
0.69%
5.04%
4.
VOL
T
AGE
UN
B
A
L
AN
CE
M
I
T
I
GA
T
I
ON
I
n
thi
s
wor
k,
a
T
C
R
r
e
a
c
ti
ve
powe
r
c
ompens
a
tor
a
t
the
load
s
ide
is
a
ppli
e
d
to
r
e
s
tor
e
the
volt
a
ge
ba
lanc
e
f
or
the
328
km
AQ
S
A
powe
r
s
ys
tem.
B
y
de
ter
mi
ning
the
f
i
r
ing
a
ngles
of
the
T
C
R
,
the
a
mount
of
r
e
a
c
ti
ve
powe
r
c
a
n
be
c
ont
r
oll
e
d
a
nd
ba
lanc
e
d
c
ondit
ions
c
a
n
be
a
c
hieve
d.
I
n
thi
s
s
e
c
ti
on
f
our
i
ntelli
ge
nt
models
:
R
B
F
Ns
,
H
-
R
B
F
Ns
,
P
Ns
,
a
nd
NN
s
a
r
e
pr
o
pos
e
d
to
ge
ne
r
a
te
the
r
e
qui
r
e
d
T
C
R
f
ir
ing
a
ngles
.
T
he
n
the
be
s
t
models
a
r
e
va
li
da
ted
thr
ough
the
e
mpl
oyment
on
the
AQ
S
A
powe
r
s
ys
tem
c
ons
ider
ing
the
VU
F
a
s
the
c
r
it
e
r
ion
f
or
a
s
s
e
s
s
ment.
F
inally,
the
two
s
teps
of
volt
a
ge
unba
lanc
e
e
va
luation
a
nd
m
it
igation
us
in
g
S
VU
F
a
nd
int
e
ll
igent
models
a
r
e
pe
r
f
or
med,
r
e
s
pe
c
ti
ve
ly.
All
the
pr
opos
e
d
int
e
ll
igent
models
uti
li
z
e
the
th
r
e
e
pha
s
e
volt
a
ge
s
a
s
input
s
to
pr
e
dict
the
r
e
qui
r
e
d
thr
e
e
f
ir
ing
a
ngles
f
or
volt
a
ge
ba
lanc
ing.
A
M
AT
L
AB
/S
im
uli
nk
model
of
AQ
S
A
is
us
e
d
to
ge
ne
r
a
t
e
the
da
ta
s
e
t
that
a
r
e
us
e
d
to
tr
a
in
the
p
r
opos
e
d
int
e
ll
igent
models
e
mpi
r
ica
ll
y.
T
h
is
pr
oc
e
dur
e
wa
s
f
oll
owe
d
to
r
e
duc
e
the
number
o
f
pa
r
a
mete
r
s
us
e
d
a
s
the
input
da
ta.
B
e
c
a
us
e
e
qua
ti
ons
r
e
quir
e
d
to
c
a
lcula
te
the
f
ir
in
g
a
ngles
de
pe
nd
on
a
t
lea
s
t
s
ix
pa
r
a
m
e
ter
s
,
including
thr
e
e
load
volt
a
ge
s
,
c
ur
r
e
nts
,
r
e
a
l
powe
r
s
,
a
nd
r
e
a
c
ti
ve
powe
r
s
,
ther
e
f
or
e
us
ing
thes
e
e
qua
ti
ons
to
ge
ne
r
a
te
the
da
ta
dur
ing
o
f
f
li
ne
mode
then
e
xc
ludi
ng
pa
r
t
of
them
a
s
in
[
27
]
a
nd
[
28]
a
f
f
e
c
ts
the
qua
li
ty
of
da
ta.
C
ons
e
que
nti
a
ll
y,
NN
's
w
it
h
c
ompl
e
x
s
tr
uc
tur
e
s
we
r
e
ne
c
e
s
s
a
r
y
to
pe
r
f
or
m
the
r
e
gr
e
s
s
ion
with
r
e
s
ult
s
s
howing
mode
r
a
te
pe
r
f
o
r
manc
e
dur
ing
the
tes
ti
ng
pha
s
e
.
230
s
a
mpl
e
s
of
da
ta
s
e
t
a
r
e
ge
ne
r
a
ted
to
tr
a
in
int
e
ll
igent
models
,
80%
of
thes
e
s
a
mpl
e
s
a
r
e
us
e
d
f
or
r
e
g
r
e
s
s
ion,
a
nd
20%
f
o
r
va
li
da
ti
on
(
i
.
e
.
,
tes
ti
ng)
.
