In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
Vol.
11, No.
1, Mar
ch 2020,
pp.
75~85
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
5
9
1
/ij
ped
s
.
v11
.
i
1.pp
7
5
-8
5
75
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
j
p
eds.i
a
esco
re
.com
Voltage contr
o
l of switched
reluctance g
e
nerator using
grasshopp
er optimization alg
orithm
M. Bahy
1
,
A
d
e
l
S
.
N
a
d
a
2
,
S.
H
. Elban
na
3
,
M
.
A
.
Mo
r
s
y
Sh
a
n
a
b
4
1,
4
E
l
ect
rical
P
ower an
d
M
ach
ine Dep
a
rt
m
e
nt,
t
h
e
H
i
gh
er
I
nsti
tute
o
f Eng
i
neering
at
E
l-Shorouk C
i
ty,
Egypt.
2,
3
E
l
ectri
cal P
ower an
d
M
achi
n
e
Depart
m
e
n
t
,
A
L
-Azhar U
ni
versity, E
gy
p
t
.
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
pr 18,
2
0
1
9
Re
vise
d A
ug
1
, 2019
Ac
ce
p
t
ed
No
v
1
6
,
2
019
Th
is
p
ap
er
i
n
t
ro
duces
a
t
erm
i
n
a
l
vo
lt
a
g
e
con
t
ro
l
ap
pro
ach
o
f
a
S
w
i
t
ched
Relu
ctance
Gen
e
rat
o
r
(S
RG)
b
a
sed
wi
nd
tu
rb
ine
gen
e
r
a
tin
g
s
y
s
t
em
s.
T
he
c
o
ntrol
pro
c
e
s
s
is
e
m
p
loy
e
d
u
s
i
n
g
a
c
l
ose
d
l
oo
p
sti
m
ula
t
e
d
b
y
t
he
e
rror
b
e
t
w
e
e
n
t
h
e
r
e
f
e
r
e
n
c
e
v
o
l
t
a
g
e
a
n
d
t
h
e
g
e
n
e
r
a
t
o
r
o
u
t
p
u
t
v
o
l
t
a
g
e
d
u
e
t
o
l
oad
and
w
i
n
d
s
p
eed
v
ari
a
tio
n.
T
his
error
f
eeds
t
h
e
tu
ned
P
r
o
port
i
o
n
al
I
n
t
egral
con
t
ro
ller
(
P
I).
T
he
t
un
in
g
b
y
c
o
n
v
e
nt
ion
a
l
anal
yti
cal
m
et
ho
ds
of
t
h
e
P
I
con
t
ro
ller
i
s
d
i
fficu
lt
d
ue
t
o
s
u
b
s
t
a
n
t
ia
l
n
on-l
i
n
earit
y.
A
n
e
w
s
t
r
ategy
app
r
oach
f
o
r
e
v
a
l
u
atin
g
op
timu
m
P
I
c
on
troll
e
r
p
a
ramet
e
rs
o
f
vo
l
tage
c
on
trol
of
S
RG
u
s
i
ng
t
he
G
rass
hopper
O
p
timization
Algorit
h
m
(GOA)
i
s
ad
dre
sse
d
here.
This
a
pproach
i
s
a
s
i
mp
le
a
n
d
e
ff
ectiv
e
alg
o
rit
h
m
,
capabl
e
of
s
olv
i
n
g
numerous
o
p
timization
i
s
sues
.
Th
e
s
i
m
p
l
e
a
lg
orithm
ensu
res
t
h
at
t
h
e
op
tim
u
m
P
I
contro
ll
er
p
aram
eters
are
opt
imi
zed
w
it
h
great
qual
i
ty
.
T
h
e
perf
ormance
of
t
he
p
ropos
ed
GOA-PI
c
on
troll
e
r
is
a
chieved
by
u
s
ing
the
integral
o
f
t
i
m
e
w
ei
ghted
squared
error
(IT
SE)
.
T
he
e
ffect
iven
e
ss
o
f
the
pro
p
o
s
ed
s
trat
e
g
y
is
t
es
ted
w
i
t
h
t
he
t
hree-ph
ase
1
2
/
8
s
truc
t
u
re
S
R
G
.
Ou
tco
m
es
i
ndicate
the
su
premacy
o
f
GO
A
over
W
h
al
e
O
p
timizati
on
Al
gor
ithm
(
W
OA)
a
nd
P
art
i
c
l
e
Swarm
Op
ti
mi
zat
ion
(PS
O
)
in
t
erms
of
con
t
ro
l p
e
rf
orm
a
nce m
eas
ures.
K
eyw
ord
s
:
G
r
a
s
shop
per
o
p
t
i
miza
tio
n
a
l
go
rith
m
Pa
rti
c
le sw
a
rm opt
imiza
tio
n
P
I
contro
l
l
er
Switche
d re
l
u
c
t
ance
ge
n
e
r
at
or
W
h
al
e op
ti
mi
zat
ion
al
g
o
r
i
t
h
m
Th
is
is a
n
o
p
en
acces
s a
r
ticle u
n
d
e
r t
h
e
CC
BY-S
A
li
cens
e
.
Corres
pon
d
i
n
g
Au
th
or:
M.
B
a
hy,
D
e
pa
rtme
nt
o
f
P
o
w
e
r a
nd Ele
c
tr
i
c
a
l
Mac
hin
e
Eng
inee
r
i
n
g
,
The
H
i
ghe
r I
n
st
i
t
u
te o
f En
g
i
n
eer
i
n
g
at El-S
horo
uk C
i
t
y
,
4J9
4
+Q
F
El S
hor
ou
k C
ity,
Al
S
horo
uk,
C
a
i
r
o
,
Egy
p
t
.
Em
ail:
eng.m
o
ham
e
dba
h
y
@
g
m
a
il.c
o
m
1.
I
N
TR
OD
U
C
TI
O
N
The
S
w
it
c
h
ed
R
e
l
uc
t
a
nce
G
e
nera
tor
(S
RG
)
offer
s
s
eve
r
a
l
a
dva
nta
g
e
s
o
ver
ot
her
gene
rators
t
ypes,
like
hi
g
h
p
ow
er
d
ens
ity,
m
echa
n
ica
l
r
obus
tne
ss,
no
w
i
n
d
i
n
g
s
a
n
d
p
er
ma
nen
t
m
ag
net
s
on
the
r
o
t
o
r,
h
ig
h
efficie
n
c
y
,
perform
ance
i
n
a
broa
d
r
a
nge
o
f
spe
e
ds,
l
o
w
manu
fa
c
turi
n
g
c
os
ts,
and
h
i
gh
fau
l
t
t
o
l
e
ra
nc
e
[1-
3
].
Th
is
t
y
p
e
of
m
achi
n
e
is
v
i
a
b
l
e
for
m
a
n
y
a
pp
lica
t
i
ons
w
i
t
h
varia
ble
spee
d
de
ma
nd
s
i
n
h
a
r
sh
e
n
v
i
ronm
e
n
t
s
,
as
in t
he
f
iel
d
o
f
w
i
n
d
pow
er
ge
n
e
r
at
io
n,
a
ircr
a
f
t
pow
er
s
yste
m
s
,
battery
c
ha
r
g
i
ng
an
d e
l
e
c
t
rica
l
trac
ti
on [
4
,
5].
Ene
r
g
i
es
w
ere
use
d
t
o
a
d
ju
st
t
he
S
RG
t
o
l
o
w
an
d
m
e
d
i
um
s
pee
d
s
i
n
w
i
n
d
a
pp
l
i
ca
ti
o
n
s,
r
educ
ing
t
h
e
to
t
a
l
cos
t
t
o
el
imina
t
i
ng
t
h
e
gear
box.
S
ome
tec
hni
q
u
es
h
a
v
e
be
e
n
su
gge
ste
d
i
n
mo
de
rn
s
tu
di
e
s
t
o
a
v
o
i
d
th
e
effec
t
s
o
f
l
oa
d
a
nd
s
p
ee
d
va
ri
ati
o
n
o
f
t
he
v
o
l
ta
ge
g
e
n
era
t
io
n
f
o
r
S
R
G
s
y
s
t
e
m
s
[
6
,
7
]
.
S
e
v
e
r
a
l
c
o
n
t
r
o
l
l
e
r
s
h
a
v
e
bee
n
i
n
t
r
o
du
c
e
d
for
S
R
G
t
o
a
c
h
ie
ve
b
e
t
ter
dy
na
mic
p
e
rform
ance
.
Exam
pl
e
s
f
or
t
hese
c
o
n
tro
lle
rs
a
r
e
Pr
op
or
tio
na
l
Integra
l
(
PI)
cont
rol w
h
ic
h
i
s
s
i
m
ple in
r
ea
liza
t
i
o
n
t
o
be
e
m
p
l
oye
d
i
n
S
RG
c
on
tro
l
[7,
8].
