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fo
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k
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o
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m
o
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(
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fo
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t
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latio
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e
n
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ra
ti
o
n
a
n
d
imp
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sy
n
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ro
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iza
ti
o
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.
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e
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l
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LI
to
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o
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f
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e
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stra
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o
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p
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to
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l
P
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b
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se
d
sy
ste
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ts
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li
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n
d
re
d
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c
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d
THD.
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h
e
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s
c
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ffe
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ti
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o
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p
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d
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t
ro
l
sc
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e
m
e
fo
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re
l
iab
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a
n
d
e
fficie
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t
P
V
g
ri
d
in
teg
ra
ti
o
n
.
K
ey
w
o
r
d
s
:
Dir
ec
t
m
o
d
el
p
r
e
d
ictiv
e
co
n
t
r
o
l
Gr
id
-
co
n
n
e
cted
PV sy
s
tem
Mu
ltil
ev
el
in
v
er
ter
Su
p
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twis
tin
g
s
lid
in
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m
o
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co
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tr
o
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T
o
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ar
m
o
n
ic
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is
to
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tio
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T
h
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s
a
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o
p
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c
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rticle
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d
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CC B
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SA
li
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se
.
C
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r
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s
p
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A
uth
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:
Kam
b
h
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p
ati
Ven
k
ata
Go
v
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an
R
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Dep
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tm
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t o
f
E
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an
d
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lectr
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ics E
n
g
in
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r
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,
St.
Ma
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tin
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s
E
n
g
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C
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Secu
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d
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T
elan
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5
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,
I
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d
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m
ail:
k
v
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g
o
v
ar
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co
m
1.
I
NT
RO
D
UCT
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O
N
T
h
e
wo
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ld
wid
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s
h
if
t
to
war
d
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e
n
ewa
b
le
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y
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as
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o
tab
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d
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en
th
e
ad
v
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e
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t
o
f
g
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i
d
-
co
n
n
ec
ted
p
h
o
to
v
o
ltaic
s
y
s
tem
s
[
1
]
.
Am
o
n
g
th
e
r
en
ewa
b
le
tech
n
o
lo
g
i
es,
p
h
o
t
o
v
o
ltaic
(
PV)
s
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s
tem
s
ar
e
wid
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a
d
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p
te
d
d
u
e
to
t
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m
o
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lar
ity
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en
v
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o
n
m
en
tal
f
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ien
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lin
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,
an
d
s
tead
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d
ec
lin
in
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co
s
t.
A
c
r
u
cial
ch
allen
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e
i
n
th
ese
s
y
s
tem
s
i
s
th
e
d
esig
n
o
f
r
elia
b
le
an
d
ef
f
icien
t
p
o
wer
co
n
v
er
s
io
n
an
d
co
n
tr
o
l
s
tr
ateg
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th
at
ca
n
h
an
d
le
th
e
n
o
n
lin
ea
r
an
d
tim
e
-
v
ar
y
in
g
n
at
u
r
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o
f
s
o
lar
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n
er
g
y
wh
ile
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s
u
r
in
g
s
tab
le
p
o
wer
in
jectio
n
in
t
o
g
r
id
[
2
]
.
M
u
ltil
ev
el
in
v
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ter
s
(
ML
I
s
)
,
esp
ec
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th
o
s
e
u
tili
zin
g
H
-
b
r
id
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e
co
n
f
ig
u
r
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s
,
ar
e
wid
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p
r
ef
er
r
ed
in
m
ed
iu
m
-
an
d
h
ig
h
-
p
o
wer
s
y
s
tem
s
d
u
e
to
t
h
eir
c
ap
ab
ilit
y
to
p
r
o
d
u
ce
h
ig
h
-
q
u
a
lity
o
u
tp
u
t
v
o
ltag
es
with
m
in
i
m
al
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
(
T
HD)
an
d
r
ed
u
ce
d
v
o
ltag
e
s
tr
ess
o
n
p
o
wer
s
witch
es.