Dif
f
e
r
e
nt
models
a
r
e
c
om
pa
r
e
d
a
c
c
or
ding
to
s
e
ve
r
a
l
f
a
c
tor
s
is
be
ing
a
s
:
−
T
he
number
of
pa
r
a
mete
r
s
c
ons
ti
tut
e
s
the
model.
−
T
he
c
oe
f
f
icie
nt
of
de
ter
mi
na
ti
on
(
R
2
)
,
whic
h
r
e
f
le
c
ts
the
model's
a
bil
it
y
to
p
r
oduc
e
the
e
xpe
c
ted
ou
tput
,
a
nd
the
opti
mal
va
lue
f
or
thi
s
f
a
c
to
r
is
1
.
−
T
he
pr
e
dicte
d
e
r
r
o
r
s
um
of
s
qua
r
e
s
R
2
(
P
R
E
S
S
R
2
)
,
whic
h
r
e
f
lec
ts
the
model
c
a
pa
bil
it
y
in
pr
e
diction
,
a
nd
the
opti
mal
va
lue
f
or
thi
s
f
a
c
tor
is
1.
−
T
he
r
oot
mea
n
s
qua
r
e
e
r
r
or
(
R
M
S
E
)
,
whic
h
indi
c
a
tes
the
mod
e
l's
a
bil
it
y
to
c
ha
s
e
the
da
ta
po
int
s
,
a
n
d
the
opti
mal
va
lue
f
o
r
thi
s
f
a
c
tor
is
z
e
r
o
.
−
P
r
e
dicte
d
e
r
r
or
s
um
of
s
qua
r
e
s
R
M
S
S
(
P
R
E
S
S
R
M
S
E
)
,
whic
h
he
lps
in
a
voidi
ng
ove
r
f
it
ti
ng
dur
ing
model
ge
ne
r
a
ti
on.
As
thi
s
f
a
c
tor
de
c
r
e
a
s
e
the
model
wi
ll
ha
ve
a
be
tt
e
r
pr
e
de
c
ti
vit
y.
R
e
duc
ing
the
R
M
S
E
va
lue
doe
s
not
gua
r
a
ntee
that
model
will
p
r
oduc
e
good
r
e
s
ult
s
whe
n
ne
w
da
ta
a
r
e
p
r
e
s
e
nted.
T
he
r
e
f
or
e
,
it
is
us
e
f
ul
to
c
ons
ider
mi
nim
izing
both
the
R
M
S
E
a
nd
P
R
E
S
S
R
M
S
E
.
4.
1
.
Radi
al
b
as
is
f
u
n
c
t
ion
n
e
t
wor
k
s
S
e
ve
r
a
l
types
of
R
B
F
Ns
a
r
e
c
ons
ider
e
d
to
pr
e
dict
the
f
ir
ing
a
ngles
.
I
n
ge
ne
r
a
l
,
the
r
a
dial
ba
s
is
f
unc
ti
on
c
a
n
be
r
e
pr
e
s
e
nted
by
(
11
)
[
35
]
.
(
)
=
(
‖
−
‖
)
(
11)
W
he
r
e
r
e
pr
e
s
e
nts
the
input
ve
c
tor
a
nd
is
the
c
e
nter
of
the
r
a
dial
ba
s
e
s
f
unc
ti
on.
I
n
te
r
ms
of
,
it
i
s
a
univa
r
iate
f
unc
ti
on
that
c
ha
r
a
c
ter
ize
s
R
B
F
Ns
'
va
r
ious
f
unc
ti
ons
,
whic
h
a
r
e
known
a
s
ke
r
ne
l
f
unc
ti
on
s
.
E
a
c
h
model
obtaine
d
us
ing
R
B
F
Ns
c
ons
i
s
ts
of
li
ne
a
r
ly
c
ombi
ne
d
N
of
R
B
F
s
that
ha
ve
dis
ti
nc
t
c
e
nter
s
.
T
he
output
of
the
model
buil
t
is
given
by
(
12
)
.
̂
(
)
=
∑
(
)
=
1
(
12)
W
he
r
e
̂
(
)
is
the
a
ppr
ox
im
a
ted
output
of
a
tar
ge
t
s
e
t
a
nd
is
the
we
ight
of
the
j
th
R
B
F
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
594
-
605
600
I
n
thi
s
wor
k
the
ke
r
ne
l
f
unc
ti
ons
c
ons
ider
e
d
a
r
e
:
mul
ti
qu
a
dr
ics
(
M
Q)
,
thi
n
-
plate
s
pli
ne
(
T
P
S
)
,
a
nd
logi
s
ti
c
ba
s
is
f
unc
ti
on
(
L
B
F
)
.
