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.
1, Mar
ch 20
19,
p
p.
242~
2
5
5
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
1.pp
2
42-
25
5
242
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
Rev
i
ew
o
f th
ree-p
h
ase i
n
verters
co
n
trol for unbalanced load
compensation
Ra
ef
A
bo
el
s
a
u
d
1,
,
A
. Ibrahim
2
,
A
l
exan
d
e
r G. Garg
a
n
e
ev
3
1,
2
D
e
p
a
rtm
e
nt
of El
ectrical P
ow
e
r
and
M
achi
n
es Eng
in
eerin
g
,
Z
agazi
g Univers
ity,
E
gypt
1,
2
,
3
Dep
a
rt
m
e
n
t
o
f
Electri
cal E
ngin
eer
i
n
g
, N
atio
na
l
Research
Tom
s
k
P
o
l
y
t
ech
ni
c U
n
ivers
i
t
y
,
Russ
ia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
May
5
, 2018
Re
vise
d O
c
t
2
9
,
2018
A
c
c
e
pte
d
D
ec 11,
2
0
1
8
In
t
h
e
m
i
c
rog
r
id
s
yst
e
m
s
,
t
h
re
e-ph
ase
in
verter
b
eco
m
e
s
th
e
m
a
in
pow
er
elect
roni
c
i
n
t
e
rfac
e
f
or
r
enewa
b
le
d
istri
b
u
t
ed
e
nerg
y
resou
r
c
e
s
(
D
E
R
s
),
esp
eciall
y
f
or
t
he
i
s
l
an
ded
micro
g
ri
ds
i
n
w
h
i
c
h
the
po
wer
qual
i
t
y
i
s
easily
af
f
ected
b
y
un
b
a
l
a
nced
a
nd
n
on
l
i
n
ear
l
o
a
ds,
t
h
is
i
s
du
e
to
t
he
fa
ct
t
hat
the
vo
lt
age
and
f
r
equ
e
ncy
o
f
t
he
m
icrog
r
id
a
re
n
o
t
s
u
ppo
rted
b
y
th
e
m
ai
n
po
w
e
r
gri
d
but
d
eterm
i
n
e
d
onl
y
by
t
h
e
i
nvert
ers.
T
h
e
refo
re,
t
h
e
co
m
p
e
nsa
t
io
n
o
f
t
he
lo
ad
u
n
b
alan
ces
a
nd
harm
o
n
i
c
s
in
a
ut
on
o
m
o
u
s
m
i
cro
g
rid
inv
e
rters
a
re
get
t
i
n
g
more
a
tt
enti
on
i
n
power
quality
r
esearch
a
reas.
T
h
e
mai
n
p
u
r
po
se
o
f
th
is
p
aper
i
s
to
r
epresen
t
a
n
o
v
erv
i
ew
o
f
t
h
e
co
ntro
l
strateg
i
e
s
of
v
a
r
iou
s
in
vert
ers
f
o
r un
b
a
lan
ced l
oad
com
p
ensatio
n.
K
eyw
ord
s
:
Control
Inver
t
e
r
Loa
d
unba
lanc
e
s
M
i
c
r
ogr
id
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:
R
a
ef Ab
o
el
sau
d
,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
P
o
w
e
r a
nd Mac
h
i
n
e
s
Eng
ineer
i
n
g
,
Za
g
azi
g
Uni
v
ersi
ty
, Eg
yp
t.
Em
ail:
rsahm
e
d@e
n
g.
zu.
e
du.
e
g
1.
I
N
TR
OD
U
C
TI
O
N
To
da
y,
R
ene
w
able
E
ner
gy
S
ource
s
(R
ES
s)
s
uc
h
a
s
p
h
o
t
o
v
o
l
taic
s
o
l
ar
s
ys
t
e
ms,
w
i
nd
t
u
rb
ines,
fue
l
ce
l
l
s,
h
y
d
r
o
po
we
r
turb
ines,
e
t
c
be
com
e
a
p
a
r
t
o
f
f
u
t
ur
e
p
o
wer
g
ener
a
tio
n
sys
t
em
s
[1]
–
[4]
wh
ic
h
a
r
e
use
d
i
n
mic
r
ogri
d
s
a
s
D
istri
b
ut
e
d
E
ne
rgy
Re
so
u
r
ce
s
(D
ERs)
a
nd
t
h
eir
ap
p
l
i
cat
i
o
ns
a
re
p
rom
i
si
ng
a
p
proa
c
h
es
t
o
c
o
pe
w
ith
t
he
e
nv
i
r
onme
n
ta
l
a
n
d
t
e
c
h
n
i
ca
l
pro
b
l
e
m
s
.
Many
r
e
s
e
a
rc
hes
a
r
e
p
r
e
s
ent
e
d
fo
r
d
e
vel
o
pi
ng
m
i
c
ro
gri
d
s
t
o
enha
nc
e
e
n
er
g
y
e
ffic
ienc
y,
i
m
p
r
ove
p
ow
e
r
qua
li
ty,
reduc
e
tra
n
sm
iss
i
o
n
l
osses,
a
nd
decr
ease
con
s
ume
r
price
s
[
5]–[
7].
M
i
cr
o
g
r
i
ds
c
a
n
b
e
c
l
ass
i
f
i
e
d
i
nto
tw
o
m
a
i
n
c
la
ss
i
f
ica
tio
ns
:
gri
d-co
nne
c
t
ed
m
i
c
ro
gri
d
s
and
s
t
an
d-
alo
n
e
m
i
c
r
o
g
ri
ds
[
8].
The
grid-c
onne
c
t
e
d
m
ic
ro
grid
c
a
n
o
p
e
ra
t
e
e
i
t
h
e
r
a
g
r
i
d
-
c
o
n
n
e
c
t
e
d
m
o
d
e
o
r
a
n
i
s
l
a
n
d
i
n
g
mode
[
9].
The
e
f
ficie
n
t
o
p
e
r
ati
o
n
i
s
t
he
k
ey
c
o
n
tr
ol
i
s
s
ue
i
n
t
he
g
r
i
d-co
n
n
e
c
te
d
m
ode
w
he
n
the
ma
i
n
pow
er
gri
d
s
u
ffe
rs
f
ro
m
abnor
ma
l
c
o
nd
iti
o
n
s
the
mi
cr
ogri
d
i
s
c
o
nve
rte
d
t
o
t
he
i
s
l
a
n
d
i
ng
m
o
de
a
nd
the
v
o
lta
ge
a
n
d
fre
que
nc
y
co
n
t
rol
be
c
o
m
e
t
he
m
ain
i
s
s
u
e in
t
hi
s
m
ode.
O
n
t
he
o
t
her
ha
n
d
,
t
h
e
s
t
a
nda
l
o
n
e
m
i
c
rogri
d
i
s
a
l
w
a
ys
opera
tin
g
i
n
t
he
i
sla
n
din
g
m
ode
w
i
t
ho
u
t
c
on
nec
tin
g
w
ith
t
he
m
ai
n
p
o
w
er
s
ys
t
e
m
b
e
cau
se
i
t
i
s
u
su
al
ly
in
sta
l
led
in
t
he r
em
ot
e
a
r
ea
s
such
a
s m
o
u
n
t
a
ino
u
s
are
a
s or
i
sl
a
nd w
i
th
out
t
he
pow
e
r
grid
[10].
The
D
E
Rs
i
nc
l
ude
p
rime
m
ove
rs
a
nd
c
o
n
v
e
r
sion
i
n
ter
f
ac
e
s
.
The
ou
t
p
u
t
o
f
the
prime
move
rs
i
s
D
C
f
o
r
m
(
s
u
c
h
a
s
P
V
s
,
f
u
e
l
c
e
l
l
s
,
b
a
t
t
e
r
i
e
s
,
e
t
c
.
)
o
r
A
C
f
o
r
m
(
s
u
c
h
a
s
w
ind
g
e
nera
tor
s
,
mic
r
ot
urb
i
ne
g
e
n
er
ators)
bu
t
u
s
ua
l
l
y
c
o
nve
r
t
ed
t
o
D
C
f
orm
a
t
firs
t.
T
he
i
n
v
e
r
ters
a
re
u
se
d
a
s
t
h
e
i
n
t
e
r
f
a
c
e
s
b
e
t
w
e
e
n
t
h
e
p
r
i
m
e
m
o
v
e
r
s
and
the
l
o
ca
l
A
C
b
us of
the
m
i
cro
g
rid.
The
m
a
i
n fu
nc
ti
o
n
of t
h
e
i
nve
rt
ers is the
p
ow
er
tra
nsfer
an
d c
o
n
t
r
o
l
.
Th
e
po
wer
q
u
a
l
i
t
y
in
a
u
t
onomo
u
s
m
i
c
ro
g
r
id
s
ca
n
b
e
a
ff
e
c
t
e
d
u
n
d
e
r
u
n
b
a
l
a
n
c
ed
a
nd
nonl
in
ea
r
lo
a
d
s,
th
i
s
i
s
d
u
e
t
o
t
he
f
a
c
t
tha
t
t
h
e
vol
ta
ge
a
nd
fr
eque
nc
y
a
r
e
not
s
u
p
p
o
rte
d
by
the
uti
l
i
t
y
[1
1].
U
nbala
nc
e
d
a
nd
harm
on
ic-di
s
t
o
rted vo
l
ta
ge ca
n
ca
u
se se
v
ere
pro
b
lem
s
on e
q
u
i
pme
n
t
su
c
h
as
vi
b
rat
i
on
,
ov
er-v
ol
t
a
g
e
,
ove
rh
e
a
t
and
s
o
o
n.
T
he
p
r
oble
m
s
of
l
ow
pow
er
qua
l
i
t
y
i
n
m
i
c
r
o
g
ri
ds
c
a
n
be
m
it
iga
t
e
d
b
y
u
s
in
g
a
c
ti
ve
p
ow
e
r
f
i
l
t
ers
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Rev
i
ew
of
t
h
ree-p
h
a
s
e i
n
v
e
rt
e
r
s
c
o
nt
rol
fo
r
un
ba
l
a
n
ced
l
oad
co
mp
en
sa
t
i
on
(Ra
e
f
Abo
e
l
s
a
u
d
)
24
3
(AP
F
s)
w
hic
h
c
ompe
n
s
ate
th
e
l
o
a
d
u
n
b
a
l
an
ce
s
an
d
harm
o
n
ic
s
by
c
o
mp
en
sat
i
ng
t
h
e
n
eg
a
t
iv
e
-
se
qu
ence
a
nd
harm
on
ic
v
olta
ge
a
n
d
c
urrent
s
t
h
r
o
ugh
c
o
u
p
l
i
n
g
trans
f
o
r
me
rs
[
12
].
