I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
(
I
J
P
E
DS
)
Vo
l.
11
,
No
.
4
,
Dec
em
b
er
2
0
2
0
,
p
p
.
1
9
6
6
~
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8
I
SS
N:
2088
-
8
6
9
4
,
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: 1
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.
1
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ed
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.
v
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.
i4
.
pp
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9
6
6
-
1
9
7
8
1966
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Im
pro
v
ement of
t
he per
forma
nce o
f
STAT
C
O
M
in
t
erms o
f
v
o
ltag
e profile usi
ng
ANN
co
ntrolle
r
M
o
ha
m
m
ed
Sa
lheen A
la
t
s
ha
n
1
,
I
bra
him
Alha
m
ro
un
i
2
, T
o
le
Su
t
ik
no
3
,
Awa
ng
J
us
o
h
4
1,
2
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
S
e
c
ti
o
n
,
Un
iv
e
rsit
y
Ku
a
la L
u
m
p
u
r
(
Un
iK
L
BM
I),
G
o
m
b
a
k
5
3
1
0
0
,
M
a
la
y
si
a
3
De
p
a
rtme
n
t
o
f
E
lec
tri
c
a
l
En
g
i
n
e
e
rin
g
,
U
n
iv
e
rsitas
Ah
m
a
d
Da
h
lan
,
Yo
g
y
a
k
a
rta,
I
n
d
o
n
e
sia
4
S
c
h
o
o
l
o
f
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
Un
i
v
e
rsiti
Te
k
n
o
lo
g
i
M
a
lay
sia
,
8
1
3
0
0
S
k
u
d
a
i,
M
a
la
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Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Feb
1
0
,
2
0
20
R
ev
is
ed
May
2
,
2
0
2
0
Acc
ep
ted
May
19
,
2
0
20
Th
e
e
lec
tro
n
ic
e
q
u
i
p
m
e
n
ts
a
re
e
x
trem
e
ly
se
n
siti
v
e
to
v
a
riatio
n
i
n
e
lec
tri
c
su
p
p
l
y
.
Th
e
i
n
c
re
a
sin
g
o
f
a
n
o
n
li
n
e
a
r
sy
ste
m
with
se
v
e
ra
l
in
te
rc
o
n
n
e
c
ted
u
n
p
re
d
icte
d
a
n
d
n
o
n
-
li
n
e
a
r
lo
a
d
s
a
re
c
a
u
sin
g
so
m
e
p
ro
b
lem
s
to
t
h
e
p
o
we
r
sy
ste
m
.
Th
e
m
a
jo
r
p
ro
b
lem
fa
c
in
g
th
e
p
o
we
r
sy
ste
m
is
p
o
w
e
r
q
u
a
li
ty
,
c
o
n
tro
ll
in
g
o
f
re
a
c
ti
v
e
p
o
we
r
a
n
d
v
o
lt
a
g
e
d
ro
p
.
A
sta
ti
c
sy
n
c
h
ro
n
o
u
s
c
o
m
p
e
n
sa
to
r
(
S
TATCOM
)
is
a
n
im
p
o
rtan
t
d
e
v
ice
c
o
m
m
o
n
ly
u
se
d
fo
r
c
o
m
p
e
n
sa
ti
o
n
p
u
rp
o
se
s,
it
c
a
n
p
ro
v
id
e
re
a
c
ti
v
e
su
p
p
o
rt
t
o
a
b
u
s
to
c
o
m
p
e
n
sa
te v
o
lt
a
g
e
lev
e
l
.
In
t
h
is p
a
p
e
r,
th
e
Artif
icia
l
Ne
u
ra
l
Ne
two
rk
(AN
N)
c
o
n
tro
ll
e
d
S
TATCOM
h
a
s
b
e
e
n
d
e
sig
n
e
d
to
re
p
lac
e
th
e
c
o
n
v
e
n
ti
o
n
a
l
P
I
c
o
n
tro
ll
e
r
to
e
n
h
a
n
c
e
t
h
e
S
TAT
COM
p
e
rfo
rm
a
n
c
e
.
T
h
e
AN
N
c
o
n
tr
o
ll
e
r
is
p
ro
p
o
se
d
d
u
e
t
o
it
s
sim
p
le
stru
c
t
u
re
,
a
d
a
p
tab
il
it
y
,
r
o
b
u
stn
e
ss
,
c
o
n
si
d
e
rin
g
th
e
p
o
we
r
g
ri
d
n
on
-
li
n
e
a
rit
ies
.
Th
e
AN
N
is
train
e
d
o
ffli
n
e
u
si
n
g
d
a
ta
f
ro
m
th
e
P
I
c
o
n
tro
ll
e
r.
Th
e
p
e
rfo
rm
a
n
c
e
o
f
S
TATCOM
with
c
a
se
o
f
Lo
a
d
in
c
r
e
a
sin
g
a
n
d
th
re
e
-
p
h
a
se
fa
u
lt
s
c
a
se
wa
s
a
n
a
ly
z
e
d
u
sin
g
M
ATLAB/S
imu
li
n
k
so
ftwa
re
o
n
th
e
IEE
E
1
4
-
b
u
s
sy
ste
m
.
Th
e
c
o
m
p
re
h
e
n
siv
e
re
su
l
t
o
f
t
h
e
P
I
a
n
d
AN
N
c
o
n
tro
ll
e
rs
h
a
s
d
e
m
o
n
stra
ted
t
h
e
e
ffe
c
ti
v
e
n
e
ss
o
f
th
e
p
ro
p
o
se
d
AN
N
c
o
n
tro
ll
e
r
i
n
e
n
h
a
n
c
in
g
t
h
e
S
TATCOM
p
e
rf
o
rm
a
n
c
e
fo
r
V
o
lt
a
g
e
p
ro
fil
e
a
t
d
iffere
n
t
o
p
e
ra
ti
n
g
c
o
n
d
i
ti
o
n
s.
F
u
rth
e
rm
o
re
,
i
t
h
a
s
p
ro
d
u
c
e
d
b
e
t
ter
re
su
lt
s
th
a
n
t
h
e
c
o
n
v
e
n
ti
o
n
a
l
P
I
c
o
n
tr
o
ll
e
r.
K
ey
w
o
r
d
s
:
ANN
co
n
tr
o
ller
I
E
E
E
1
4
b
u
s
s
y
s
tem
MA
T
L
AB
/S
im
u
lin
k
PI
co
n
tr
o
ller
SP
W
M
STAT
C
OM
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
I
b
r
ah
i
m
Al
h
a
m
r
o
u
n
i,
E
lectr
ical
E
n
g
in
ee
r
in
g
Sectio
n
,
Un
iv
er
s
iti
Ku
ala
L
u
m
p
u
r
-
B
r
itis
h
Ma
lay
s
ian
I
n
s
titu
te,
B
atu
8
,
J
alan
Su
n
g
ai
Pu
s
u
,
5
3
1
0
0
,
Go
m
b
ak
,
Selan
g
o
r
,
Ma
lay
s
ia.
E
m
ail:
ib
r
ah
im
.
m
o
h
am
ed
@
u
n
ik
l.e
d
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
elec
tr
ic
p
o
wer
s
y
s
tem
is
a
h
ig
h
ly
n
o
n
lin
ea
r
s
y
s
tem
th
at
o
p
er
ates
in
a
c
o
n
s
tan
tly
ch
an
g
in
g
en
v
ir
o
n
m
en
t;
lo
ad
s
,
g
en
er
at
o
r
o
u
tp
u
ts
,
an
d
k
ey
o
p
er
atin
g
p
ar
am
eter
s
ch
an
g
e
co
n
tin
u
all
y
[
1
]
.
T
h
e
s
tab
ilit
y
d
ep
en
d
s
o
n
th
e
n
atu
r
e
o
f
th
e
d
is
tu
r
b
an
ce
th
at
m
ay
s
u
b
ject
to
th
e
s
y
s
tem
,
wh
er
e
th
e
d
is
tu
r
b
an
ce
m
ay
o
cc
u
r
f
o
r
a
lo
n
g
o
r
s
h
o
r
t
p
er
i
o
d
[
2
]
.
T
h
e
r
e
co
u
l
d
b
e
d
a
m
ag
es
to
th
e
m
a
ch
in
es
co
n
n
ec
ted
t
o
th
e
s
y
s
tem
,
ca
u
s
e
h
ea
tin
g
in
th
e
elec
tr
ical
eq
u
ip
m
e
n
t,
an
d
m
alf
u
n
ctio
n
o
f
t
h
e
s
en
s
itiv
e
eq
u
ip
m
en
t.
Sm
all
d
is
tu
r
b
an
ce
s
in
th
e
f
o
r
m
o
f
lo
a
d
ch
an
g
es
o
cc
u
r
c
o
n
tin
u
ally
,
a
n
d
th
e
s
y
s
tem
ad
ju
s
ts
to
th
e
c
h
an
g
in
g
co
n
d
itio
n
s
.
T
h
e
s
y
s
tem
m
u
s
t
b
e
ab
le
to
o
p
er
ate
s
atis
f
ac
to
r
ily
u
n
d
er
th
ese
co
n
d
itio
n
s
an
d
s
u
cc
ess
f
u
lly
m
ee
t
th
e
lo
a
d
d
em
a
n
d
.
I
t
m
u
s
t
also
b
e
ab
le
to
su
r
v
iv
e
n
u
m
er
o
u
s
d
is
tu
r
b
an
ce
s
o
f
a
s
ev
er
e
n
atu
r
e
,
s
u
ch
as
a
s
h
o
r
t
-
cir
cu
it
o
n
a
tr
an
s
m
is
s
io
n
lin
e
o
r
lo
s
s
o
f
a
lar
g
e
g
e
n
er
ato
r
[
3
]
.
I
n
th
e
p
ast,
tr
ad
itio
n
ally
it
h
as
b
ee
n
u
s
ed
f
ix
ed
o
r
m
ec
h
an
ically
s
witch
ed
s
h
u
n
t
an
d
s
er
ies
ca
p
ac
ito
r
s
,
r
ea
cto
r
s
an
d
s
y
n
ch
r
o
n
o
u
s
g
en
er
at
o
r
s
to
s
o
lv
e
m
an
y
o
f
t
h
ese
p
r
o
b
le
m
s
.