T
he
s
e
k
e
r
ne
l
f
unc
ti
ons
a
r
e
given
by
(
13
)
-
(
15
)
r
e
s
pe
c
ti
ve
ly.
All
thes
e
f
unc
ti
ons
ha
ve
a
width
pa
r
a
mete
r
r
e
late
d
to
the
f
unc
ti
on
s
pr
e
a
d
a
r
ound
it
s
c
e
nter
.
(
)
=
(
⁄
)
2
log
(
⁄
)
(
13)
(
)
=
1
1
+
e
x
p
(
)
(
14)
(
)
=
√
2
+
2
(
15)
T
a
ble
2
s
hows
that
a
ll
Ke
r
ne
l
f
unc
ti
ons
r
e
s
ult
e
d
in
a
n
outs
tanding
pe
r
f
o
r
manc
e
in
te
r
ms
of
R
2
,
whic
h
ha
s
a
va
lue
of
1.
W
hich
pr
ove
s
the
models
a
bil
it
y
to
pr
oduc
e
the
e
xpe
c
ted
output
.
Als
o,
it
c
a
n
be
s
e
e
n
that
P
R
E
S
S
R
2
is
ve
r
y
high
,
a
lm
os
t
1
f
or
a
ll
models
,
whic
h
mani
f
e
s
ts
high
pe
r
f
o
r
ma
nc
e
in
t
e
r
ms
of
pr
e
dicta
bil
it
y.
M
or
e
ove
r
,
the
lea
s
t
R
M
S
E
s
a
r
e
p
r
o
vided
by
M
Q,
L
B
F
,
a
nd
L
B
F
.
T
he
r
e
f
o
r
e
,
a
c
ombi
na
ti
on
of
thes
e
f
unc
ti
ons
is
a
ppli
e
d
in
the
S
im
uli
nk
model
to
pe
r
f
or
m
volt
a
ge
unba
lanc
e
mi
t
igation.
T
a
ble
2.
R
B
F
Ns
models
r
e
s
ult
s
T
C
R
f
ir
in
g a
ng
le
s
K
e
r
ne
l
F
unc
ti
on
P
a
r
a
me
te
r
s
R
2
P
R
E
S
S
R
2
R
M
S
E
P
R
E
S
S
R
M
S
E
α1
MQ
62
63
60
1
1
1
0.999
0.999
0.998
1.19
1.38
1.26
3.25
3.75
4.29
T
P
S
L
B
F
α2
MQ
63
63
63
1
1
1
0.999
0.996
0.999
1.91
1.92
1.85
4.36
7.39
3.97
T
P
S
L
B
F
α3
MQ
63
63
63
1
1
1
0.999
0.999
0.999
1.78
1.57
1.53
3.5
3.49
3.7
T
P
S
L
B
F
4.
2
.
Hyb
r
id
r
ad
ial
b
as
is
f
u
n
c
t
ion
n
e
t
wor
k
s
T
he
s
e
f
unc
ti
ons
a
r
e
a
c
ombi
na
ti
on
of
R
B
F
Ns
a
nd
li
ne
a
r
models
.
T
he
H
-
R
B
F
Ns
c
on
s
ider
e
d
a
r
e
hybr
id
-
L
B
F
(
HL
B
F
)
,
hyb
r
id
-
M
Q
(
HM
Q)
,
a
nd
hybr
id
-
li
ne
r
R
B
F
(
HL
R
B
F
)
with
P
Ns
.
T
a
ble
3
s
ho
ws
that
a
high
va
lue
o
f
R
2
f
o
r
the
th
r
e
e
f
i
r
ing
a
ngles
of
mor
e
than
o
r
e
qua
l
to
0
.
99
is
r
e
a
c
he
d
f
o
r
a
ll
models
.
I
t
s
hows
the
models
a
bil
it
y
to
pr
oduc
e
the
e
xpe
c
ted
output
.
F
ur
ther
mor
e
,
P
R
E
S
S
R
2
is
a
c
c
e
ptable
a
nd
s
ho
ws
good
pr
e
diction
c
a
pa
bil
it
ies
.
I
n
ter
ms
of
lea
s
t
R
M
S
E
,
i
t
is
a
c
c
ompl
is
he
d
by
the
L
B
F
P
model;
he
nc
e
it
is
us
e
d
in
s
e
c
ti
on
4.
5
f
o
r
volt
a
ge
unba
lanc
e
mi
ti
ga
ti
on.
T
a
ble
3.