H
ow
e
v
er,
it
is
u
nec
o
nom
i
c
t
o i
n
s
t
a
l
l
e
x
tra
A
P
F
s
f
or
e
a
c
h
of
t
he
D
E
R
i
n
m
i
cro
g
ri
d.
O
n
t
h
e
othe
r
han
d
,
t
h
e
i
nve
r
t
e
r
f
or
e
ac
h
D
E
R
ca
n
b
e
u
sed
t
o
com
p
en
sate
t
h
e
load-
di
s
t
ort
i
o
n
by m
e
a
n
s of
a
pr
oper
con
t
ro
l [1
3
],
[14].
Th
is
p
a
p
e
r
s
h
o
w
s
a
n
o
v
ervi
ew
o
f
the
c
o
nfi
gura
t
i
o
n
s
a
nd
t
h
e
c
o
nt
r
o
l
strate
gi
e
s
o
f
t
h
r
ee-
p
h
ase
in
verter
s
a
s
a
p
ar
o
f
D
E
Rs
f
or
l
oa
d
un
b
a
la
nce
c
o
m
p
e
n
sat
i
o
n
s.
T
h
e
p
a
p
e
r
i
s
o
rg
an
iz
ed
a
s
fo
llo
w
s.
S
e
c
t
i
on
2
gi
ves
a
c
o
m
p
ara
t
i
v
e
r
e
view
o
f
var
i
o
u
s
inve
rt
er
t
o
p
o
l
ogie
s
u
sed
un
der
s
y
s
t
em
unba
la
nc
i
n
g
c
o
n
d
iti
on
w
h
i
c
h
i
s
fo
l
l
ow
e
d
b
y
a
descr
i
pt
i
on
of
a
va
ila
ble
c
o
n
t
r
o
l
stra
te
g
i
e
s
f
rom
the
u
nba
la
nced
l
oad
c
o
m
p
ensa
t
i
o
n
p
o
i
n
t
o
f
view
i
n
sec
t
i
o
n
3.
C
ompar
a
ti
ve
a
na
l
y
sis
of
c
on
tro
l
s
t
r
uct
u
res
a
nd
som
e
s
ug
ges
t
i
o
ns
f
or
t
he
f
u
t
ur
e
re
se
ar
ches
are
put forw
a
r
d
in S
ecti
o
n 4.
S
om
e
conc
l
u
si
ons a
re
g
ive
n
i
n S
e
c
tio
n 5.
2.
INVERTER TOPOLOG
I
E
S
I
n
t
h
i
s
pa
per,
t
w
o
c
omm
only
use
d
t
w
o
-le
v
e
l
i
n
v
erte
r
t
o
p
o
l
o
g
i
es
are
disc
u
ssed
bas
i
ng
o
n
t
he
n
um
ber
o
f
p
rovi
din
g
wi
re
s.
2.1.
T
h
ree-phase
thr
ee-
wire
inver
t
er
t
opol
og
y
H
o
w
e
ver,
t
he
vol
tage
u
n
b
a
l
a
n
ces
a
nd
har
m
on
ics
c
o
m
p
e
n
s
a
ti
o
n
a
bil
it
y
c
a
n
be
a
c
h
i
e
ve
d
b
y
p
r
o
p
e
r
c
o
nt
rol
o
f
t
h
e
3
l
e
g
V
SI.
Th
is
t
o
pol
ogy
i
s
le
ss
in
t
e
re
sti
n
g
fo
r
t
he
l
ow
-vo
l
t
a
ge
d
istri
b
u
t
ion
n
e
t
w
or
ks
i
n
w
h
ic
h
[1
5]
a
n
e
u
t
r
al
c
on
nec
t
i
o
n
i
s
u
sed
to
a
ll
ow
t
h
e
c
irc
u
la
tio
n
o
f
z
er
o
se
que
nce
c
u
rre
nt
c
omp
o
n
en
ts.
A
lterna
tive
l
y
one
c
a
n
u
se
t
h
e
t
hr
ee-
l
e
g
in
v
e
rte
r
w
i
t
h
a
D
-
Y
transfor
me
r
[1
6]
or
z
i
g
za
g
trans
f
or
me
r
[1
7]
w
hic
h
i
s
hea
vy
an
d
cos
tly
a
n
d
t
h
u
s
not
d
e
s
i
r
ed
i
n
ma
ny app
l
ica
t
i
ons.
The
ze
ro
s
e
q
u
e
nce
curre
n
t
c
om
po
ne
nt
w
ou
ld
b
e
f
ilter
e
d
i
n
t
he
z
i
gzag
t
r
a
nsform
er
o
r
c
i
rculating
in
the
D
w
i
n
d
in
g
of
D
-
Y
t
r
a
nsfo
rm
e
r
a
nd
the
c
o
n
t
ro
l
circ
ui
t
o
f
t
he
i
n
v
erter
w
o
u
l
d
on
l
y
h
a
v
e
t
o
c
om
pe
ns
ate
t
h
e
un
ba
lanc
e
s
fr
o
m
negati
ve
s
e
q
uence
c
u
rren
t
s.
2.2.
T
h
ree-phase
four
-wire
inve
rte
r
t
opolog
y
2.2.
1. C
ap
acitor
mid
p
o
in
t
top
o
lo
gy
Ca
pa
ci
tor
midpo
i
n
t
to
p
o
l
o
gy
,
show
n
i
n
Erro
r!
R
efere
n
ce
s
o
u
rce
n
o
t
fo
und.
,
i
s
t
h
e
s
i
m
p
l
e
s
t
to
pol
o
g
y
w
i
t
h
t
he
l
ea
st
n
um
b
e
r
of
s
w
i
tches.
T
he
n
e
u
tral
i
s
c
o
n
n
e
c
t
ed
t
o
th
e
mid
poi
nt
o
f
th
e
spl
i
t
d
c
-l
in
k
ca
paci
t
o
rs.
A
not
her
a
d
van
t
a
g
e
is
t
ha
t
t
h
is
t
o
p
o
l
ogy
a
c
t
s
a
s
thr
ee
si
n
g
l
e
-
p
h
a
se
h
a
l
f-bri
dge
i
n
v
erter
s
,
thus
e
a
c
h
l
e
g
of
t
h
e
i
nv
ert
e
r
o
f
c
a
n
b
e
c
o
nt
roll
e
d
i
nd
ep
e
n
d
e
n
tly
[
18
].
T
h
e
m
a
i
n
d
isa
dva
n
t
age
o
f
t
hi
s
t
opo
l
o
gy
is
i
n
th
e
expe
ns
i
v
e
an
d
large
c
a
pa
c
i
t
o
r
w
h
ic
h
is
r
equ
i
red
to
ach
ie
ve
e
qua
l
vo
lta
ge
s
har
i
ng
be
tw
e
e
n
t
he
s
p
l
i
t
c
apa
c
i
t
o
rs
[1
9].
A
n
o
t
her
w
e
a
k
n
e
ss
w
i
t
h
thi
s
c
onfig
ur
atio
n
i
s
t
ha
t
u
nde
r
se
vere
u
nb
alance
d
an
d
non
l
i
nea
r
c
o
n
d
i
t
i
o
n
s,
a
large
ne
utra
l
curr
ent f
l
ow
t
h
r
ou
g
h
the ne
u
t
r
al pa
t
h
an
d c
a
u
s
es
a pe
rturbat
i
on i
n
t
he
c
on
tr
ol sc
h
e
m
e
.
F
i
gure
1.
C
a
p
a
c
it
or m
idp
o
i
n
t
to
p
o
l
o
gy
2.2.
2. Th
ree
H-b
rid
g
e
in
ver
t
e
r
Th
is
t
y
p
e
o
f
pow
er
c
on
vert
er
c
onsis
ts
o
f
t
h
ree
si
n
g
le-
pha
se
H
-
b
ri
dg
es
t
o
inte
rfa
c
e
w
it
h
t
h
e
in
div
i
dua
l
ou
t
p
u
t
p
hase
s,
w
hich
a
re
c
ou
ple
d
t
o
t
h
e
l
o
a
d
s
w
ith
a
n
iso
l
a
t
ion
trans
f
or
me
r
a
s
s
how
n
i
n
Err
o
r!
Ref
erence
so
urce
n
o
t
f
o
u
n
d
.
.
Th
i
s
t
opo
logy
h
a
s
b
e
e
n
p
ro
po
sed
fo
r
f
our-wi
r
e
a
c
t
i
v
e
p
o
w
er
f
i
l
t
e
r
i
n
g
[20]
,
[2
1].
Com
p
ar
ed
t
o
the
othe
r
t
o
p
o
l
o
g
i
es,
th
is
t
o
p
o
l
og
y
ha
s
adva
n
tage
s
lik
e
low
e
r
dc-li
n
k
v
o
lta
ge
r
equ
i
rem
e
nt
for
a
g
i
ven
o
u
t
p
u
t
v
o
ltage
,
w
h
ic
h
i
s
h
a
l
f
as
c
ompa
red
to
a
c
a
p
a
ci
t
o
r
m
i
d
poi
n
t
i
n
v
erter
.
A
lt
ho
u
gh
the
hi
g
h
er
numbe
r
of
d
e
v
ice
s
i
s
re
qu
ire
d
i
n
t
h
is
pow
e
r
c
on
ver
t
e
r
,
t
h
e
ou
t
p
u
t
v
ol
ta
ge
o
b
t
a
i
ne
d
is
e
q
u
i
va
le
nt
t
o
t
h
e
t
h
ree
-
leve
l
i
n
ver
t
e
r
r
esulti
n
g
i
n
b
e
tter
harm
on
ic
p
r
o
f
i
le
a
n
d
r
e
duce
d
r
e
quir
e
me
nt
f
or
p
as
sive
f
i
l
t
e
r
s.
