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
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
731~
7
4
3
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
7
31-
74
3
731
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
A co
mp
arative study and exp
eri
mental valida
t
ion on
sing
l
e
p
h
ase series active power filter
control strategies usi
n
g
PI, F
LC
and sliding mode
controllers
A
b
da
l
l
a
h
B
e
n
A
b
d
e
l
k
a
d
er
,
O
t
h
ma
n
e
Ab
d
elk
h
alek
,
I
s
mail Khalil Bou
sse
rha
n
e,
M
o
hame
d A
m
ine
Ha
r
t
an
i
,
Aym
en
O
m
a
ri
F
acul
t
y
o
f
T
ech
no
lo
gy
, Univ
ersity
o
f T
a
hri M
ohamm
ed
Bechar, Alg
eria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
Sep
2
3
,
2
018
Re
vise
d N
ov
1
9
,
201
8
Ac
ce
p
t
ed
J
an
26
,
2
0
19
S
e
ns
it
ive
lo
ads
a
r
e
wid
e
ly
u
sed
i
n
i
ndustr
ial,
w
hi
ch
i
s
t
h
e
ma
i
n
caus
e
o
f
sag
-
sw
ell
a
n
d
h
a
rmo
n
i
c
s
v
o
lt
ages
p
rob
l
em
s
that
c
an
a
f
f
ect
t
he
p
o
w
er
q
uali
ty.
Am
o
ng
t
h
e
dev
i
ces
t
h
a
t
so
lv
e
such
p
ow
er
q
uali
ty
p
ertu
rbati
o
n
s
,
th
e
series
acti
v
e
p
o
w
e
r
Filter
APF
S
i
s
consid
ered
i
n
this
p
a
p
er.
T
h
u
s
,
a
s
ing
l
e
ph
ase
AP
FS
i
s
d
e
ve
l
o
p
e
d
t
h
rou
gh
an
a
naly
ti
c
anal
ys
is,
su
pp
o
r
t
e
d
b
y
a
n
exp
e
rim
e
nt
al
v
a
l
id
a
tio
n
,
w
here
w
e
ap
pl
ied
cl
a
ssi
cal
p
ro
po
rtio
n
a
l
in
te
g
r
a
t
or
P
I
, f
u
zz
y
l
ogic F
L
C and sl
id
i
n
g
m
o
d
e
S
M
con
t
ro
ll
ers
t
o
im
p
ro
ve
th
e
dy
na
m
i
c
r
e
sp
on
se o
f
t
h
e AP
FS
.
I
n
ad
d
i
t
i
on,
a
com
p
a
r
a
t
i
v
e
st
u
d
y
b
et
w
een
t
h
es
e
con
t
rol
st
rateg
i
es
h
as
m
ad
e
in
o
rder
t
o
m
i
t
i
g
a
te
v
ol
ta
g
e
s
ag
-swel
l
a
n
d
es
peci
ally
h
a
rmon
ic
s,
w
he
re
t
h
e
S
MC
h
a
s
s
ho
we
d
mo
re
e
ffe
c
t
iv
e
a
n
d
ro
b
u
st
r
esu
l
ts
c
o
mpa
r
e
d
t
o
PI
a
n
d
FLC
a
n
d
pro
v
e
d
b
y
the
To
ta
l
ha
rm
on
ic
d
ist
o
rt
i
o
n
THD
rati
o.
R
es
ult
s
o
f
the
p
r
op
ose
d
c
on
trollers
a
re
s
im
u
l
ated
i
n
M
A
T
LAB
sim
u
link
®
a
n
d
v
ali
d
at
ed
t
hro
ugh
exp
e
ri
m
e
nt
al
t
est
s
a
pplied
o
n
o
ur
s
y
s
te
m
p
r
ototy
p
e
.
K
eyw
ord
s
:
Ser
i
es ac
tive p
o
w
e
r
f
ilter
apfs
Propo
r
tional integrator PI
Sa
g-swell,
harmonics volta
ges
Fuz
z
y logic
FLC
Sl
id
i
n
g
mo
de
S
M
Power quality
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
A
bda
lla
h Be
n
A
bde
lka
d
e
r
,
F
acul
t
y
o
f
Electri
cal Eng
in
eering,
Unive
r
sit
y
of
T
a
hri Moha
m
m
e
d Bec
h
ar,
A
l
g
eria
Em
ail:
A
bda
lla
hbe
na
bde
lka
d
e
r
@ya
h
oo.
fr
1.
I
N
TR
OD
U
C
TI
O
N
G
i
ve
n
t
h
e
de
ma
nd
o
f
i
mpr
ovi
ng
the
p
o
w
er
qua
lit
y
e
s
pe
c
i
al
l
y
i
n
i
nd
us
t
r
y,
w
here
t
he
c
ri
t
i
ca
l
equ
i
pme
n
t
a
n
d
se
ns
iti
ve
l
o
a
ds
a
re
w
idel
y
use
d
a
n
d
t
he
i
r
p
ow
er
s
up
pl
y
sh
ou
ld
n
o
t
i
nt
e
r
ru
pt
e
d
.
He
re
,
u
n
i
n
t
e
rrup
t
ed
, c
l
e
an
a
nd
r
e
g
ul
at
ed
p
o
w
er
s
upp
ly
i
s
re
q
u
i
r
e
d
wh
e
n fee
d
in
g loa
d
s tha
t
ha
v
e im
por
tan
t
tas
k
s
. O
n
the
ot
her
ha
nd,
m
ost
com
m
o
n
vo
l
t
a
g
e
d
i
s
t
ur
bance
s
a
p
p
ea
r
in
a
l
t
e
r
n
at
i
v
e
cur
r
ent
a
p
p
l
i
a
nc
es
A
C
pro
v
i
d
i
ng
a
reduc
tio
n
i
n
v
ol
t
a
ge
a
mpl
i
t
u
d
e
k
now
n
as
s
ag.
Thus,
sa
g
and
i
n
te
rrup
t
i
ons
p
ro
vi
d
e
m
ost
of
t
he
i
n
d
u
s
t
ria
l
pro
b
lem
s
(
90
%
)
t
ha
t
a
f
fe
c
t
t
heir
s
u
p
p
l
y
qu
ali
t
y
[
1]
.
M
o
reove
r,
sw
el
l
pr
o
b
l
e
m
is
a
l
s
o
a
m
ong
d
is
t
u
rba
n
ce
s
th
at
affec
t
t
he
p
ow
e
r
qua
lit
y,
w
h
i
c
h
i
s
de
fi
ned
by
a
r
isi
n
g
i
n
vol
ta
ge
a
mp
li
tude
a
b
o
v
e
it
s
nomi
n
a
l
v
al
ue
[
2].