T
h
e
n
o
v
el
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
[
3
]
to
p
o
lo
g
y
f
u
r
th
e
r
en
h
an
ce
s
s
y
s
tem
p
er
f
o
r
m
an
ce
b
y
r
ed
u
cin
g
th
e
n
u
m
b
er
o
f
s
witch
e
s
r
eq
u
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d
,
th
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r
eb
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2252
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8
7
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2
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u
p
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tw
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lid
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l fo
r
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…
(
C
H.
V
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465
m
in
im
izin
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c
o
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d
u
ctio
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lo
s
s
es,
s
y
s
tem
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p
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,
a
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c
o
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t.
T
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ter
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o
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tim
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f
o
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m
an
ce
in
th
e
s
y
s
tem
,
a
r
eliab
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co
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tr
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s
tr
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is
r
eq
u
ir
e
d
th
at
ca
n
m
ax
im
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p
o
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ex
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ac
tio
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f
r
o
m
th
e
PV
p
an
els
wh
ile
m
ain
tain
in
g
g
r
id
cu
r
r
en
t
with
lo
w
T
HD
[
4
]
.
D
ir
ec
t
m
o
d
el
p
r
ed
ictiv
e
co
n
tr
o
l
(
DM
PC
)
h
as
r
ec
en
tly
em
er
g
ed
as
a
p
r
o
m
is
in
g
alter
n
ativ
e
to
tr
ad
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o
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m
eth
o
d
s
,
o
f
f
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in
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s
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aster
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am
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ea
s
e
o
f
h
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d
lin
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u
ltip
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o
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an
d
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p
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ir
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tly
m
an
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te
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m
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m
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v
e
n
tio
n
al
p
r
o
p
o
r
tio
n
al
in
teg
r
al
(
PI)
co
n
tr
o
ller
f
o
r
DC
-
lin
k
v
o
ltag
e
r
eg
u
latio
n
[
5
]
.
Desp
ite
its
wid
esp
r
ea
d
u
s
e
o
wi
n
g
to
its
s
im
p
licity
an
d
ea
s
e
o
f
in
teg
r
atio
n
,
th
e
PI
c
o
n
tr
o
ller
h
as
n
o
tab
le
lim
itatio
n
s
,
it
s
u
f
f
er
s
f
r
o
m
s
ev
er
al
d
r
awb
ac
k
s
in
n
o
n
lin
ea
r
an
d
tim
e
-
v
ar
y
in
g
s
y
s
tem
s
s
u
ch
a
s
PV
g
en
er
atio
n
[
6
]
.
T
h
e
lim
itatio
n
s
in
clu
d
e
s
lo
we
r
r
esp
o
n
s
e
to
ab
r
u
p
t
ch
a
n
g
es
in
en
v
ir
o
n
m
en
tal
c
o
n
d
itio
n
s
,
s
tead
y
-
s
tate
er
r
o
r
s
u
n
d
er
v
ar
y
in
g
lo
ad
s
,
an
d
lac
k
o
f
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
c
es.
T
h
ese
is
s
u
es
b
ec
o
m
e
m
o
r
e
p
r
o
m
in
e
n
t
in
PV
s
y
s
tem
s
wh
er
e
ir
r
ad
ia
n
ce
a
n
d
tem
p
er
atu
r
e
f
lu
ctu
ate
r
ap
id
ly
,
m
ak
i
n
g
it
ch
allen
g
in
g
f
o
r
a
lin
ea
r
co
n
tr
o
ller
to
m
ain
tain
ac
cu
r
ate
v
o
ltag
e
tr
ac
k
in
g
an
d
en
s
u
r
e
s
m
o
o
th
p
o
wer
in
jectio
n
[
7
]
.
T
o
o
v
er
co
m
e
th
ese
lim
itatio
n
s
,
th
i
s
p
ap
er
p
r
o
p
o
s
es
a
n
in
teg
r
atio
n
o
f
a
s
u
p
e
r
-
twis
tin
g
s
lid
in
g
m
o
d
e
co
n
tr
o
ller
(
STSMC)
in
p
lac
e
o
f
th
e
PI
co
n
tr
o
ller
u
s
ed
in
th
e
o
r
ig
in
al
DM
PC
.