H
ig
h
e
r
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
24
2 –
25
5
24
4
re
l
i
a
b
ili
t
y
c
a
n
b
e
ac
hi
ev
e
d
s
in
ce
e
ac
h
p
h
a
se
i
s
ind
e
p
e
nd
en
t
a
n
d
dur
in
g
a
fa
ul
t
in
a
ny
o
n
e
phase
,
the
o
t
h
e
r
tw
o
pha
ses
can
s
til
l
source
pow
e
r
to the
gr
id [
22].
F
i
gure
2.
Thre
e
-H
-
b
ridge i
nv
er
t
e
r
2
.
2
.
3
. Fo
u
r
-
l
e
g
0
202
I
n
t
his
t
o
po
l
o
g
y
,
t
h
e
ne
u
t
r
a
l
li
ne
i
s
c
o
nne
c
t
i
n
g
t
o
t
he
m
i
d
p
o
in
t
of
t
he
a
dd
it
io
na
l
f
o
urt
h
l
e
g
,
as
s
h
o
w
n
in
F
i
gure
3.
T
he
m
a
i
n
ad
va
n
t
age
of
t
h
i
s
c
o
nfi
gurat
i
on
i
s
t
ha
t
i
t
does
no
t
nee
d
t
o
u
til
ize
la
rge
a
nd
e
x
p
e
ns
iv
e
ca
paci
t
o
rs
a
n
d
p
r
o
vide
l
ow
e
r
r
ipple
v
o
lta
ge
i
n
the
D
C
-l
i
n
k
c
a
pa
c
i
t
o
r
[23].
M
o
r
e
over,
t
he
m
odu
la
tio
n
in
d
e
x
is
abo
u
t
%
1
5
h
ighe
r
in
c
om
p
a
ri
son
w
i
th
t
he
s
pl
it
D
C
-l
in
k
[
1
8].
H
o
w
ev
e
r
,
Th
e
ext
r
a
t
w
o
swi
t
ch
es
a
re
r
e
s
ul
ti
n
g
in
h
i
g
her
cost
m
ore
com
p
li
cated
c
on
tro
l
[
2
4
].
T
he
m
a
j
or
d
isa
d
va
n
t
a
g
e
o
f
t
hi
s
to
pol
ogy
i
s
t
h
e
n
e
e
d
f
o
r
isola
t
io
n tra
n
sf
orm
e
r(s)
,
w
hi
c
h
m
ay
n
o
t
b
e d
e
si
r
e
d i
n
m
a
n
y
app
l
ica
t
i
o
ns.
F
i
gur
e 3.
F
our-leg
i
n
v
e
r
ter
top
o
l
o
gy
2.2.
4. Fou
r
l
e
g imp
e
d
a
n
ce sou
r
ce
in
v
e
r
te
rs (Z
S
I)
O
n
e
o
f
t
he
m
ain
l
i
mi
tat
i
o
ns
o
f
t
h
e
V
S
Is
i
s
t
h
a
t
t
he
D
C
in
pu
t
v
o
lta
ge
m
u
s
t
be
g
rea
t
er
t
h
a
n
the
pea
k
val
u
e
o
f
t
he
l
i
n
e-
to-li
n
e
o
u
t
p
u
t
vo
l
t
age
.
S
o
a
dc-dc
b
o
os
t
con
v
erter
is
n
eeded
for
all
DC
p
rime
m
over
s
,
such
as
g
rid-c
o
n
n
ec
t
e
d
ph
o
t
o
v
o
lta
i
c
(
P
V
)
gener
a
t
i
o
n
a
n
d
f
ue
l
c
e
ll
po
w
e
r
c
o
n
v
e
r
si
on,
i
n
w
h
ich
a
low
-
v
o
l
t
a
ge
d
c
source
h
a
s
to b
e
bo
o
st
e
d
t
o
a
de
s
i
r
a
ble ac o
u
t
pu
t v
o
lta
ge
[
2
5
]
.
Mo
r
eover
,
D
ea
d
time
is
r
equ
i
red to pre
v
e
nt the
sh
oo
t
-
t
h
rou
gh
o
f
t
h
e
s
wit
c
h
i
ng
d
evi
c
e
s
o
f
ea
ch
i
nvert
e
r
l
eg
,
t
h
is
r
esul
t
s
i
n
di
stor
tio
n
i
n
o
u
t
p
u
t
vo
lta
ge w
a
v
e
f
o
r
m
[26].
The
s
e
lim
i
t
a
t
i
o
ns
can
b
e
s
o
l
v
e
d
by
the
Z-so
urc
e
i
nve
rter
s
(ZS
I
s
)
[27]
i
n
w
h
i
c
h
t
h
e
dc
-d
c
in
put
s
ta
ge
is
r
ep
lac
e
d
w
i
t
h
a
s
p
ec
i
a
l
L
C
Z
-n
e
t
w
o
rk
a
s
sh
ow
n
i
n
F
ig
ure
4.
T
h
e
Z
S
I
c
a
n
p
rovid
e
o
utp
u
t
A
C
v
olt
a
ge
grea
ter
t
h
a
n
t
h
e
a
v
a
il
a
b
l
e
d
c
l
i
n
k
v
ol
ta
ge
[
28]
.
The
Z-
ne
t
w
ork
ca
n
bo
os
t
the
dc
v
o
l
t
a
ge
b
y
me
ans
of
t
he
sho
o
t-
thro
ug
h
ze
ro
s
ta
t
e
o
f
th
e
in
verte
r
s
w
i
t
c
hi
n
g
c
yc
le
i
n
w
h
i
c
h
s
h
o
r
t
-
c
ir
cui
t
acr
oss
the
dc
lin
k
i
s
c
r
e
a
t
e
d
b
y
clo
s
in
g
tw
o
swit
c
h
es
i
n
one
l
e
g
s
im
ulta
neo
u
s
ly.
In
t
his
ca
se
,
e
nergy
is
t
ra
nsfer
r
ed
t
o
the
Z-
netw
ork
fr
o
m
t
he
ca
paci
t
o
rs to t
h
e
ind
u
c
t
ors,
caus
i
n
g
a
bo
o
sti
n
g in
t
he
dc
v
o
l
t
a
ge.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Rev
i
ew
of
t
h
ree-p
h
a
s
e i
n
v
e
rt
e
r
s
c
o
nt
rol
fo
r
un
ba
l
a
n
ced
l
oad
co
mp
en
sa
t
i
on
(Ra
e
f
Abo
e
l
s
a
u
d
)
24
5
The
ZS
I
has
som
e
s
i
g
n
i
fi
c
a
n
t
dr
aw
bac
k
s
;
n
am
ely
t
h
a
t
i
n
t
h
e
b
o
o
s
t
m
o
d
e
m
a
k
e
s
t
h
e
i
n
p
u
t
c
u
r
r
e
n
t
di
sc
o
n
t
i
n
uo
us
a
nd
t
h
a
t
l
ar
ge
c
apa
c
itor
s
a
re
n
e
e
d
e
d
t
o
s
us
t
a
i
n
a
h
ig
h
vo
lta
ge
.
The
q
u
a
s
i-Z-
sour
ce
i
n
ver
t
e
r
(qZS
Is) is c
ons
i
d
e
r
e
d
a
s a
soluti
on f
o
r th
is d
ra
w
b
acks
[2
9].
(a)
(
b
)
Fi
g
u
r
e 4
.
(a
)
Z
-s
o
u
r
c
e
f
o
u
r-l
eg
i
nv
e
r
t
e
r t
opol
ogy
, (b
) Th
e
q
Z
S
four-le
g
i
n
v
erter
to
po
lo
gy
2.2.
5. F
o
u
r
l
e
g mat
r
ix c
on
ve
r
t
er
(M
C
)
I
n
c
a
s
e
o
f
v
ari
a
bl
e
spe
e
d
ge
n
e
r
a
tion
syste
m
s,
s
uch
a
s
v
ari
a
ble
spe
e
d
d
i
e
s
el-dri
ve
n
or
w
in
d
turb
i
n
e
P
e
rm
anent
M
a
gne
t S
y
n
c
hron
ous
G
e
n
era
t
or
(P
M
S
G
),
the
g
ener
at
or i
s
connect
e
d to
a
bridge r
ec
tifie
r or
a 3-le
g
V
S
I
a
s
f
irst
c
onve
r
tin
g
s
t
age
a
n
d
t
h
e
sec
ond
c
onve
rt
ing
sta
g
e
i
s
perfor
m
e
d
b
y
a
4-le
g
vo
lta
ge
s
o
u
rce
in
ve
rter
(VS
I
)
at
t
he
o
u
t
pu
t
[3
0],
[3
1].
The
4-
l
e
g
V
S
I
is
u
til
ize
d
f
or
p
r
o
vid
i
n
g
a
n
e
u
tra
l
c
on
ne
c
t
i
o
n
to
t
he
l
oa
d.
T
hes
e
tw
o
V
S
Is
a
re
p
rese
n
t
e
d
a
s
7
-
leg
back-
t
o-
ba
ck
t
o
p
o
l
og
y
w
h
ic
h
ca
n
b
e
repla
c
e
d
by
a
4-le
g
ma
t
r
i
x
c
on
ver
t
er
(MC),
as
s
ho
w
n
i
n
F
i
gure
5
[3
2
]
.
This
t
o
p
o
l
ogy
pr
o
v
ide
s
b
i-d
i
re
c
tio
na
l
p
o
w
e
r
flow
a
n
d
c
on
trol
la
bl
e
sinus
o
i
da
l
inp
u
t
/
out
pu
t
c
u
rre
nts
[3
3].
The
a
b
se
nce
o
f
t
h
e
D
C
L
i
nk
ca
pa
ci
tor
is
c
o
n
s
ide
r
ed
a
s
the
m
a
in
adva
n
t
a
g
e
of
M
C
m
a
ki
ng
th
e
MC
m
or
e
robus
t
an
d
rel
i
ab
le
a
n
d
s
av
i
ng
the
spac
e
o
f
M
C
[34]
,
re
sul
t
i
ng
in
a
bet
t
er
o
ve
rall
e
f
f
i
c
i
e
n
c
y
.