Ho
wev
er
,
th
er
e
ar
e
lim
itatio
n
s
to
th
e
u
s
e
o
f
th
e
s
e
co
n
v
en
tio
n
al
co
m
p
en
s
ato
r
s
.
r
eq
u
ir
e
d
p
e
r
f
o
r
m
an
ce
was
n
o
t
b
ein
g
ab
le
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
r
o
ve
men
t o
f th
e
p
erfo
r
ma
n
ce
o
f S
TATC
OM in
term
s
o
f
… (
Mo
h
a
mme
d
S
a
lh
ee
n
A
la
ts
h
a
n
)
1967
ac
h
iev
e
ef
f
ec
ti
v
ely
.
W
ea
r
a
n
d
tear
in
th
e
m
ec
h
an
ical
c
o
m
p
o
n
en
ts
an
d
s
lo
w
r
esp
o
n
s
e
we
r
e
th
e
m
aj
o
r
o
f
th
e
p
r
o
b
lem
s
[
4
]
.
W
ith
th
e
r
ap
id
in
cr
ea
s
e
in
p
o
wer
elec
tr
o
n
ics
d
ep
lo
y
m
en
t,
th
er
e
was
g
r
ea
ter
n
ee
d
f
o
r
th
e
alter
n
ativ
e
tech
n
o
l
o
g
y
m
ad
e
o
f
s
o
lid
-
s
tate
d
ev
ices w
ith
f
ast r
esp
o
n
s
e
ch
ar
ac
ter
is
tics
.
R
ec
en
tly
,
f
lex
ib
le
AC
tr
an
s
m
is
s
io
n
s
y
s
tem
s
(
F
AC
T
S)
co
n
tr
o
ller
s
h
av
e
b
ee
n
m
ain
l
y
u
s
ed
f
o
r
s
o
lv
in
g
v
ar
io
u
s
s
tead
y
-
s
tate
co
n
tr
o
l
p
r
o
b
lem
s
an
d
en
h
a
n
ce
p
o
wer
s
y
s
tem
s
tab
ilit
y
in
ad
d
itio
n
to
th
eir
m
ain
f
u
n
ctio
n
o
f
p
o
wer
f
lo
w
co
n
tr
o
l.
E
m
p
lo
y
m
en
t
o
f
FAC
T
S
d
ev
ices
in
p
o
wer
s
y
s
tem
s
lead
s
to
b
etter
p
er
f
o
r
m
an
ce
o
f
th
e
s
y
s
tem
,
f
o
r
in
s
t
an
ce
,
v
o
ltag
e
s
tab
ilit
y
,
v
o
ltag
e
r
eg
u
latio
n
,
an
d
p
o
wer
s
y
s
tem
s
tab
ilit
y
,
d
am
p
in
g
,
ca
n
b
e
im
p
r
o
v
e
d
b
y
u
s
in
g
th
ese
d
e
v
ic
es
[
5
]
.
A
Static
Sy
n
ch
r
o
n
o
u
s
C
o
m
p
en
s
ato
r
(
STAT
C
OM
)
is
o
n
e
o
f
th
e
p
a
r
allel
FAC
T
S
d
ev
ices
th
at
is
u
s
u
ally
u
s
ed
f
o
r
v
o
ltag
e
r
e
g
u
latio
n
.
I
t
ca
n
also
b
e
u
s
ed
to
im
p
r
o
v
e
p
o
wer
s
y
s
tem
s
tab
ilit
y
b
y
in
jectin
g
o
r
ab
s
o
r
b
in
g
r
ea
ctiv
e
p
o
wer
to
t
h
e
n
etwo
r
k
.
I
t
is
b
ased
o
n
a
p
o
wer
elec
tr
o
n
ics
v
o
ltag
e
-
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
an
d
if
c
o
n
n
ec
ted
to
a
s
o
u
r
ce
o
f
p
o
wer
it
ca
n
also
p
r
o
v
id
e
ac
t
iv
e
p
o
wer
[4
-
6]
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
STAT
C
OM
is
m
ain
ly
d
ep
en
d
en
t
u
p
o
n
h
o
w
ac
cu
r
ately
an
d
q
u
ick
ly
er
r
o
r
s
ig
n
als
ar
e
co
m
p
en
s
ate
d
.
wh
er
e
th
e
b
est
co
m
p
en
s
atio
n
e
f
f
ec
t
ca
n
b
e
o
b
tain
ed
b
y
p
r
o
p
er
c
o
n
tr
o
l
o
f
t
h
e
STAT
C
OM
[
7
]
.
C
o
n
v
en
tio
n
ally
,
a
STAT
C
OM
is
co
n
tr
o
l
led
b
y
th
e
PI
co
n
tr
o
ller
,
wh
ich
r
eq
u
ir
es
p
r
ec
is
e
lin
ea
r
m
ath
em
atica
l
m
o
d
els,
wh
er
e
ar
e
d
if
f
icu
lt
t
o
o
b
tain
an
d
f
ail
to
p
er
f
o
r
m
s
at
is
f
ac
to
r
ily
u
n
d
er
p
a
r
am
eter
v
ar
iatio
n
s
n
o
n
lin
ea
r
ity
lo
ad
d
is
tu
r
b
an
ce
.
T
h
u
s
,
th
e
b
est
p
o
s
s
ib
le
p
er
f
o
r
m
an
ce
f
r
o
m
a
STAT
C
OM
m
ig
h
t
n
o
t
b
e
o
b
tain
ed
f
r
o
m
co
n
v
e
n
tio
n
al
co
n
tr
o
ller
s
f
o
r
d
if
f
er
en
t
o
p
er
atin
g
p
o
i
n
ts
[
8
,
9
]
.
T
o
av
o
id
th
e
a
b
o
v
e
-
m
en
tio
n
e
d
d
r
awb
ac
k
s
.
T
h
e
n
ee
d
was
f
o
r
th
e
d
ev
el
o
p
m
en
t
o
f
n
ew
c
o
n
tr
o
ller
s
with
m
o
r
e
im
p
r
o
v
e
d
p
e
r
f
o
r
m
an
ce
[
7
]
.
R
ec
en
tly
,
a
m
ajo
r
e
f
f
o
r
t
h
as
b
ee
n
u
n
d
e
r
way
to
d
ev
elo
p
n
ew
a
n
d
u
n
co
n
v
en
tio
n
al
c
o
n
tr
o
l
tec
h
n
i
q
u
es
th
at
ca
n
o
f
ten
au
g
m
en
t
o
r
r
ep
lace
c
o
n
v
e
n
tio
n
al
co
n
tr
o
l
tech
n
iq
u
es,
ANN
tech
n
iq
u
es
h
av
e
b
ee
n
s
ig
n
if
ic
an
tly
u
s
ef
u
l
in
p
o
wer
elec
tr
o
n
ics
f
o
r
th
e
m
ain
ten
a
n
ce
o
f
t
h
e
s
tab
ilit
y
o
f
s
y
s
te
m
s
o
v
er
a
wid
e
r
a
n
g
e
o
f
o
p
e
r
atio
n
.
ANN
co
n
tr
o
ller
ca
n
lear
n
,
r
em
em
b
er
an
d
m
a
k
e
d
ec
is
io
n
s
.
Fu
r
th
er
m
o
r
e,
it
p
r
o
v
id
es
a
f
ast
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
th
eir
co
n
tr
o
l
r
eq
u
i
r
e
s
n
o
m
ath
em
atica
l
m
o
d
el
o
f
th
e
s
y
s
tem
[
1
0
,
1
1
]
.
Sev
er
al
s
tu
d
ies
h
av
e
p
r
o
p
o
s
ed
th
e
ap
p
licatio
n
o
f
ANN
-
b
ased
co
n
tr
o
l
o
f
STAT
C
OM
in
p
o
wer
s
y
s
tem
d
is
tr
ib
u
tio
n
.
I
n
th
is
p
a
p
er
,
th
e
ANN
co
n
tr
o
ller
h
as
b
ee
n
d
es
ig
n
ed
in
s
tead
o
f
c
o
n
v
e
n
tio
n
al
PI
f
o
r
STAT
C
OM
co
n
tr
o
l
cir
cu
it.
E
x
h
au
s
tiv
e
s
i
m
u
latio
n
s
tu
d
ies
ar
e
ca
r
r
ied
o
u
t
f
o
r
th
e
I
E
E
E
1
4
-
b
u
s
s
y
s
tem
to
s
tu
d
y
th
e
p
er
f
o
r
m
an
ce
o
f
d
esig
n
e
d
ANN
co
n
tr
o
ller
f
o
r
STAT
C
OM
.
2.
ST
A
T
I
C
SYNCH
RO
NO
US
CO
M
P
E
N
SAT
O
R
(
S
T
A
T
C
O
M
)
A
co
m
p
lete
d
etailed
ex
p
lan
ati
o
n
ab
o
u
t ST
AT
C
OM
f
u
n
ctio
n
ality
an
d
co
n
tr
o
llab
ilit
y
is
as f
o
llo
ws:
2
.
1
.
T
he
ba
s
ic
o
pera
t
ing
princ
ipl
e
o
f
ST
AT
CO
M
Static
Sy
n
ch
r
o
n
o
u
s
C
o
m
p
en
s
ato
r
(
STAT
C
OM
)
as
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
tan
t
m
em
b
er
s
o
f
th
e
FAC
T
S
f
am
ily
,
wh
ich
is
in
cr
ea
s
in
g
ly
u
s
ed
in
m
o
d
e
r
n
p
o
wer
s
y
s
tem
s
,
is
co
n
n
ec
ted
in
s
h
u
n
t
to
th
e
s
y
s
tem
as
s
h
o
wn
in
Fig
u
r
e
1
.
I
t is a
3
Ø
v
o
lta
g
e
s
y
s
tem
th
at
let
s
b
o
th
g
en
er
atio
n
an
d
a
b
s
o
r
p
tio
n
o
f
r
ea
ctiv
e
p
o
wer
.
W
h
en
s
y
s
tem
v
o
ltag
e
is
lo
w,
th
e
STAT
C
OM
g
en
er
ates
r
ea
ctiv
e
p
o
wer
(
STAT
C
OM
ca
p
ac
itiv
e)
.
W
h
en
s
y
s
tem
v
o
ltag
e
is
h
ig
h
,
it
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
(
STAT
C
OM
in
d
u
ctiv
e)
.