P
I
c
ontro
ller
i
s
w
ide
l
y
im
p
l
e
m
ented
i
n
t
he
p
r
oduc
tio
n
pr
o
c
e
ss
a
s
the
control
strate
g
y
.
B
a
sica
ll
y,
t
he
syste
m
r
e
s
po
ns
e,
s
te
ady-s
t
a
t
e
err
o
r,
a
nd
t
h
e
s
y
stem
s
t
a
b
ili
t
y
w
il
l
be
i
m
p
ro
ved
b
y
P
I
cont
rol
l
e
r
.
Moreo
v
e
r,
t
he
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
75
–
85
76
P
I
p
ar
a
m
eters
a
r
e
de
p
e
n
d
e
n
t
on
t
h
e
sys
t
em
f
e
a
t
u
res.
T
he
refore,
the
pr
o
p
er
o
r
opt
im
um
P
I
par
a
me
ter
s
a
r
e
ne
cessar
y
t
o
a
c
hie
v
e
t
h
e
des
i
r
e
d
per
f
or
ma
n
ce.
T
r
a
di
ti
o
n
al
a
nd
i
nte
l
l
i
ge
n
t
a
djustm
en
ts
a
r
e
m
etho
ds
o
f
tun
i
n
g
P
I
p
a
r
a
m
e
t
e
r
s
.
Z
i
e
g
l
e
r
a
nd
N
i
c
ho
ls
s
ugg
e
s
t
e
d
th
e
c
onve
n
tio
n
a
l
P
I
a
d
apta
t
i
o
n
t
o
t
h
e
f
o
r
m
ula
bas
e
d
o
n
obs
er
vat
i
on
o
f
t
he
s
e
n
si
t
i
v
i
t
y
,
a
m
p
l
i
t
u
d
e
,
and
natur
a
l
fr
eque
nc
y
of
s
ys
tem
s
[
9]
.
For
these
pur
p
o
se
s,
i
ncre
asi
n
g
the
c
a
pa
b
i
lit
ies
of
P
I
con
t
rol
l
e
rs
b
y
addi
n
g
n
e
w
f
e
a
t
u
r
e
s
i
s
h
i
g
hly
de
sira
ble.
P
arti
cle
Sw
arm
Op
ti
m
i
z
a
t
i
on
(PSO),
A
rti
f
ic
ial
Bee
C
o
lo
ny
(
AB
C
)
,
D
i
ff
e
r
en
ti
a
l
E
vol
uti
o
n
(DE),
Te
ach
in
g
Lea
r
nin
g
Base
d
O
pt
i
m
iza
tio
n
(
T
LBO
)
,
G
r
a
v
i
t
a
t
i
o
nal
S
e
ar
c
h
A
lg
or
i
t
hm
(
G
S
A)
,
B
a
t
A
l
g
o
r
i
t
h
m
(
B
A
)
,
P
a
t
t
e
r
n
S
e
a
r
c
h
A
lgor
i
t
h
m
(
P
S
A
)
,
F
iref
ly
A
l
g
or
it
hm
(
F
A
),
B
i
o
-Ge
o
g
r
ap
hy
B
ased
O
p
t
i
m
i
z
at
ion
(B
B
O
),
A
n
t
C
o
l
o
ny
O
p
t
i
m
i
za
tio
n
(
A
C
O
)
,
C
uc
ko
o
S
e
a
r
ch
(
C
S
)
Al
g
o
r
i
t
h
m
,
W
h
ale
Opt
i
mization
Alg
o
r
ith
m
(
W
OA),
I
m
pe
r
i
alist
C
o
m
p
etit
i
v
e
A
l
go
r
i
t
h
m
(
I
C
A
)
a
nd
G
e
ne
tic
A
l
gor
i
t
hm
(
G
A
)
a
r
e
the
m
e
t
h
od
s
of
t
un
i
n
g
ba
se
d
o
n
he
ur
ist
i
c
o
p
t
im
izat
i
on
to
i
m
p
r
ove
t
he
e
ff
ic
ie
nc
y
o
f
t
he
m
enti
o
n
ed
cont
r
o
l
l
er
ty
p
e
s.
[
10
,
1
1
]
.
Gras
sh
o
p
p
e
r
Op
timiza
tion
Al
go
r
ith
m
(G
OA)
i
s
S
a
r
e
mi
'
s
p
o
pulatio
n
-
b
a
s
ed
s
i
ngl
e
obj
ect
iv
e
st
ocha
st
ic
a
nd
h
e
u
r
i
st
ic
o
ptim
izat
i
o
n
tec
h
n
i
q
u
e
[1
2],
which
em
u
l
a
t
e
s
Gr
a
ssh
opp
e
r
'
s
b
e
h
av
io
r
in
n
a
t
u
r
e
,
a
nd
m
a
them
at
ica
l
l
y
m
od
e
l
s i
t
to
so
lve pro
b
l
em
s
of o
ptim
iza
t
io
n
w
ith
c
ont
e
n
ti
o
u
s
v
a
r
ia
bl
e
s
.
Test
s
we
r
e
c
ond
u
c
t
e
d
wit
h
d
i
ffe
re
nt
t
es
t
f
unc
t
i
o
n
s
suc
h
a
s
u
n
imo
d
a
l
,
m
u
ltim
o
d
a
l
,
c
o
m
p
o
s
ite
a
nd
C
E
C
2
0
05,
a
n
d
r
ea
l
s
t
r
u
ctur
a
l
d
e
sign
p
rob
l
ems,
s
h
o
w
t
h
a
t
GOA
can
ef
ficiently
r
es
olv
e
m
an
y
p
r
o
ble
m
s
of
o
p
t
i
m
iz
ati
o
n
(
a
ls
o
tho
s
e
w
i
t
h
un
k
now
n
sear
ch
a
r
e
as)
[1
2]
.
A
s
G
O
A
c
onside
r
s
a
cer
t
a
in
p
r
o
blem
of
o
pt
i
m
i
zat
ion
as
a
b
l
a
c
k
-box
a
nd
d
o
e
sn'
t
ne
ed
g
rad
i
e
n
t
inf
o
rm
ation
fr
o
m
t
he
s
ear
ch
a
re
a,
t
his
e
n
ab
le
s
i
t
a
h
ig
h
l
y
a
p
pr
opr
i
a
te
o
pti
m
i
z
at
io
n
te
c
h
n
i
q
u
e
in
di
ff
er
e
n
t
ar
e
a
s
f
o
r
a
ny
c
o
r
r
e
c
t
l
y
f
or
m
u
la
te
d
op
t
i
m
i
z
a
t
i
on
pr
ob
l
em
[
10]
.
S
i
nce
the
n
o
n
l
inear
n
at
ur
e
a
n
d
/
or
m
agn
itu
de
o
f
a
pr
o
b
le
m
does
n
ot
a
f
f
ect
th
e
GOA
an
d
W
O
A
,
Where
e
a
rl
y
co
nver
g
e
n
ce
u
s
u
all
y
s
h
o
ws
c
erta
i
n
g
lo
ba
l
o
p
t
i
m
iza
t
i
o
n
s
t
r
ate
g
ie
s,
t
he bes
t
s
o
l
u
tio
n
is
f
ou
n
d
w
it
h
fa
st
e
r
c
onv
e
r
gen
c
e
mo
re
e
f
f
i
c
i
e
nt
l
y
.
In
t
hi
s
stud
y
,
t
a
k
i
n
g
i
n
to
a
cc
o
unt
t
he
se
a
d
v
a
n
ta
ges
of
t
he
G
O
A
a
l
g
o
r
i
t
h
m
,
a
G
O
A
-
ba
se
d
P
I
(
G
O
A
-
P
I
)
con
t
r
o
l
l
e
r
s
pr
o
p
o
se
d
f
o
r
S
R
G
vol
ta
ge
c
o
n
t
r
o
l.
I
t
sho
u
l
d
be
n
o
t
e
d
t
ha
t
no
s
u
c
h
a
na
l
y
s
i
s
has
be
en
s
u
g
g
es
ted
bef
o
r
e
i
n
t
h
e
l
ite
r
a
tur
e
.
S
om
e
com
p
arati
v
e
resu
l
t
s
be
t
w
een
t
he
p
r
o
p
o
se
d
GOA-P
I
c
o
n
t
r
o
ller
a
nd
b
oth
WOA-PI
a
n
d
PSO-P
I
co
n
t
r
o
llers
will
b
e
pr
ese
n
t
e
d
i
n
o
r
d
e
r
t
o
c
o
n
f
ir
m
the
r
obust
n
ess
a
n
d
ef
fec
t
i
v
e
n
ess
of
t
he
p
r
opo
se
d
m
e
tho
d
.
This
p
a
p
er
i
ntr
o
du
ces
t
h
e
d
ev
elop
men
t
p
roced
u
r
es
o
f
GOA-
b
a
sed
P
I
co
ntr
o
l
l
ers,
W
OA
and
PSO
op
t
i
miza
tio
n
t
e
c
h
n
i
que
s.