Bu
t
the
ma
in
d
isa
d
va
n
t
a
g
e
o
f
M
C
is
t
ha
t
t
h
e
ma
ximum
o
u
tp
ut
v
o
l
t
a
ge
i
s
lim
it
e
d
t
o
a
b
out
8
7
%
o
f
t
h
e
a
v
a
i
l
a
bl
e
in
put
A
C
vo
l
t
a
g
e
.
M
o
re
ov
e
r
,
i
t
i
s
p
a
r
t
i
c
u
larl
y
se
ns
iti
ve
t
o
t
h
e
d
i
s
t
ur
ba
nce
s
o
f
t
h
e
in
put
v
olta
ge
[33]
.
F
i
gure
5.
A
4-l
e
g
m
atrix c
onv
e
r
ter
A
c
o
mp
a
r
i
s
o
n
b
et
we
en
t
h
e
f
ou
r
wi
re
i
n
v
ert
e
r
t
opo
log
i
es
i
s
p
r
e
s
e
n
t
e
d
i
n
Ta
bl
e
1.
I
t
is
g
e
n
era
lly
conc
l
ude
d t
h
at
e
ach top
ol
o
g
y
ha
s it
s ow
n
a
d
van
t
a
g
es a
nd
disa
dva
n
t
a
g
es, a
n
d
the
r
e is n
o t
o
p
o
l
o
gy ca
n
be
use
d
for
all a
p
p
l
ica
t
i
ons.
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
24
2 –
25
5
24
6
Tab
l
e 1.
Comp
a
riso
n of
t
hr
ee-
pha
se
f
o
u
r-w
ire
inver
t
e
r
to
p
o
l
og
i
e
s
C
a
p
ac
itor m
i
dpoint
F
o
u
r
-
le
g
V
S
I
T
h
ree
H-
B
r
idge
Inve
rte
r
Fo
u
r
le
g
ZS
I
F
o
u
r
leg
M
C
Pow
e
r c
onve
rsion
D
C
-AC
D
C
-
A
C
D
C
-A
C
D
C
-A
C
A
C
-A
C
I
s
ol
a
tion
tra
n
sf
orm
e
r
no
n
o
n
o
no
N
o
.
o
f
sw
itc
h
e
d
6
8
12
8
12
bidi
r
e
c
tiona
l
Inp
u
t
ca
p
a
c
itor s
i
ze
V
e
r
y
hi
gh
m
e
diu
m
l
ow
h
i
gh
N
o
n
ee
d
output
v
olt
a
g
e
a
s a
pe
rce
n
ta
g
e
o
f
inpu
t
volt
a
ge
<
50%
o
f
input
D
C
Volta
g
e
<
60%
o
f
input
DC volta
g
e
<
10
0%
t
he
i
nput
D
C
volt
a
g
e
C
a
n
be
g
ra
te
r
o
r
le
ss
t
h
a
n
i
nput
DC
Vo
l
t
a
g
e
<
87
%
of
i
n
put
A
C
volta
ge
D
e
sign c
o
m
p
l
e
xi
t
y
l
ow
h
igh
m
e
diu
m
h
i
gh
high
Si
ze
/wi
ght
m
ediu
m
low
hi
gh
m
e
diu
m
l
o
w
A
pplic
a
t
i
on i
n
D
ER
Se
c
ond
st
a
g
e
c
onve
rt
e
r
f
or
a
ll
ty
p
e
s of
DER
S
e
c
ond
st
a
g
e
c
onve
rt
e
r
f
or
a
ll
ty
p
e
s of DER
Se
c
ond
st
a
g
e
c
o
nve
rt
e
r
f
or
a
l
l
ty
p
e
s of
DER
Si
n
g
l
e s
t
ag
e
c
onve
r
t
e
r
f
or
P
V
an
d
f
u
el
c
el
l
DE
R
Si
n
g
l
e s
t
ag
e
c
onve
r
t
e
r
for
V
a
r
i
ab
l
e
sp
e
e
d
d
i
e
se
l
a
nd
w
i
nd
DER
3.
CONT
ROL S
T
RATEG
IES
UNDER
UNBALANCE LOAD
CONDIT
I
ON
The
a
v
ai
la
b
l
e
c
o
n
t
r
o
l
s
t
rate
gi
e
s
o
f
thr
ee-
pha
se
t
wo-
l
eve
l
i
n
v
er
t
e
rs
f
o
r
c
omp
e
n
s
at
i
n
g
lo
ad
unb
al
an
ce
in m
i
c
ro
gri
d
s a
r
e
i
l
l
u
st
r
a
ted
in
t
he
fol
low
i
n
g
sub
sect
i
o
n
s
.
3.1.
S
ymme
tric
a
l
c
omp
o
n
e
n
t
b
ased
c
ontr
ol
s
trat
egy
S
y
mm
etric
a
l
se
que
nce
dec
o
m
pos
i
t
i
on
(S
S
D
)
is
u
se
d
m
a
in
l
y
i
n
p
o
w
e
r
elec
t
r
i
c
f
au
l
t
a
nal
y
s
i
s
[
35].
The
S
S
D
i
s
a
ble
t
o
r
epre
se
nt
t
he
u
nba
la
n
c
e
d
t
hre
e
-p
ha
se
s
i
gna
l
(
v
o
lta
ge/c
urre
nt)
as
a
s
um
o
f
p
o
s
i
tive
,
nega
t
i
ve
a
n
d
z
er
o
se
q
u
ence
s.
T
he
p
os
i
tive
and
ne
ga
ti
ve
c
ompo
ne
n
t
s
a
r
e
t
h
r
e
e
-
p
h
a
s
e
s
y
m
m
e
t
r
i
c
a
l
s
i
g
n
a
l
s
,
wher
eas
t
he
z
er
o
seq
u
enc
e
i
s
a
sin
g
l
e-p
h
a
s
e
one.
In
t
e
r
ms
o
f
co
n
t
rol
l
e
r
de
sign,
t
he
c
on
ve
nti
ona
l
c
ontr
o
l
st
r
a
te
gy
uses
v
ol
t
a
ge
a
n
d
c
urre
n
t
d
q
0
-c
omp
o
n
en
t
i
n
a
r
e
f
er
ence
f
r
ame
ro
t
a
t
i
n
g
at
t
h
e
f
un
d
a
me
nt
al
f
requ
e
n
cy
(ω
).
If
the
loa
d
i
s
ba
lanc
e
d
,
t
h
e
d-
a
n
d
q
-c
om
po
ne
nt
s
are
dc
q
u
ant
i
t
i
e
s
and
t
h
e
0
-
co
mp
on
en
t
i
s
a
bsen
t
.
U
n
d
e
r
u
n
b
a
l
a
n
ced
c
on
dit
i
on
s,
t
h
e
n
eg
a
tiv
e
se
qu
ence
a
p
p
e
a
r
s
as
a
d
i
s
tu
rba
n
ce
i
n
d
a
n
d
q
c
ompo
ne
nt
a
t
a
fre
que
nc
y
of
2
ω.
T
his
is
b
ec
au
se
t
he
d
q
0
r
efe
r
enc
e
fra
m
e
i
s
r
o
t
at
i
n
g
i
n
t
he
p
osi
t
i
v
e
di
r
e
c
t
i
o
n
a
t
a
n
a
n
g
u
l
a
r
f
re
q
u
e
n
cy
o
f
ω
,
w
here
as
t
he
n
e
g
a
t
ive
se
q
u
e
nce
dist
urba
n
c
e
rota
te
s
a
t
a
n
an
gu
l
a
r
f
r
e
q
u
e
n
c
y
o
f
ω
i
n
t
h
e
o
p
p
o
s
i
t
e
d
i
r
e
c
t
i
o
n
.
In
t
h
i
s
c
a
se,
the
ze
ro
s
e
q
u
e
nce
ap
pe
ars
at
a
f
r
e
quenc
y
of
ω
i
n
t
h
e
0
-
com
p
o
n
en
t,
b
eca
use
t
h
e
ze
ro-a
x
i
s
is
s
ta
tio
na
ry.
I
n
[
36],
a
c
ontro
l
s
t
ra
t
e
gy
b
a
sed
o
n
s
ym
me
t
r
i
c
a
l
s
e
q
ue
nc
e
de
c
o
m
p
o
s
itio
n
i
s
p
ro
po
sed
t
o
c
ont
rol
fo
ur-
l
e
g
i
nver
t
er
.
The
pro
pos
ed
c
on
tro
l
m
et
ho
d
i
nde
pe
nde
nt
l
y
r
e
g
u
la
tes
t
h
e
t
h
r
ee
se
que
nce
s
c
om
po
ne
nt
s
o
f
loa
d
v
o
l
ta
ge
s
a
nd
c
u
rren
t
s.
E
a
c
h
c
o
m
p
o
n
e
n
t
is
c
o
n
tro
l
l
e
d
in
o
w
n
dq
re
fe
re
nce
fram
a
s
dc
s
i
gna
l
[
37].
F
i
rstl
y,
t
h
e
sy
mmet
ri
c
a
l
co
mp
on
en
t
s
o
f
th
e
u
n
b
a
l
a
n
c
ed
v
o
l
t
a
g
e
s
a
n
d
c
u
rre
nt
s
a
r
e
d
e
riv
e
d
in
t
hre
e
c
h
a
nn
e
l
s
fo
r
each
com
p
o
n
e
n
t
w
h
ic
h
is
t
he
n
tra
n
sfer
red
i
n
to
t
he
dq
refere
nc
e
fra
m
e
s
o
t
h
at
t
he
c
o
n
t
r
ol
v
ari
a
b
l
es
c
an
b
e
a
d
j
u
st
ed
in
de
pen
d
e
n
t
l
y
i
n
thre
e
differe
nt
s
e
q
u
e
nc
e
c
o
m
p
o
n
e
n
ts
a
s
show
n
i
n
F
i
g
u
r
e
6.