In
a
d
dit
i
o
n
,
h
armo
ni
c
di
st
o
r
ti
on
c
an
p
rov
i
d
e
hug
e
p
r
ob
l
e
ms
i
n
th
e
w
h
o
l
e
of
t
he
p
ow
er
c
on
v
e
r
s
i
o
n
c
h
a
i
n
su
ch
a
s
hea
t
i
ng
the
sy
stem
c
ompo
ne
nt
s,
m
echa
n
i
c
a
l
o
sc
illa
t
i
ons,
un
pr
ed
i
c
t
ab
le
b
eha
v
ior
o
f
p
r
o
tec
t
in
g
de
v
i
c
e
s,
a
nd
ma
y c
a
use
dam
a
ge
[
3,
4
].
D
u
e
t
o
t
he
se
p
rob
l
em
s,
it
i
s
n
e
cessar
y
t
o
a
p
pro
v
e
pr
ote
c
t
ing
de
v
i
ce
s
an
d
ef
f
ecti
v
e
so
l
u
ti
on
t
o
so
lv
e
suc
h
d
is
turba
n
ces.
In
t
h
i
s
pa
per,
w
e
focu
s
on
s
erie
a
c
t
ive
p
o
we
r
f
i
lter
(APFS)
i
n
o
r
d
e
r
to
m
iti
g
a
te
s
ag
-swell
and
ha
rm
on
i
c
s
[5-8]
tha
t
a
ffe
c
t
o
u
r
system
.
Th
us,
a
ser
i
e
compe
nsa
t
or
i
n
s
erted
be
tw
ee
n
the
so
urc
e
a
n
d
t
he
loa
d
c
a
l
l
e
d
d
y
n
am
ic
v
o
lta
ge
r
estore
r
D
V
R
i
s
a
l
so
i
m
p
l
e
me
nte
d
i
n
t
h
i
s
w
o
rk
t
o
pr
o
t
e
c
t
oper
a
tin
g
v
o
l
t
a
g
e
o
f
s
e
n
s
i
t
i
v
e
a
n
d
c
r
i
t
i
c
a
l
a
p
p
l
i
a
n
c
e
s
a
g
a
i
n
s
t
s
a
g
p
r
o
b
l
e
m
e
s
p
e
c
i
a
l
l
y
[
9
-12
]
.
APFS
h
a
v
e
t
h
e
s
a
me
t
o
pol
ogy
a
s
th
e
ac
t
i
ve
f
i
l
ter,
w
ith
a
n
e
x
ce
l
l
en
t
dy
nam
i
c
ca
pa
bil
i
t
y
t
o
re
stor
e
the
l
o
a
d
vol
t
a
ge
t
o
i
n
o
m
i
n
a
l
val
u
e
w
i
t
h
i
n
a
f
ew
mi
l
l
i
s
econ
d
s
as
w
el
l
p
r
ovi
ding
p
o
w
er
d
i
s
rupt
ion
to
t
h
e
s
upp
li
ed
l
o
a
d
s
.
I
n
o
t
h
e
r
r
e
s
e
a
r
c
h
e
s
,
t
h
e
s
e
r
i
e
t
o
p
o
l
o
g
y
aim
s
t
o
c
o
mpe
n
sa
te
t
he
s
a
g
w
it
h
a
c
t
i
v
e
p
o
w
er
[
13].
I
n
po
w
e
r
qual
it
y
do
m
a
in,
var
i
o
u
s
paper
ha
s
use
d
c
lass
ical
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
731
–
7
43
73
2
and
i
n
t
e
ll
i
g
en
t
con
t
ro
l
l
e
r
s
in
o
rder
t
o
impr
ove
t
he
s
ta
bi
l
ity,
ro
bu
stn
e
ss
a
nd
e
x
cel
l
e
nt
d
y
n
a
mi
c
res
p
on
se
o
f
t
h
e
A
P
F
S
a
s
m
e
ntione
d
i
n
[
4,
1
5-18].
T
he
c
o
n
t
ro
l
s
t
rate
g
i
e
s
u
se
d
in
t
h
i
s
p
a
p
e
r
s
u
c
h
a
s
P
I
,
F
L
C
a
n
d
S
M
C
p
r
e
s
e
n
t
s
rob
u
st
a
nd
e
f
f
i
c
i
e
n
t
re
su
lts
w
it
h
d
i
ffe
r
en
t
TH
D
r
a
ti
o,
w
he
re
S
M
C
ha
s
prov
i
d
ed
t
he
b
es
t
ra
tio
w
i
t
h
3%
.
Mo
de
ls
o
f
t
h
e
t
h
r
ee
c
o
n
t
r
o
lle
r
s
a
re
d
e
v
el
op
ed
m
athem
a
t
i
c
a
ll
y
as
c
ite
d
in
v
ario
us
w
or
ks
s
uch
as
[
1
9
-2
4]
,
an
d
ada
p
te
d to o
ur
s
ystem
t
o
p
o
l
o
g
y
.
The
rest
o
f
the
paper
is
o
rga
n
i
zed
a
s
f
o
ll
ows:
s
e
c
t
i
on1
p
rese
n
t
s
t
h
e
A
P
F
S
m
ode
l
w
i
th
m
ode
l
i
n
g
o
f
t
h
e
po
we
r
sy
ste
m
,
se
ct
i
o
n
2
f
o
cu
ses
on
t
h
e
c
on
t
r
ol
s
t
r
a
t
eg
i
e
s
w
it
h
a
comp
ara
t
iv
e
st
udy
b
et
we
en
t
h
e
u
sed
st
r
a
te
gie
s
a
nd f
i
na
lly,
th
i
s
p
a
p
er
ends
w
i
t
h
a c
onc
l
u
s
i
o
n
.
2.
DESCRIPTIO
N
O
F
TH
E
S
Y
S
TEM
2.1.
Se
ries
a
ctive
powe
r
fi
l
t
er
APFS
I
n
t
h
i
s
pape
r,
t
he
s
t
u
d
i
e
d
s
yste
m
is
c
om
pose
d
m
ai
nly
b
y
t
h
r
e
e
b
loc
k
s,
a
p
rogram
m
a
ble
A
C
s
ourc
e
t
o
pro
v
i
d
e
sa
g-sw
ell
a
nd
h
a
rm
on
i
c
s
v
o
l
t
a
g
es
s
cena
r
i
o
s,
a
s
e
n
s
i
t
i
ve
l
o
a
d
(med
i
c
al
e
qui
pmen
t
)
a
nd
A
P
FS.