H
-
R
B
F
Ns
models
r
e
s
ult
s
T
C
R
f
ir
in
g a
ngl
e
s
H
-
R
B
F
P
a
r
a
me
te
r
s
R
2
P
R
E
S
S
R
2
R
M
S
E
P
R
E
S
S
R
M
S
E
α1
H
L
B
F
67
67
67
0.997
0.997
0.997
0.929
0.941
0.945
1.00
1.00
1.10
4.6
4.06
4.18
H
M
Q
H
L
R
B
F
α2
H
L
B
F
67
67
67
0.99
0.99
0.99
0.971
0.977
0.972
1.59
1.65
1.68
3.54
4.98
3.14
H
M
Q
H
L
R
B
F
α3
H
L
B
F
67
67
67
0.994
0.993
0.994
0.971
0.97
0.96
1.37
1.44
1.49
3.18
3.76
3.28
H
M
Q
H
L
R
B
F
4.
3
.
P
o
lyn
om
ial
s
L
inea
r
r
e
gr
e
s
s
ion
pr
ovides
s
im
pler
models
c
ompa
r
e
d
to
other
r
e
gr
e
s
s
ion
types
.
Ne
ve
r
thele
s
s
,
whe
n
de
a
li
ng
with
P
Ns
models
,
a
tt
e
nti
on
mus
t
be
given
to
the
numbe
r
of
ter
ms
.
T
his
number
mus
t
be
s
e
l
e
c
ted
s
o
that
a
c
ompr
o
mi
s
a
ti
on
be
twe
e
n
r
e
duc
ing
the
e
r
r
or
a
nd
a
voidi
ng
ove
r
f
it
ti
n
g
is
a
c
hieve
d
[
35
]
.
R
e
ga
r
ding
that,
a
s
the
number
of
ter
ms
incr
e
a
s
e
s
,
the
e
r
r
or
de
c
r
e
a
s
e
s
.
T
o
pr
ovide
a
be
tt
e
r
ge
ne
r
a
li
z
a
ti
on
(
i.
e
.
,
model
pr
e
dicta
bil
it
y)
,
s
tepw
is
e
r
e
gr
e
s
s
ion
is
us
e
d
to
s
e
lec
t
model
ter
ms
s
o
that
the
P
R
E
S
S
R
M
S
E
is
mi
n
im
i
z
e
d.
S
e
ve
r
a
l
polynom
ial
models
a
r
e
e
xa
mi
ne
d
to
pr
e
dic
t
the
f
i
r
ing
a
ngles
.
A
th
ir
d,
f
our
th,
a
nd
f
if
th
-
or
de
r
polynom
ials
a
r
e
inves
ti
ga
ted,
a
s
s
hown
in
T
a
ble
4.
I
t
c
a
n
be
noti
c
e
d
that
a
s
the
o
r
de
r
of
the
po
lynom
ial
incr
e
a
s
e
s
a
nd
c
ons
e
que
nti
a
ll
y,
the
number
o
f
te
r
ms
incr
e
a
s
e
s
,
the
R
M
S
E
de
c
r
e
a
s
e
d
s
li
ghtl
y.
How
e
ve
r
,
the
P
R
E
S
S
R
M
S
E
incr
e
a
s
e
d
numer
ous
ly
a
nd
P
R
E
S
S
R
2
de
c
r
e
a
s
e
d,
r
e
f
lec
ti
ng
a
r
e
duc
ti
on
in
the
pr
e
diction
c
a
pa
bil
it
y
of
the
higher
-
or
de
r
models
a
nd
ove
r
f
it
ti
ng.
As
a
r
e
s
ult
,
the
thi
r
d
-
or
de
r
po
lynom
ial
will
be
c
ons
ider
e
d
f
or
volt
a
ge
unba
lanc
e
c
ont
r
ol.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mple
me
ntat
ion
of
r
e
ac
ti
v
e
c
ompe
ns
ator
for
v
olt
age
balancing
us
ing
…
(
Dana
M
.
R
agab
)
601
T
a
ble
4.
P
olynom
ials
models
r
e
s
ult
s
T
C
R
f
ir
in
g a
ngl
e
s
P
ol
ynomi
a
l
O
r
de
r
P
a
r
a
me
te
r
s
R
2
P
R
E
S
S
R
2
R
M
S
E
P
R
E
S
S
R
M
S
E
α1
3
rd
15
35
38
0.964
0.966
0.968
0.931
0.215
-
10.695
4.32
3.5
3.46
4.51
15.27
58.94
4
th
5
th
α2
3
rd
14
35
38
0.939
0.972
0.973
0.926
0.623
-
13.155
5.3
3.86
3.77
5.61
10.81
77.81
4
th
5
th
α3
3
rd
14
23
33
0.96
0.96
0.97
0.951
-
0.094
0.945
3.9
3.82
3.47
4.16
19.63
4.41
4
th
5
th
4.