T
he
f
irst
c
ha
nne
l
co
ntr
o
ls
t
he
pos
it
ive
se
que
nc
e
of
v
o
lta
ges
an
d
c
u
r
r
ents
i
n
a
p
o
s
i
t
i
ve
d
q
re
f
.
fram
e
,
w
h
ich
ro
tate
s
c
o
u
n
terc
loc
k
w
i
se,
w
h
i
l
e
the
se
co
n
d
c
ha
nne
l
r
e
g
u
l
a
t
e
s
t
he
n
e
g
a
t
i
v
e
se
que
nce
of
v
o
l
t
a
ge
s
a
nd
c
u
rr
ent
s
i
n
a
ne
gat
i
v
e
refere
nce
fra
m
e
,
w
h
ic
h
ro
ta
te
s
cl
ockw
ise
a
t
t
he
s
am
e
a
n
gula
r
f
r
e
que
nc
y.
T
he
t
hir
d
c
h
an
ne
l
a
l
s
o
c
ompe
n
s
a
t
es
t
he
z
ero
seq
u
enc
e
vol
ta
ge
s
a
nd
c
u
rr
ent
s
i
n
a
ne
ga
t
i
ve
r
efe
r
e
n
ce
fram
e
,
t
his
c
a
n
b
e
d
one
a
f
t
e
r
a
pp
ly
ing
s
p
a
t
i
a
ll
y
di
sp
lac
e
d
a
t
1
20
deg.
f
or
t
he
z
ero
seq
u
e
n
c
e
s
eque
nc
e
[38].
F
i
na
l
l
y,
t
he
c
onve
n
t
i
o
nal
P
I
r
egu
l
a
t
ors
a
r
e
a
p
p
l
ied
to re
g
ul
a
t
e
t
h
e
vo
ltage
and
c
urre
n
t
l
oo
ps.
The
i
d
ea
o
f t
h
e
SS
D
ha
s bee
n
de
v
e
l
o
p
e
d
u
si
n
g
t
he com
b
i
na
tio
n o
f
s
yn
c
h
ron
o
u
s
a
nd
s
t
a
t
i
on
a
r
y
f
r
a
m
e
con
t
ro
l
stra
te
g
y
f
or
a
f
o
u
r-
l
e
g
ma
t
r
ix
c
on
ve
rter
i
n
[3
2].
The
s
ug
g
e
st
ed
s
ch
eme
i
s
p
a
r
t
l
y
si
mi
l
a
r
t
o
t
he
pro
pose
d
c
o
n
t
rol
i
n
a
g
r
i
d-
in
t
e
r
f
ac
i
n
g
p
o
w
e
r
qua
lit
y
com
p
e
n
sa
to
r
us
i
ng
t
h
re
e-pha
se
f
o
u
r-le
g
V
S
I
i
n
[4
0
]
a
nd
three
le
g
V
S
I
in
[
41].
I
n
t
he
p
ro
pose
d
c
o
n
tro
l
s
trateg
y,
t
he
p
o
s
i
tive
a
n
d
ne
ga
t
i
ve
c
o
m
pone
n
t
s
of
t
he
l
oa
d
vo
lta
ge
a
r
e
r
e
gula
t
e
d
w
it
ho
ut
t
he
n
ee
d
o
f
c
a
l
c
u
la
t
i
o
n
t
he
s
ymm
e
tric
a
l
c
om
po
ne
n
t
d
e
c
om
p
o
s
iti
o
n
.
Tw
o
sy
nc
h
r
ono
us
r
e
f
e
r
en
c
e
f
rames
a
r
e
u
s
ed
,
on
e
i
s
r
o
t
a
t
i
n
g
c
l
ock
w
i
s
e
a
n
d
th
e
ot
h
e
r
i
s
r
ot
a
t
in
g
c
oun
t
e
rcl
o
ck
wi
se
i
n
o
rd
er
t
o
con
t
ro
l
th
e
p
o
s
itiv
e
a
n
d
n
e
g
a
t
i
v
e
se
qu
e
n
c
e
re
sp
ec
ti
ve
ly.
T
w
o
n
o
tc
h
fi
lter
s
a
r
e
u
se
d
t
o
f
il
te
r
the
nega
t
i
ve
s
e
que
nc
e
vo
lta
ge
s
fr
om
t
he
pos
it
iv
e
seq
u
e
n
c
e
s
ync
hro
n
o
u
s
r
ot
a
t
in
g
f
r
ame
and
th
e
p
o
s
it
i
v
e
se
qu
en
c
e
vo
lta
ge
s
fr
om
t
he
n
e
g
a
t
i
v
e
se
que
nce
fr
am
e
as
s
h
o
w
n
i
n
F
i
gure
7.
T
he
z
e
r
o
com
p
o
n
en
t
o
f
t
he
l
o
a
d
v
o
l
t
age
is
regu
la
t
e
d
by
a
sepa
rate
r
eso
n
a
nt
c
o
n
t
r
olle
r
(RC)
i
n
the
s
t
a
t
io
n
ary
fr
am
e;
w
hile
t
w
o
P
I
c
o
mpe
n
sa
tor
s
a
re
u
se
d
for
pos
it
ive
an
d ne
ga
t
i
ve
se
q
ue
nce
v
o
l
t
a
ge
re
g
u
l
a
tio
n.
I
n
[
39],
fo
ur-leg
V
S
I
i
s
em
p
l
oye
d
as
l
oad
u
nba
la
n
c
e
c
o
mp
e
n
sa
t
o
r
(
LUC
)
.
Th
e
co
nt
rol
co
mp
e
n
sa
tes
the
un
ba
lanc
in
g
c
u
rre
nts
of
t
he
s
ta
nda
l
one
m
icr
ogri
d
b
y
i
n
j
e
c
t
i
ng
t
he
u
nba
la
nc
e
c
u
r
r
ent
r
e
q
u
ire
d
f
or
t
he
loa
d
s. Eac
h
ph
ase curr
en
t of
t
h
e
m
icro
gr
id
i
m
g_a
, i
mg
_b
, and
i
mg
_c
is tra
nsfor
m
e
d
i
nt
o a
ro
ta
ti
n
g
d–
q
-0
co
o
r
di
nate
i
m
g_d
,
i
mg_
q
,
an
d
i
mg
_0
.
In
t
hi
s
case
,
t
he
f
u
nda
me
nta
l
p
os
iti
ve
s
e
q
u
e
nce
c
u
rre
nt
h
a
s
D
C
v
a
lu
e
whil
e
th
e
un
ba
lanc
e
c
u
rre
nt
c
om
p
o
n
en
t
s
,
posi
t
i
v
e
a
n
d
ne
ga
t
i
ve
c
urre
nt
s
eq
ue
nc
es,
h
a
ve
a
c
va
l
u
e
s
a
nd
ar
e
co
nside
r
ed
a
s
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
Revie
w
o
f
thre
e-
ph
ase
inve
rte
rs c
o
n
t
ro
l f
o
r u
n
b
a
l
a
n
ce
d lo
a
d
com
p
e
n
s
a
t
i
o
n (
R
aef Ab
oe
ls
au
d)
24
7
ha
r
m
onic
s
i
n
d
q
r
efe
r
enc
e
f
r
a
m
e
w
hich
a
r
e
e
xtr
a
c
t
ed
b
y
usin
g
lo
w
pa
ss
f
ilter
(
L
PF
)
as
s
how
n
i
n
F
i
gur
e
8.
I
n
the
pr
op
ose
d
c
on
tr
o
l
s
ys
t
e
m,
thr
e
e
P
I
contr
o
ll
e
r
s
a
r
e
used
t
o
r
egu
l
ate
d
–
q
-
0
c
ur
r
e
nt
c
om
p
one
n
t
s.
F
i
gur
e
6.
C
o
n
t
r
ol
s
t
r
ateg
y
bas
e
d
on
s
y
mm
etric
a
l
com
p
o
n
e
n
t
s
in
[3
6
]
F
i
gur
e
7.
T
he
p
r
o
pose
d
c
o
n
tr
ol
s
tr
ateg
y
f
o
r
4-
le
g
M
C
i
n
[
3
2]
F
i
gur
e
8.
T
he
p
r
o
pose
d
u
nba
l
a
nc
e
com
p
e
n
sa
tor
in
[
3
9
]
(
a
)
c
o
n
t
r
o
l
a
l
go
r
i
t
h
m
,
(
b)
C
ur
r
e
nt
c
on
t
r
o
ller
P
o
w
e
r
qual
ity
i
mpr
o
vem
e
nt
t
hr
o
u
g
h
t
hr
ee
-
l
eg
V
S
I
b
a
s
ed
b
at
ter
y
i
nv
e
r
t
e
r
s
i
n
mi
cro
g
r
i
d
s
i
s
p
ropo
se
d
i
n
[
42
].
T
h
e
p
ro
po
se
d
c
ont
rol
st
rat
e
gy
d
e
v
e
l
o
p
s
a
n
Unb
a
la
n
c
e
d
C
ur
r
e
n
t
(
U
C
)
a
n
d
H
a
r
m
onic
Cur
r
e
nt
(
H
C
)
c
o
mpe
n
sa
t
i
on
us
in
g
bat
t
e
r
y
i
nver
t
er
s
base
d
on
t
h
e
s
t
r
u
ct
ur
e
of
Pr
o
port
i
o
n
a
l
-
R
e
s
o
n
a
n
ce
(
P
R)
c
ontr
o
l
l
er
i
n
sta
t
i
o
nary
r
efe
r
enc
e
f
ra
m
e
[
4
3
]
.
For
m
i
cr
ogrids,
t
he
b
at
terie
s
c
a
n
be
u
se
d
no
t
o
n
l
y
f
or
p
e
a
k
s
hap
i
ng
b
u
t
a
ls
o
f
o
r
p
o
w
e
r
qua
lit
y
im
pr
o
v
em
ent.
T
he
t
r
a
n
s
fe
r
f
u
nc
tio
n
o
f
a
P
R
co
n
t
r
o
l
l
er
i
s
sh
ow
n
in F
i
gur
e
9,
w
her
e
K
p
is
th
e
pr
opor
ti
ona
l
g
a
in
a
n
d
K
ih
i
s
t
h
e
r
e
so
na
nce
g
a
i
n
f
or
eac
h
ha
r
m
onic
or
de
r
.