T
h
e
APF
S
conta
i
ns
a
s
ing
l
e-p
h
ase
P
W
M
vo
l
t
age source
i
n
v
er
t
e
r
in ord
er
t
o
i
n
j
e
c
t
t
he
c
ompe
n
s
at
i
n
g v
o
lta
g
e
by a
n
in
j
e
c
t
ion
trans
f
or
me
r
and
a
n
L
f
,
Cf
s
ec
o
nd
or
de
r
fi
l
e
r
to
e
l
i
m
i
n
a
t
e
h
i
gh
fre
qu
en
cy
c
au
sed
by
i
n
v
e
rt
er
sw
it
c
h
i
n
g
act
io
ns.
Thi
s
i
n
v
e
r
t
e
r
i
s
s
upp
l
i
ed
b
y a
D
C
s
ource
a
s
show
n i
n
F
i
gur
e 1.
F
i
gure
1.
S
ing
l
e
-
phase
ser
i
e
s ac
tive
p
o
w
e
r
fi
lter
(A
S
F
)
2.2.
M
o
de
l
i
n
g
o
f
t
he
A
P
F
S
s
y
s
t
e
m
Th
is
s
ec
t
i
o
n
d
ea
ls
w
it
h
t
h
e
m
a
them
at
ica
l
m
ode
li
ng
o
f
t
h
e
se
ries
a
ct
ive
pow
er
f
ilter
A
PFS.
The
fu
ll
st
r
u
c
t
ure of the
A
PF
S
can
b
e
re
p
r
esen
ted b
y
a
c
on
verter
a
s show
n
i
n
F
i
gur
e
2,
w
her
e
K
irchh
o
f
f’s
v
o
lta
g
e
l
aw
i
s
a
pp
li
ed
t
o
t
h
e
A
C
c
l
o
s
e
d
c
i
r
c
u
i
t
t
o
g
et
t
h
e
f
oll
o
wi
ng
m
at
hem
at
i
cal
e
x
p
r
essi
o
n
[5
]:
(
1
)
(
2
)
w
ith:
:
Con
t
r
ol
in
put
t
o
t
h
e
seri
e
s
con
v
e
rt
e
r
:
I
nduc
tor c
u
rre
nt
o
f t
h
e
serie
s
c
on
ver
t
e
r
:
O
utp
u
t
v
o
l
ta
ge
of the
se
ries c
on
verter
:
d
c lin
k v
o
l
t
a
g
e
:
The
in
duc
ta
nc
e
of the f
ilter
:
The
c
apac
ita
nc
e
of the
f
i
l
t
e
r
:
Equ
iva
l
e
n
t se
ries r
esista
nce
ES
R of i
nd
uc
t
o
r
:
The ESR of the
capacitor
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
A com
par
a
tive
st
udy
a
n
d
e
x
pe
rim
e
n
t
al
v
a
l
i
d
a
tio
n on
s
i
n
g
l
e ph
ase
se
rie
s
ac
tive ..
. (Abda
llah Be
n
Abde
l
k
ade
r)
73
3
F
i
gure
2. E
q
u
i
v
ale
n
t
circu
it o
f
serie
s
con
v
e
r
t
e
r.
̂
3
̂
4
3.
CONT
ROL S
T
RATEG
IES
O
F
T
HE S
YS
TE
M
T
h
e
c
o
n
t
r
o
l
s
t
r
a
t
e
g
i
e
s
u
s
e
d
i
n
t
h
i
s
w
o
r
k
a
r
e
P
I
,
F
L
C
a
n
d
S
M
c
o
n
t
r
oller
s
.
Th
us,
a
com
p
ar
ati
v
e
stud
y
is
m
a
d
e
be
t
w
een
t
he
t
hree
m
e
t
h
ods
i
n
or
de
r
to
i
m
p
ro
ve
t
he
i
r
p
er
form
ance
a
nd
ro
bus
tn
e
s
s
in
pow
e
r
q
ua
li
ty
.
The
3 m
e
th
ods
a
r
e
de
s
cribe
d
s
epar
ate
l
y a
s
f
ol
l
o
w
:
3.1.
C
l
ass
i
c
a
l
p
r
op
ort
i
on
al in
t
e
g
rator
PI c
on
trol
l
e
r
Th
e
PI
s
t
r
u
c
tu
re
c
on
si
st
s
of
a
s
in
gl
e
ou
t
e
r
v
o
l
t
ag
e
l
o
op
t
o
reg
ul
at
e
t
h
e
i
n
j
ect
ed
v
ol
t
a
g
e
o
f
th
e
APFS.
T
h
e
o
u
t
p
u
t
o
f
t
h
i
s
l
o
o
p
i
s
t
h
e
p
h
a
s
e
a
n
g
l
e
t
h
a
t
i
s
p
r
o
v
i
d
e
d
b
y
the
P
W
M
s
i
g
n
a
l
g
e
n
e
r
ator.
Thus,
th
e
P
W
M
gene
ra
tes
pu
lse
si
gna
ls
t
o
the
ga
te
o
f
sw
itc
h
i
n
g
d
e
v
ice
I
G
B
T
[
5
]
.
T
he
f
o
l
l
o
w
i
n
g
t
ra
nsfe
r
fu
nc
ti
on
de
fi
nes
th
e
P
I
contro
l
l
er
a
s:
5
The
P
I
c
ont
r
o
l
l
e
r
c
anno
t c
h
a
n
ge abru
p
t
l
y i
n
t
he err
or e
ps (Vr
ef
– Vrms). There
f
ore,
P
I contr
o
l
l
e
r
c
an
deter
m
i
n
es
t
he
i
ns
t
a
nt
a
n
e
ous
v
a
l
ue
s
o
f
t
he
e
r
r
or
w
it
h
o
u
t
c
onsi
d
er
i
n
g
the
i
r
d
i
ver
g
en
c
e
a
nd
per
t
urba
t
i
o
n
s,
w
h
ic
h is de
f
i
n
e
d
by
t
h
e de
ri
va
te
o
f t
h
e
err
o
r a
nd de
n
o
te
d
∆
e
[5
].
The
tra
n
sfer
f
u
n
ct
i
on o
f
v
olta
ge
-cl
o
sed
lo
op
i
n
s
eries
co
n
v
e
r
t
e
r is def
ined
i
n
(6) using (
4
):
̂
6
F
i
gure
3.
Co
n
t
r
o
l
ler
with PWM and
V
SC
3.2.
Fu
zzy
l
o
g
ic
c
o
n
troller
FLC
Th
e
se
con
d
c
o
n
t
r
o
l
l
e
r
u
s
ed
i
n
t
h
i
s
p
ap
er
i
s
t
h
e
FLC
i
n
o
rder
t
o
i
m
p
r
o
v
e
t
h
e
b
e
h
a
v
i
o
r
o
f
t
h
e
A
P
F
S
.