4
.
Ne
u
r
al
n
e
t
wor
k
s
M
a
ny
publi
c
a
ti
ons
in
the
li
ter
a
tu
r
e
dis
c
us
s
e
d
the
us
e
of
NN
f
o
r
f
i
r
ing
a
ngles
ge
ne
r
a
ti
on
.
T
ypica
ll
y,
NN
's
us
e
is
wide
s
pr
e
a
d
dur
ing
onli
ne
ope
r
a
ti
on
due
to
it
s
f
a
s
t
r
e
s
pons
e
c
ompar
e
d
to
other
a
lgor
it
hms
s
uc
h
a
s
gr
a
vit
a
ti
ona
l
s
e
a
r
c
h,
pa
r
t
icle
s
wa
r
m,
a
nd
ge
ne
ti
c
a
lgor
it
hm
that
a
r
e
us
ua
ll
y
us
e
d
to
ge
ne
r
a
te
the
f
ir
in
g
a
ngles
dur
ing
o
f
f
li
ne
mode
[
28
]
.
T
wo
s
tr
uc
tu
r
e
s
of
NN
a
r
e
s
ugge
s
ted.
F
ir
s
t,
th
r
e
e
NN
s
a
r
e
us
e
d
with
the
th
r
e
e
load
volt
a
ge
s
a
s
input
a
nd
one
of
the
f
ir
ing
a
ngles
a
s
e
a
c
h
ne
twor
k's
output
.
E
a
c
h
NN
c
ons
is
ts
of
one
hidd
e
n
laye
r
with
ten
ne
ur
ons
a
nd
a
n
output
laye
r
with
one
ne
ur
on;
the
tans
igm
oid
tr
a
ns
f
e
r
f
unc
ti
on
is
c
ons
ider
e
d
in
both
l
a
ye
r
s
.
T
a
ble
5
s
hows
the
da
ta
r
e
late
d
to
NN
s
tr
a
i
ning.
I
t
c
a
n
be
s
e
e
n
that
in
a
ll
c
a
s
e
s
,
R
2
is
ve
r
y
hig
h
a
lm
os
t
one
,
whic
h
mea
ns
that
the
NN
s
ha
ve
a
n
e
xc
e
ll
e
nt
p
e
r
f
or
manc
e
dur
ing
the
t
r
a
ini
ng
pha
s
e
.
I
n
ter
ms
of
the
s
e
c
ond
s
tr
uc
tur
e
,
one
NN
with
th
e
thr
e
e
load
volt
a
ge
s
a
s
input
a
nd
the
th
r
e
e
f
i
r
ing
a
ngles
a
s
output
is
s
ugge
s
ted.
T
he
NN
c
ons
is
ts
of
one
hidden
laye
r
with
ten
ne
u
r
ons
,
whic
h
r
e
duc
e
s
c
a
lcula
ti
ons
s
igni
f
ica
ntl
y.
R
e
pe
a
tedly,
the
tans
ig
moi
d
t
r
a
ns
f
e
r
f
unc
ti
on
is
us
e
d
f
or
both
the
hidde
n
a
nd
the
outp
ut
laye
r
s
.
F
igur
e
5
s
hows
the
pe
r
f
or
manc
e
of
t
he
pr
opos
e
d
NN
dur
ing
the
tr
a
ini
ng,
va
li
da
ti
on,
a
nd
tes
ti
ng
pha
s
e
s
.
Outs
tanding
pe
r
f
or
manc
e
is
a
c
hieve
d
wh
e
r
e
R
2
is
mor
e
than
0.
97
dur
ing
a
ll
pha
s
e
s
while
a
tt
a
ini
ng
c
ons
ider
a
ble
s
im
pli
f
ica
ti
on
in
the
s
tr
uc
tur
e
c
ompar
e
d
to
other
NN
s
a
ppli
e
d
f
o
r
the
s
a
me
p
r
oblem.
T
a
ble
5.
R
e
s
ult
s
of
NN
models
T
C
R
f
ir
in
g a
ngl
e
s
P
a
r
a
me
te
r
s
R
2
R
M
S
E
α1
51
0.97
3.27
α2
51
0.95
5.16
α3
51
0.979
3.01
F
igur
e
5.
NN
pe
r
f
or
manc
e
4.
5
.
M
od
e
ls
v
ali
d
a
t
ion
T
he
be
s
t
models
obtaine
d
in
the
p
r
e
vious
s
e
c
ti
ons
a
r
e
va
li
da
ted
th
r
ough
33
tes
t
c
a
s
e
s
.