T
he
c
on
tr
o
l
s
tr
uc
tur
e
i
s
a
l
so
s
how
n
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
ow
E
l
e
c
&
Dr
i
S
y
st,
Vol.
10,
N
o.
1
,
Mar
c
h
2
0
1
9
:
24
2
–
255
24
8
in
F
i
g
ur
e
9,
w
her
e
o
nly
fir
s
t
or
der
an
d
sec
ond
or
der
c
o
n
t
r
o
l
l
e
r
a
re
d
ra
wn
.
T
h
e
ref
e
re
n
c
e
cu
rre
n
t
s
o
f
the
pr
opose
d
c
on
t
r
ol
(
i
α_
r
e
f
and
i
β_
re
f
)
a
r
e
the
ne
gat
i
v
e
seq
u
e
n
c
e
a
nd
ha
r
m
on
ic
c
ur
r
e
nts
of
t
he
m
icr
o
g
ri
d
i
n
α
β
r
e
f
e
re
n
c
e
f
r
ame.
A
s
i
g
n
a
l
c
ond
iti
oni
ng
u
nit
is
u
sed
t
o
e
x
t
ra
c
t
t
h
ese
s
c
ur
r
e
nt
s
o
f
t
he
m
icr
ogr
id
m
a
i
n
c
u
r
r
e
nt
a
s
show
n
i
n
F
i
gur
e
9.
F
i
gur
e
9.
T
he
p
r
o
pose
d
c
o
n
tr
ol
s
tr
ate
g
y
i
n
[
42]
(
a
)
P
R
cont
r
o
l
l
e
r
s
t
r
u
c
tu
re
,
(b
)
si
g
n
a
l
co
nd
i
t
i
oni
ng
uni
t
I
n
[
1
4
]
,
P
I
and
m
u
lt
i-
Res
on
ant
c
o
n
t
r
o
l
l
er
a
r
e
c
om
bi
ne
d
i
n
a
s
i
n
g
l
e
sy
nchr
on
ous
r
efe
r
enc
e
f
r
a
m
e
(
S
RF)
a
nd
us
ed
f
or
b
o
t
h
t
h
e
vo
lta
ge
u
n
b
a
l
a
nce
a
n
d
ha
r
m
onic
c
o
mp
e
n
sa
tio
n.
T
he
f
un
dam
e
n
t
a
l
p
osit
i
v
e
se
que
nce
(
F
PS
)
volt
a
ge
is
c
o
nver
t
ed
to ‘
D
C
’
un
d
er
t
he f
u
n
d
am
ent
a
l
p
os
itive
S
R
F
.
The fun
dam
e
n
t
a
l
n
e
g
at
i
v
e
-
se
que
nce
vo
l
t
a
g
e
i
s
2
f
0
(
f
0
i
s
the
f
unda
me
nta
l
f
r
e
q
u
e
n
c
y
)
‘
A
C
’
c
om
po
ne
nt
u
n
d
e
r
t
he
s
a
m
e
S
R
F.
The
typ
i
ca
l
vo
l
t
age
ha
r
m
onic
s
s
uc
h
a
s
t
he
5
th,
7
t
h,
1
1t
h
an
d
so
o
n
ar
e
sti
l
l
‘
A
C’
c
om
po
nen
t
s
u
nde
r
t
h
e
f
u
n
d
a
m
enta
l
pos
i
tive
S
R
F
.
T
he
d
eta
iled
tr
ans
f
or
me
d
r
e
sul
t
s
of
eac
h
c
o
mp
o
n
en
t
f
r
o
m
‘
a
bc’
coor
di
na
ti
o
n
t
o
t
h
e
f
u
nda
me
nta
l
pos
it
ive
S
R
F
ar
e
gi
ven
in
T
a
b
l
e
2
,
w
h
er
e
‘
+
’
and
‘
−
’
m
eans
positive
-
s
eque
nce
a
n
d
ne
gat
i
ve
-
se
que
nce
,
r
esp
e
ctive
l
y
.
T
he
P
I
contr
o
l
l
e
r
i
s
r
e
sp
ons
ible
t
o
r
e
g
u
l
a
t
e
t
h
e
F
P
S
w
h
i
c
h
i
s
i
n
‘
D
C’
c
om
po
ne
nt.
O
n
the
ot
h
e
r
han
d
,
t
he
r
e
s
onan
t
c
on
tr
o
l
ler
s
a
r
e
u
sed
t
o
a
c
h
i
e
ve
t
h
e
zero
-err
o
r
t
rack
in
g
on
th
e
2f
0
,
6
f
0
a
n
d
1
2
f
0
‘
A
C
’
c
om
pone
nt
s.
Tab
l
e
2.
C
on
ve
r
t
e
d
r
e
s
ul
ts
f
r
o
m
‘
a
bc
’
c
oor
di
nat
i
on
t
o
t
he
f
u
nda
me
nt
al
po
s
it
i
v
e SR
F
1
s
t
1
s
t
5th
7th
11th
13th
17th
...
In
a
bc c
oor
di
na
tion
+
-
-
+
-
+
-
.
.
.
In
positi
ve
f
0
SRF
0
2f
0
6
f
0
6
f
0
12f
0
12f
0
18f
0
...
3.
2.
P
er
p
h
ase
-
b
a
se
d
con
t
rol
st
rat
e
gy
The
pe
r
-
p
hase
c
on
t
r
o
l
s
tr
a
t
e
gy
c
a
n
b
e
on
l
y
a
p
p
l
i
e
d
o
n
the
thr
e
e
p
h
a
s
e
f
o
u
r
w
i
r
e
i
n
v
e
r
t
e
r
s
w
h
i
c
h
pr
ovi
de a
n
e
u
tr
a
l
c
on
nec
tio
n.
H
e
n
ce,
e
ac
h
p
h
ase
vo
l
t
a
g
e a
n
d
c
u
r
r
e
n
t
ca
n
be c
o
n
t
r
o
l
l
ed
i
nde
pe
nde
n
tly.
I
n
[
44]
,
a
reso
n
a
nt-filter
b
a
nk
i
n
comb
in
at
ion
w
i
th
a
P
ro
po
rtio
nal
(P
)
c
on
tr
ol
le
r
is
u
ti
lize
d
t
o
r
e
gul
a
t
e
eac
h
phas
e
vo
l
t
age
of
a
n
a
u
t
o
nom
o
u
s
thr
e
e-
pha
se
f
o
u
r
-
l
e
g
i
n
ver
t
er
[
4
5
]
,
as
s
how
n
i
n
F
igur
e
10.
A
nove
l
m
i
ni
m
u
m
l
o
s
s
di
sco
n
t
i
nuo
us
P
WM
m
et
ho
d
ba
se
d
o
n
t
he
C
a
r
r
i
er
-
b
ased
3
-
D
S
pa
ce
V
e
c
t
o
r
P
W
M
i
s
u
s
e
d
.
A
c
a
p
a
c
i
t
o
r
c
u
r
r
e
n
t
fe
e
d
b
ack
l
oop
i
s
ad
de
d
t
o
t
he
c
o
n
t
r
ol
s
ch
eme
to
p
ro
v
i
d
e
a
c
t
i
v
e
dam
p
i
n
g.
F
ur
t
h
er
mor
e
,
a vo
lta
ge
f
ee
d
-
f
o
r
w
a
r
d
lo
o
p
i
s
a
dde
d
to
t
he
f
i
l
t
er
f
o
r
a
ccur
a
tel
y
t
r
a
c
k
i
ng.
T
h
i
s
c
o
n
t
r
o
l
s
tr
ate
g
y
i
s
a
lso
use
d
i
n
[
4
6]
w
i
t
h
o
u
t
t
he
ha
r
m
onic
fr
e
q
uenc
y
r
e
so
nan
t
f
il
ter
con
t
r
o
l
l
e
r
s.
3
D
space
v
ec
tor
P
WM
i
n
abc
co
o
r
di
nat
i
on
i
s
u
se
d
as
PW
M
t
ech
ni
q
u
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Rev
i
ew
of
t
h
ree-p
h
a
s
e i
n
v
e
rt
e
r
s
c
o
nt
rol
fo
r
un
ba
l
a
n
ced
l
oad
co
mp
en
sa
t
i
on
(Ra
e
f
Abo
e
l
s
a
u
d
)
24
9
F
i
gure
1
0
.
Blo
c
k dia
g
r
a
m
of
t
he c
on
t
r
o
l
s
yst
e
m
p
r
esented
b
y
[44
]
The
w
o
rk
i
n
[31]
p
rese
n
t
s
a
re
pet
i
t
i
ve
c
o
n
t
rol
tech
n
i
q
u
e
of
a
f
o
u
r-
l
e
g
m
a
trix
c
onve
rt
er
t
o
m
iti
ga
te
the
t
o
ta
l
ha
rmon
i
c
d
is
tor
tio
n
(
T
H
D
)
in
t
he
l
oa
d
vo
l
t
a
g
es
i
n
cas
e
o
f
n
o
n
linea
r
an
d
un
ba
la
n
c
e
d
l
oa
ds.
I
n
t
he
pro
pose
d
c
on
tr
ol
s
tra
t
e
g
y,
t
he
r
epe
tit
i
v
e
co
n
t
rol
l
er
i
s
a
dde
d
t
o
th
e
c
onv
e
n
tio
n
a
l
co
nt
roll
er
C
(z
),
w
h
i
ch
c
a
n
b
e
the
P
R
c
o
n
tr
ol
ler,
a
s
show
n
i
n
F
i
g
ure
1
1
w
here
t
he
r
epe
t
i
tive
c
ontro
l
l
er
(
RC(
z
))
i
s
use
d
f
or
l
oa
d
har
m
on
i
c
com
p
en
sat
i
on,
w
here
as
t
he
c
o
nve
n
tio
na
l
c
o
n
t
ro
ller
(C(z)
)
i
s
use
d
to pro
vid
e
t
he bala
n
c
e
d
l
o
a
d
v
o
l
tage fo
r
t
he
un
ba
lanc
e
d
l
oa
d.
P
l
a
nt
pha
ses
a,
b
,
and c
r
e
prese
n
t
d
i
ffe
r
en
t
s
i
n
g
l
e
ph
as
e lo
a
d
s co
nn
e
c
t
e
d
t
o
t
h
e
i
nv
ert
e
r.