The
co
ntro
l
l
e
r
in
ba
sed
on
Ma
m
d
ani’s sys
t
e
m
and
i
t
s
struc
t
ur
e i
s
show
n
in
F
igure
4.
L
i
n
g
u
i
s
t
i
c
v
a
r
i
a
b
l
e
s
a
r
e
t
h
e
e
r
r
o
r
e
a
n
d
i
t
s
d
e
r
i
v
a
t
e
∆
e
,
w
h
i
c
h
a
r
e
m
appe
d
from
ma
t
h
e
m
a
t
ic
a
l
i
npu
t
val
u
es
i
n
t
o
fu
z
z
y
m
e
m
b
e
r
ship
f
u
n
c
tio
ns.
A
f
ter,
e
xec
u
t
i
ng
a
l
l
ap
pl
i
c
a
b
le
r
u
l
es
i
n
the
r
u
l
e
b
ase
aim
s
t
o
c
o
mp
ut
e
th
e
fu
zz
y
out
put
f
un
c
t
io
ns
.
Fi
n
a
l
l
y
,
b
y
d
e
-fu
z
z
if
yin
g
t
he
f
uzz
y
o
u
t
pu
t
func
t
i
o
n
s,
w
e
ge
t
"
c
r
i
sp
"
o
u
t
p
ut
v
al
ue
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
731
–
7
43
73
4
F
i
gure
4.
F
uz
zy
c
on
tro
l
l
e
r
The
s
e
ou
tpu
t
s
are
deter
m
ine
d
u
si
n
g
t
he
i
nfe
r
e
n
c
e
e
ngi
ne
a
nd
t
h
e
r
ule
bas
e
(
i
f-the
n
ru
les
)
a
s
fol
l
ow
:
IF
e
A
N
D
∆
e,
T
HEN
Kp
AND
Ki
.
Th
e
v
a
ri
ati
o
n
of
K
p
and
K
i
c
on
st
an
t
s
d
ep
e
nd
on
(
e
a
n
d
∆e
).
T
h
e
me
mbe
r
ship
f
unc
t
i
o
n
c
urve
s
of
e
,
∆e,
K
p
a
n
d
K
i
are
show
n
in
F
ig
ur
e
5
a
n
d
6,
w
h
e
re
a
ll
m
em
be
r
s
h
i
ps
’
fu
nc
ti
o
n
s have
t
ria
n
g
u
l
ar
s
hap
e
[
4].
(a)
(b)
F
i
gure
5.
Mem
ber
s
h
i
p f
u
nct
i
o
n
c
ur
ve
s (a
) error
e, (b) D
errived
of t
he
er
r
or ∆e
F
i
gure
6. Me
m
be
rsh
i
p
fu
nct
i
o
n
cur
ves o
f
b
o
t
h
in
p
u
t
s
K
p and
K
i
T
h
u
s
,
t
h
e
f
u
z
z
y
s
u
b
s
e
t
f
o
r
e
a
n
d
∆
e
a
r
e
(
N
L
;
N
M
,
N
S
,
Z
E
,
P
S
,
P
M
,
PL
).
T
ab
l
e
1
p
re
se
n
t
s
t
h
e
fu
zzy
lo
gic
con
t
ro
l r
u
l
e
s for
the
var
i
ab
les
K
i
a
n
d
K
p.
Ta
b
l
e
1.
Ru
l
e
base
for
fuz
z
y
c
on
t
r
o
lle
r
de
(n
)
NB
NM
NS
ZE
PS
PM
PB
e(
n
)
NB
NB
NB
NB
NB
NM
NS
ZE
NM
NB
NB
NB
NM
NS
NZ
PS
NS
NB
NB
NM
NS
NZ
PS
PM
ZE
NB
NM
NS
ZE
PS
PM
PB
PS
NM
NS
ZE
PS
PM
PB
PB
PM
NS
ZE
PS
PM
PB
PB
PB
PB
ZE
PS
PM
PB
PB
PB
PB
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
A com
par
a
tive
st
udy
a
n
d
e
x
pe
rim
e
n
t
al
v
a
l
i
d
a
tio
n on
s
i
n
g
l
e ph
ase
se
rie
s
ac
tive ..
. (Abda
llah Be
n
Abde
l
k
ade
r)
73
5
In
a
d
di
tio
n
,
a
3D
c
urve
o
f
the
relation
b
e
tween
i
nputs
and
ou
t
puts
of
t
h
e
FLC
controll
er
i
s
a
l
so
plotte
d
and sh
own
in Fig
ure
7.
F
i
g
u
r
e
7.
The
re
lat
i
on
s
u
rfac
e
betw
ee
n in
p
u
ts
a
nd ou
t
p
u
t
o
f
F
L
C
3.3.
S
lid
in
g mod
e
c
on
t
r
ol
l
e
r
S
M
C
The
las
t
c
on
t
r
o
l
ler
use
d
i
s
the
S
M
c
on
trol
ler
descr
i
be
d b
y
t
h
e
fol
l
ow
ing
sta
t
e
spac
e
mode
l
:
01
⁄
1
⁄
⁄
1
⁄
0
01
⁄
7
wher
e
i
a
nd
i
a
re the
f
i
l
t
e
r i
n
d
u
c
t
or
c
urr
e
nt a
n
d
s
ource
c
u
r
rent
r
espec
tive
l
y.
Ta
k
i
n
g
t
he
i
nj
ec
t
e
d
vo
l
t
age
Vin
j
x
and
b
y
d
e
r
i
v
a
t
e
x
,
x
1
x
2
.
Th
e
n
,
t
h
e
d
e
sc
ri
pti
o
n
of
t
he
mode
l bec
o
me
:
x
x
x
x
x
i
u
u
8
first,
we
consider a
g
eneral
s
ec
o
nd or
der dynamic
system a
s fol
low
:
,
(
9
)
Where,
.
,
1
,
2
a
r
e
s
m
o
o
t
h
f
unc
t
i
ons
w
i
t
h
c
on
ti
n
u
o
u
s
fini
te
tim
e
de
riva
t
i
ve
s
t
o
e
x
i
s
t
and
.
i
s
i
nve
r
tib
l
e
.
The
ar
gume
n
ts
o
f
.
a
nd
.
ha
ve
b
e
e
n
r
e
m
o
v
e
d
for
simpl
i
c
i
ty
i
n
the
ana
l
y
s
es
t
o
fo
l
l
ow
.