I
t
co
n
s
is
ts
o
f
b
lo
ck
s
a
n
d
th
ey
ar
e
co
u
p
lin
g
tr
an
s
f
o
r
m
er
,
m
ea
s
u
r
em
e
n
t
s
y
s
tem
,
in
v
er
ter
/co
n
v
er
ter
cir
cu
it,
co
n
tr
o
ller
an
d
a
d
c
-
lin
k
c
ap
ac
ito
r
.
T
h
e
b
asic
o
p
er
atio
n
p
r
in
cip
le
o
f
th
e
ST
AT
C
OM
is
b
ased
o
n
two
AC
s
o
u
r
ce
s
(
Sy
s
tem
an
d
STAT
C
OM
)
with
th
e
s
am
e
f
r
eq
u
e
n
cy
th
r
o
u
g
h
c
o
u
p
lin
g
in
d
u
ctan
ce
.
T
h
e
e
x
ch
an
g
e
o
f
r
ea
ctiv
e
p
o
wer
b
etwe
en
th
e
s
y
s
tem
an
d
STAT
C
OM
is
ac
h
iev
ed
b
y
ad
ju
s
tin
g
th
e
a
m
p
litu
d
e
o
f
th
e
VSC
o
u
tp
u
t
v
o
ltag
e
(
Vo
u
t)
.
I
f
th
e
am
p
litu
d
e
o
f
th
e
VSC
o
u
tp
u
t
v
o
ltag
e
is
g
r
ea
ter
t
h
an
t
h
e
s
y
s
tem
v
o
ltag
e
(
Vac
)
,
th
e
S
T
AT
C
OM
g
en
er
ates
ca
p
ac
i
tiv
e
r
ea
ctiv
e
p
o
wer
.
Oth
er
wis
e,
th
e
STAT
C
OM
ab
s
o
r
b
s
in
d
u
ctiv
e
r
ea
ctiv
e
p
o
we
r
.
I
f
th
e
a
m
p
litu
d
e
o
f
th
e
VS
C
o
u
tp
u
t
v
o
ltag
e
is
eq
u
al
to
th
e
s
y
s
tem
v
o
ltag
e,
th
e
ex
ch
an
g
e
o
f
r
ea
ctiv
e
p
o
wer
b
etwe
en
th
e
STAT
C
OM
an
d
th
e
s
y
s
tem
will b
e
ze
r
o
[
8
,
1
0
,
1
2
]
.
Fig
u
r
e
1
.
STAT
C
OM
in
p
o
we
r
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
11
,
No
.
4
,
Dec
em
b
er
2
0
2
0
:
1966
–
1
9
7
8
1968
T
h
e
r
elatio
n
b
etwe
en
th
e
f
u
n
d
am
en
tal
co
m
p
o
n
en
t
o
f
th
e
c
o
n
v
er
ter
ac
v
o
ltag
e
o
u
tp
u
t a
n
d
th
e
v
o
ltag
e
ac
r
o
s
s
th
e
d
c
ca
p
ac
ito
r
is
g
iv
e
n
as:
=
(
1
)
W
h
er
e
k
is
th
e
co
ef
f
icien
t
th
a
t
d
ep
en
d
s
o
n
th
e
n
u
m
b
er
o
f
s
witch
in
g
p
u
ls
es,
co
n
v
er
ter
c
o
n
f
ig
u
r
atio
n
an
d
th
e
co
n
v
er
ter
co
n
tr
o
ls
.
T
h
e
f
u
n
d
am
e
n
tal
co
m
p
o
n
e
n
t
o
f
th
e
c
o
n
v
er
te
r
v
o
ltag
e
o
u
tp
u
t
i.e
.
Vo
u
t
is
d
ep
en
d
e
n
t
o
n
Vd
c
,
ca
n
b
e
c
o
n
tr
o
lled
b
y
v
ar
y
i
n
g
th
e
d
c
v
o
ltag
e
ac
r
o
s
s
th
e
ca
p
ac
ito
r
wh
i
ch
ca
n
b
e
d
o
n
e
b
y
v
ar
y
in
g
th
e
p
h
ase
an
g
le
α
o
f
th
e
co
n
v
er
ter
s
witch
in
g
.
T
h
e
d
ir
ec
tio
n
o
f
r
ea
ctiv
e
p
o
wer
f
l
o
w
eith
er
f
r
o
m
t
h
e
s
y
s
tem
to
th
e
co
u
p
lin
g
tr
a
n
s
f
o
r
m
er
o
r
f
r
o
m
th
e
co
u
p
lin
g
tr
an
s
f
o
r
m
er
to
t
h
e
s
y
s
tem
is
d
ec
id
ed
b
y
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
c
o
n
v
e
r
ter
v
o
ltag
e
o
u
tp
u
t a
n
d
th
e
ac
s
y
s
tem
b
u
s
v
o
ltag
e
[
8
]
.
T
h
e
r
ea
ctiv
e
p
o
wer
ex
c
h
an
g
e
d
ca
n
b
e
g
iv
en
as f
o
llo
ws:
=
2
−
∝
(
2
)
T
h
e
r
ea
l p
o
wer
ex
ch
a
n
g
e
b
etwe
en
th
e
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
e
r
ter
an
d
th
e
ac
s
y
s
tem
ca
n
b
e
g
i
v
en
as:
=
∝
(
3
)
W
h
er
e:
-
co
n
v
e
r
ter
o
u
tp
u
t v
o
ltag
e,
-
ac
s
y
s
tem
v
o
ltag
e
m
a
g
n
itu
d
e,
–
leak
ag
e
r
ea
ctan
ce
o
f
th
e
co
u
p
lin
g
tr
a
n
s
f
o
r
m
er
.
α
-
p
h
ase
an
g
le
b
etwe
en
th
e
c
o
n
v
er
ter
o
u
tp
u
t v
o
ltag
e
an
d
t
h
e
s
y
s
tem
v
o
ltag
e.
2
.
2
.
Sin
us
o
i
da
l pul
s
e
width
m
o
du
la
t
io
n (
SPWM)
t
ec
hn
iq
ue
T
h
e
m
o
s
t
co
m
m
o
n
PW
M
ap
p
r
o
ac
h
is
s
in
u
s
o
id
al
PW
M.
I
n
th
is
m
eth
o
d
,
a
tr
ia
n
g
u
la
r
wav
e
is
co
m
p
ar
ed
to
a
s
in
u
s
o
id
al
wav
e
o
f
th
e
d
esire
d
f
r
eq
u
en
cy
a
n
d
th
e
r
elativ
e
le
v
el
o
f
th
e
two
wav
es
is
u
s
ed
t
o
co
n
tr
o
l th
e
s
witch
in
g
o
f
d
ev
ic
es in
ea
ch
p
h
ase
leg
o
f
th
e
i
n
v
er
ter
.
T
h
e
in
v
er
ter
o
u
tp
u
t v
o
ltag
e
h
a
s
th
e
f
o
llo
win
g
f
ea
t
u
r
es.
1
-
SP
W
M
f
r
eq
u
en
c
y
is
th
e
s
a
m
e
as th
e
f
r
eq
u
en
cy
o
f
V
tr
i.
2
-
Am
p
litu
d
e
is
co
n
tr
o
lled
b
y
th
e
p
ea
k
v
alu
e
o
f
V
C
o
n
tr
o
l.
3
-
Fu
n
d
a
m
en
tal
f
r
e
q
u
en
c
y
is
co
n
tr
o
lled
b
y
th
e
f
r
eq
u
en
cy
o
f
V
C
o
n
tr
o
l.
T
h
e
aim
o
f
t
h
e
co
n
t
r
o
ller
an
d
s
in
u
s
o
id
al
PW
M
s
ch
em
e
is
to
m
ain
tain
co
n
s
tan
t
v
o
ltag
e
m
a
g
n
itu
d
e
at
th
e
p
o
in
t
wh
er
e
a
s
en
s
itiv
e
lo
ad
is
co
n
n
ec
te
d
,
u
n
d
er
s
y
s
tem
d
is
tu
r
b
an
ce
s
.
T
h
e
co
n
tr
o
l
s
y
s
tem
o
n
ly
m
ea
s
u
r
es
th
e
R
MS
v
o
ltag
e
at
th
e
lo
ad
p
o
in
t,
i.e
.
,
n
o
r
ea
ctiv
e
p
o
wer
m
ea
s
u
r
em
en
ts
ar
e
r
eq
u
ir
ed
.
T
h
e
VSC
s
witch
in
g
s
tr
ateg
y
is
b
ased
o
n
a
s
in
u
s
o
id
al
PW
M
tech
n
iq
u
e
wh
ich
o
f
f
e
r
s
s
im
p
licity
an
d
g
o
o
d
r
esp
o
n
s
e.
SP
W
M
m
eth
o
d
s
o
f
f
er
a
m
o
r
e
flex
ib
le
o
p
tio
n
th
an
th
e
f
u
n
d
am
en
tal
f
r
eq
u
en
cy
s
witch
in
g
m
eth
o
d
s
f
a
v
o
u
r
e
d
in
FAC
T
S
ap
p
licatio
n
.
2
.
3
.
Vo
lt
a
g
e
s
o
urce
co
nv
er
t
er
(
V
SC)
VSC
i
s
a
p
o
wer
elec
tr
o
n
ic
t
o
o
l
ab
le
o
f
g
en
er
atin
g
a
s
in
u
s
o
id
al
v
o
ltag
e
o
f
r
eq
u
ir
ed
f
r
eq
u
en
c
y
,
m
ag
n
itu
d
e
an
d
p
h
ase
a
n
g
le.
I
t
co
n
v
er
ts
th
e
d
.
c
v
o
ltag
e
t
h
r
o
u
g
h
th
e
s
to
r
ag
e
ca
p
ac
ito
r
in
to
th
r
ee
-
p
h
ase
a
.
c
o
u
tp
u
t
v
o
ltag
es.
T
h
e
v
o
ltag
es
ar
e
in
p
h
ase
an
d
co
u
p
l
ed
w
ith
th
e
a.
c
s
y
s
tem
th
r
o
u
g
h
th
e
c
o
u
p
lin
g
tr
an
s
f
o
r
m
er
[
1
3
]
.
T
h
e
m
ajo
r
f
u
n
ctio
n
o
f
VSC
as
an
i
n
teg
r
al
p
ar
t
o
f
STAT
C
OM
is
to
co
n
t
r
ib
u
te
in
m
itig
atin
g
p
o
wer
q
u
ality
d
is
tu
r
b
an
ce
s
b
y
in
jectin
g
o
r
a
b
s
o
r
b
in
g
th
e
r
e
q
u
ir
ed
v
o
ltag
e.