T
h
e
t
ask
of
t
ha
t
co
n
t
r
o
l
l
e
r
i
s
t
o
g
e
n
e
r
a
te
t
he
t
ur
n
o
f
f
ang
l
e
(
θ
o
f
f
)
of
t
he
m
a
gne
tiz
a
t
i
o
n
sta
g
e
of
S
RG
t
o
r
e
g
u
l
ate
th
e
ge
n
e
r
a
t
e
d
v
o
lta
ge
u
n
d
e
r
di
ff
e
r
en
t
op
e
r
at
in
g
co
nd
i
t
i
o
n
s
,
suc
h
a
s
l
o
ad
a
nd
wi
n
d
sp
eed
v
a
r
i
a
tions.
2.
OPERA
T
ION
OF
T
HREE
-
P
H
A
S
E
SWI
T
CHE
D
R
E
L
UCTANCE GENE
R
A
T
OR
A
S
R
G
i
s
a
m
a
c
h
i
n
e
t
h
a
t
a
d
o
u
b
l
y
s
a
l
i
e
n
t
p
o
l
e
s
u
p
p
l
i
e
d
b
y
u
n
i
p
o
la
r
pow
er
c
on
v
e
r
t
er
s.
T
he
c
o
n
f
ig
u
r
at
io
n
of
a
3
-
p
hase
m
ac
hine
w
ith 12
po
les
on
the
s
t
a
t
or
a
n
d
8
p
o
l
e
s
on
the
r
o
tor
i
s
d
is
p
l
aye
d
i
n
F
i
gur
e
1(
a)
.
The
asy
m
me
tr
ic
h
al
f-
b
r
idge
c
on
ver
t
e
r
(
A
H
B
)
f
o
r
a
t
h
r
e
e
-
ph
ase
S
R
G
s
how
n
i
n
F
i
gur
e
1
(
b
)
,
m
a
i
n
l
y
be
cau
se
it ena
b
l
e
s t
h
e
ma
chin
e to
b
e dr
ive
n
b
o
t
h as
a
g
ener
ator
and
as
a m
o
to
r.
(a)
(b
)
F
i
gur
e
1.
(
a)
M
ac
hine
s
tr
uc
t
u
r
e
,
(
b)
A
symm
e
t
r
i
c
ha
lf
b
r
i
d
g
e
c
o
n
ver
t
er
f
or
a
3
-
ph
S
R
G
The
wi
n
d
in
gs
o
f
the
s
t
at
or
a
r
e
o
f
a
co
nce
n
tr
a
t
ed
t
y
p
e
a
n
d
s
i
mpl
e
sha
p
e
,
t
he
r
otor
h
a
s
n
o
w
i
ndi
n
g
,
no
m
a
gne
ts
a
n
d
l
ow
i
ner
tia
[
3,
13]
.
The
cha
r
acte
r
ist
i
cs
o
f
the
S
R
G
d
e
p
e
nd
on
num
er
o
u
s
fea
t
ur
es,
main
ly:
m
a
c
h
i
n
e
st
r
u
c
t
ur
e
(
numbe
r
o
f
phas
e
s,
numb
e
r
of
s
t
a
t
o
r
a
n
d
r
o
t
o
r
pol
es,
st
a
t
o
r
a
nd
r
ot
o
r
a
rc
s)
,
ma
g
n
e
tiz
at
ion
c
h
ara
c
teris
t
ic
o
f
t
h
e
la
mi
na
t
i
o
n
s,
c
on
fig
u
rati
o
n
o
f
t
h
e
c
o
n
v
e
r
t
e
r
a
n
d
m
e
t
h
o
d
o
l
o
g
y
o
f
c
o
n
t
r
o
l
l
e
r
[
1
3
,
1
4
]
.
Co
n
c
e
n
t
r
at
ed
s
t
a
to
r
win
d
i
ng
s
are
di
vid
e
d
in
t
o
f
ou
r
di
a
m
et
ri
ca
ll
y
s
y
mm
etr
i
c
a
l
pa
ir
s
li
nk
ed
i
n
ser
i
e
s
t
o
f
o
r
m
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Vo
lt
a
g
e c
o
n
t
r
o
l of s
w
i
t
c
h
e
d
re
l
u
c
t
anc
e
g
e
ner
a
t
o
r us
i
n
g
g
r
assho
p
p
er
o
p
tim
i
z
a
tio
n
alg
o
ri
th
m
(
M
. Bahy
)
77
pha
se
s.
D
ue
t
o
The
v
a
r
i
a
t
i
on
in
t
he
a
ir
g
a
p
a
nd
n
on-
li
near
i
r
o
n
m
a
gne
t
i
z
a
ti
o
n
,
the
m
a
c
h
i
n
e
fl
u
x
l
inka
ge
i
s
a
no
n
l
i
n
ear
f
u
n
c
tio
n
o
f
t
he
s
ta
to
r
cur
r
ent
a
nd
th
e
angu
lar
posi
t
i
o
n
o
f
t
h
e
ro
t
o
r a
s
i
n
,
(1
)
Where
i
s
t
h
e
f
l
u
x
lin
ke
d
by
t
h
e
w
i
n
d
i
n
g,
is the
p
h
ase
cur
r
ent a
n
d
θ
is
t
he
pos
it
io
n
of
t
he
r
otor
r
e
l
ated
t
o
t
h
e
a
lig
ne
d
po
si
ti
o
n
(
θ
= 0
o
)
.
By t
he use
the
f
i
n
i
t
e-
e
l
em
ent fie
l
d ca
lc
u
l
a
tio
n s
u
ch a
s M
o
tor
S
o
lve
s
o
f
t
w
a
r
e
w
it
h
de
f
i
ne
d
pa
r
a
m
e
te
r
s
,
t
h
i
s
c
o
m
pl
e
x
f
ea
t
u
re
can
b
e
re
al
i
z
e
d
[
15
].
T
h
e
S
R
M
c
h
a
ract
eri
s
t
i
c
o
f
m
a
gne
t
i
za
t
i
o
n
c
o
n
s
i
der
e
d
i
n
t
he
p
r
e
sen
t
pa
per
is
i
l
l
ust
r
a
t
e
d
i
n
F
i
g
u
r
e
2
(
a
)
.
T
h
e
c
har
acte
r
ist
i
c
o
f
m
agn
e
t
iza
t
i
o
n
com
p
r
i
se
s
i
s
a
f
am
il
y
of
c
ur
ves
si
gn
if
y
i
n
g
t
he
m
achine
f
l
ux
l
i
n
k
a
g
e
as
a
f
u
n
ct
i
o
n
of
c
ur
r
e
nt
o
f
t
he
p
ha
se
f
or
v
ar
i
o
us
r
otor
p
osi
t
i
o
n
s
fr
om
al
ign
e
d po
si
tion
(θ =
0
o
)
t
o
una
l
i
g
n
e
d
po
si
t
i
on
(
θ
=
22
.5
o
)
.
T
he
a
r
e
a u
n
d
e
r
t
he
c
ur
ve
i
s t
h
e
co-
e
ner
gy
m
a
gne
t
i
c
fi
e
l
d
W
c
,
w
hic
h
t
he
r
e
l
a
tio
ns
hi
p
co
ul
d
be
d
e
s
c
r
ibe
d
,
,
(2
)
The
elec
t
r
oma
gne
t
i
c
tor
que
T
i
s
pr
op
or
t
i
o
n
a
l
t
o
the
cha
nge
o
f
t
h
e
m
a
c
h
i
n
e
'
s
m
a
gnet
i
c
co-
e
ne
rgy
W
c
a
t
e
ve
r
y
p
ha
se
o
f
t
h
e
S
R
M
,
w
hi
le
t
he
m
ac
hine
r
ota
t
e
s
:
(3
)
Wh
e
r
e L
,
i
s t
h
e
u
n
sa
t
u
ra
t
e
d
ph
ase
i
n
du
ct
an
ce
, t
h
e
n
t
h
e
fl
u
x ψ
w
ill be
:
.
(4
)
Th
e
n
th
e
f
amiliar simp
lified
r
el
at
io
nshi
p
f
o
r
SR
M
to
rqu
e
T
i
s [
16
]
(5
)
Whe
r
e
i
s
posi
t
i
v
e
for
m
o
tor
i
ng
a
n
d
ne
ga
ti
v
e
f
or
g
e
n
er
a
tin
g
mode
s
as
show
n
i
n
F
i
gur
e
2(
b
)
.
By
in
jec
t
in
g
c
u
r
r
ent
i
n
to
p
hase
w
indi
n
g
s
dur
i
ng
the
per
i
od
w
h
en
t
h
e
de
ve
lo
pe
d
tor
q
ue
i
s
ne
ga
ti
ve,
ele
c
t
r
i
ca
l
e
n
er
g
y
can
b
e
gener
a
ted
a
s
θ
c
han
g
es
f
r
o
m
0
t
o
2
2.
5
o
as
ill
us
t
r
ated
i
n
Fig
u
re
2
(b).