The
pa
ram
e
ter
s
.
,
1
,
2
a
re
know
n.
L
et
t
he
o
u
t
pu
t
o
f
t
he
s
ys
tem
be
x
.
.1
,
2
.
Def
i
ne
t
he
err
o
r a
s
[18].
The
e
rror
dyna
m
i
c
is de
f
i
n
e
d
a
s
fol
l
o
w
:
10
11
The
sl
idi
ng s
u
r
f
ac
e w
i
t
h
its
d
e
r
i
v
a
tio
n
can
b
e
de
fi
ne
d
as fol
l
o
w:
12
13
A
f
ter,
usin
g
t
h
e
foll
o
w
i
ng l
y
a
p
u
n
ov f
u
nct
i
on
:
Vs
s
,
w
i
t
h
its
tim
e d
e
ri
vat
i
v
e a
s
fol
l
o
w
:
14
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
731
–
7
43
73
6
F
o
r
st
abl
e
o
perat
i
on,
V
<0,
which
results
S
<
0
f
o
r
S
>
0
a
n
d
S
>
0
f
or
S
<0.
The
n
,
the
co
n
t
rol
la
w
c
a
n
b
e
repr
esente
d
as fo
llow
usin
g e
q
1
3
a
nd
eq1
1
:
(15)
F
i
gure
8
de
sc
ribes
t
h
e
fe
e
d
back
c
on
tro
l
d
ia
gram
o
f
t
h
e
A
P
F
S
.
A
s
s
how
n,
t
he
V
l
o
adre
f
i
s
t
he
refere
nce
l
o
a
d
vol
tage
d
e
s
ire
d
a
t
t
h
e
P
CC. T
he er
r
or b
e
t
w
e
en V
l
o
a
d
r
ef
a
nd
V
lo
ad
g
i
v
es
t
h
e
r
e
f
e
r
en
c
e
i
nj
ec
t
e
d
vo
lta
ge
s
ig
na
l
pro
v
i
d
e
d
b
y
the
in
ject
i
on
transfor
me
r.
B
y
com
p
in
g
the
o
u
t
put
o
f
t
h
e
l
o
w
-
pa
ss
f
i
l
t
e
r
w
i
t
h
t
h
e
i
n
j
ect
ed
r
e
f
e
r
en
c
e
vol
t
a
g
e
,
we
g
e
t
t
h
e
i
n
s
t
a
nt
an
eou
s
e
rro
r
si
gn
a
l
c
al
l
e
d
z
1
.
A
f
ter,
t
he er
r
or w
it
h it
s deri
v
a
te (e
,
∆e)
a
r
e
used
b
y
the
sli
d
in
g
m
ode
c
o
n
t
ro
ller
to
g
e
n
er
ate
the
co
n
tr
ol
l
a
w
u
,
w
h
ic
h
i
s
c
on
v
e
rted
t
o
P
W
M
si
gna
l
of
t
he
sw
itc
h
i
ng
dev
i
ce
IG
B
T
of the
i
n
v
e
r
ter
[18].
F
i
gure
8.
F
e
e
dbac
k
c
on
tro
l
c
han
g
e
abr
u
p
t
l
y
diagr
am
of
A
P
F
S
Th
e
e
r
ro
r ca
n
b
e
d
ef
in
ed
as
f
o
ll
o
w
1
6
The
n
,
the
error dynam
i
c
is
d
erive
d
u
s
i
ng
(2):
17
18
19
Th
e
s
e
l
e
ct
ed
sl
i
d
in
g
su
rfa
c
e
was
s
K
z
K
z
a
l
o
n
g
w
ith
t
he
c
o
n
tro
l
l
a
w
:
∗
20
wher
e
21
1
|
|
|
|
22
The
ne
xt ste
p i
s
to
o
b
t
a
in
t
h
e
s
l
i
di
ng
mode
c
on
tro
l
law
u us
i
n
g
(
1
4
)
.
F
i
nal
l
y
,
t
h
e
c
o
n
t
r
o
l
l
a
w
c
a
n b
e
de
r
ive
d
usi
n
g
eq
14,
19 and
20
as
f
o
l
l
o
w
:
23
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
A c
o
mpar
ative
study and
expe
r
i
m
enta
l
validation
on single phase
ser
i
es
ac
ti
v
e
... (
A
bdal
l
ah B
e
n Abde
l
k
ade
r)
73
7
4.
RESU
L
T
S
A
ND DIS
C
U
S
S
I
ON
In
t
hi
s
se
cti
o
n
,
w
e
d
i
s
c
u
s
s
t
h
e
an
a
l
y
t
i
cal
a
nd
e
xp
e
r
i
m
e
n
t
a
l
re
s
ults
o
f
t
h
e
di
ffe
r
e
nt
c
on
t
r
ol
m
e
t
ho
d
s
use
d
i
n
t
h
is
s
tu
dy.
F
ir
st,
we
p
r
e
se
nt
s
i
m
ula
t
io
n
data
,
the
n
we
d
iscuss
t
h
e
r
e
s
u
l
t
s
.
T
h
u
s
,
we
p
re
s
e
n
t
e
xper
i
m
e
nta
l
r
esu
l
ts
w
ith
a
d
e
t
a
i
l
e
d
d
i
scu
ssion.
4.
1.
Si
m
u
l
a
t
i
o
n
r
e
s
ul
t
s
S
i
m
u
l
a
t
i
o
n
t
e
s
t
has
m
a
de
i
n
MA
TLA
B
S
i
mul
i
nk®
i
n
or
de
r
t
o
i
m
p
r
o
v
e
t
h
e
per
f
or
m
a
nce
of
t
he
u
se
d
c
o
n
t
r
o
l
st
r
a
te
g
i
es
s
uc
h
as
P
I,
F
LC
a
nd
S
M
C.
T
he
s
im
ul
a
tio
n
c
i
r
c
uit is s
h
o
wn
in
Figu
re
9
.
F
i
g
u
r
e
9
:
S
i
m
u
l
a
ti
on
dia
g
r
a
m
of
t
he
s
ys
tem
Th
us,
simu
lat
i
on
da
ta
a
r
e
s
u
m
m
a
r
i
z
e
d
i
n
T
able
2
.
The
si
m
u
lat
i
on
r
esul
ts
o
f
th
e
APFS
are
p
r
esen
ted
in
o
rder
t
o
im
p
r
o
v
e
its
c
a
p
a
b
i
l
i
t
y
o
f
am
el
i
o
ra
tin
g
the
p
o
w
er
q
u
a
l
i
t
y
.