T
h
e
STSMC
is
a
s
ec
o
n
d
-
o
r
d
e
r
s
lid
in
g
m
o
d
e
co
n
tr
o
l
s
tr
ateg
y
th
at
co
n
f
ir
m
s
f
in
ite
-
tim
e
co
n
v
er
g
en
ce
,
r
ed
u
ce
d
ch
atter
in
g
,
a
n
d
s
tr
o
n
g
r
o
b
u
s
tn
ess
ag
ain
s
t
s
y
s
tem
u
n
ce
r
tain
ties
an
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
[
8
]
.
I
t
ef
f
ec
tiv
e
ly
h
an
d
les
th
e
n
o
n
lin
ea
r
itie
s
o
f
PV
s
y
s
tem
s
an
d
en
h
an
ce
s
th
e
r
eg
u
latio
n
o
f
DC
-
lin
k
v
o
ltag
es,
wh
ic
h
in
tu
r
n
im
p
r
o
v
es th
e
q
u
ality
o
f
th
e
g
r
id
cu
r
r
en
t
r
ef
er
en
ce
g
en
er
a
tio
n
[
9
]
,
[
1
0
]
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
tr
ateg
y
r
etain
s
th
e
DM
PC
f
o
r
g
r
id
cu
r
r
en
t
co
n
tr
o
l
wh
ile
m
o
d
if
y
in
g
th
e
r
ef
er
en
ce
cu
r
r
en
t
g
en
er
atio
n
lo
o
p
b
y
in
t
r
o
d
u
cin
g
STSMC
in
th
e
v
o
lta
g
e
co
n
tr
o
l
s
tag
e
[
1
1
]
.
T
h
is
in
t
eg
r
atio
n
lea
d
s
to
a
m
o
r
e
r
o
b
u
s
t
an
d
ad
ap
tiv
e
co
n
tr
o
l
s
y
s
tem
th
at
n
o
t
o
n
ly
im
p
r
o
v
es
tr
an
s
ien
t
an
d
s
tead
y
-
s
tate
p
e
r
f
o
r
m
a
n
ce
b
u
t
also
en
s
u
r
es
b
etter
tr
ac
k
in
g
o
f
m
a
x
im
u
m
p
o
wer
p
o
in
t
u
n
d
er
d
y
n
am
ic
o
p
er
atin
g
co
n
d
itio
n
s
[
1
2
]
.
Fu
r
th
er
m
o
r
e,
it
co
n
tr
ib
u
tes
to
th
e
r
ed
u
ctio
n
o
f
T
HD
in
th
e
in
jecte
d
g
r
id
cu
r
r
en
t
an
d
en
h
a
n
ce
s
p
o
wer
q
u
a
lit
y
[
1
3
]
.
T
h
is
p
ap
er
o
f
f
er
s
d
etailed
m
o
d
elin
g
an
d
s
im
u
latio
n
o
f
th
e
en
h
an
ce
d
c
o
n
tr
o
l
s
y
s
tem
.
A
co
m
p
ar
ativ
e
ex
p
lo
r
atio
n
b
etwe
en
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
an
d
p
r
o
p
o
s
ed
STSMC
-
b
ased
s
ch
em
e
is
co
n
d
u
cte
d
u
n
d
er
v
a
r
i
o
u
s
test
co
n
d
itio
n
s
in
clu
d
in
g
s
tep
a
n
d
r
am
p
c
h
an
g
es
in
ir
r
ad
ian
ce
a
n
d
tem
p
er
atu
r
e
[
1
4
]
.
T
h
e
o
u
tc
o
m
es
clea
r
ly
v
alid
ate
s
u
p
er
io
r
ity
o
f
p
r
o
p
o
s
ed
m
et
h
o
d
s
in
ter
m
s
o
f
f
aster
v
o
ltag
e
r
e
g
u
latio
n
,
r
e
d
u
ce
d
o
v
e
r
s
h
o
o
t,
im
p
r
o
v
ed
cu
r
r
en
t
tr
ac
k
in
g
,
an
d
lo
wer
T
HD.