T
h
e
r
eq
u
ir
e
d
v
o
ltag
e
in
th
is
ca
s
e
i
s
th
e
d
if
f
er
e
n
ce
b
etwe
en
r
ef
er
e
n
ce
an
d
ac
t
u
al
v
o
ltag
e
.
T
h
e
VSC
i
s
u
s
u
ally
b
ased
o
n
s
o
m
e
ty
p
e
o
f
en
er
g
y
s
to
r
ag
e
th
at
will
s
u
p
p
ly
th
e
d
.
c
v
o
ltag
e.
T
h
e
r
e
q
u
ir
ed
v
o
ltag
e
ca
n
th
en
b
e
g
ettin
g
b
y
s
witch
in
g
th
e
s
o
lid
-
s
tate
elec
tr
o
n
ic
d
ev
ices in
th
e
co
n
v
er
ter
[
1
4
]
.
2
.
4
.
Str
uct
ure
o
f
ST
AT
CO
M
co
ntr
o
l c
ircuit
T
h
e
m
ain
f
u
n
ctio
n
o
f
th
e
S
T
AT
C
OM
co
n
tr
o
l
cir
cu
it
is
to
in
d
ep
en
d
en
tly
co
n
t
r
o
l
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
s
u
p
p
lied
to
th
e
p
o
wer
s
y
s
tem
to
r
eg
u
late
t
h
e
v
o
ltag
e
g
en
er
ate
d
o
v
er
th
e
d
c
-
lin
k
ca
p
ac
ito
r
.
Fig
u
r
e
3
d
e
p
icts
th
e
b
asic c
o
n
t
r
o
l stra
teg
y
em
p
l
o
y
ed
f
o
r
t
h
e
STAT
C
OM
.
T
h
e
co
n
tr
o
l
s
y
s
tem
co
n
s
is
ts
o
f
:
T
h
e
Ph
ase
-
L
o
ck
ed
L
o
o
p
(
PLL
)
,
m
ea
s
u
r
em
en
t
s
y
s
tem
s
,
ab
c
-
d
q
0
tr
an
s
f
o
r
m
atio
n
,
PI
co
n
t
r
o
ller
,
cu
r
r
en
t r
e
g
u
lato
r
a
n
d
t
h
e
p
u
ls
e
g
en
er
ato
r
.
A
p
h
ase
-
lo
ck
e
d
lo
o
p
(
PLL
)
wh
ich
s
y
n
ch
r
o
n
izes
o
n
th
e
p
o
s
itiv
e
-
s
eq
u
en
ce
c
o
m
p
o
n
en
t
o
f
th
e
th
r
ee
-
p
h
ase
p
r
im
ar
y
v
o
ltag
e
V1
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
PLL
(
an
g
l
e
θ=
ω
t)
is
u
s
ed
to
co
m
p
u
te
th
e
d
ir
ec
t
-
ax
is
an
d
q
u
ad
r
atu
r
e
-
ax
is
co
m
p
o
n
e
n
ts
o
f
th
e
AC
th
r
ee
-
p
h
ase
v
o
ltag
e
an
d
cu
r
r
en
ts
(
lab
eled
as
Vd
,
Vq
o
r
I
d
,
I
q
o
n
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
r
o
ve
men
t o
f th
e
p
erfo
r
ma
n
ce
o
f S
TATC
OM in
term
s
o
f
… (
Mo
h
a
mme
d
S
a
lh
ee
n
A
la
ts
h
a
n
)
1969
d
iag
r
am
)
.
Me
asu
r
e
m
en
t
s
y
s
tem
s
th
at
m
ea
s
u
r
e
th
e
d
an
d
q
co
m
p
o
n
en
ts
o
f
AC
p
o
s
itiv
e
-
s
eq
u
en
ce
v
o
ltag
e
an
d
cu
r
r
en
ts
to
b
e
co
n
tr
o
lled
as
w
ell
as
th
e
DC
v
o
ltag
e
Vd
c.
A
n
o
u
ter
co
n
tr
o
l
lo
o
p
co
n
s
is
ti
n
g
o
f
a
PI
co
n
tr
o
ller
f
o
r
AC
v
o
ltag
e
a
n
d
an
o
th
er
PI
co
n
tr
o
ller
f
o
r
DC
v
o
ltag
e.
T
h
e
o
u
tp
u
t
o
f
th
e
PI
c
o
n
tr
o
ller
f
o
r
AC
v
o
ltag
e
is
th
e
r
ef
er
en
ce
cu
r
r
en
t
I
q
r
ef
f
o
r
th
e
cu
r
r
en
t
r
eg
u
lato
r
(
I
q
=
cu
r
r
en
t
in
q
u
ad
r
atu
r
e
with
a
v
o
ltag
e
wh
ich
co
n
tr
o
ls
r
ea
ctiv
e
p
o
wer
f
lo
w)
.
T
h
e
o
u
tp
u
t
o
f
t
h
e
PI
co
n
tr
o
ller
f
o
r
th
e
DC
v
o
ltag
e
is
th
e
r
ef
er
e
n
ce
c
u
r
r
en
t
I
d
r
ef
f
o
r
t
h
e
cu
r
r
en
t
r
eg
u
lato
r
(
I
d
=
c
u
r
r
e
n
t
in
p
h
ase
with
a
v
o
lta
g
e
wh
i
ch
co
n
tr
o
ls
ac
tiv
e
p
o
wer
f
lo
w
)
.
An
in
n
er
c
u
r
r
e
n
t
r
eg
u
latio
n
lo
o
p
co
n
s
is
tin
g
o
f
a
cu
r
r
en
t
r
eg
u
lato
r
.
T
h
e
cu
r
r
e
n
t
r
eg
u
lato
r
c
o
n
tr
o
ls
th
e
m
ag
n
itu
d
e
an
d
p
h
ase
o
f
th
e
v
o
ltag
e
g
en
er
ate
d
b
y
th
e
SP
W
M
co
n
v
er
ter
(
V2
d
,
V2
q
)
f
r
o
m
th
e
I
d
r
e
f
an
d
I
q
r
ef
r
ef
er
en
ce
c
u
r
r
e
n
ts
p
r
o
d
u
ce
d
r
esp
ec
tiv
ely
b
y
th
e
PI
co
n
tr
o
ller
f
o
r
AC
v
o
ltag
e
a
n
d
th
e
PI
co
n
t
r
o
ller
f
o
r
t
h
e
D
C
v
o
ltag
e
(
in
v
o
ltag
e
co
n
tr
o
l
m
o
d
e)
.
T
h
e
cu
r
r
e
n
t
r
eg
u
lato
r
is
ass
is
ted
b
y
a
f
ee
d
-
f
o
r
war
d
ty
p
e
r
eg
u
lato
r
w
h
ich
p
r
ed
icts
th
e
V2
v
o
ltag
e
o
u
tp
u
t (
V2
d
,
V2
q
)
f
r
o
m
th
e
V1
m
ea
s
u
r
e
m
en
t (
V1
d
,
V1
q
)
[
1
5
]
.
Fig
u
r
e
2
.
VSC
u
s
in
g
I
GB
T
-
b
ased
SP
W
M
in
v
er
ter
s
Fig
u
r
e
3
.
C
o
n
tr
o
l sy
s
tem
b
lo
c
k
d
iag
r
am
o
f
STAT
C
OM
2
.
5
.
P
I
co
ntr
o
ller
PI
C
o
n
tr
o
ller
is
r
eq
u
ir
ed
to
c
o
n
tr
o
l
o
r
to
o
p
er
ate
STAT
C
OM
d
u
r
in
g
a
d
is
tu
r
b
a
n
ce
in
th
e
s
y
s
tem
,
s
u
ch
as
d
r
o
p
in
th
e
v
o
ltag
e
le
v
el.
T
h
e
v
o
ltag
e
o
f
Po
in
t
o
f
C
o
m
m
o
n
C
o
u
p
lin
g
(
PC
C
)
is
s
e
n
s
ed
an
d
f
o
r
war
d
ed
th
r
o
u
g
h
a
s
eq
u
en
ce
a
n
aly
ze
r
.
R
ea
ctiv
e
p
o
wer
co
n
tr
o
l
lo
o
p
(
co
n
tr
o
l
u
n
it
o
f
q
-
co
o
r
d
in
ate
)
an
d
ac
tiv
e
p
o
wer
co
n
tr
o
l
lo
o
p
(
c
o
n
tr
o
l
u
n
it
o
f
d
-
co
o
r
d
in
ate
)
h
a
v
e
a
s
ep
ar
ate
PI
co
n
tr
o
ller
.
As
a
s
am
e
o
f
f
e
ed
b
ac
k
co
n
tr
o
ller
s
,
th
e
PI
c
o
n
tr
o
ller
o
p
er
ates
b
y
s
u
m
m
in
g
t
h
e
er
r
o
r
an
d
in
teg
r
al
o
f
th
ese
v
alu
es
[
1
6
]
.
Stru
ctu
r
e
o
f
PI
co
n
t
r
o
ller
d
ep
icted
in
Fig
u
r
e
4
.
T
h
e
d
if
f
er
en
ce
v
alu
e
b
etwe
en
th
e
ac
tu
al
a
n
d
r
ef
er
e
n
ce
v
o
ltag
e
is
th
e
in
p
u
t
o
f
th
e
PI
co
n
t
r
o
ller
.
Fo
r
th
e
q
-
co
o
r
d
i
n
ate
co
n
t
r
o
l
u
n
it,
th
e
r
ef
er
e
n
ce
v
al
u
e
f
o
r
v
o
ltag
e
is
1
p
.
u
,
wh
e
r
e
in
t
h
is
co
n
tr
o
l,
th
e
p
r
o
p
o
r
tio
n
al
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
11
,
No
.
4
,
Dec
em
b
er
2
0
2
0
:
1966
–
1
9
7
8
1970
g
ain
(
Kp
)
is
5
an
d
th
e
in
teg
r
a
l
g
ain
(
Ki)
is
1
0
0
0
.
I
n
th
e
co
n
tr
o
l
u
n
it
o
f
d
-
co
o
r
d
in
ate,
th
e
p
r
o
p
o
r
tio
n
al
g
ain
(
Kp
)
a
n
d
in
teg
r
al
g
ain
(
Ki)
ar
e
0
.
0
2
5
.