(a
) Ma
g
n
et
i
z
a
t
i
on cur
v
es
(b
)
To
rq
u
e
p
rof
i
le
F
i
gur
e
2.
M
a
g
net
i
z
a
t
io
n
an
d
t
o
r
que
p
r
o
f
i
l
e
of
1
2
/
8
S
R
G
3.
M
A
TH
E
M
A
T
IC
A
L
M
O
D
EL
O
F
TH
E
S
R
G
A
MATLAB/S
I
MULINK
too
l
s
a
r
e
use
d
t
o
r
e
pr
esen
t
t
h
e
n
onl
i
n
ea
r
mod
e
l
o
f
12
/8
S
R
G
.
Th
e
SR
G
is
a
no
n
-
l
i
n
e
ar
e
le
ct
ri
cal
s
y
s
t
e
m
a
c
c
o
m
p
a
n
i
ed
b
y
a
me
ch
an
i
c
a
l
s
y
s
t
em
w
h
i
ch
d
i
s
pl
ay
s
t
h
e
mec
h
a
n
ic
al
dyn
a
m
i
c
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
75
–
85
78
of
t
he gener
at
o
r
.
A
si
ngle
p
h
a
s
e ter
m
inal vol
tage
o
f
S
R
G is
lin
ke
d
to the
f
l
ux linke
d
of
t
he w
ind
i
ng as se
e
n
be
low
[1
6]
(6
)
wh
ere,
R
s
is
t
he
re
s
i
s
tanc
e o
f
t
he
s
t
a
t
o
r
. T
h
e
m
agne
tic
flu
x l
i
n
k
a
g
e
with
t
he
wi
n
di
ng
s i
s
de
l
ib
e
r
a
t
ed
by
.
7
The
cur
r
ents
f
or
m
e
d
by
the
no
n
l
i
n
ea
r
fu
nc
ti
on
(ψ
,
θ
),
a
re
p
r
e
sented
a
s
a
lo
oku
p
table
I
T
BL.
Th
e
no
n
l
i
n
ear
f
un
c
t
i
on
T
e
(
,
θ
)
,
w
hich
i
s
als
o
u
se
d
a
s
a
TTBL
loo
k
-
u
p
ta
ble
pr
o
v
ide
s
f
or
t
h
e
ele
c
trom
ag
net
i
c
tor
que
s
cr
eate
d
by
the
s
t
a
t
or
p
hase
s.
T
he
t
w
o
l
o
o
k
u
p
t
a
b
l
e
s
I
T
B
L
an
d TT
B
L
use
d i
n
m
od
eli
n
g o
f
t
h
e
S
RG
a
r
e
il
l
u
s
t
r
a
t
e
d
in
F
i
gur
e
3.
,
(8
)
Whe
r
e
T
e
is
t
h
e
e
le
c
t
r
i
c
a
l
t
o
r
q
u
e
a
n
d
j
i
s
t
h
e
num
ber
o
f
p
ha
ses
of S
R
G
.
Th
e
r
e
sul
t
i
n
g t
o
r
q
ue
eq
u
a
t
i
o
n
fo
r th
e
SRG can
b
e
r
ep
resen
t
ed
as:
(9
)
Whe
r
e
T
m
i
s
t
h
e
prim
e
m
o
v
e
r
torq
ue,
J
i
s
th
e
iner
t
i
a
o
f
t
he
r
otor
,
a
nd
B
i
s
t
h
e
co
ef
fi
ci
e
n
t
o
f
f
ri
ct
ion
.
The
sum
m
a
tio
n
of
e
lec
t
r
i
c
ou
tp
u
t
p
ow
e
r
o
f
eac
h
p
h
a
s
e
in
one
e
le
ctr
i
c
cy
cle
P
ou
t
i
s
the
a
v
era
g
e
p
o
w
e
r
of
S
RG
pha
se
s
(
10)
Whe
r
e
T,
N
s
,
V
j
a
nd
i
sj
a
r
e
t
h
e
c
on
du
ct
i
on
p
e
r
i
o
d
o
f
o
n
e
p
h
a
s
e,
t
he
num
b
e
r
of
m
otor
p
h
a
s
es,
vol
t
a
g
e
a
nd cur
r
en
t of
P
h
ase
j
.
(
a
)
Cur
r
ent
ver
s
u
s
r
ot
or
pos
i
tion
an
d
f
l
ux.
(
b
)
Tor
que
v
er
sus
r
o
tor
pos
i
t
i
on
a
n
d
c
u
r
r
e
nt.
Fig
u
r
e 3
.
S
R
G
Loo
kup
tables I
T
B
L
a
n
d
TTBL
4.
PERFORMANC
E
STUDY
O
F
SRG
A
S
I
MU
LI
NK
d
i
agr
a
m
t
h
a
t
u
se
d
t
o
d
e
t
er
m
i
ne
t
he
g
e
n
e
r
at
or
p
er
f
o
r
m
a
n
ce
is
s
h
o
w
n
i
n
the
F
i
gur
e
4.
A
thr
e
e-
pha
se
a
sym
m
e
t
r
i
c
p
o
w
er
c
onver
t
e
r
s
up
p
lie
s
t
h
e
S
R
G
.
W
ith
t
h
i
s
str
u
c
t
ur
e,
t
he
c
ur
r
e
nt
s
of
t
he
pha
ses
c
a
n
be
c
on
tr
o
l
l
e
d
i
nde
pe
n
d
en
tly.
To
i
m
p
le
me
nt
t
ur
n-
o
n
a
nd
tur
n
-
o
ff
a
n
g
l
es
o
f
ea
ch
p
h
a
se
p
erf
ectl
y
,
a
ro
t
o
r
pos
i
tio
n
se
nso
r
i
s
use
d
.
To
c
alcu
la
te
t
he
d
if
fer
e
nt
v
a
r
ia
ble
s
o
f
t
h
e
sy
ste
m
a
nd
ma
r
k
t
he
m
ea
sur
e
m
e
nts,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
Vo
lt
a
g
e c
o
n
t
r
o
l of s
w
i
t
c
h
e
d
re
l
u
c
t
anc
e
g
e
ner
a
t
o
r us
i
n
g
g
r
assho
p
p
er
o
p
tim
i
z
a
tio
n
alg
o
ri
th
m
(
M
. Bahy
)
79
m
e
a
s
ur
ing
de
v
i
c
e
s
a
nd
s
i
gna
l
pr
oc
e
s
si
n
g
b
l
o
c
k
s
a
r
e
a
p
p
lie
d
t
o
t
he
s
ys
t
e
m.
T
able
1
p
r
o
vi
des
the
S
R
G
pa
r
a
m
e
ter
s
u
sed
i
n
t
his
pa
per
.
F
i
gur
e
4.
D
iagr
a
m
o
f
t
h
e
simu
li
n
k
f
or
t
he
1
2
/
8
S
R
G
F
i
gur
e
5
sh
ow
s
w
a
ve
f
o
r
m
s
of
t
he
f
l
u
x,
c
ur
r
e
nt,
v
o
l
tage
a
n
d
t
or
q
ue
w
ave
f
or
m
s
f
or
t
ur
n-
on
a
n
d
t
u
r
n
-
of
f
a
n
g
l
e
s
(
α
=
-
7°,
β
=
9.
5°)
.
T
he
m
ain
si
m
u
lat
i
on
r
e
su
l
t
s
o
b
ta
i
n
ed
f
or
w
i
n
d
sp
e
e
d
12
(
m
/s)
or
N
=
1000
r
p
m
.
Ta
ble
1.
S
RG
Pa
r
a
m
e
te
r
SR
G
Vol
t
a
g
e
(V)
600
Torqu
e
(N.m
)
650
Out
put
P
ow
e
r
(
k
W
)
100
Sta
t
or
pole
s
12
R
o
tor
pole
s
8
B
a
se
sp
eed
(
r
.
m
i
n
-1
)
1200
Re
s
i
st
a
n
ce
/
p
h
a
s
e
(
Ω)
0
.
0310
9
Mo
me
nt
of ine
r
tia
/
(
kg.m
2
)
0.
05
Fric
t
i
on c
o
e
f
fic
i
e
n
t/
(
N
.m
.
s
)
0.
02
F
i
gur
e
5.
S
R
G
f
l
u
x,
c
ur
r
e
nt,
vol
ta
ge
a
nd
tor
q
ue
w
avef
or
ms
a
t
α
=
-
7o,
β
=
9
.
5oa
n
d
a
c
ons
t
a
n
t
l
oad
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
75
–
85
80
The
pe
r
f
o
r
m
an
c
e
o
f
the
12
/
8
S
RG
f
or
r
ot
or
s
pee
d
o
f
1
0
0
0
r
pm
w
it
h
α
=
-
7
o
,
β
=
9
.
5
o
a
t
a
cons
ta
nt
loa
d
o
f 10
0
k
W
is i
l
l
u
str
a
te
d
in
T
ab
le 2.
Tab
l
e
2.