T
he
s
e
c
a
s
e
s
a
r
e
c
onduc
ted
on
the
AQ
S
A
powe
r
s
ys
tem
mo
de
l
us
ing
M
AT
L
AB
/S
im
uli
nk.
A
thi
r
d
-
or
de
r
pol
ynomi
a
l,
R
B
F
N,
H
-
R
B
F
N,
a
nd
NN
a
r
e
us
e
d
to
ge
ne
r
a
te
t
he
r
e
quir
e
d
T
C
R
f
i
r
ing
a
ngles
f
o
r
vo
lt
a
ge
ba
lan
c
ing.
As
mentioned
e
a
r
li
e
r
,
the
a
c
c
e
ptable
va
lue
of
the
VU
F
is
les
s
than
3%
.
Ac
c
or
ding
to
thi
s
c
r
i
ter
ion,
the
pr
opos
e
d
models
a
r
e
e
va
luate
d.
T
a
ble
6
s
hows
the
unba
lanc
e
d
volt
a
ge
s
a
nd
the
VU
F
be
f
o
r
e
a
nd
a
f
ter
c
or
r
e
c
ti
on
us
ing
dif
f
e
r
e
nt
models
,
f
o
r
di
f
f
e
r
e
nt
load
c
ha
nge
s
a
t
AQ
S
A.
All
models
pr
ovide
a
c
c
e
ptable
pe
r
f
or
manc
e
a
nd
a
c
hieve
the
goa
l
o
f
r
e
duc
ing
VU
F
to
les
s
than
3%
e
xc
e
pt
f
o
r
polyno
mi
a
ls
,
whic
h
s
c
r
e
we
d
in
s
ome
c
a
s
e
s
a
nd
ge
ne
r
a
ll
y
maintaine
d
higher
VU
F
.
Als
o,
it
c
a
n
be
s
e
e
n
that
the
R
B
F
N
pr
o
v
ides
the
be
s
t
pe
r
f
or
manc
e
,
with
a
n
a
ve
r
a
ge
VU
F
o
f
0.
76
%
.
T
his
r
e
s
ult
c
a
n
be
e
lucida
t
e
d
by
R
B
F
N
models
'
high
pe
r
f
or
manc
e
in
ter
ms
of
P
R
E
S
S
R
2
a
nd
R
2
,
indi
c
a
ti
ng
thes
e
models
'
a
bil
it
ies
to
pr
e
dict
a
nd
f
it
da
ta.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8694
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
,
Vol.
13
,
No.
1
,
M
a
r
c
h
20
22
:
594
-
605
602
T
a
ble
6.
VU
F
us
ing
di
f
f
e
r
e
nt
models
B
e
f
or
e
vo
lt
a
ge
unba
la
nc
e
mi
ti
ga
ti
on
A
f
te
r
vol
ta
ge
unba
la
nc
e
mi
ti
ga
ti
on
VUF
V
ab
V
bc
V
ca
V
U
F
(
P
ol
ynomi
a
l)
VUF
(H
-
R
B
F
N
)
VUF
(
R
B
F
N
)
VUF
(
N
N
)
3.68
225
234
219
0.36
0.33
0.49
1.01
6.68
220
230
205
1.93
0.67
0.67
0.9
4
225
233
217
0.15
0.26
0.33
1.07
6.48
218
235
210
2.8
0.6
0.6
0.85
4.5
219
230
213
0.88
0.4
0.36
0.4
6.3
219
232
208
0.96
0.49
0.47
0.521
6
216
232
210
1.23
0.96
0.7
0.37
5.9
214
232
215
0.48
0.75
0.72
0.22
5
222
236
217
0.4
0.66
0.64
0.78
7.5
221
229
202
2.97
1.93
1.65
1.68
3.37
227
238
224
0.55
0.45
0.34
1.5
3.7
228
225
240
1.94
1.71
0.86
1.26
3.9
229
222
238
1.65
0.774
1.06
1.07
4.84
223
220
238
1.32
0.58
1.31
1.17
6
223
218
240
2.8
0.36
0.92
0.85
5.37
223
220
239
2
0.26
0.4
0.37
7.11
222
216
242
3.89
1.06
1.71
1.65
3.48
218
222
232
0.84
0.74
0.52
1.02
3.47
216
214
226
1.16
0.25
0.17
0.7
4.77
205
213
223
0.64
0.32
0.35
0.27
6.3
200
210
223
1.4
1.5
1.13
1.1
5.25
202
213
221
0.77
0.58
0.59
0.23
4.29
202
209
218
0.95
0.55
0.47
0.8
3.28
231
231
220
1.09
0.34
0.37
1.4
5.05
226
232
214
0.21
0.14
0.23
0.29
4.1
229
231
217
0.69
0.56
0.72
0.91
6
227
230
208
1.66
1.39
1.06
0.08
7.17
224
231
205
2.82
2.41
1.29
1.12
6.9
224
227
203
1.9
1.845
0.91
0.67
4.79
219
221
205
0.35
0.64
0.67
0.55
5.94
221
221
204
1.11
0.85
0.71
0.49
7.9
226
224
199
2.43
3.5
2.04
1.27
3.99
229
227
215
0.6
0.3
0.52
0.19
A
ve
r
a
ge
VUF
5.24
1.36
0.85
0.76
0.81
F
igur
e
6
s
hows
the
r
e
s
pons
e
of
the
thr
e
e
-
load
volt
a
ge
s
a
t
AQ
S
A
with
5.