I
n
[48]
, t
h
e
h
y
s
t
e
r
esis v
ol
ta
ge
r
egu
l
a
t
or is
em
pl
o
y
ed
t
o c
o
n
t
r
o
l t
h
e ou
t
p
u
t
v
ol
t
a
ges of 4-le
g
V
S
I
. Thi
s
st
r
a
te
gy
uses
m
easure
s
t
he
d
i
f
fer
e
nce
s
b
e
t
w
een
t
he
f
ee
d
b
a
c
k
v
o
l
ta
ge
a
nd
t
h
e
re
fer
e
nc
e
val
u
e
;
a
fter
w
a
rd,
this
di
ffe
re
nce
is
s
e
n
t
t
o
t
he
hyst
e
r
e
sis
c
o
m
p
en
sa
tor
as
d
e
p
ic
t
e
d
i
n
F
ig
ure
1
2
.
Base
d
o
n
t
h
i
s
di
ffe
r
ence
a
nd
t
h
e
w
i
d
t
h
of
t
he
h
yster
e
sis
l
o
o
p
t
he
s
ta
te
o
f
sw
itc
hes
c
a
n
b
e
c
h
a
n
g
e
d
.
Thi
s
m
etho
d
i
s
e
asi
e
r
t
o
i
m
p
lem
e
nt
t
ha
n
c
o
nv
en
tio
n
a
l
c
o
nt
rol
l
e
rs
w
it
h
ca
rri
e
r-b
as
ed
m
o
d
u
l
a
t
i
o
n
app
r
o
ach
e
s
.
Neve
rt
h
e
l
e
s
s
,
it
i
s
c
h
a
r
ac
t
e
ri
zed
b
y
th
e
li
m
i
ta
t
i
o
n
o
f a
no
n-c
o
nstan
t
s
w
itc
hi
n
g
frequ
e
n
cy,
irregu
la
r sw
i
tc
h
i
n
g
an
d
s
low
dyn
am
i
c
re
s
po
nse
[4
9]
.
F
i
gure
1
1
. (
a
)
The
re
pet
iti
ve
c
on
tro
l
sys
tem
(b)
T
hree
pha
se
c
o
n
tro
l
s
ys
tem
incl
u
d
i
n
g the
repe
t
i
t
i
ve
c
o
nt
rol
to
pol
o
gy
Fi
g
u
r
e
12
. Vo
l
t
ag
e h
y
st
e
r
esi
s
c
o
n
t
r
ol
sc
h
eme
f
o
r
t
h
e
th
ree
-
p
h
ase fo
u
r-l
eg
i
nv
erte
r
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, Vol. 10,
N
o.
1, Mar
c
h 2
0
1
9
:
24
2 –
25
5
25
0
A
u
t
hors
i
n
[
47
]
sugge
st
a
n
im
prove
d
per-p
ha
se
c
o
n
tr
ol
a
ppr
oa
ch
fo
r
a
fo
u
r-l
eg
a
u
t
onomo
u
s
V
SI
t
o
regu
la
t
e
o
u
t
pu
t
vo
lta
ge
u
n
d
e
r
h
i
gh
unba
lan
c
e
d
l
oa
d
c
o
n
d
i
t
i
ons
[
4
7
].
T
his
con
t
ro
l
l
e
r
i
s
i
m
plem
en
te
d
i
n
t
hre
e
di
ffe
re
nt
c
ha
nn
els
i
n
t
h
e
d
q
fr
am
e.
T
he
s
truc
ture
o
f
the
s
u
g
g
es
ted
c
o
ntro
l
sche
me
f
or
t
he
a
-phase
i
s
pr
e
s
en
ted
in
F
igur
e.
13.
I
n
eac
h
p
h
a
s
e
,
t
he
c
on
t
r
o
l
s
y
s
te
m
cons
ists
o
f
vo
l
t
age
a
n
d
curr
ent
l
o
ops
a
nd
a
dd
i
t
i
o
na
l
fe
ed-
forw
a
r
d
pa
th
s
w
h
i
c
h
are
e
m
plo
y
e
d
t
o
dec
o
u
p
le
t
he
d
a
nd
q
chan
ne
l
s
f
r
o
m
ea
ch
o
ther.
T
h
e
dq
c
o
mpo
n
e
n
t
s
o
f
ea
ch
o
u
t
p
u
t
phase
v
ol
ta
ge
c
a
n
b
e
de
term
in
ed
b
y
a
p
p
l
yi
n
g
the
P
a
rk
t
r
a
nsform
ati
o
n,
a
ft
e
r
c
re
ati
ng
t
h
e
p
s
eu
do-
tw
o-p
h
ase
syst
e
m
. The
PI c
ontro
ller
s
a
re
e
mpl
o
yed
in
t
he v
ol
ta
g
e
and
c
u
rre
nt
l
o
o
p
s
.
F
i
gure
.
13. S
che
m
a
t
ic
d
iagra
m
o
f the
per-
phase
c
o
n
tro
l
str
ateg
y
p
ropo
se
d i
n
[
47
]
3.3.
A
lte
r
n
a
t
i
ve
c
on
tr
ol
s
trategie
s
The
fo
l
l
ow
i
n
g
ap
proa
c
h
es
a
r
e
b
a
s
e
d
on
ne
i
t
he
r
s
y
m
m
e
trica
l
c
omp
o
ne
nt
s
co
n
t
rol
s
t
r
a
t
e
gy
n
or
t
he
per-
phase
c
o
n
t
rol
st
r
a
te
g
y
.
Henc
e,
t
hese
a
p
p
roac
hes
a
r
e
usin
g
o
ther
s
tr
ateg
ies
to
c
o
m
pe
nsa
t
e
t
h
e
syste
m
un
ba
lanc
e c
o
n
d
i
t
i
o
n
s.
The
M
ode
l
P
r
e
d
ic
t
i
v
e
C
o
n
t
r
o
l
(MP
C
)
is
r
e
cent
l
y
c
on
side
red
as
o
n
e
of
t
h
e
m
o
s
t
ef
fe
cti
v
e
wa
y
s
t
o
con
t
ro
l
pow
e
r
e
lec
t
r
o
n
i
c
s
c
on
ve
rters
due
t
o
i
t
s
fa
st
r
e
s
po
ns
e
a
nd
hig
h
c
ontr
o
l
ac
cura
cy
.
The
basic
i
d
ea
of
t
h
i
s
appr
oa
ch
i
s
to
m
inimize
t
h
e
pre
d
i
c
te
d
err
o
r,
by
eva
l
ua
t
i
n
g
t
he
o
b
jec
tive
func
tio
n
so
t
ha
t
the
r
e
fe
renc
e
vo
lta
ge
s
or
c
u
rre
nt
s
ca
n
be
t
ra
cked
a
c
c
u
ra
te
ly
u
n
d
er
l
oad
d
i
sto
rt
io
n
c
ond
it
i
o
n
s
.
A
numb
e
r
o
f
s
tu
di
es
h
ave
bee
n
pre
se
n
t
e
d
u
n
d
e
r
t
he nam
e of M
P
C
f
or
c
ur
rent c
on
tro
l
of 4-l
e
g
V
S
I
[50],
[51], 4-leg
ZS
I
[28]
, 4-leg
qZS
I
[5
2],
a
nd for
vol
t
a
ge c
on
t
r
o
l
o
f
4-le
g V
S
I
[53].
The
w
o
rk
i
n
[5
4]
,
uses
F
in
it
e
Con
t
ro
l
Set
M
ode
l
Pre
d
ic
t
i
ve
C
o
n
t
rol
(
F
CS-M
P
C
)
for
an
a
utonom
ous
fo
ur-
l
e
g
V
SI
t
o
ma
in
ta
in
b
a
l
anc
e
d
o
u
t
pu
t
v
o
lta
ges
for
u
n
b
a
lanc
e
d
l
o
a
d
s
wi
th
l
o
w
h
armo
ni
c
di
st
o
r
t
i
on
f
o
r
t
he
no
n
l
i
n
ea
r
l
o
a
d
.
F
u
rtherm
ore,
T
he
c
o
n
t
rol
a
l
gor
it
hm
i
s
de
v
e
lo
pe
d
t
o
redu
c
e
t
he
n
umbe
r
of
t
he
m
athe
m
a
tica
l
opera
tio
ns
r
eq
uire
d
for
the
c
o
n
t
ro
l
s
y
stem
w
it
ho
u
t
a
f
f
ec
ti
ng th
e
cont
ro
l
p
e
rf
o
r
ma
n
c
e.
A
s
a
re
su
l
t
,
th
e
si
z
e
and
cos
t
o
f
the
m
i
c
r
oproce
ssor
s
u
se
d
for
c
o
n
t
rol
s
y
stem
i
mp
l
e
m
e
nta
t
i
o
n
ar
e
de
cre
a
sed.
I
n
t
h
is
s
tra
t
eg
y,
t
he
t
w
o
ze
ro
v
e
c
t
or
s
t
a
t
e
s
a
r
e
c
o
n
s
i
d
e
r
e
d
a
s
one
c
om
bi
ne
d
zer
o
ve
c
t
or
s
ta
te
a
nd
t
h
e
co
ntr
o
l
a
l
gor
i
t
hm
s
e
l
e
c
ts
b
e
t
w
e
e
n
them
r
a
n
dom
l
y
.
Ther
efore
,
t
he
c
on
tro
l
a
l
g
ori
t
hm
w
i
ll
re
qu
i
r
e
th
e
cal
cul
a
tio
n
of
1
5
sta
t
e
s
i
ns
t
ead
o
f
1
6
f
o
r
ea
ch
s
a
m
p
l
i
n
g
per
i
o
d
.
M
o
re
over,
t
he
r
efer
e
n
ce
v
o
l
ta
g
e
i
s
a
s
sum
e
d
to
b
e
co
ns
tan
t
t
h
r
ou
gh
the
sam
p
l
i
ng
peri
od.
T
his
as
sum
p
t
i
o
n
w
i
l
l
e
l
im
ina
t
e
the
c
a
l
c
u
l
a
tio
n
time
req
u
i
red
f
o
r
refere
nce
v
o
l
ta
ge
e
x
t
r
a
p
o
l
at
i
on.