T
h
e
o
u
tp
u
t
o
f
th
e
PI
co
n
tr
o
ller
is
c
o
n
v
e
r
ted
i
n
to
t
h
r
ee
-
p
h
ase
v
o
ltag
e
an
d
g
iv
en
t
o
th
e
SP
W
M
p
u
ls
e
g
en
er
ato
r
to
p
r
o
d
u
ce
th
e
p
u
ls
e
an
d
th
en
it
will
b
e
d
eliv
er
ed
to
th
e
VSC
to
tr
ig
g
er
th
e
I
GB
T
s
witch
es.
Fig
u
r
e
4
.
PI
c
o
n
tr
o
ller
[
1
0
]
2
.
6
.
ANN
co
ntr
o
ller
Neu
r
al
n
etwo
r
k
s
h
av
e
n
o
w
b
ec
o
m
e
o
n
e
o
f
th
e
n
ew
co
n
tr
o
l
tech
n
o
lo
g
ies,
it
is
a
h
ig
h
ly
in
ter
co
n
n
ec
ted
n
etwo
r
k
o
f
a
g
r
ea
t
n
u
m
b
e
r
o
f
p
r
o
ce
s
s
in
g
elem
en
ts
ca
lled
n
eu
r
o
n
s
in
a
d
esig
n
in
s
p
ir
ed
b
y
th
e
h
u
m
an
b
r
ain
.
i
n
g
en
e
r
ally
,
th
e
b
o
d
y
o
f
t
h
e
n
eu
r
al
n
etwo
r
k
c
o
n
tain
s
s
ev
er
al
lay
er
s
o
f
n
eu
r
o
n
s
,
an
in
p
u
t
lay
er
,
h
id
d
en
la
y
er
s
,
an
d
an
o
u
tp
u
t la
y
er
[
1
7
]
.
As s
h
o
wn
in
Fig
u
r
e
5
.
Fig
u
r
e
5
.
G
en
e
r
al
s
tr
u
ctu
r
e
o
f
n
eu
r
al
n
etwo
r
k
[
1
0
]
T
h
e
m
ajo
r
o
b
ject
o
f
th
e
ANN
co
n
tr
o
ller
is
to
g
et
p
r
o
p
er
v
al
u
es
f
o
r
weig
h
ts
an
d
b
iases
wh
i
ch
ar
e
th
e
lear
n
ab
le
p
ar
a
m
eter
s
in
s
id
e
th
e
co
n
tr
o
ller
s
tr
u
ct
u
r
e
t
h
at
g
iv
e
s
th
e
r
eq
u
ir
ed
o
u
tp
u
t
[
1
6
]
.
I
n
th
is
r
esear
ch
,
a
m
u
ltil
ay
er
B
P
-
ty
p
e
ANN
co
n
tr
o
ller
was
u
tili
ze
d
to
im
p
r
o
v
e
t
h
e
p
er
f
o
r
m
an
ce
o
f
STAT
C
OM
.
T
h
e
ANN
was
tr
ain
ed
b
y
u
s
in
g
t
h
e
MA
T
L
AB
to
o
lb
o
x
;
L
ev
en
b
e
r
g
M
ar
q
u
ar
d
t
(
L
M)
B
P
alg
o
r
ith
m
was
ap
p
lied
as
th
e
tr
ain
in
g
alg
o
r
ith
m
in
th
is
ar
tific
ial
n
eu
r
al
n
etwo
r
k
co
n
tr
o
ll
er
.
T
h
er
e
ar
e
th
r
ee
m
eth
o
d
s
to
f
i
n
d
t
h
e
l
o
ca
l
m
in
im
u
m
f
o
r
an
y
g
iv
en
f
u
n
ctio
n
.
Gr
ad
ien
t
Descen
t
(
G
D)
is
a
f
ir
s
t
-
o
r
d
e
r
o
p
tim
izatio
n
f
r
am
ewo
r
k
,
L
e
v
en
b
er
g
-
Ma
r
q
u
ar
d
t
B
ac
k
p
r
o
p
ag
atio
n
(
L
MBP
)
alg
o
r
ith
m
is
a
s
ec
o
n
d
-
o
r
d
er
o
p
tim
izatio
n
f
r
am
ewo
r
k
,
a
n
d
Gau
s
s
-
New
to
n
(
GN)
f
r
am
e
wo
r
k
.
G
r
ad
ien
t
Descen
t
(
GD
)
is
a
s
tr
o
n
g
m
eth
o
d
esp
ec
i
ally
wh
en
it
b
e
g
in
s
f
ar
f
r
o
m
th
e
f
i
n
al
m
in
im
u
m
;
m
ea
n
tim
e,
it
is
p
r
o
n
e
to
p
o
o
r
co
n
v
er
g
en
ce
.
L
M
alg
o
r
ith
m
ca
n
g
et
s
o
lu
tio
n
s
ev
en
in
itiatin
g
f
a
r
f
r
o
m
th
e
f
in
al
s
o
lu
tio
n
.
W
h
er
e
th
e
L
MBP
m
eth
o
d
is
b
etwe
en
GD
an
d
Gau
s
s
-
New
to
n
(
GN)
f
r
am
ewo
r
k
s
.
L
ev
en
b
er
g
-
Ma
r
q
u
ar
d
t
B
ac
k
p
r
o
p
ag
atio
n
(
L
MBP
)
alg
o
r
ith
m
is
a
p
r
ef
er
ab
le
o
p
tio
n
t
h
an
t
o
G
N
an
d
GD
m
eth
o
d
s
[
1
8
]
as
it
co
n
v
er
g
es
q
u
ick
l
y
,
n
ee
d
lo
w
m
em
o
r
y
,
an
d
en
ab
le
to
lear
n
[
1
9
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
r
o
ve
men
t o
f th
e
p
erfo
r
ma
n
ce
o
f S
TATC
OM in
term
s
o
f
… (
Mo
h
a
mme
d
S
a
lh
ee
n
A
la
ts
h
a
n
)
1971
T
h
e
d
iag
r
am
o
f
th
e
ANN
co
n
tr
o
ller
u
tili
ze
d
in
th
is
r
esear
ch
as
s
h
o
wn
in
Fig
u
r
e
6
,
h
as
3
lay
er
s
,
co
n
s
is
t o
f
1
in
p
u
t la
y
e
r
,
1
h
i
d
d
en
lay
er
(
co
n
tain
ed
o
f
1
0
n
eu
r
o
n
s
)
,
an
d
1
o
u
t
p
u
t la
y
er
.
T
h
e
d
ata
f
o
r
tr
ain
i
n
g
th
e
ar
tific
ial
n
eu
r
al
n
etwo
r
k
ar
e
s
o
u
r
ce
d
f
r
o
m
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
.
T
h
e
i
n
p
u
t
o
f
t
h
e
ar
tific
ial
n
eu
r
al
n
etwo
r
k
is
th
e
er
r
o
r
s
ig
n
al
o
f
t
h
e
Vac
an
d
th
e
er
r
o
r
s
ig
n
al
o
f
th
e
Vd
c.
T
h
e
er
r
o
r
is
d
eter
m
in
ed
an
d
a
p
o
r
tio
n
o
f
it
is
p
r
o
p
ag
ated
b
ac
k
war
d
th
r
o
u
g
h
th
e
n
etwo
r
k
.
T
h
e
ANN
co
n
tr
o
ller
is
ex
p
ec
ted
to
m
i
n
i
m
ize
th
is
er
r
o
r
.
T
h
e
p
er
f
o
r
m
an
ce
m
etr
ic
o
f
th
e
ANN
co
n
tr
o
ller
is
th
e
Me
an
s
q
u
ar
e
er
r
o
r
wh
ich
r
ef
lects th
e
er
r
o
r
b
etwe
en
th
e
in
p
u
t
an
d
th
e
tar
g
et
v
alu
es.1
0
0
0
ep
o
ch
s
wer
e
r
eq
u
ir
e
d
f
o
r
th
e
ANN
tr
ain
in
g
in
th
e
co
n
tr
o
l
u
n
i
t
o
f
q
-
co
o
r
d
i
n
ate
th
e
b
est
-
ac
h
iev
ed
v
alid
atio
n
p
er
f
o
r
m
an
ce
(
0
.
0
0
0
2
6
4
0
4
)
was
ac
h
iev
ed
at
e
p
o
ch
1
5
.
T
h
e
n
u
m
b
er
o
f
ep
o
c
h
s
in
t
h
e
co
n
tr
o
l
u
n
it
o
f
d
-
co
o
r
d
i
n
ate
ar
e
1
0
0
0
wh
ile
th
e
b
est
-
ac
h
iev
ed
v
alid
atio
n
p
er
f
o
r
m
a
n
c
e
(
0
.
0
0
0
4
1
6
4
3
)
is
ac
h
iev
ed
at
ep
o
ch
1
3
.
T
h
e
A
NN
tr
ain
in
g
was
p
er
f
o
r
m
ed
o
f
f
lin
e
an
d
was
p
r
o
g
r
am
m
ed
t
o
co
n
tr
o
l
th
e
VSC
STAT
C
OM
.
Af
ter
th
e
o
f
f
lin
e
tr
ain
in
g
was
co
m
p
leted
,
th
e
n
ex
t
s
tag
e
is
to
r
ep
lace
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
with
th
e
cr
ea
ted
AN
N
co
n
tr
o
ller
.
Fig
u
r
e
6
.
Diag
r
a
m
o
f
n
eu
r
al
n
etwo
r
k
u
s
ed
in
t
h
is
s
tu
d
y
3.
M
O
DE
L
I
NG
O
F
T
H
E
T
E
S
T
P
O
WE
R
S
YS
T
E
M
A
test
p
o
wer
s
y
s
tem
was
m
o
d
eled
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
s
o
f
twar
e
in
th
e
I
E
E
E
-
1
4
b
u
s
.
T
h
e
s
y
s
tem
co
n
s
is
ts
o
f
1
1
lo
a
d
b
u
s
es,
two
p
o
wer
g
e
n
er
ato
r
s
,
t
h
r
ee
s
y
n
ch
r
o
n
o
u
s
co
m
p
e
n
s
ato
r
s
an
d
a
to
tal
o
f
2
1
tr
an
s
m
is
s
io
n
lin
es.
T
h
e
test
p
o
wer
s
y
s
tem
was
d
esig
n
ed
u
s
in
g
a
p
h
aso
r
s
im
u
latio
n
ty
p
e.