T
h
ese
f
in
d
in
g
s
co
n
f
ir
m
th
at
th
e
r
ep
lace
m
e
n
t
o
f
th
e
P
I
co
n
tr
o
ller
with
STSM
C
[
1
5
]
s
ig
n
if
ican
tly
en
h
an
ce
s
th
e
p
e
r
f
o
r
m
an
ce
a
n
d
r
eliab
ilit
y
o
f
s
y
s
tem
u
s
in
g
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
s
[
1
6
]
.
2.
L
I
T
E
R
AT
U
RE
SU
RVE
Y
R
ec
en
t
ad
v
an
ce
m
e
n
ts
in
r
e
n
e
wab
le
en
er
g
y
c
o
n
tr
o
l
s
y
s
tem
s
em
p
h
asize
th
e
lim
itatio
n
s
o
f
c
o
n
v
en
tio
n
al
PI
co
n
tr
o
ller
s
,
p
ar
ticu
lar
ly
th
e
ir
s
en
s
itiv
ity
to
p
ar
a
m
eter
v
a
r
i
atio
n
s
an
d
p
o
o
r
d
y
n
am
ic
p
er
f
o
r
m
an
ce
u
n
d
er
n
o
n
-
lin
ea
r
co
n
d
itio
n
s
.
I
n
co
n
tr
ast,
STSMC
[
1
7
]
,
a
s
e
co
n
d
-
o
r
d
er
s
lid
in
g
m
o
d
e
tech
n
iq
u
e,
h
as
g
ai
n
ed
r
ec
o
g
n
itio
n
f
o
r
its
r
o
b
u
s
tn
ess
,
f
in
ite
-
tim
e
co
n
v
er
g
e
n
ce
,
a
n
d
ef
f
ec
tiv
e
ch
a
tter
in
g
s
u
p
p
r
ess
io
n
[
1
8
]
.
Var
io
u
s
s
tu
d
ies
h
a
v
e
d
em
o
n
s
tr
ated
th
e
s
u
p
e
r
io
r
ity
o
f
STSMC
in
ap
p
licatio
n
s
r
an
g
in
g
f
r
o
m
s
en
s
o
r
less
in
d
u
cti
o
n
m
o
to
r
d
r
iv
es
to
s
tan
d
alo
n
e
an
d
g
r
i
d
-
co
n
n
ec
te
d
r
en
ewa
b
le
s
y
s
tem
s
[
1
9
]
.
No
tab
ly
,
th
e
in
teg
r
atio
n
o
f
STSMC
with
m
u
ltil
ev
e
l
in
v
er
ter
s
(
ML
I
s
)
en
h
a
n
ce
s
v
o
ltag
e
r
eg
u
latio
n
an
d
r
ed
u
ce
s
T
HD,
th
er
eb
y
im
p
r
o
v
in
g
p
o
wer
q
u
ality
.
Ad
d
itio
n
ally
,
r
ec
en
t
m
u
ltil
ev
el
in
v
er
ter
t
o
p
o
lo
g
ies
aim
to
r
ed
u
ce
th
e
n
u
m
b
er
o
f
s
witch
in
g
d
ev
ices
an
d
elim
in
ate
th
e
n
ee
d
f
o
r
m
u
ltip
le
DC
s
o
u
r
ce
s
,
lead
in
g
to
s
im
p
lifie
d
d
esig
n
s
with
h
ig
h
ef
f
icien
cy
[
2
0
]
,
[
2
1
]
.
T
h
ese
d
ev
elo
p
m
e
n
ts
alig
n
well
with
th
e
p
r
o
p
o
s
ed
co
n
t
r
o
l
s
tr
ateg
y
i
n
th
e
m
an
u
s
cr
ip
t,
wh
ic
h
lev
er
a
g
es
STSMC
an
d
an
o
p
tim
ized
H
-
b
r
i
d
g
e
ML
I
f
o
r
a
g
r
id
-
co
n
n
ec
ted
PV sy
s
tem
[
2
2
]
,
[
2
3
]
.