T
h
e
r
e
s
u
lts
a
r
e
d
isc
u
sse
d
se
pa
ra
t
e
l
y
,
whe
r
e
a
com
p
ara
tive
a
n
a
l
y
s
e
s
i
s
m
a
de
b
etwee
n
t
he
t
hr
ee
con
t
ro
l
l
e
r
s
in
t
he
t
wo
c
ase
(sag-swe
ll
a
n
d
ha
r
m
onic
s
)
.
Tab
l
e
2.
E
lectric
a
l par
a
m
e
ter
s
Pa
r
a
m
e
te
rs
V
alue
s
Sourc
e
v
o
l
t
a
g
e
f
r
e
q
ue
ncy
f
50
HZ
S
our
c
e
volta
g
e
V
s
5.
7
V
r
m
s
L
o
ad
r
es
i
s
t
a
n
c
e
R
L
1
2
.
3
Ω
C
f
(
L
C
fil
te
r
induct
a
n
c
e
)
1
n
F
Lf
( LC filte
r
c
a
p
a
c
ita
n
c
e
)
9
m
H
Tra
n
sform
e
r
1
2
V
/
230V
/
1
K
V
A
D
C
-bus
c
a
p
ac
itor,
D
C
-
bus
2200
uF
–
re
fe
r
e
n
c
e
volta
g
e
V
dc
*
=
35V
K
p
,
K
i
S
i
m
u
l
a
tion
re
sult
s
K
p
=
7,
2-
K
i
=
33
Kp
,K
i Ex
p
e
r
i
men
t
a
l
r
esu
lts
K
p
=8
,8
-
Ki
=4
,2
4
S
l
id
i
n
g
mo
d
e
c
o
n
tr
o
l
ler
pa
ra
m
e
t
e
r
s
2
5
0
,
0
.
0
2
3
5
7
,
4
00,
0
.
0
0
1
,
0
.
0
1
4.
1.
1.
Case of
t
h
e
h
a
rmon
ics volt
age
:
F
i
gur
e
10,
1
1
a
nd
12
pr
esen
t
t
h
e
vol
tage
w
avef
or
ms
o
f
P
I
,
F
L
C
a
nd
th
e
S
M
C
.
T
he
T
H
D
of
t
he
sour
c
e
v
ol
ta
ge
w
a
s
4
8.
3
4
%.
A
s
sh
ow
n,
t
he
A
P
F
S
h
as
c
om
pen
s
ate
d
t
he
v
olta
ge
h
ar
m
o
n
i
cs
s
ucc
e
ssf
u
lly
.
The
thr
e
e
c
o
n
t
r
o
lle
r
s
h
ave
pr
e
s
en
ted
va
r
i
ous
e
x
c
e
l
l
e
n
t
r
esul
ts,
w
h
i
c
h
i
s
sh
o
w
n
thro
u
gh
a
m
e
l
iora
tin
g
th
e
vo
lt
a
g
e
f
o
r
m
a
n
d
r
e
d
u
c
i
n
g
t
h
e
T
H
D
v
a
l
u
e
.
T
h
e
T
H
D
h
a
s
b
e
c
o
m
e
4
.
1
5
%
w
i
t
h
P
I
c
on
tr
o
l
ler
,
3
.
88%
w
i
t
h
the
F
L
C
a
n
d
3.
29
%
w
i
t
h
t
he
S
MC.
The
f
o
ll
ow
i
ng
F
i
gur
e
1
3
,
14
and
1
5
s
how
t
he
s
pe
c
t
ra
l
analy
s
is for
th
e
thre
e
c
on
tro
lle
rs.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
731
–
7
43
73
8
F
i
gure
1
0
.
S
i
mula
tio
n v
o
l
t
a
g
e
w
a
ve
form
es for P
I
C
ontr
o
ller
F
i
gure
1
1
.
S
i
mul
a
t
i
o
n
v
o
l
ta
ge
w
ave
f
orm
e
s
for
F
u
zz
y
C
ontr
o
ller
F
i
gure
1
2
:
S
i
m
u
l
a
tio
n
vol
ta
ge
w
ave
f
orm
e
s
for
sl
id
i
n
g
mode
Con
t
ro
ll
e
r
(a)
(
b
)(
a
)
(
b
)
F
i
gure
13.
S
pe
c
t
r
a
l a
n
a
l
ysis f
or P
I c
ontro
ll
e
r
,
(
a
)
sour
ce
vo
lta
ge,
(b)
load v
ol
ta
ge
F
i
gure
1
4
.
S
p
ectra
l
ana
l
y
s
is for
f
uz
zy c
o
n
t
r
o
ller
(
a
)
so
ur
ce
vo
lta
ge,
(b).
load v
ol
ta
ge
(a)
(b)
F
i
gure
1
5
.
S
p
e
c
tral a
na
ly
si
s
for
s
l
id
in
g
m
o
de
co
n
t
ro
ller
(a) sourc
e
vo
lta
ge
,
(
b
) load
v
o
lta
g
e
.
A
s
a
r
e
s
u
l
t
,
t
h
e
s
l
i
d
i
n
g
m
o
d
e
c
o
n
t
r
o
l
l
e
r
h
a
s
p
r
e
s
e
n
t
e
d
t
h
e
l
o
w
e
st
T
HD
v
a
l
u
e
,
w
hi
ch
r
ef
l
e
c
t
s
t
h
e
ro
bu
stn
e
ss a
nd t
h
e ef
fi
ci
e
n
c
y
o
f
t
h
e con
t
ro
l
st
ru
c
t
u
r
e
.
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
4
5
-10
-2
6
10
(B
)
In
j
e
cte
d
vo
l
t
a
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
4
5
-15
-7
1
9
15
Ti
m
e
(C
)
Load
v
o
l
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
4
5
-15
-7
1
9
15
(A
)
S
ourc
e
v
ol
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
45
-1
5
-7
1
9
15
(A)
S
our
c
e
v
ol
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
45
-1
5
-7
1
9
15
(B)
I
n
j
e
c
t
ed
v
o
l
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
45
-1
5
-7
1
9
15
Ti
m
e
(C
)
Loa
d
v
o
l
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
45
-15
-7
1
9
15
(A
)
S
ourc
e
v
ol
t
a
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
45
-15
-7
1
9
15
(B
)
I
n
j
e
c
t
e
d
v
ol
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
45
-15
-7
1
9
15
Ti
m
e
(C
)
Load
v
o
l
t
age
0
50
0
1
000
0
10
20
30
F
r
equ
enc
y
(H
z
)
F
u
n
d
a
m
e
n
ta
l
(
5
0
H
z)
= 8
.7
9
2
, T
H
D
=
4
8
.