P
er
for
m
a
n
c
e
o
f
S
R
G
un
der
loa
d
in
g
c
ond
it
i
ons
Re
s
u
l
t
s
α=
-
7
o
,
β
=
9.
5
o
R
M
S
pha
s
e
c
ur
re
n
t
I
rm
s
(
A)
173.
1
Ave
r
a
g
e
pha
s
e
c
ur
re
nt
I
avg
(A)
112.
3
DC
bus
output
V
o
l
ta
g
e
V
o
(V)
350
DC
bus
output
C
ur
r
e
nt
I
dc
(A)
286.
5
Out
put
powe
r
P
ou
t
(kW)
100.
2
E
l
ec
tro
m
a
gne
t
i
c
Torq
ue
(
N
.
m
)
950
5.
CLOSED LO
O
P
O
P
E
RATIO
N
OF SRG
A
contr
o
l
te
c
hni
que
i
s
de
si
gne
d
f
o
r
the
c
l
ose
d
-
l
oop
o
p
e
r
at
io
n
r
e
qui
r
e
d
to
c
o
n
t
r
o
l
th
e
v
o
l
t
a
ge
pr
oduc
e
d
.
The
ma
gnet
i
za
t
i
o
n
p
er
i
od
w
i
d
t
h
o
f
t
he
S
RG
p
ha
se
v
ar
ie
s
a
c
c
o
r
d
in
g
t
o
t
h
i
s
a
ppr
oac
h
,
Mai
n
t
a
in
in
g
the
va
lue
of
θ
on
f
i
x
e
d
(
-
7
0
)
and
c
o
n
t
r
o
lli
n
g
t
he
v
a
l
ue
o
f
th
e
θ
off
t
hr
ou
g
h
P
I
c
ontr
o
l
l
e
r
.
If
t
he
s
pe
e
d
o
f
w
i
n
d
tur
b
i
n
e
or
t
he
l
oa
ds
v
ar
i
e
s,
t
he
v
al
ue
o
f
θ
of
f
wi
l
l
b
e
ch
ange
s
by
t
h
e
P
I
co
nt
r
o
l
l
e
r
[
7
,
1
6
,
1
7
].
A
s
a
c
o
nt
ro
l
s
t
r
a
t
e
g
y
i
n
t
h
e
p
r
o
d
u
c
t
i
o
n
p
r
o
c
e
s
s
,
t
h
e
P
I
c
o
n
t
r
o
l
l
e
r
i
s
c
o
m
m
o
n
l
y
u
s
e
d
.
B
asi
c
a
lly
,
T
h
e
re
sp
on
se
s
p
eed
,
t
h
e
stea
dy-s
t
a
t
e
er
ror
and
sy
stem
p
erform
ance
a
re
e
nha
nc
ed
by
th
e
P
I
c
ontr
o
ll
e
r
.
N
e
ver
t
he
l
e
ss,
t
h
e
P
I
par
a
me
t
e
r
se
tti
n
g
is re
fer
r
ed
t
o as
s
y
s
tem
proce
s
s
char
acte
r
istic
s.
The
P
I
contro
ller
'
s
t
r
ansfer
fu
n
c
t
i
o
n
is.
(
11)
Th
e
Integ
r
al
o
f
Time-Mu
l
tiplied
S
q
u
a
re
E
r
r
or
(IT
S
E
)
i
s
u
sed
in
t
h
i
s
p
ap
e
r
t
o
ev
alu
a
t
e
a
n
d
d
e
s
i
g
n
th
e
pr
opose
d
c
o
n
tr
ol
ler
for
th
e
pe
r
f
or
m
a
nc
e
i
n
de
x,
a
nd
it
'
s
a
s
gi
ve
n
[
1
8
]
.
(
12)
The P
I
cont
r
o
ller
will
be
t
une
d off line us
i
ng both of PSO,
W
O
A
a
nd
G
O
A
as
p
r
e
sente
d
i
n
Figu
re 6
.
F
i
gur
e
6.
S
t
r
uctur
e
o
f
S
R
G
vo
lta
ge
c
o
n
t
r
o
l
l
e
r
u
si
ng
P
I
w
i
t
h
evo
lu
t
i
o
n
a
r
y
t
un
i
ng
6.
MO
DELL
IN
G OF PSO,
W
O
A
AN
D
G
O
A
6.
1.
Par
t
ic
le
s
war
m
o
ptimizat
io
n
(
P
SO)
T
h
e
P
S
O
-
P
I
c
o
n
t
r
o
l
l
e
r
i
s
r
e
c
o
m
m
e
n
d
e
d
i
n
t
h
i
s
s
e
c
t
i
o
n
.
P
S
O
w
i
l
l
study
t
h
e
m
e
t
hod
o
f
t
uni
ng
P
I
c
o
n
t
r
o
ller
par
a
me
ter
s
.
A
s
t
he
f
o
l
l
o
w
i
ng
e
q
u
a
t
i
on,
t
he
o
p
e
r
a
ting
a
l
g
or
i
t
hm
i
s
base
d
o
n
t
he
b
e
s
t
l
o
c
a
l
a
nd
gl
o
b
al
s
ol
u
tio
n
[18,
19]
.
(
13)
wher
e,
a
t
k
i
te
r
a
ti
on
i
s
t
he
v
e
l
oc
i
t
y
of
p
ar
tic
le
i,
is
t
h
e
p
ar
ticle
i
u
pda
t
e
d
vel
o
c
i
t
y
,
i
s
t
h
e
w
e
ight
a
nd
di
f
f
e
r
e
nt
i
ner
t
ia
o
f
par
t
icl
e
i
,
C
1
a
nd
C
2
a
re
c
on
sta
n
ts
o
f
pos
i
t
i
v
e
acc
elera
t
ion
,
a
t
itera
tio
n
k
i
s
c
u
r
r
e
nt
p
osi
t
i
o
n o
f
p
ar
t
i
c
l
e
i
,
ran
d
i
s
be
tw
ee
n 0
an
d
1
r
a
nd
om
num
ber
,
is
th
e
i
th
par
tic
le
's best pre
v
i
o
us
pos
i
tio
n,
a
nd
i
s
t
h
e
bes
t
p
a
r
tic
l
e
i
n
th
e
po
pul
at
io
n
a
m
on
g
al
l
p
a
rti
c
l
e
s.
T
h
e new
pos
iti
o
n
c
an,
ther
e
f
or
e
,
be
m
odif
i
e
d
w
i
t
h
t
h
e
pr
ese
n
t
p
o
sit
i
on
an
d
u
p
d
ate
d
v
e
l
o
c
i
t
y
as
[
19,
20]
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Vo
l
t
a
g
e
con
t
r
o
l
of s
w
i
t
c
h
e
d
reluc
t
ance
g
e
ne
rat
o
r us
i
ng g
r
as
shop
pe
r o
p
t
i
m
i
za
tio
n
alg
o
ri
t
h
m
(M
.
Bahy)
81
(
1
4
)
Th
e
con
s
t
a
n
t
s
p
o
s
iti
v
e
a
c
cel
erat
io
n
C
1
a
n
d
C
2
a
re
s
et
t
o
1.
6.
T
he
w
e
i
g
h
te
d
i
n
ert
i
a
w
i
i
s
set
within
t
he
range
(0.
4 to 0.
9
).
6.2.
Wh
ale op
timi
zati
on
alg
or
ith
m
(WOA
)
I
n
201
6,
M
i
r
j
a
l
i
l
i
a
n
d
l
ew
is
d
eve
l
ope
d
a
n
o
p
t
imiz
a
tio
n
t
e
c
h
n
i
qu
e
t
h
at
i
s
in
sp
i
r
e
d
b
y
t
h
e
wh
al
e
s
’
beha
v
i
or,
so-
c
alle
d
WO
A
[2
1,
2
2].
Wha
l
es
a
re
p
r
e
sen
t
e
d
a
s
sma
r
t
a
nd
qu
ic
k
a
n
ima
l
s
in
f
ind
i
ng
a
p
r
e
y.
A
whale
first
l
y se
ar
ches
t
he
pr
e
y
,
e
ncirc
l
es it a
n
d
the
n
,
by a
st
rateg
y
a
t
t
ac
ks t
he
pre
y, c
alle
d bu
b
b
le-
n
et h
u
n
tin
g.
WOA
assum
e
s
t
h
a
t
a
p
osition
i
s
t
he
b
es
t
so
lut
i
on
for
a
pr
ey
a
n
d
t
he
n
trie
s
to
c
ha
n
g
e
the
i
r
p
o
si
t
i
on
s
tow
a
rds
this
a
gen
t
b
y
t
h
e
o
t
her
re
sear
ch
a
gen
t
s.
L
i
k
e
all
he
ur
i
st
ic-
b
a
s
ed
a
l
gor
ithm
s
,
WO
s
imulat
e
s
t
he
beha
v
i
or
o
f
s
w
a
r
m
expl
ora
tio
n
a
nd
e
x
pl
o
i
t
a
ti
on.