T
h
e
c
o
m
b
in
e
d
ap
p
r
o
a
ch
n
o
t o
n
l
y
en
s
u
r
es
im
p
r
o
v
e
d
d
y
n
am
ic
r
esp
o
n
s
e
a
n
d
r
eliab
ilit
y
u
n
d
er
en
v
ir
o
n
m
e
n
tal
d
is
tu
r
b
an
ce
s
[
2
4
]
,
[
2
5
]
b
u
t
also
m
ee
ts
m
o
d
er
n
g
r
id
co
m
p
lian
ce
s
tan
d
ar
d
s
f
o
r
r
en
ewa
b
le
en
er
g
y
in
teg
r
ati
o
n
[
2
6
]
,
[
27
]
.
T
ab
le
1
(
s
ee
Ap
p
en
d
ix
)
g
iv
es
th
e
d
ata
o
f
th
e
liter
atu
r
e
s
u
r
v
ey
[
1
0
]
,
[
1
2
]
,
[
2
1
]
,
[
2
2
]
,
[
2
8
]
-
[
3
0
]
.
3.
SYST
E
M
M
O
D
E
L
I
NG
T
h
e
s
y
s
tem
ex
am
in
ed
is
a
g
r
id
-
co
n
n
ec
ted
PV
s
etu
p
f
ea
tu
r
in
g
a
n
ew
H
-
b
r
id
g
e
ML
I
to
p
o
lo
g
y
,
i
llu
s
tr
ated
in
Fig
u
r
e
1
.
I
t
is
en
g
in
ee
r
ed
t
o
m
ax
im
ize
p
o
wer
e
x
tr
ac
tio
n
f
r
o
m
PV
m
o
d
u
les.
T
h
at
in
jects
a
h
ig
h
-
q
u
ality
cu
r
r
en
t
in
to
th
e
g
r
id
.
T
h
e
to
p
o
lo
g
y
co
m
p
r
is
es th
r
ee
PV m
o
d
u
les,
tw
o
DC
-
lin
k
ca
p
ac
ito
r
s
,
a
n
o
v
el
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
,
a
n
o
u
t
p
u
t f
ilter
,
a
n
d
a
s
in
g
le
-
p
h
ase
g
r
i
d
co
n
n
ec
tio
n
.
3
.
1
.
P
V
a
rr
a
y
a
nd
DC
-
lin
k
co
nfig
ura
t
io
n
T
h
e
PV
s
o
u
r
ce
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
co
m
p
r
is
es
th
r
ee
in
d
iv
i
d
u
al
PV
m
o
d
u
les,
d
en
o
ted
as
PV1
,
PV2
a,
an
d
PV2
b
.
T
h
ese
m
o
d
u
les
ar
e
s
tr
ateg
ically
ar
r
an
g
ed
t
o
f
o
r
m
two
d
is
tin
ct
DC
-
lin
k
s
th
at
s
u
p
p
ly
th
e
r
e
q
u
ir
e
d
v
o
ltag
e
lev
els
to
th
e
in
v
er
ter
.
Sp
ec
if
ically
,
PV1
f
o
r
m
s
th
e
f
i
r
s
t
DC
-
lin
k
o
n
its
o
wn
,
wh
ile
PV2
a
an
d
PV2
b
ar
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
464
-
479
466
co
n
n
ec
ted
in
s
er
ies to
co
n
s
titu
te
th
e
s
ec
o
n
d
DC
-
lin
k
.
T
h
is
h
y
b
r
id
c
o
n
f
ig
u
r
atio
n
en
ab
les th
e
in
v
er
ter
to
ac
h
iev
e
m
u
ltip
le
o
u
tp
u
t
v
o
ltag
e
le
v
els
wh
ile
m
in
im
izin
g
th
e
n
u
m
b
e
r
o
f
PV
m
o
d
u
les
an
d
ass
o
ciat
ed
p
o
wer
elec
tr
o
n
ic
co
m
p
o
n
en
ts
.
E
ac
h
PV
m
o
d
u
le
is
in
ten
d
e
d
to
o
p
er
ate
at
its
in
d
iv
id
u
al
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
,
wh
ich
f
lu
ctu
ates
b
ased
o
n
e
n
v
ir
o
n
m
e
n
tal
f
ac
to
r
s
lik
e
s
u
n
lig
h
t
in
ten
s
ity
an
d
tem
p
er
atu
r
e.