T
h
e
test
p
o
wer
s
y
s
tem
o
p
er
ates
b
ase
o
n
a
1
0
0
MV
A
an
d
b
ase
v
o
ltag
e
o
f
1
3
8
KV.
T
h
e
d
esig
n
was
in
a
cc
o
r
d
an
ce
with
th
e
IEEE
-
1
4
b
u
s
test
s
y
s
tem
as
s
h
o
wn
in
Fig
u
r
e
7
.
T
h
is
s
y
s
tem
was
u
s
ed
th
r
o
u
g
h
o
u
t
all
ca
s
es
th
at
wer
e
s
im
u
lated
.
Fig
u
r
e
7
.
Mo
d
el
o
f
th
e
IEEE
-
1
4
b
u
s
s
y
s
tem
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
11
,
No
.
4
,
Dec
em
b
er
2
0
2
0
:
1966
–
1
9
7
8
1972
Af
ter
r
u
n
n
in
g
th
e
test
s
y
s
tem
s
im
u
latio
n
,
u
n
d
er
th
e
s
tan
d
a
r
d
I
E
E
E
-
1
4
b
u
s
s
y
s
tem
d
ata
with
n
o
d
is
tu
r
b
an
ce
an
d
with
o
u
t
STAT
C
OM
.
T
h
e
b
u
s
v
o
ltag
e
(
p
.
u
)
r
esu
lt
was
o
b
tain
ed
as
p
r
esen
ted
in
Fig
u
r
e
8
.
T
h
e
r
esu
lt
s
h
o
ws
th
at
th
e
v
o
ltag
e
a
t
b
u
s
1
,
b
u
s
7
an
d
b
u
s
8
h
as
th
e
h
ig
h
est
v
o
ltag
e
(
p
.
u
)
at
1
.
0
5
7
p
.
u
,
1
.
0
5
4
p
.
u
a
n
d
1
.
0
8
3
p
.
u
r
esp
ec
tiv
ely
.
w
h
er
e
th
ese
b
u
s
es
ar
e
n
o
t
c
o
n
n
ec
te
d
to
an
y
lo
ad
.
An
d
b
y
m
o
n
ito
r
in
g
th
e
r
est
o
f
th
e
s
y
s
tem
b
u
s
es
th
at
c
o
n
n
ec
t
to
lo
ad
s
.
I
t
was
n
o
te
d
th
at
all
v
o
l
tag
es
wer
e
with
in
th
e
p
er
m
itt
ed
o
p
er
atin
g
r
an
g
e.
W
h
er
e
th
e
v
o
ltag
e
at
b
u
s
es
2
,
3
,
4
,
5
,
6
,
9
,
1
0
,
1
1
,
1
2
,
1
3
an
d
1
4
ar
e
1
.
0
4
1
p
.
u
,
1
.
0
0
8
p
.
u
,
1
.
0
1
1
p
.
u
,
1
.
0
1
4
p
.
u
,
1
.
0
5
p
.
u
,
1
.
0
4
8
p
.
u
,
1
.
0
4
3
p
.
u
,
1
.
0
4
9
p
.
u
,
1
.
0
4
7
p
.
u
,
1
.
0
4
2
p
.
u
an
d
1
.
0
2
6
r
esp
ec
tiv
ely
.
Fig
u
r
e
8
.
Vo
ltag
e
(
p
.
u
)
f
o
r
all
b
u
s
es a
t stan
d
ar
d
d
ata
4.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S O
F
T
H
E
T
E
S
T
CAS
E
S
I
n
th
is
s
tu
d
y
,
two
ca
s
es
wer
e
cr
ea
ted
to
ca
u
s
e
a
d
is
tu
r
b
a
n
ce
in
th
e
test
s
y
s
tem
,
th
ey
wer
e
L
o
ad
in
cr
ea
s
in
g
ca
s
e
an
d
th
r
ee
-
p
h
ase
f
au
lts
ca
s
e.
T
h
is
was
d
o
n
e
to
ac
h
iev
e
t
h
e
o
b
jectiv
e
o
f
th
is
s
tu
d
y
.
Fo
r
clar
if
icatio
n
,
th
e
o
b
jectiv
e
w
as
to
in
v
esti
g
ate
th
e
p
er
f
o
r
m
an
ce
o
f
a
STAT
C
OM
r
eg
ar
d
to
im
p
r
o
v
em
e
n
t
o
f
b
u
s
es
v
o
ltag
e
an
d
d
am
p
in
g
r
a
tio
wh
en
th
e
d
esig
n
e
d
ANN
co
n
tr
o
ller
was
in
tr
o
d
u
ce
d
as
a
n
alter
n
ativ
e
to
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
in
a
p
o
wer
s
y
s
tem
.
T
h
e
r
esu
lt
o
f
u
s
in
g
th
e
STAT
C
OM
wit
h
PI
co
n
tr
o
ller
was
p
r
esen
ted
,
th
en
f
o
llo
wed
b
y
t
h
e
r
esu
lt
o
f
u
s
in
g
th
e
ANN
i
n
co
n
t
r
o
llin
g
th
e
STAT
C
OM
.
At
ev
er
y
s
tag
e
o
f
im
p
lem
en
tatio
n
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
y
s
tem
was c
o
m
p
ar
ed
.
4
.
1
.
L
o
a
d incre
a
s
e
ca
s
e
I
n
th
is
ca
s
e
an
in
cr
ea
s
e
o
f
3
0
0
%
f
r
o
m
th
e
s
tan
d
ar
d
v
alu
e
o
f
th
e
lo
ad
s
wer
e
in
cr
ea
s
ed
f
o
r
all
b
u
s
es
th
at
co
n
n
ec
tin
g
with
a
lo
a
d
.
T
h
e
ju
s
tific
atio
n
f
o
r
an
i
n
cr
ea
s
e
in
th
e
lo
ad
was
to
p
r
o
d
u
ce
a
d
is
tu
r
b
an
ce
in
th
e
test
s
y
s
tem
an
d
o
b
s
er
v
e
t
h
e
ef
f
ec
t
o
n
th
e
p
o
wer
s
y
s
tem
to
lo
ca
te
th
e
wea
k
est
b
u
s
f
o
r
th
e
in
s
tallatio
n
o
f
STAT
C
OM
.
4
.
1
.
1
.
L
o
a
d incre
a
s
e
ca
s
e
wit
h o
ut
ST
A
T
CO
M
W
h
en
th
e
lo
ad
was
in
cr
ea
s
ed
u
p
to
3
0
0
%
with
o
u
t
STAT
C
O
M
th
e
v
o
ltag
e
ass
o
ciate
d
with
ea
ch
b
u
s
is
p
r
esen
ted
in
Fig
u
r
e
9
.
B
y
o
b
s
er
v
in
g
th
e
r
esu
lts
,
we
n
o
t
e
th
e
b
u
s
es
th
at
co
n
n
ec
te
d
to
th
e
g
e
n
er
ato
r
s
a
n
d
th
o
s
e
clo
s
e
to
th
e
s
u
p
p
ly
s
id
e
wer
e
n
o
t
a
f
f
ec
ted
s
ig
n
if
ican
t
ly
b
y
in
cr
ea
s
in
g
th
e
lo
ad
.
W
h
er
e
th
e
v
o
ltag
e
at
b
u
s
es
1
,
2
,
3
,
6
an
d
8
a
r
e
1
.
0
5
1
p
.
u
,
1
.
0
3
7
p
.
u
,
1
.
0
0
4
p
.
u
,
1
.
0
4
9
p
.
u
an
d
1
.
0
6
p
.
u
r
esp
ec
tiv
ely
.
On
th
e
o
th
e
r
h
an
d
,
T
h
er
e
was
o
b
s
er
v
e
a
n
e
f
f
ec
t
o
n
th
e
v
o
ltag
e
am
p
litu
d
e
at
th
e
b
u
s
9
(
1
.
0
2
6
p
.
u
)
,
b
u
s
1
0
(
1
.
0
1
1
p
.
u
)
,
b
u
s
1
1
(
1
.
0
1
4
p
.
u
)
,
b
u
s
1
2
(
0
.
9
3
9
7
p
.
u
)
,
b
u
s
1
3
(
0
.
9
3
0
7
p
.
u
)
,
an
d
b
u
s
1
4
(
0
.
8
9
8
7
p
.
u
)
.
T
h
er
ef
o
r
e,
b
u
s
es
1
2
,
1
3
an
d
1
4
wer
e
i
d
e
n
tifie
d
as
th
e
m
o
s
t
v
u
ln
er
ab
le
b
u
s
es
o
f
th
e
test
ca
s
es.
As
th
e
v
o
ltag
e
o
f
th
ese
b
u
s
es
is
b
elo
w
th
e
p
er
m
itted
lev
el
f
o
r
o
p
e
r
atin
g
lo
ad
s
.
T
h
u
s
,
th
er
e
was
n
ee
d
to
ad
d
co
m
p
e
n
s
atio
n
tech
n
o
lo
g
y
.
W
h
er
e
in
th
is
s
tu
d
y
,
a
STAT
C
OM
d
ev
ice
was
ad
d
ed
to
th
e
s
y
s
tem
.
Pr
ev
io
u
s
s
tu
d
ies
h
ad
r
ep
o
r
ted
t
h
at
th
e
p
lace
m
en
t
cr
iter
io
n
o
f
STAT
C
OM
is
to
h
av
e
it
co
n
n
ec
ted
at
th
e
wea
k
est
b
u
s
o
f
th
e
s
y
s
tem
[
2
0
]
.
T
h
e
wea
k
est
b
u
s
wa
s
id
en
tifie
d
as
b
u
s
1
4
.
T
h
is
is
i
d
en
tical
to
th
e
s
tu
d
ies
th
at
h
a
v
e
b
ee
n
d
o
n
e
to
i
d
en
tify
th
e
wea
k
est
b
u
s
o
n
I
E
E
E
1
4
B
US sy
s
tem
[
2
,
6
,
2
1
,
2
2
]
.
Fu
r
th
er
m
o
r
e
,
a
c
o
m
p
ar
ativ
e
a
n
aly
s
is
o
f
th
e
e
f
f
ec
t
o
f
th
e
in
c
r
ea
s
ed
lo
ad
is
p
r
esen
ted
in
T
a
b
le
1
.