I
n
the
beg
i
nn
in
g
of
t
he
a
l
g
ori
t
hm,
the
o
p
t
i
mum
de
s
i
g
n
pos
it
io
n is
n
o
t
kn
o
w
n
i
n
t
h
e s
ear
ch
s
pa
ce,
t
h
e
in
itia
l
se
arc
h
a
gen
t
is
e
x
p
e
c
t
ed t
o be t
he ta
r
get pr
ey or
c
l
o
s
e
th
e
op
tim
um
one.
The
o
t
her
sear
ch
a
ge
n
t
s
a
tte
m
p
t
t
o
c
h
a
n
g
e
the
po
si
t
i
o
n
s
tow
a
rds
t
h
e
be
st
o
ne
w
he
n
th
e
be
st
sear
ch a
genc
y
is de
t
er
mine
d.
The
bes
t a
g
en
t
is de
s
c
r
i
b
e
d
be
l
ow
:
⃗
1
⃗
.
⃗
⃗
(1
5
)
⃗
⃗
.
⃗
⃗
(1
6
)
Where
⃗
a
nd
⃗
s
tand
for
best
s
ol
u
t
i
on
of
pos
it
io
n
a
nd
t
h
e
w
h
a
l
e
c
u
rre
nt
p
o
s
i
tio
n,
r
e
s
p
e
cti
v
el
y,
a
n
d
t
i
n
dica
te
s
the
numbe
r
o
f
c
u
r
r
e
nt
i
ter
a
t
i
o
n
.
T
h
e
vec
t
ors
⃗
a
nd
⃗
a
r
e
g
i
v
e
n
by
e
qua
tio
n
(17)
i
n
ter
m
s
o
f
a
rand
om
v
ect
or
⃗
i
n
[0,
1]
a
nd
a
s
h
r
inki
n
g
b
ub
ble
s
v
e
c
t
or
⃗
w
hich
i
s
de
cr
e
a
sed
l
i
ne
arl
y
f
rom
2
to
0
,
as
expre
s
se
d i
n
(
18).
⃗
2
⃗.
⃗
⃗;
⃗
2
.
⃗
(1
7
)
⃗
2
2
(1
8
)
The
b
ubble
net
hun
ti
n
g
i
s
also
c
all
e
d
the
s
p
iral
s
y
s
tem
and
has
a
d
iff
e
r
e
n
t
m
echan
is
m
,
b
e
c
a
u
s
e
t
h
e
h
u
m
p
b
a
c
k
w
i
l
l
t
r
a
v
e
l
t
o
t
h
e
p
r
e
y
i
n
t
h
e
f
o
r
m
o
f
a
h
eli
x
.
The
s
p
iral
m
otion
is
e
xpre
s
sed
in Eq (
1
9)
⃗
1
⃗
.
.
2
⃗
(1
9
)
Where
⃗
⃗
⃗
a
nd
t
h
e
dis
t
a
n
ce
b
e
t
w
e
en
t
he
p
re
y
a
nd
t
h
e
i
th
w
ha
le
i
s
de
te
rmin
e
d
,
b
is
t
h
e
lo
g
a
r
i
th
m
i
c
s
p
ir
a
l
c
o
n
s
t
a
n
t,
a
n
d
l
in
[
-
1
,
1]
i
s
a
ra
n
d
o
m
n
u
mbe
r
.
The
de
v
e
l
ope
rs
o
f
WO
a
ssum
e
d
t
h
a
t
pro
b
ab
i
lit
y
(ρ
)
determ
ine
s
t
h
e
m
ovem
e
nt
t
ype
,
so
a
ny
v
a
l
u
e
of
ρ
˂
0
.5
m
eans
t
h
at
s
hri
n
k
i
ng
m
e
c
h
an
ism
app
l
ies.
T
he
n,
t
he
s
pira
l
me
chan
ism
app
l
i
e
s
i
n
case
of
ρ
≥
0
.5.
T
hi
s
a
l
l
o
w
s
W
O
to
c
on
duc
t
a
glo
b
a
l
s
e
a
rc
h.
A
d
d
iti
ona
l
l
y
. Re
a
d
er
s
ma
y refe
r to
W
O
for m
o
re inform
a
tio
n.
[
2
1
].
6.3.
Grassh
op
p
e
r
op
timiz
a
ti
on
a
l
g
or
i
t
h
m
(
GO
A
)
G
O
A
is
a
n
e
w
l
y
p
ro
po
se
d
sing
le
t
a
r
ge
t,
a
p
op
u
l
a
t
i
o
n-base
d
he
uri
s
t
i
c
a
l
gori
t
hm
t
hat
e
m
ula
t
e
s
grassh
op
per
sw
a
r
m
s
'
b
e
h
a
v
ior
i
n
n
a
t
ure
a
nd
m
o
d
e
ls
t
he
m
ma
t
h
e
m
a
ti
c
a
ll
y
t
o
o
pt
imi
z
a
t
i
o
n
pro
b
le
m
s
w
i
t
h
lit
iga
t
i
ng
var
i
a
b
le
s
[
12]
.
A
m
ong
G
ra
ssho
p
p
e
r
s,
t
he
a
l
g
or
it
h
m
s
i
mula
te
s
re
puls
i
on
a
n
d
a
t
t
raction
forces.
W
h
ile
forc
es
o
f
repu
l
s
ion
a
l
l
o
w
gra
ssh
op
per
t
o
s
e
a
rc
h
spac
e,
f
or
ce
s
o
f
a
ttra
c
tio
n
urge
t
hem
to
e
xp
l
o
i
t
p
rom
i
sin
g
regi
ons.
S
o
t
h
a
t
the
ex
p
l
orat
io
n
is
b
a
l
a
n
ce
d
a
n
d
e
x
trac
ti
on
p
r
o
ce
ss,
G
O
A
w
a
s
prov
ide
d
w
ith
a
c
o
e
fficie
n
t
dec
r
ea
si
ng
t
he
g
rassh
o
ppers
c
omfort
z
o
n
e.
T
h
i
s
a
l
l
o
w
s
G
O
A
no
t
t
o
ge
t
tra
p
ped
i
n
l
oca
l
u
lt
ima
t
e
a
nd
fi
n
d
a
relia
ble
g
l
o
b
a
l
o
p
t
imum
calc
u
la
ti
on.
B
eca
us
e
t
h
e
be
st
s
olu
t
i
on
t
h
e
sw
ar
m
has
ac
hie
v
e
d
s
o
fa
r
is
r
e
g
a
r
de
d
as
a
cha
s
e
d
o
bje
c
t
i
v
e,
t
he
g
ra
ssh
o
p
p
er
s
ha
ve
a
s
tro
ng
op
p
o
rt
un
ity
o
f
f
ind
i
ng
t
h
e
g
l
o
ba
l
op
ti
mu
m
th
roug
h
th
e
impro
v
e
m
e
n
t
o
f
t
he
t
ar
ge
t
ove
r
the
c
ourse
o
f
the
i
t
era
t
ions
[
23
,
2
4
].
T
he
G
O
A
equa
ti
o
n
o
f
p
o
s
i
t
i
o
n
up
da
t
e
i
s
gi
ve
n by
∑
(
20)
Where,
is
t
he
posi
t
i
o
n
i
n
d
-
t
h
d
i
m
e
ns
ion
t
h
e
curre
nt
s
ol
ut
i
o
n
,
r
is
a
c
oe
fficie
nt
o
f
d
i
m
i
n
i
s
h
i
n
g,
w
h
ic
h narrow
s
the are
a
of
c
omfort, repuls
i
on and at
trac
ti
o
n
zon
e,
in
d
-th
di
m
e
nsi
o
n
up
pe
r
b
o
und
,
in
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
nt
J
P
o
w
E
l
e
c
&
D
r
i
S
yst
V
o
l.
11,
N
o.
1
,
Mar
202
0
:
75
–
85
82
d
-t
h
di
m
e
ns
io
n
low
e
r
bou
n
d
,
S
des
c
ribes
the
social
f
orces among
grasshoppers,
shal
l
be
a
bso
l
u
t
e
val
u
e
f
o
r
the
di
sta
n
ce
a
mong
j
-
t
h
gr
as
sho
p
p
er
and
i
-
t
h
gr
a
s
s
h
o
p
p
e
r
an
d
in
d
-
t
h
val
u
e
o
f
d
ime
n
s
i
o
n
t
ar
ge
t,
w
h
ic
h
sol
u
tio
n
ha
s
bee
n
f
o
und
t
o
da
te
.