2
%
volt
a
ge
unba
lanc
e
oc
c
ur
s
a
t
0.
08
s
e
c
.
T
he
n
a
t
0.
13
s
e
c
,
R
B
F
N
is
us
e
d
to
ge
ne
r
a
te
the
r
e
quir
e
d
T
C
R
f
ir
ing
a
ngles
(
99
°
,
96
°
,
130
°
)
a
nd
the
volt
a
ge
unba
lanc
e
is
mi
ti
ga
ted
to
0
.
75
%
. To
f
ur
the
r
de
mons
tr
a
te
the
a
dva
ntage
of
the
pr
opos
e
d
S
VU
F
,
two
c
a
s
e
s
f
or
vol
tage
unba
lanc
e
e
va
luation
a
nd
mi
ti
ga
ti
on
a
r
e
c
ons
ider
e
d.
I
n
both
c
a
s
e
s
,
a
f
ter
volt
a
ge
unba
lanc
e
de
tec
ti
on,
10
ms
e
c
a
r
e
c
ons
ider
e
d
to
c
a
l
c
ulate
the
thr
e
e
load
volt
a
ge
s
us
e
d
a
s
NN
input
s
.
Ne
xt,
the
thr
e
e
f
i
r
ing
a
ngles
a
r
e
pr
oduc
e
d
by
the
NN
ins
tantly.
F
igur
e
7
s
hows
that
the
tot
a
l
ti
me
r
e
quir
e
d
to
r
e
tr
ieve
the
ba
lanc
e
c
ondit
ion
is
30
ms
e
c
whe
n
VU
F
is
u
s
e
d
to
e
va
luate
the
volt
a
ge
unba
lanc
e
.
On
the
oth
e
r
ha
nd,
F
igur
e
8
s
hows
that
thi
s
ti
me
is
r
e
duc
e
d
to
20
ms
e
c
whe
n
S
VU
F
is
uti
l
ize
d
f
o
r
the
e
va
luation.
T
he
r
e
f
or
e
,
the
a
c
tual
ti
me
r
e
quir
e
d
f
or
volt
a
ge
unba
lanc
e
de
tec
ti
on
a
nd
e
va
luation
whe
n
the
VU
F
us
e
d
is
20
ms
e
c
,
while
in
the
c
a
s
e
of
S
VU
F
,
th
e
ti
me
is
r
e
duc
e
d
to
10
ms
e
c
.
I
t
is
wo
r
th
to
mention
that
in
both
c
a
s
e
s
volt
a
ge
un
ba
lanc
e
oc
c
ur
s
a
t
0.
1s
.
F
igu
r
e
9
s
hows
one
of
the
li
ne
vol
tage
s
Vc
a
in
both
c
a
s
e
s
.
T
he
c
ontr
o
l
a
c
ti
on
take
s
plac
e
a
t
0.
12
s
in
the
c
a
s
e
of
S
VU
F
,
while
in
the
c
a
s
e
of
V
UF,
it
take
s
plac
e
a
t
0
.
13
s
.
F
igur
e
6
T
hr
e
e
pha
s
e
load
vo
lt
a
ge
s
with
R
B
F
Ns
to
r
e
tr
ieve
vol
tage
ba
lanc
ing
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
P
ow
E
lec
&
Dr
i
S
ys
t
I
S
S
N:
2088
-
8694
I
mple
me
ntat
ion
of
r
e
ac
ti
v
e
c
ompe
ns
ator
for
v
olt
age
balancing
us
ing
…
(
Dana
M
.
R
agab
)
603
F
igur
e
7
.
Voltage
unba
lanc
e
mi
ti
ga
ti
on
a
nd
e
va
lua
ti
on
us
ing
NN
s
a
nd
VU
F
F
igur
e
8
.