I
t
is
clea
r
f
r
o
m
th
e
tab
le
th
at
th
e
i
n
cr
ea
s
e
in
lo
ad
h
ad
a
s
ig
n
if
ic
an
t
ef
f
ec
t
o
n
th
e
t
h
r
ee
m
o
s
t
v
u
ln
er
ab
le
b
u
s
es
(
1
2
,
1
3
,
an
d
1
4
)
.
W
h
er
e
th
e
v
o
ltag
e
at
n
o
r
m
al
lo
ad
s
in
th
ese
b
u
s
es
was
1
.
0
4
7
p
.
u
,
1
.
0
4
2
p
.
u
a
n
d
1
.
0
2
6
p
.
u
.
Af
ter
th
e
in
cr
ea
s
e
i
n
th
e
lo
ad
,
th
e
v
o
ltag
e
f
o
r
th
e
th
r
ee
b
u
s
es
was
0
.
9
3
9
7
1
p
.
u
,
0
.
9
3
0
7
p
.
u
an
d
0
.
8
9
8
7
p
.
u
r
esp
ec
tiv
ely
.
T
h
e
a
n
aly
s
is
s
h
o
wed
th
at
1
0
.
2
5
%,
1
0
.
6
8
%
an
d
1
2
.
4
1
%
wer
e
th
e
v
o
ltag
e
d
r
o
p
r
atio
in
b
u
s
es
1
2
,
1
3
an
d
1
4
r
esp
ec
tiv
ely
.
T
h
is
d
ec
r
ea
s
e
in
v
o
ltag
e
d
u
e
to
th
e
s
ite
o
f
th
ese
b
u
s
es
f
ar
f
r
o
m
th
e
p
o
wer
s
o
u
r
ce
s
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1.057
1.041
1.008
1.011
1.014
1.05
1.054
1.083
1.048
1.043
1.049
1.047
1.042
1.026
0.95
1
1.05
1.1
VOLT
AG
E
(P.U
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
r
o
ve
men
t o
f th
e
p
erfo
r
ma
n
ce
o
f S
TATC
OM in
term
s
o
f
… (
Mo
h
a
mme
d
S
a
lh
ee
n
A
la
ts
h
a
n
)
1973
(
g
en
er
ato
r
s
)
[
2
1
]
,
wh
er
e
th
e
s
y
s
tem
ca
n
n
o
t
m
ee
t
th
e
r
eq
u
i
r
e
d
o
f
r
ea
ctiv
e
p
o
wer
d
u
e
t
o
th
e
in
cr
ea
s
ed
lo
ad
,
a
n
d
if
th
is
r
ea
ctiv
e
p
o
wer
d
o
es n
o
t
c
o
m
p
en
s
ate
it will le
ad
to
v
o
l
tag
e
in
s
tab
ilit
y
o
r
ev
e
n
v
o
ltag
e
co
llap
s
e
[
2
3
]
.
Fig
u
r
e
9
.
Vo
ltag
e
(
p
.
u
)
f
o
r
all
b
u
s
es a
t lo
ad
in
cr
ea
s
e
ca
s
e
with
o
u
t ST
AT
C
OM
)
T
ab
le
1
.
Vo
ltag
e
d
r
o
p
at
b
u
s
es 1
2
,
1
3
an
d
1
4
b
etwe
en
n
o
r
m
a
l a
n
d
l
o
ad
in
cr
ea
s
e
ca
s
e.
B
u
s
e
s
V
o
l
t
a
g
e
w
h
e
n
n
o
r
mal
c
a
se
(
p
.
u
)
V
o
l
t
a
g
e
w
h
e
n
l
o
a
d
i
n
c
r
e
a
se
c
a
se
(
p
.
u
)
V
o
l
t
a
g
e
d
r
o
p
(
%)
12
1
.
0
4
7
0
.
9
3
9
7
1
0
.
2
5
%
13
1
.
0
4
2
0
.
9
3
0
7
1
0
.
6
8
%
14
1
.
0
2
6
0
.
8
9
8
7
1
2
.
4
1
%
4
.
1
.
2
.
L
o
a
d incre
a
s
e
ca
s
e
wit
h S
T
AT
CO
M
I
n
th
is
s
ec
tio
n
,
STAT
C
OM
w
ill
b
e
in
tr
o
d
u
ce
d
to
th
e
test
s
y
s
tem
,
to
im
p
r
o
v
e
th
e
r
esu
lt
o
b
tain
ed
in
th
e
lo
ad
in
cr
ea
s
e
ca
s
e.
A
s
ig
n
if
ican
t
d
ec
r
ea
s
e
in
v
o
ltag
e
was
o
b
s
er
v
ed
o
n
b
u
s
es
1
2
,
1
3
a
n
d
1
4
.
I
t
will
f
o
cu
s
o
n
th
ese
th
r
ee
b
u
s
es
an
d
ex
p
l
ain
th
e
ef
f
ec
tiv
en
es
s
o
f
th
e
STAT
C
OM
to
im
p
r
o
v
e
th
e
v
o
ltag
e
lev
el.
Fro
m
th
e
p
r
ev
io
u
s
ca
s
e,
a
s
u
itab
le
p
lace
to
co
n
n
ec
t
th
e
STAT
C
OM
to
th
e
s
y
s
tem
was
d
eter
m
in
ed
o
n
b
u
s
1
4
.
T
h
e
ef
f
ec
t
o
f
a
co
n
v
en
tio
n
al
PI
co
n
t
r
o
lle
d
STAT
C
OM
an
d
th
at
o
f
AN
N
co
n
tr
o
lled
STAT
C
OM
ar
e
p
r
esen
ted
.
T
h
e
aim
was to
co
m
p
ar
e
th
e
ef
f
icien
cy
o
f
th
e
PI
an
d
ANN
co
n
tr
o
ller
s
[
2
4
,
2
5
]
a.
STAT
C
OM
b
ased
o
n
a
co
n
v
e
n
tio
n
al
PI
co
n
t
r
o
ller
I
n
th
is
ca
s
e,
th
e
STAT
C
OM
was
u
s
ed
with
co
n
v
en
tio
n
al
PI
co
n
tr
o
l
to
m
itig
ate
th
e
v
o
ltag
e
wea
k
n
ess
an
d
th
e
r
esu
lts
wer
e
as
d
is
p
la
y
ed
in
Fig
u
r
e
1
0
.
T
h
e
b
u
s
es
c
o
n
n
ec
ted
to
g
en
er
atio
n
s
o
u
r
ce
s
ar
e
s
till
at
ab
o
u
t
th
e
s
am
e
v
alu
e
.
b
u
s
1
(
1
.
0
5
p
.
u
)
b
u
s
2
(
1
.
0
3
7
p
.
u
)
,
b
u
s
3
(
1
.
0
0
3
p
.
u
)
,
b
u
s
6
(
1
.
0
5
p
.
u
)
a
n
d
b
u
s
8
(
1
.
0
5
5
p
.
u
)
.
W
h
ile
th
e
v
o
ltag
e
o
n
b
u
s
es
4
,
5
,
7
,
9
,
1
0
,
1
1
is
0
.
9
8
6
p
.
u
,
1
.
0
0
1
p
.
u
,
1
.
0
2
7
p
.
u
,
1
.
0
2
1
p
.
u
,
1
.
0
0
8
p
.
u
a
n
d
1
.
0
1
2
p
.
u
r
esp
ec
tiv
ely
.
W
ith
p
ar
ticu
lar
in
te
r
est
to
th
e
wea
k
est
b
u
s
es,
STAT
C
OM
with
th
e
PI
c
o
n
tr
o
ller
h
ad
a
n
ef
f
ec
t
o
n
im
p
r
o
v
e
v
o
ltag
e
lev
el,
wh
e
r
e
b
u
s
1
2
h
ad
a
v
o
ltag
e
am
p
litu
d
e
o
f
0
.
9
5
5
p
.
u
,
wh
ile
1
3
an
d
1
4
h
ad
0
.
9
6
p
.
u
a
n
d
0
.
9
7
2
p
.
u
r
esp
ec
tiv
ely
.
As d
is
p
lay
ed
in
t
h
e
f
o
llo
win
g
Fig
u
r
e
1
1
.
Fig
u
r
e
1
0
.
Vo
ltag
e
(
p
.
u
)
f
o
r
al
l b
u
s
es a
t
(
lo
ad
in
cr
ea
s
e
ca
s
e
u
s
e
StatC
o
m
with
PI
co
n
tr
o
ller
)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1.051
1.037
1.004
0.989
1
1.049
1.031
1.06
1.026
1.011
1.014
0.94
0.931
0.899
0.8
0.85
0.9
0.95
1
1.05
1.1
VOLT
AG
E
(P.U
)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
CA
S
E
3
1.051
1.037
1.003
0.986
1.001
1.05
1.027
1.055
1.021
1.008
1.012
0.955
0.96
0.972
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
VOLT
AG
E
(P.U
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2088
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t,
Vo
l.
11
,
No
.
4
,
Dec
em
b
er
2
0
2
0
:
1966
–
1
9
7
8
1974
Fig
u
r
e
1
1
.
Vo
ltag
e
at
B
1
2
,
B
1
3
,
B
1
4
,
(
lo
a
d
in
cr
ea
s
e
ca
s
e
u
s
e
StatC
o
m
with
PI
co
n
tr
o
ller
)
b.
STAT
C
OM
b
ased
o
n
an
ANN
co
n
tr
o
ller
T
h
e
PI
co
n
tr
o
ller
h
as
b
ee
n
r
e
p
lace
d
with
th
e
d
esig
n
e
d
ANN
co
n
tr
o
ller
in
t
h
e
co
n
tr
o
l
cir
cu
it
o
f
th
e
STAT
C
OM
.
T
h
is
was
in
f
u
r
th
er
an
ce
to
th
e
o
b
jectiv
e
o
f
th
i
s
s
tu
d
y
,
wh
ich
is
to
c
o
m
p
a
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
PI
-
co
n
tr
o
lled
STAT
C
OM
with
th
e
ANN
-
co
n
tr
o
lled
ST
AT
C
OM
[
2
6
,
2
7
]
Fo
r
clar
if
ic
atio
n
s
,
th
e
f
u
n
ctio
n
o
f
th
e
ANN
was
to
d
eliv
er
a
s
wif
t
an
d
d
y
n
am
ic
r
esp
o
n
s
e
a
n
d
im
p
r
o
v
e
th
e
s
tab
ilit
y
o
f
th
e
s
y
s
tem
f
o
r
a
lar
g
e
o
p
er
atin
g
r
an
g
e.