Eq
(
20)
s
h
o
w
s
t
ha
t
a
gr
a
ssh
op
per
'
s
ne
xt
p
os
i
t
i
o
n
de
p
e
n
d
s
on
his
pos
i
tio
n
c
u
r
r
ent,
a
l
l
o
t
h
er
g
r
a
ssh
o
p
p
e
r
’
s
posi
t
i
on,
a
nd
the
tar
ge
t
p
o
s
iti
o
n
.
in
E
q
(
2
0)
t
he
f
unc
t
i
on
of
s
ocia
l
fo
rces
i
s d
e
fin
e
d
as
(
21)
Wh
i
l
e,
f
i
ndi
cat
es
t
h
e
a
t
t
r
ac
ti
on
s
t
r
e
n
gth
a
n
d
l
is
l
e
n
g
t
h
sca
l
e
of
a
tt
r
a
cti
v
e.
I
n
pr
op
or
tio
n
t
o
t
h
e
iter
a
tio
ns
n
umbe
r
to
b
a
l
a
n
c
e
of
e
x
p
lor
a
t
i
on
a
nd
ex
p
l
o
i
t
a
ti
on,
p
a
r
am
eter
r
in
E
q
(
20)
s
hou
ld
b
e
r
e
du
c
e
d.
I
t
faci
l
i
t
a
t
e
s
t
h
e
use
a
s
t
he
i
nc
rea
s
ing
n
u
mbe
r
o
f
itera
ti
o
n
s.
I
t
a
l
s
o
r
e
duc
es
t
he
c
om
for
t
z
one
acc
or
di
n
g
t
o
t
h
e
iter
a
tio
ns
n
um
ber
and
is
m
easur
e
d
a
ccor
d
i
n
gl
y
[
25]
r
r
t
(
22)
W
h
erev
er
i
s
t
h
e
v
a
l
u
e
o
f
m
a
x
i
m
u
m
,
is
t
he v
alue o
f min
i
mu
m
,
t
is t
he
c
ur
re
nt
i
t
e
r
a
t
i
on,
and
T
is
t
he
numbe
r
of
iter
a
tio
ns
m
axim
um.
I
n
t
his
paper
a
nd
i
s
1
a
nd
0.
0
0
0
0
1
r
e
s
p
e
ct
ive
l
y.
7.
S
I
M
U
L
A
TI
O
N
R
ES
U
L
T
S
7.
1.
S
y
stem
r
espo
nse w
i
th PI
co
nt
ro
ller
tu
n
e
d b
y
P
S
O
, WOL a
nd
GOA
To
m
ain
t
a
i
n
t
h
e
o
u
t
p
ut
v
olt
a
ge
o
f
t
h
e
S
R
G
a
t
3
5
0
V
,
f
o
r
t
he
o
ut
p
ut
c
heck
i
ng
of
t
he
c
on
tr
o
l
l
e
r
pa
r
a
m
e
ter
s
P
S
O
-
P
I
acc
or
di
ng
t
o
the
eva
l
ua
ti
on,
t
he
p
a
r
am
ete
r
s
o
f
PSO are
u
sed
as fo
l
lo
w
s
:
S
i
z
e
o
f
p
opu
l
a
ti
on
=
25;
w
ma
x
=
0.
9,
w
mi
n
=
0.
1;
C
1
=
C
2
=
1
.6;
I
t
e
r
ati
on
=
6
0
;
F
o
r
the
WO
A
,
t
her
e
a
r
e
only
tw
o
con
t
r
o
l
pa
r
a
m
e
te
r
s
;
⃗
w
h
ic
h
w
a
s
dir
e
ctl
y
r
educ
e
d
f
r
o
m
2
to
0
a
nd
the
ran
dom
ve
c
tor
⃗
in
[
0,
1
]
.
T
he
b
es
t
r
e
sults
w
er
e
obtai
ne
d
usin
g
the
ty
p
i
c
a
l
va
l
u
e
s, I
terat
i
on
=60
To
v
e
r
i
f
y
t
h
e
P
e
r
f
or
m
a
n
c
e
of
t
he
GOA-PI
c
ontr
o
l
l
er
p
ara
m
eters,
the
f
o
l
l
ow
in
g
pa
r
a
m
e
te
r
s
o
f
G
O
A
a
r
e
used:
Num
b
er
of
sear
ch a
gen
t
s = 2
5
Num
b
er
of
it
e
r
ati
o
ns =
6
0
F
i
gur
e
7.
s
h
o
w
s
t
he
c
onve
r
g
e
n
c
e
c
ur
ve
s
of
t
he
W
O
A
,
P
S
O
,
a
nd
G
O
A
a
lgor
i
t
hm
s.
I
t
ca
n
be
c
l
e
ar
l
y
seen
t
hat
GOA
conver
g
es
t
o
the
gl
obal
v
alue
f
as
ter
than
t
he
o
th
er
a
lgor
ithm
s
f
or
t
he
p
r
o
b
l
e
m
unde
r
c
o
n
s
i
d
er
at
io
n.
By he
ur
is
tic
t
u
n
in
g m
e
th
o
d
s f
o
r
the
tune
d
a
n
d o
p
ti
m
i
ze
d P
I
c
ontr
o
l
l
er
,
t
h
e
pa
r
a
m
e
ter
s
ob
t
aine
d
a
f
ter
the s
i
m
u
la
t
i
o
n
p
roce
ss
a
re
illustra
t
e
d i
n
Ta
b
l
e
3.
.
F
i
gur
e
7.
T
he
f
it
ness
f
u
nct
i
on
ver
s
us
n
um
ber
of
i
t
e
r
a
t
i
ona
Tab
l
e
3.
P
arameter
s of
o
ptim
iz
ed
P
I
C
ontrolle
r
T
y
p
e
K
p
K
i
PS
O_P
I
0.
0231
2.
0121
WOA_
P
I
0.
0985
2.
9537
GO
A_
P
I
0.
0665
2.
745
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Vo
l
t
a
g
e
con
t
r
o
l
of s
w
i
t
c
h
e
d
reluc
t
ance
g
e
ne
rat
o
r us
i
ng g
r
as
shop
pe
r o
p
t
i
m
i
za
tio
n
alg
o
ri
t
h
m
(M
.
Bahy)
83
A
s
show
n
i
n
F
igure 8(a)
, t
h
e
pr
opose
d
c
o
n
t
rol
l
er ca
n
h
ol
d
t
h
e v
ol
t
a
ge ge
n
era
t
ed
a
t
t
h
e rate
d val
u
e o
f
35
0
V
.
F
igur
e
8(b)
s
h
o
w
s
t
h
e
p
ow
er
s
upp
l
i
e
d
t
o
t
h
e
l
o
ad.
The
pe
rfor
m
a
n
ce
fea
t
ure
s
t
ha
t
de
fi
ne
t
he
t
ra
ns
ien
t
re
sp
on
se
o
f
a
un
i
t
st
ep
i
npu
t
a
r
e
max
i
mu
m
o
v
e
rsho
ot
,
set
t
l
in
g
t
ime
,
r
ise
t
i
m
e
a
nd
ste
a
dy
sta
t
e
er
ror.
T
h
u
s,
t
h
e
impl
ica
t
io
ns
o
f
these
fea
t
ure
s
a
re
s
how
n
i
n
T
ab
le
4
.
The
p
e
rfor
m
a
nc
e
of
t
he
p
r
o
pose
d
G
O
A
-P
I
control
l
er
i
n
com
p
aris
on w
ith o
t
h
er
con
tro
llers
i
s
veri
fie
d
f
or
t
hese
e
ffec
ts
.
(a)
S
y
stem
out
pu
t v
o
l
t
a
g
e
(
b
) S
y
st
e
m
o
u
t
pu
t
pow
er
F
i
gure
8.
S
tep
respo
n
se
o
f t
h
e
syst
e
m
w
it
h
P
I
contro
ller
t
une
d
by
P
S
O
,
W
O
A
and G
O
A
Tab
l
e
4.
R
e
s
ult
s
of the
system
for tra
nsi
e
nt
r
espo
nse
ana
l
ys
i
s
.
C
ontrolle
r
T
y
p
e
O
ve
rshot
%
S
e
t
t
ling T
i
m
e
(
se
c
)
R
i
s
i
n
g
Ti
me (
s
ec)
P
e
a
k
Ti
me
(
s
ec)
I
TS
E v
a
lu
e
PSO
_PI
0.
258
0
.
0569
0
.
0249
0
.
0919
0
.
2107
WO
A
_
PI
0.
2388
0
.
0508
0
.
022
0
.
0895
0
.
2068
6
G
O
A
_P
I
0.
238
0
.
0506
0
.
0214
0
.
0869
0
.
2068
G
O
A-PI
h
a
s
b
etter
re
su
lts t
ha
n
P
S
O-P
I
f
or
m
aximum
ove
rsho
o
t
by
7.7
5
%
a
nd
0.3
3
5
%
com
p
ar
ed
t
o
W
OA-
P
I
.
F
o
r
s
e
tt
ling time,
GOA
-PI
has
better
results
by 11.07%
c
o
m
p
a
r
ed t
o P
S
O-P
I
and 0.
3
9
4
%
c
ompa
red
t
o
W
OA-PI.
F
o
r
r
i
se
t
i
m
e,
GOA-
P
I
h
as
b
et
ter
resu
l
t
s
b
y
14
.