Voltage
unba
lanc
e
mi
ti
ga
ti
on
a
nd
e
va
lua
ti
on
us
ing
NN
s
a
nd
S
VU
F
F
igur
e
9
.
Vc
a
li
ne
vo
lt
a
ge
with
NN
C
c
ons
ider
ing
u
nba
lanc
e
e
va
luation
us
ing
VU
F
a
nd
S
VU
F
5.
CONT
RI
B
U
T
I
ON
T
O
KNOWL
E
DGE
Voltage
unba
lanc
e
e
va
luation
wa
s
e
nha
nc
e
d
by
us
ing
the
S
VU
F
,
whic
h
r
e
duc
e
s
the
ti
me
r
e
quir
e
d
f
or
e
va
luation
by
ha
lf
while
maintaining
good
a
c
c
ur
a
c
y
a
nd
e
li
mi
na
ti
ng
the
ne
e
d
to
us
e
s
ymm
e
tr
ica
l
c
omponent.
T
a
ble
7
s
hows
a
c
ompar
is
on
be
twe
e
n
the
pr
opos
e
d
R
B
F
Ns
a
nd
NN
models
a
nd
other
NN
s
us
e
d
in
the
li
ter
a
tur
e
.
T
he
to
ta
l
number
o
f
pa
r
a
mete
r
s
include
s
the
pa
r
a
mete
r
s
of
models
s
uc
h
a
s
the
nu
mber
of
we
ight
s
a
nd
bias
e
s
us
e
d
in
the
NN
s
.
T
he
r
e
s
pons
e
ti
me
is
the
ti
me
ne
c
e
s
s
a
r
y
to
r
e
s
tor
e
volt
a
ge
ba
lanc
e
e
xc
ludi
ng
the
ti
me
f
or
volt
a
ge
unba
lanc
e
e
va
luation.
I
n
[
26]
a
nd
[
27]
,
thr
e
e
NN
s
with
mo
r
e
than
on
e
hidden
laye
r
we
r
e
us
e
d,
r
e
s
ult
ing
in
lar
ge
numbe
r
s
of
pa
r
a
mete
r
s
c
a
us
ing
a
n
e
xc
e
s
s
ive
incr
e
a
s
e
in
c
omput
a
ti
ons
.
A
s
im
pler
model
o
f
one
NN
with
thr
e
e
input
s
wa
s
p
r
opos
e
d
in
[
28
]
.
How
e
ve
r
,
thi
s
r
e
duc
ti
on
in
the
nu
mber
of
ne
twor
ks
a
n
d
input
s
wa
s
c
ompens
a
ted
by
g
r
a
dua
ll
y
incr
e
a
s
ing
the
number
of
ne
ur
ons
lea
ding
a
ga
in
to
lar
ge
number
s
of
pa
r
a
mete
r
s
a
nd
e
xc
e
s
s
ive
c
omput
a
ti
ons
.
Als
o,
the
NN
s
ugge
s
ted
ha
s
moder
a
te
pe
r
f
or
manc
e
dur
ing
tes
ti
ng,
with
R
2
e
qua
ls
0
.
814.
T
he
NN
s
ugge
s
ted
in
[
29]
h
a
s
the
s
im
ples
t
s
tr
uc
tur
e
with
163
pa
r
a
mete
r
s
only
a
nd
a
r
e
s
pons
e
ti
me
of
40
ms
e
c
.
I
n
thi
s
wor
k,
a
much
s
im
pler
NN
s
tr
uc
tur
e
is
c
ons
i
de
r
e
d,
with
a
tot
a
l
nu
mber
of
pa
r
a
mete
r
s
e
qua
l
to
73.
S
im
ul
tane
ous
ly,
high
pe
r
f
or
manc
e
is
maintain
e
d
dur
ing
the
tes
ti
ng
ph
a
s
e
,
with
R
2
e
qua
ls
0.
976
.
I
n
ter
ms
of
R
B
F
Ns
,
a
lt
hough
it
ha
s
a
s
li
ghtl
y
higher
num
be
r
o
f
pa
r
a
mete
r
s
,
it
s
ti
ll
pr
ovides
the
be
s
t
pe
r
f
or
manc
e
in
ter
ms
of
R
2
a
nd
P
R
E
S
S
R
2
lea
ding
to
h
igher
a
bil
it
y
in
ge
ne
r
a
ti
ng
the
f
ir
ing
a
ngles
with
the
lea
s
t
VU
F
.
Als
o,
the
tot
a
l
r
e
s
pons
e
ti
me
o
f
T
C
R
is
r
e
duc
e
d
to
30
ms
e
c
.
Evaluation Warning : The document was created with Spire.PDF for Python.