3
4
%
M
a
g
(
%
o
f
F
undam
e
n
t
a
l)
0
500
1000
0
0.
1
0.
2
0.
3
F
r
equenc
y
(Hz
)
F
und
am
ent
al
(
50Hz
)
=
6
.
79
,
T
H
D
=
4
.
15%
M
a
g
(
%
o
f
F
undam
e
n
t
a
l
)
0
200
400
600
800
1000
0
10
20
30
F
r
equenc
y
(H
z
)
F
undam
ent
a
l
(
5
0H
z
)
=
8
.
791
,
T
H
D
=
48.
34%
M
a
g
(
%
o
f
F
u
nda
m
e
nt
al
)
0
20
0
40
0
600
80
0
10
00
0
0.
2
0.
4
F
r
eq
uen
c
y
(
H
z
)
F
u
n
d
a
m
ent
al
(
5
0
H
z
)
=
6.
81
7
,
T
H
D
=
3
.
8
8
%
M
a
g
(
%
o
f
F
u
nda
m
e
nt
al
)
0
20
0
40
0
60
0
800
100
0
0
10
20
30
F
r
equ
enc
y
(
H
z
)
F
u
n
d
a
m
e
n
ta
l
(
5
0
H
z
)
= 8
.
7
9
1
, T
H
D
= 4
8
.3
4
%
M
a
g
(
%
o
f
F
un
dam
en
t
a
l
)
0
20
0
40
0
60
0
80
0
10
0
0
0
0.
2
0.
4
0.
6
F
r
eq
ue
nc
y
(
H
z
)
F
u
nd
am
e
n
t
a
l
(
50
H
z
)
=
6.
82
,
T
H
D
=
3
.
2
9
%
M
a
g
(
%
o
f
F
un
dam
en
t
a
l
)
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
A com
par
a
tive
st
udy
a
n
d
e
x
pe
rim
e
n
t
al
v
a
l
i
d
a
tio
n on
s
i
n
g
l
e ph
ase
se
rie
s
ac
tive ..
. (Abda
llah Be
n
Abde
l
k
ade
r)
73
9
4.1.2.
Case
o
f the
sa
g-swell voltage:
I
n
t
hese
c
ases
o
f
sa
g
a
n
d
s
w
e
l
l
v
o
lta
ge
,
w
e
p
rove
t
he
a
bi
l
i
t
y
o
f
the
APFS
t
o
com
p
en
sate
t
h
e
un
ba
lanc
e
v
o
l
t
a
ge
s
a
g
s
a
nd
sw
e
l
l
s
.
F
i
g
u
re
16,
1
8
a
n
d
2
0
s
how
s
t
he
pha
se
v
ol
ta
ge
s
ou
rc
e
w
i
th
s
a
g
o
f
5
0
%,
w
h
ic
h
oc
c
u
rre
d
d
u
ri
ng
[0.
1
4
s
–
0.
3
s].
The
thr
ee
co
ntr
o
l
l
e
r
s
h
a
s
c
orr
ected
t
h
e
l
oa
d
vo
l
t
age
(
V
lao
d
RMS
=
6.
87
1
V
)
w
ith
c
om
pen
s
at
in
g t
h
e
missed vo
l
t
age
(5
0
%
i
n
t
h
i
s
case
re
fer
to 3.
435
5
V
)
.
The
sw
el
l
v
o
l
t
a
ge
p
he
nom
en
on
is
s
h
o
w
n
i
n
F
i
gure
1
7
,
19
and
21
,
wh
ere
we
u
sed
a
50
%
as
s
wel
l
vo
lta
ge
d
u
r
i
n
g
the
sam
e
t
a
m
e
dom
ai
n
as
m
e
n
t
i
o
n
ed
i
n
sa
g
c
a
s
e.
T
hus,
the
t
h
r
ee
c
ontro
l
l
ers
has
als
o
c
orre
cted
the
sw
e
ll
vo
l
t
a
g
e
p
h
en
om
en
o
n
b
y
i
n
je
ct
i
ng
a
vo
lta
ge
i
n
ph
a
s
e
po
sit
i
on
i
n
o
r
d
e
r
t
o
m
it
ig
at
e
th
e
ov
er-v
ol
t
a
g
e
ratio (
50% in this case r
e
f
e
r
to
3
.4355 V)
.
Figure
1
6
.
Simu
la
tio
n v
o
l
t
a
g
e
w
a
vefor
m
e
s
for P
I Con
t
r
o
l
l
e
r
F
i
g
u
r
e
17.
S
i
m
ula
t
io
n v
o
l
t
a
g
e
waveform
es
f
or PI
C
o
ntroller
F
i
gur
e 1
8
.
S
i
mula
t
i
o
n
v
ol
t
a
ge
w
a
vef
o
rme
s
for
fuz
zy c
on
t
r
o
lle
r
F
i
gur
e 1
9
.
S
i
mula
t
i
o
n
v
ol
t
a
ge
w
a
vefor
m
e
s
for
fuz
zy c
on
t
r
o
ller
con
t
ro
l
l
er
Fi
g
u
r
e 20
. Si
mu
l
a
t
i
o
n
vo
lt
ag
e
w
a
vefor
m
e
s
for
sliding m
ode
co
nt
rol
l
e
r
F
i
gur
e 2
1
.
S
i
mula
t
i
on
v
o
lta
ge
waveform
es for
sliding
m
o
d
e
con
t
ro
l
l
er
4.2.
Exp
e
r
i
m
e
nt
al
results
The
e
x
per
i
m
e
nta
l
r
es
ults
t
o
val
i
da
te
t
he
s
im
ulat
i
o
n
t
e
sts
an
d
i
m
p
ro
ve
t
he
r
obus
t
n
ess
o
f
t
he
u
s
e
d
con
t
ro
l
m
e
t
h
o
d
s.
A
s
i
n
s
im
ula
t
io
n,
t
he
e
x
p
erim
en
tal
re
sul
t
s
are
d
is
cu
ss
ed
s
ep
a
r
a
t
ed
i
n
e
a
c
h
p
h
e
n
o
me
n
on
(sag-
s
w
e
ll
a
n
d
h
arm
o
n
i
c
s
vo
l
ta
ge
case
s
)
.
The
e
x
p
e
rime
nt
a
l
t
es
t
has
r
ealize
d
a
n
d
e
l
a
bora
t
ed
i
n
S
m
art
G
r
id
a
nd
R
e
n
ewab
l
e
E
ne
rg
i
e
s
Lab
o
ra
tor
y
(
S
G
RE-La
b
)
in
t
he
U
n
i
versi
t
y
of
T
A
H
R
I
Mo
ha
me
d-Bé
c
h
a
r
-A
lger
i
a
.