T
he
bl
oc
k
d
i
agra
m
of
t
h
e
s
u
g
g
es
ted
c
o
n
t
ro
l
sc
he
me
i
s
prese
n
te
d
in
F
ig
ure
14.
T
o
ha
nd
l
e
t
he
d
e
s
i
r
ed
c
ontro
l
ob
jec
t
i
v
es,
the
c
o
st
f
u
n
ct
i
on
is
c
om
pose
d
of t
h
ree
c
o
st
f
unc
t
i
o
ns
a
s fo
llow
s
:
2
*
o
g
vv
(
k
1
)
(1
)
wher
e
v
*
is
t
he
r
e
f
e
r
enc
e
o
utp
u
t
v
o
lta
ge
v
e
c
t
o
r
a
nd
v
o
(
k
+
1
)
i
s
t
he
p
re
dic
t
e
d
o
ut
p
u
t
vol
t
a
ge
v
e
c
t
or.
I
(
k
)
a
nd
io
(
k
)
ar
e
the
o
u
t
put
i
nve
r
t
er
c
urre
nt
a
nd
lo
a
d
c
ur
ren
t
v
e
c
t
o
rs,
res
pe
ctive
l
y.
T
he
p
re
d
i
c
tive
m
o
d
e
l
is
u
sed
t
o
pred
ic
t
v
o
*
for
i
n
stant
(
k
+
1
)
from
t
he
m
ea
sur
e
d
va
lue
s
o
f th
e
l
o
a
d
c
urre
nt
i
0
(
k
)
a
nd
o
u
t
p
ut
i
n
v
erter
c
u
rrent i
a
t
a
n
i
n
s
t
a
n
t
(
k
)
.
T
he
o
b
j
ec
t
i
ve
f
unc
ti
on
se
le
cts
the
bes
t
s
w
i
t
c
hin
g
s
ta
te
acc
o
rdi
n
g
t
o
t
he
e
rr
or
b
etw
e
en
t
he
refere
nce
vo
lt
a
g
e a
nd t
h
e
pred
icte
d
v
o
lta
ge.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
I
S
S
N
:
2088-
86
94
Rev
i
ew
of
t
h
ree-p
h
a
s
e i
n
v
e
rt
e
r
s
c
o
nt
rol
fo
r
un
ba
l
a
n
ced
l
oad
co
mp
en
sa
t
i
on
(Ra
e
f
Abo
e
l
s
a
u
d
)
25
1
F
i
g
u
r
e
14.
The
prop
o
sed
F
C
S
-
M
P
C
schem
e
for
q
ZS
f
our-
l
e
g
in
v
erte
r
i
n
[
54
]
In
[
5
5
]
,
a
nove
l
co
nt
rol
st
ra
te
g
y
i
s
de
v
e
lo
pe
d
f
o
r
a
st
and-a
l
on
e
s
p
l
i
t
d
c
b
u
s
V
S
I.
I
n
this
c
ontro
l
tech
n
i
q
u
e,
a
n
in
ner
discre
te
-time
sli
d
i
n
g
mode
-con
tro
l
led
(D
SMC
)
curr
ent
l
o
op
w
i
t
h
a
n
o
u
te
r
r
obust
servom
ec
ha
ni
sm
c
on
t
r
olle
d
(
R
S
C
)
vo
lta
ge
l
oo
p
i
s
c
om
bi
n
e
d
as
s
ho
w
n
i
n
F
i
g
u
r
e
1
5
.
T
h
i
s
m
e
t
h
o
d
i
s
u
s
e
d
t
o
ac
hi
e
v
e
v
o
lta
g
e
r
egu
l
at
i
o
n
w
i
t
h
l
ow
s
tea
d
y
-
state
e
rror
an
d
l
o
w
t
o
ta
l
ha
rm
onic
dist
ort
i
on
a
n
d
fa
st
t
ra
nsien
t
respo
n
se
u
nde
r
vario
u
s
l
o
a
d
d
isturba
n
ces
a
nd
u
n
b
a
l
a
n
ce
s.
T
he
c
o
ntro
l
al
gor
it
hms
a
r
e
de
ve
lope
d
u
nder
st
a
tio
na
ry
α
β0
r
e
f
er
ence
fram
e
a
nd
a
m
o
d
i
fi
ed
s
p
a
c
e
v
ec
t
o
r
pu
l
s
e
w
i
dt
h
m
odu
l
a
tio
n
(M
S
V
P
W
M)
i
s prop
ose
d
to
i
m
p
lem
e
n
t
t
he
a
lg
ori
t
hm
u
nder
αβ
0
r
e
fe
r
e
nc
e
fra
m
e
.
A
ft
e
r
c
o
n
ve
rtin
g
the
q
u
a
n
t
i
tie
s
f
r
om
r
efe
r
enc
e
f
r
a
m
e
in
to
α
β0
r
efere
n
ce
fram
e,
a
p
p
ly
i
ng
s
y
mm
etry
o
f
t
h
e
t
h
ree
dime
ns
i
o
ns,
and
con
duc
tin
g
per
un
i
t
trans
f
or
ma
t
i
o
n
,
t
h
e
s
y
ste
m
m
ode
l
ca
n
be
r
educe
d
i
n
t
o
a
si
ng
le-p
h
a
s
e
p
e
r
-
u
n
i
t
e
q
u
i
v
a
l
e
n
t
c
i
r
c
u
i
t
,
a
n
d
t
h
e
n
a
st
a
t
e
s
p
ac
e
repre
s
en
t
a
t
i
on
m
od
e
l
o
f
t
h
e
p
l
ant
i
s
d
ev
e
l
op
e
d
.
M
S
V
P
W
M
is
a
m
odifie
d
s
pa
ce
vec
t
or
p
u
l
se
w
id
t
h
modu
la
ti
o
n
i
n
v
erte
r,
v
ref
i
s
th
e
re
f
e
re
n
ce
loa
d
v
ol
t
a
g
e
,
i
cmd
*
i
s
t
he
d
es
ire
d
i
n
v
er
t
e
r
c
u
rre
nt
c
om
ma
nd,
i
cm
d
i
s
the
true
i
n
v
er
te
r
c
u
r
r
ent
c
o
m
m
a
nd,
v
pwm
*
is
t
he
P
WM
v
o
ltage
c
om
mand,
v
pwm
a
n
d
i
s
t
h
e
t
r
u
e
m
o
d
u
l
a
t
e
d
in
verter
ou
t
put
volta
ge
.
A c
u
rrent
lim
i
t
e
r
is a
dde
d be
t
w
een
t
he
tw
o
l
oo
ps f
or ove
r-cur
rent
pr
o
t
e
c
t
i
o
n.
F
i
gure
1
5
.
The
prop
ose
d
c
o
n
t
r
ol
s
ys
tem
bl
oc
k
dia
g
ram
i
n
[
5
5
]
4.
COMPARATIVE
ANALYS
IS
OF
CONTROL
STRUC
TURES
The
co
n
t
rol
s
t
r
a
teg
i
es
o
f
t
h
re
e-pha
se
i
n
v
erter
s
can
b
e
cl
assi
fi
e
d
i
n
t
o
s
e
ver
a
l
cate
g
o
r
ie
s
based
o
n
di
ffe
re
nt
c
o
n
si
der
a
t
i
o
n
a
s
s
h
o
w
n
in
T
a
b
l
e
3
.
F
rom
t
h
e
v
i
e
w
o
f
mo
du
la
ti
on,
t
he
m
o
d
u
la
tio
n
sc
hem
e
s
can
b
e
broa
dl
y
c
l
ass
i
fied
a
s
the
f
o
ll
o
w
in
g:
c
arr
i
e
r
l
ess
(hy
s
t
e
re
sis
c
o
n
t
r
o
l
a
n
d
m
o
d
e
l
p
r
e
d
i
c
t
i
v
e
c
o
n
t
r
o
l
)
a
n
d
c
a
r
r
i
e
r
-
b
a
sed
(sin
u
s
oid
a
l
pul
se
w
i
d
th
m
od
ul
at
i
o
n
(S
P
W
M
)
,
Di
sc
o
n
ti
nuo
us
PWM
(DPW
M
)
[
4
4
]
)
a
n
d
3
-
D
sp
ace
vec
t
or
m
od
u
l
a
tio
n
(3D
-
S
V
M)
[
24]
.
H
o
w
e
v
e
r,
t
he
c
arr
i
e
r
-less
m
o
d
u
la
tio
n
me
tho
d
p
rov
i
de
s
a
fas
t
d
y
n
am
ic
respo
n
se,
the
y
c
ause
a
v
a
r
iab
l
e
sw
i
t
c
h
ing
fr
e
que
nc
y
o
p
e
r
at
i
on.
In
c
on
trast,
t
he
c
arrie
r-ba
s
e
d
m
et
h
ods
i
m
pos
e
a
con
s
ta
n
t
s
w
itc
hi
ng
fre
q
uen
c
y
o
p
er
at
ion.
T
he
3
D
-
S
V
M
offers
g
oo
d
d
c
b
u
s
u
t
i
l
i
z
a
t
i
o
n
a
s
w
e
l
l
a
s
a
l
o
w
e
r
THD
i
n
c
o
m
pa
ri
ng
w
it
h
th
e
SPWM
;
th
e
s
e
adv
a
nt
ag
e
s
m
a
k
e
t
h
i
s
m
et
h
o
d
m
ore
i
n
tere
st
i
n
g.
H
ow
e
v
er,
t
h
i
s
me
tho
d
i
s
co
m
p
lex
in
r
ea
l-ti
m
e
i
mple
me
nt
a
tio
n.
T
he
d
i
s
c
o
n
t
i
n
uo
u
s
P
W
M
(DPW
M)
i
s
in
trod
u
ced
a
n
alter
n
a
t
i
v
e
app
r
oa
ch
i
nstea
d
o
f
3D
-SV
M
as it m
a
ke
use
o
f
the
m
e
rits of
b
o
t
h
P
W
M
and
S
V
M m
e
tho
d
s.
Evaluation Warning : The document was created with Spire.PDF for Python.