T
h
e
r
esu
lt
o
b
tain
ed
is
p
r
es
en
ted
in
Fig
u
r
e
1
2
.
I
t
is
clea
r
f
r
o
m
th
e
r
esu
lts
;
th
e
ANN
was
ab
le
to
p
r
o
v
id
e
m
o
r
e
s
tab
ilit
y
to
t
h
e
p
o
wer
s
y
s
tem
as
it
im
p
r
o
v
ed
th
e
v
o
ltag
e
lev
el
o
n
th
e
wea
k
b
u
s
es
th
at
wer
e
co
n
n
ec
ted
to
STAT
C
OM
.
On
th
e
o
th
e
r
h
a
n
d
,
th
er
e
is
n
o
c
h
a
n
g
e
was
o
b
s
er
v
ed
in
th
e
r
e
s
t
o
f
th
e
b
u
s
es
wh
ich
f
ar
f
r
o
m
th
e
STAT
C
OM
co
n
n
ec
tio
n
p
o
in
t.
Fig
u
r
e
1
2
.
Vo
ltag
e
(
p
.
u
)
f
o
r
al
l b
u
s
es a
t
(
lo
ad
in
cr
ea
s
e
ca
s
e
u
s
e
StatC
o
m
with
PI
co
n
tr
o
ller
)
Fig
u
r
e
1
3
s
h
o
ws
th
e
ef
f
ec
t
o
f
ANN
o
n
wea
k
b
u
s
es,
as
th
e
le
v
el
o
f
v
o
ltag
e
at
b
u
s
es
1
2
,
1
3
an
d
1
4
is
0
.
9
6
0
2
p
.
u
,
0
.
9
7
1
p
.
u
an
d
1
.
0
0
6
p
.
u
,
r
esp
ec
tiv
ely
.
A
n
d
also
,
t
h
e
d
am
p
i
n
g
tim
e
is
b
etter
th
a
n
u
s
e
PI
co
n
tr
o
ller
.
Fig
u
r
e
1
3
.
Vo
ltag
e
at
B
1
2
,
B
1
3
,
B
1
4
,
(
lo
a
d
in
cr
ea
s
e
ca
s
e
u
s
e
StatC
o
m
with
ANN
co
n
tr
o
ller
)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
CA
S
E
4
1.051
1.037
1.003
0.987
1.001
1.05
1.028
1.056
1.022
1.009
1.013
0.96
0.971
1.006
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
1.06
1.08
VOLT
AG
E
(P.U
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2
0
8
8
-
8
694
I
mp
r
o
ve
men
t o
f th
e
p
erfo
r
ma
n
ce
o
f S
TATC
OM in
term
s
o
f
… (
Mo
h
a
mme
d
S
a
lh
ee
n
A
la
ts
h
a
n
)
1975
4
.
1
.
3
.
P
er
f
o
rma
nce
co
m
pa
riso
n o
f
ANN
co
ntr
o
ller
a
g
a
ins
t
P
I
co
ntr
o
ller
du
ring
lo
a
d incre
a
s
e
ca
s
e.
T
o
ac
h
iev
e
a
c
o
m
p
ar
is
o
n
b
et
wee
n
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
two
co
n
tr
o
ller
s
(
PI
an
d
ANN)
d
u
r
in
g
th
e
lo
ad
in
cr
ea
s
in
g
ca
s
e,
f
r
o
m
th
e
r
esu
lts
s
h
o
wn
in
th
e
f
ig
u
r
e
1
0
,
1
1
a
n
d
1
3
.
I
t
s
h
o
u
ld
b
e
n
o
t
ed
th
at
th
e
wea
k
est
b
u
s
es
d
u
r
in
g
th
is
ca
s
e
b
u
s
1
2
,
1
3
an
d
1
4
,
wer
e
th
e
m
o
s
t
af
f
e
cted
b
y
th
e
ad
d
itio
n
o
f
STAT
C
OM
.
T
ab
les
2
an
d
3
s
h
o
w
th
e
r
ate
o
f
im
p
r
o
v
e
m
e
n
t f
o
r
b
o
th
c
o
n
tr
o
ller
s
o
n
th
es
e
b
u
s
es.
T
ab
le
2
.
Vo
ltag
e
im
p
r
o
v
em
en
t
r
ate
wh
en
u
s
e
StatC
o
m
with
PI
co
n
tr
o
ller
B
u
s
e
s
V
o
l
t
a
g
e
w
h
e
n
l
o
a
d
i
n
c
r
e
a
se
c
a
se
(
p
.
u
)
V
o
l
t
a
g
e
w
h
e
n
s
t
a
t
c
o
m w
i
t
h
p
i
(
p
.
u
)
V
o
l
t
a
g
e
i
m
p
r
o
v
e
m
e
n
t
(
%)
D
a
mp
i
n
g
t
i
m
e
(
s)
12
0
.
9
3
9
7
0
.
9
5
4
6
1
.
5
9
%
0
.
0
9
13
0
.
9
3
0
7
0
.
9
6
0
1
3
.
1
6
%
14
0
.
8
9
8
7
0
.
9
7
1
6
8
.
1
1
%
T
ab
le
3
.
Vo
ltag
e
im
p
r
o
v
em
en
t
r
ate
wh
en
u
s
e
StatC
o
m
with
ANN
co
n
tr
o
ller
B
u
s
e
s
V
o
l
t
a
g
e
w
h
e
n
l
o
a
d
i
n
c
r
e
a
se
c
a
se
(
p
.
u
)
V
o
l
t
a
g
e
w
h
e
n
s
t
a
t
c
o
m w
i
t
h
a
n
n
V
o
l
t
a
g
e
i
m
p
r
o
v
e
m
e
n
t
(
%)
D
a
mp
i
n
g
t
i
m
e
(
s)
12
0
.
9
3
9
7
0
.
9
6
0
2
2
.
1
8
%
0
.
0
5
13
0
.
9
3
0
7
0
.
9
7
1
0
4
.
3
3
%
14
0
.
8
9
8
7
1
.
0
0
6
1
1
.
9
4
%
I
t
is
clea
r
f
r
o
m
th
e
r
esu
lt
in
T
ab
le
2
t
h
at
wh
en
th
e
l
o
ad
w
as
in
cr
ea
s
ed
in
b
u
s
1
2
,
th
e
v
o
ltag
e
was
0
.
9
3
9
7
p
.
u
.
h
o
wev
er
,
wh
en
t
h
e
im
p
lem
en
tatio
n
o
f
STAT
C
OM
wi
th
th
e
PI
co
n
tr
o
ller
,
th
e
v
o
ltag
e
lev
el
im
p
r
o
v
e
d
to
0
.
9
6
0
2
p
.
u
.
Als
o
,
wh
e
n
th
is
r
esu
lt
was
c
o
m
p
ar
ed
with
th
e
in
itial
ca
s
e
o
f
in
cr
ea
s
ed
l
o
ad
,
an
im
p
r
o
v
em
e
n
t
o
f
2
.
1
8
%
was
o
b
s
er
v
ed
.
T
h
e
r
esu
lt
g
o
t
b
etter
in
s
u
b
s
eq
u
en
t
b
u
s
es
h
e
r
ein
r
ep
o
r
ted
with
4
.
3
3
%%
an
d
1
1
.
9
4
%
im
p
r
o
v
e
m
en
ts
o
b
tain
e
d
in
b
u
s
es
1
3
a
n
d
1
4
r
esp
ec
tiv
ely
.
A
c
o
m
p
ar
is
o
n
o
f
th
e
r
esu
lt
in
th
e
th
r
ee
b
u
s
es
as
p
r
esen
ted
i
n
T
ab
le
3
s
h
o
we
d
a
b
etter
an
d
m
o
r
e
im
p
r
o
v
ed
p
e
r
f
o
r
m
an
c
e
o
f
th
e
STAT
C
OM
wh
en
th
e
ANN
was
u
s
ed
as
a
co
n
tr
o
ller
[
2
8
]
.
Her
e,
th
e
im
p
r
o
v
em
e
n
t
o
b
tain
ed
was
2
.
1
8
%
%,
4
.
3
3
%
%
an
d
1
1
.
9
4
%
%
in
b
u
s
1
2
,
1
3
,
an
d
1
4
r
esp
ec
tiv
ely
.
T
h
e
d
am
p
i
n
g
tim
e
was
also
r
e
d
u
ce
d
f
r
o
m
0
.
0
9
s
w
h
en
u
s
in
g
PI
to
0
.
0
5
s
wh
en
ANN
co
n
tr
o
lled
STAT
C
OM
.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
a
g
r
ea
t
im
p
r
o
v
e
m
en
t
was
o
b
tain
ed
in
th
e
wea
k
est
b
u
s
1
4
wh
er
e
th
e
STAT
C
OM
wa
s
p
lace
d
[
2
9
]
.
Fo
r
in
s
tan
ce
,
th
e
v
o
ltag
e
lev
el
in
th
e
r
esp
ec
tiv
e
b
u
s
es
was
0
.
9
6
0
2
p
.
u
,
0
.
9
7
1
0
p
.
u
a
n
d
1
.
0
0
6
p
.
u
wh
en
ANN
was
u
s
e
d
as
ag
ain
s
t
th
e
0
.
9
3
9
7
p
.
u
,
0
.
9
3
0
7
p
.
u
an
d
0
.
8
9
8
7
p
.
u
o
b
tain
e
d
wh
en
th
e
lo
ad
was
in
c
r
ea
s
ed
with
o
u
t
STAT
C
OM
.
Fig
u
r
e
1
4
s
h
o
ws
th
e
co
m
p
ar
is
o
n
o
f
b
u
s
es
1
2
,
1
3
an
d
1
4
f
o
r
lo
a
d
in
cr
ea
s
e
ca
s
es.
An
d
a
c
o
m
p
r
e
h
en
s
iv
e
co
m
p
ar
is
o
n
o
f
th
e
r
e
s
u
lt
in
all
th
e
lo
a
d
in
cr
ea
s
e
ca
s
es is
p
r
esen
ted
in
Fig
u
r
e
1
5
.
Fig
u
r
e
1
4
.
C
o
m
p
ar
is
o
n
o
f
b
u
s
es 1
2
,
1
3
a
n
d
1
4
f
o
r
lo
a
d
in
cr
e
ase
ca
s
es
Evaluation Warning : The document was created with Spire.PDF for Python.