E
m
p
lo
y
i
n
g
two
in
d
ep
en
d
en
t
DC
-
lin
k
co
n
f
ig
u
r
atio
n
s
en
ab
le
s
s
ep
ar
ate
v
o
ltag
e
r
eg
u
latio
n
f
o
r
ea
ch
m
o
d
u
le,
th
er
eb
y
im
p
r
o
v
in
g
th
e
s
y
s
tem
’
s
ad
ap
tab
ilit
y
u
n
d
er
p
ar
tial
s
h
a
d
in
g
o
r
n
o
n
-
u
n
if
o
r
m
o
p
er
atin
g
c
o
n
d
itio
n
s
.
T
h
e
DC
-
lin
k
c
ap
ac
i
to
r
s
,
d
en
o
ted
as
C1
an
d
C2
,
ar
e
co
n
n
ec
ted
ac
r
o
s
s
th
e
o
u
tp
u
ts
o
f
PV1
a
n
d
t
h
e
s
e
r
ies
-
co
n
n
ec
ted
PV2
a
–
PV2
b
,
r
esp
ec
tiv
ely
.
T
h
ese
ca
p
ac
ito
r
s
s
er
v
e
as e
n
er
g
y
b
u
f
f
er
s
,
s
m
o
o
th
o
u
t v
o
lta
g
e
r
ip
p
le
s
,
an
d
p
r
o
v
id
e
a
s
tead
y
DC
s
u
p
p
ly
to
i
n
v
er
ter
s
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
m
o
d
el
o
f
PV
g
r
id
s
y
s
tem
T
h
e
r
atio
n
ale
f
o
r
co
n
n
ec
tin
g
P
V2
a
an
d
PV2
b
in
s
er
ies
is
to
ac
h
iev
e
a
h
i
g
h
er
v
o
ltag
e
le
v
el
p
v
2
≈
2
p
v
2
,
wh
ich
is
es
s
en
tial
f
o
r
en
ab
lin
g
th
e
n
o
v
el
H
-
b
r
id
g
e
in
v
er
ter
to
s
y
n
th
esize
s
ev
en
d
is
tin
ct
o
u
tp
u
t
v
o
ltag
e
lev
els.
T
h
ese
lev
els
ar
e
{
0
,
±
1
,
±
2
,
±
(
1
+
2
}.
T
h
is
s
elec
tiv
e
v
o
ltag
e
g
en
e
r
atio
n
im
p
r
o
v
es
th
e
q
u
ality
o
f
th
e
o
u
tp
u
t
wav
ef
o
r
m
an
d
r
ed
u
ce
s
T
HD
with
o
u
t
r
eq
u
i
r
in
g
a
lar
g
er
n
u
m
b
er
o
f
s
witch
in
g
d
ev
ices
o
r
co
m
p
le
x
m
o
d
u
latio
n
tech
n
iq
u
es.
I
n
a
d
d
itio
n
to
im
p
r
o
v
in
g
v
o
lt
ag
e
r
eso
lu
tio
n
at
th
e
i
n
v
er
ter
o
u
tp
u
t,
t
h
e
s
ep
ar
ate
DC
-
lin
k
s
tr
u
ctu
r
e
f
ac
ilit
ates
d
is
tr
ib
u
ted
MPPT
co
n
tr
o
l.
T
h
is
allo
ws
ea
ch
DC
-
lin
k
to
tr
ac
k
its
o
w
n
MPP
in
d
ep
en
d
en
tly
,
ev
en
wh
e
n
d
if
f
er
en
t
p
o
r
tio
n
s
o
f
th
e
PV
ar
r
ay
ex
p
er
ien
ce
v
a
r
y
in
g
le
v
e
ls
o
f
s
u
n
lig
h
t.