The
expe
r
i
me
nta
l
p
r
o
tot
y
pe
inc
l
ude
s
a
dS
P
A
CE
car
d
11
04
p
la
tform
Texa
s
In
st
r
u
me
nt
w
i
t
h
a
T
M
S
32F
24
0
D
S
P
c
o
nnec
t
e
d
w
i
t
h
a
P
C
(P
entium
)
i
n
or
de
r
to
e
na
ble
a
u
t
o
m
a
t
i
c i
m
p
l
e
m
entat
i
on
o
f
th
e
c
o
nt
r
o
l
m
e
th
ods
d
irec
tl
y fro
m
M
a
tla
b
S
i
m
u
l
i
nk
as il
l
us
t
r
ate
d
i
n
F
i
gure
22.
Th
us,
the
tes
t
b
e
n
c
h
c
o
n
s
i
st
s
of
a
v
o
l
ta
ge
i
n
v
e
r
ter,
a
n
ind
u
c
t
o
r,
a
n
in
jec
t
ion
trans
f
o
r
mer,
H
a
l
l
curr
ent/ volt
a
ge sens
o
r
s
, linea
r
load
a
n
d
a
program
me
d sou
r
c
e
.
0
0.
0
5
0.
1
0.
1
5
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
-1
0
-5
0
5
10
(A
)
Sour
c
e
v
ol
t
age
0
0.
0
5
0.
1
0.
1
5
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
-1
0
-5
0
5
10
(B
)
I
n
j
e
c
t
ed
v
ol
t
a
g
e
0
0.
0
5
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
4
5
-1
0
-5
0
5
10
Ti
m
e
(C
)
Load
v
o
l
t
ag
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-20
-10
0
10
20
(A
)
Sour
c
e
v
ol
t
age
0
0.
05
0.
1
0.
1
5
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-10
-5
0
5
10
(B
)
I
n
j
e
c
t
ed
v
o
l
t
age
0
0.
05
0.
1
0.
1
5
0.
2
0.
25
0.
3
0.
3
5
0.
4
0.
45
-20
-10
0
10
20
Ti
m
e
(C
)
Load
v
o
l
t
a
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-1
0
-5
0
5
10
(A
)
S
our
c
e
v
ol
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-1
0
-5
0
5
10
(B
)
I
n
j
e
c
t
e
d
v
ol
t
a
ge
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-2
0
-1
0
0
10
20
Ti
m
e
(C
)
Loa
d
v
o
l
t
a
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-1
5
-1
0
-5
0
5
10
15
(A
)
S
o
u
r
c
e
v
ol
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-1
0
-5
0
5
10
(B
)
I
n
j
e
c
t
ed
v
o
l
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-2
0
-1
0
0
10
20
Ti
m
e
(C
)
Load
v
o
l
t
age
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-10
-5
0
5
10
(A
)
S
o
u
r
c
e
v
o
l
ta
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-10
-5
0
5
10
(B
)
I
n
j
e
ct
e
d
vo
l
t
a
g
e
0
0.
05
0.
1
0.
15
0.
2
0.
25
0.
3
0.
35
0.
4
0.
45
-20
-10
0
10
20
Ti
m
e
(C
)
Loa
d
v
o
l
t
ag
e
0
0.
05
0.
1
0.
15
0.
2
0.
2
5
0.
3
0.
3
5
0.
4
0.
45
-1
5
-1
0
-5
0
5
10
15
(A
)
S
o
u
r
c
e
v
o
l
ta
g
e
0
0.
05
0.
1
0.
1
5
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
4
5
-1
0
-5
0
5
10
(B
)
In
j
e
ct
e
d
vo
l
t
a
g
e
0
0.
05
0.
1
0.
1
5
0.
2
0.
2
5
0.
3
0.
35
0.
4
0.
4
5
-2
0
-1
0
0
10
20
Ti
m
e
(C
)
L
oad
v
ol
t
a
g
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
7
3
1
–
7
43
74
0
F
i
gur
e
2
2
:
Ex
p
e
r
i
m
e
nta
l
t
e
s
t
ban
s
hee
4.
2.
1.
C
a
se
o
f
th
e
h
a
rm
on
ics
v
o
lt
a
g
e
The
PW
M
sw
i
t
c
h
ing
ga
tes
was
selec
t
e
d
1
5
KHz,
whic
h
a
r
e
gener
a
te
d
fr
om
t
he
d
S
P
ACE,
c
a
r
d
i
n
re
a
l
t
i
m
e
ex
p
e
ri
men
t
a
l
t
est
s
.
T
h
u
s
,
a
l
i
n
ea
r
l
o
a
d
w
a
s
s
el
ect
e
d
.
A
s
seen,
t
h
e
AP
FS
h
as
t
he
a
b
ili
ty
t
o
mit
i
g
at
e
vo
l
t
age
har
m
onic
s
p
r
ovi
de
d
by
the
gr
id
a
n
d
s
u
p
p
l
ied
to
t
he
c
on
n
e
c
t
ed
l
oa
d.
T
he
v
o
l
t
a
ge
h
ar
m
o
nic
s
a
r
e
pr
ovi
de
d
b
y
t
h
e
v
o
l
tage
i
n
v
e
r
ter
,
w
hic
h
w
as
c
on
nec
t
e
d
i
n
pa
r
a
ll
e
l
w
it
h
th
e
s
o
ur
c
e
v
o
l
t
a
g
e
.
The
har
m
on
ics
w
a
s
a
ppl
ie
d
d
u
r
i
ng
[
5.
6
s
–
6.
3
s]
,
w
h
er
e
t
h
e
i
n
i
tia
l
TH
D
befor
e
a
p
ply
i
ng
the
co
n
t
r
o
l
w
a
s
a
bou
t
4
6
.
4
%
as
show
n
i
n
F
i
gur
e
24,
26
an
d
2
8
.
F
i
gur
e
2
3
.
Exp
e
r
i
m
e
nta
l
v
o
lta
ge
w
a
v
ef
or
m
e
s
for
PI
c
on
tr
ol
l
e
r
(a)
(b
)
F
i
gur
e
2
4
.
S
p
e
c
tr
al
a
na
lysis
o
f
t
he
s
o
u
r
ce
vo
lt
a
g
e
(
a
)
and
lo
a
d
v
o
l
t
a
ge
(
b)
f
or
P
I
c
ontr
o
ller
F
i
gur
e
2
5
.
Exp
e
r
i
me
nt
a
l
v
o
l
t
a
ge
w
avef
or
m
e
s
for
fuz
z
y
co
n
t
r
o
l
l
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.