0
56
%
c
o
m
p
a
r
e
d
t
o
P
S
O
-
P
I
,
2.73%
c
om
p
a
red
to
WO
A
-
PI.
F
o
r
pe
ak
t
im
e,
G
OA
-P
I
has
bet
t
er
r
e
s
ults
by
5.
4
4
%
c
o
mpa
red
t
o
P
S
O
-P
I
and
1.82
2%
c
om
pa
re
d
to
WOA-
PI.
In
t
h
e
s
a
m
e
Tab
l
e
4
a
r
e
a
l
so
i
n
d
i
cated
t
he
p
erfo
r
m
a
n
ce
in
de
x
va
lue
s
f
or
d
iffe
rent
c
ontr
o
l
l
e
r
s.
The
pro
pose
d
c
o
n
t
rol
l
e
r
g
ive
s
m
inim
um
o
f
ITS
E
v
a
l
ue
i
n
c
o
mpar
ing
w
i
t
h
t
h
e
o
t
h
e
r
c
o
n
t
r
o
l
l
e
r
s
,
a
s
s
e
e
n
i
n
t
h
i
s
tab
l
e.
Thi
s
r
esu
l
t
s
c
o
n
fi
rm
t
h
a
t
th
e
GOA
t
u
n
e
d
co
nt
rol
l
e
r
h
a
s
b
e
tt
er
p
e
r
f
o
r
m
a
n
c
e
t
h
a
n
t
h
e
o
t
h
e
r
P
S
O
a
n
d
WO
A
tune
d c
o
nt
r
o
l
l
er
s.
7.2.
T
e
sti
n
g
o
f
the
pro
po
se
d co
n
t
ro
l
l
er
To
c
larify
t
he
r
ob
ust
n
ess
of
t
he
s
u
g
g
es
ted
c
ontro
l
l
er,
tw
o
sc
en
ar
ios
w
i
l
l
b
e
occ
u
r
r
ed
i
n
the
l
o
a
d
a
t
0.3
sec
o
n
d
.
I
n
F
ig
ur
e
9,
t
h
e
l
oa
d
is
d
e
c
re
as
ed
s
u
d
d
en
l
y
f
r
o
m
10
0
kW
t
o
58
kW.
F
u
rth
e
rmor
e
,
t
he
l
o
a
d
i
s
incre
a
se
d
su
dd
e
n
ly
f
rom
64
k
W
to 1
0
0
k
W,
a
s
show
n
i
n
F
igure
1
0
.
F
i
gu
re
9
.
S
RG
outp
u
t
po
wer
as
t
h
e
l
o
a
d
d
ecrease
s
F
i
gu
re
10.
S
RG
ou
t
p
u
t
po
wer
as
t
h
e
l
o
a
d i
n
creases
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
11,
N
o.
1
, Ma
r
202
0
:
75
– 85
84
The
sys
t
em
v
o
lta
ge
r
e
s
p
onse
w
i
t
h
o
ptim
um
P
I
c
ont
r
o
ller
tu
ned
by
GOA,
W
OA
a
n
d
P
S
O
t
e
ch
niq
u
e
s
us
i
n
g
IT
SE
f
i
t
ne
ss
f
u
n
ct
i
on
are
show
n
i
n
F
i
gur
es
1
1
a
n
d
1
2
.
D
u
e
to
t
h
e
l
o
a
d
v
a
r
ia
t
i
on,
t
he
S
RG
t
er
minal
vo
lta
ge
i
s
e
n
ha
nc
ed
c
lose
l
y
t
o
3
5
0
V
w
i
t
h
s
m
a
ll
o
v
e
r
sh
oot
a
n
d
r
e
c
o
v
ery
t
i
me
.
The
res
u
l
t
s
o
b
t
ai
ne
d
veri
fy
t
he
eff
e
c
t
iv
en
ess
of
t
h
e
GOA-
b
a
sed
v
o
l
t
a
g
e
co
n
tro
l
sy
s
t
e
m.
F
i
gu
re
11.
T
he
out
pu
t
v
o
l
t
age
respo
n
s
e
u
s
i
n
g
(
ITSE
)
f
o
r
decre
a
si
ng
t
h
e
l
oad
Figu
re
12
.
T
he
o
utpu
t
v
o
lta
ge
re
s
po
nse
usin
g
(
ITS
E
) f
o
r
in
creasi
ng th
e load
I
n
a
ddi
t
i
o
n
,
th
e
c
h
an
g
i
ng
of
t
he
w
i
n
d
s
p
ee
d
is
d
ec
rea
s
e
d
from
1
2
m/s
to
1
0
m
/
s
a
t
0
.
4
s
ec
on
d
as
ill
us
trate
d
i
n
F
i
g
u
re
1
3.
D
uring
t
h
i
s
e
ve
nt,
the
term
ina
l
v
olta
ge
o
f
t
h
e
SRG
ter
m
inal
v
o
l
t
a
ge
i
s
reg
u
la
t
e
d
clo
s
el
y t
o
35
0
V
w
ith sm
a
l
l
o
ve
rsh
oot a
nd r
ecove
r
y
t
im
e. A
lso,
it is reve
a
led t
h
a
t
t
he
s
y
s
tem
vo
l
t
age re
spo
n
s
e
with
o
p
t
i
m
um
P
I
contro
l
l
er
t
u
n
ed
b
y
GOA
,
WOA
an
d
PS
O
t
e
ch
n
i
q
u
es
u
si
ng
ITSE
f
it
ne
ss
f
unc
t
i
on,
a
s
show
n
in
F
i
g
ure
1
4
.
The
resu
lts
o
b
t
a
i
ne
d
ver
i
f
y
t
he
e
ffe
c
t
i
v
e
n
ess
of
th
e
p
r
opo
sed
GOA
b
a
sed
co
nt
rol
l
e
r
f
o
r
vo
lt
a
g
e
con
t
ro
l sys
t
em
.
F
i
g
u
re 1
3
.
S
tep
chan
ge i
n t
h
e win
d
s
peed
Figu
re 14
. Th
e
o
u
t
p
u
t
vo
l
t
age res
p
o
n
se using
(
ITSE
)
f
o
r
incre
a
sing
t
he l
o
a
d
8.
CONCL
U
S
ION
Th
is
p
a
p
e
r
p
re
sen
t
s
o
u
t
p
ut
v
ol
t
a
ge
c
ontr
o
l
of
S
RG
b
ase
d
o
n
w
i
n
d
t
urbi
n
e
o
f
1
00
K
W
w
i
t
h
e
l
e
c
t
ric
gri
d
us
in
g
a
P
I
c
on
trol
ler
tu
ne
d
by
b
o
t
h
G
O
A
,
WO
A
a
nd
P
S
O
.
F
or
t
he
p
a
r
amet
er
t
u
n
i
n
g
t
ech
ni
que,
t
h
e
con
t
ro
l
pr
i
n
c
i
p
l
e
i
s
t
o
dire
c
t
t
he
s
w
i
t
c
hes
o
f
t
he
e
lec
t
r
i
c
a
l
c
on
verter
,
t
o
p
ro
vi
de
opt
im
al
p
a
r
am
eter
s
for
t
h
e
ITS
E
-b
ased
P
I
co
nt
roll
er,
t
h
e
GOA
al
g
o
r
it
h
m
i
s
f
r
eq
u
e
ntl
y
u
sed
.
T
he
c
on
t
r
ol
ler
is
t
e
s
t
e
d
i
n
t
hree
c
a
s
e
s
,
incre
a
ses
t
h
e
l
o
ad,
de
cre
a
ses
loa
d
a
n
d
c
ha
ng
e
s
i
n
w
i
n
d
s
pe
ed.
T
he
s
im
u
l
a
tio
n
re
su
lts
s
ho
w
tha
t
t
he
p
ro
pos
ed
G
O
A
-PI
con
t
rol
l
er
c
a
n
f
in
d
o
p
tim
um
c
on
tro
ller
par
a
m
e
ters
q
uic
k
l
y
an
d
e
f
f
i
ci
en
tly
.
T
h
e
GOA
-PI
c
o
nt
ro
ll
er
i
s
als
o
c
om
pare
d
w
i
t
h
t
he
W
O
A
-
P
I
a
nd
P
S
O-P
I
c
on
t
r
olle
rs
u
s
i
n
g
t
he
re
sul
t
s
o
f
t
r
a
n
si
en
t
a
n
a
l
y
s
es
a
n
d
v
a
lid
it
y
ana
l
ys
is.
The
r
e
sul
t
s
of
s
imula
t
io
n
us
in
g
a
G
O
A
-P
I
contr
o
l
l
e
r
f
o
r
S
R
G
b
a
s
e
d
w
i
n
d
t
u
r
b
i
n
e
s
h
o
w
b
e
t
t
e
r
perform
ance
of
vol
t
a
ge c
on
t
r
o
l
t
ha
n t
h
e
o
t
he
r
tun
i
ng m
e
t
h
o
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.