T
h
e
MPPT
alg
o
r
ith
m
ad
ju
s
ts
th
e
r
ef
er
en
ce
1
∗
an
d
2
∗
,
wh
ich
ar
e
later
u
s
ed
in
th
e
v
o
ltag
e
r
eg
u
latio
n
lo
o
p
to
d
eter
m
in
e
th
e
r
eq
u
ir
ed
p
o
wer
in
jectio
n
in
to
th
e
g
r
id
.
T
h
e
PV
m
o
d
u
les
u
s
ed
in
th
e
s
i
m
u
latio
n
ar
e
m
o
d
eled
u
s
in
g
s
tan
d
ar
d
I
–
V
ch
ar
ac
ter
is
tics
u
n
d
er
v
ar
y
in
g
co
n
d
itio
n
s
o
f
s
o
lar
.
T
h
e
s
y
s
tem
ass
u
m
es th
at
ea
c
h
m
o
d
u
le
c
an
d
eliv
e
r
a
n
o
m
in
al
v
o
ltag
e
o
f
ar
o
u
n
d
2
8
.
5
V
a
n
d
a
cu
r
r
en
t
o
f
7
.
3
A
at
s
tan
d
ar
d
test
co
n
d
itio
n
s
,
as
p
er
th
e
s
p
ec
if
icatio
n
s
.
As
PV2
a
an
d
PV2
b
ar
e
in
s
er
ies,
th
e
s
ec
o
n
d
DC
-
lin
k
v
o
ltag
e
a
p
p
r
o
x
im
ately
d
o
u
b
les,
th
u
s
en
ab
lin
g
th
e
cr
ea
tio
n
o
f
h
ig
h
er
o
u
tp
u
t
v
o
ltag
e
s
tep
s
in
th
e
m
u
ltil
ev
el
in
v
e
r
ter
.
3
.
2
.
No
v
el
H
-
b
ridg
e
m
ultile
v
el
inv
er
t
er
T
h
e
p
o
wer
c
o
n
v
e
r
s
io
n
u
n
it
in
th
e
p
r
o
p
o
s
ed
s
y
s
tem
is
b
ased
o
n
a
m
o
d
if
ied
H
-
b
r
id
g
e
ML
I
to
p
o
lo
g
y
.
T
h
is
in
v
er
ter
f
u
n
ctio
n
s
as
th
e
p
r
im
ar
y
in
ter
f
ac
e
th
at
lin
k
s
D
C
o
u
tp
u
t
f
r
o
m
t
h
e
PV
m
o
d
u
le
s
to
th
e
AC
u
tili
ty
g
r
id
.
I
n
co
n
tr
ast
to
tr
ad
itio
n
a
l
m
u
ltil
ev
el
in
v
e
r
ter
s
th
at
t
y
p
ically
r
eq
u
ir
e
n
u
m
er
o
u
s
s
witch
in
g
d
ev
ices
an
d
m
u
ltip
le
is
o
lated
DC
s
o
u
r
ce
s
,
th
e
ad
o
p
ted
H
-
b
r
i
d
g
e
co
n
f
ig
u
r
atio
n
ac
h
iev
es
s
ev
en
-
lev
el
v
o
ltag
e
o
u
tp
u
t
with
f
ewe
r
s
em
ico
n
d
u
ct
o
r
s
witch
es,
o
f
f
er
in
g
a
m
o
r
e
co
m
p
ac
t
a
n
d
ef
f
icien
t
d
esig
n
.
T
h
is
to
p
o
lo
g
y
co
n
s
is
ts
o
f
s
ix
b
id
ir
ec
tio
n
al
s
witch
es
(
ty
p
ically
r
ea
lized
u
s
in
g
MO
SF
E
T
s
)
,
s
tr
at
eg
ically
co
n
f
ig
u
r
e
d
to
p
r
o
d
u
ce
a
m
an
d
ato
r
y
m
u
ltil
ev
el
v
o
ltag
e
wav
e
f
o
r
m
.
T
h
e
v
o
ltag
e
le
v
els g
en
er
ated
a
t
th
e
o
u
tp
u
t te
r
m
in
al
o
f
th
e
in
v
er
ter
ar
e
(
1
)
.
{
0
,
±
1
,
±
2
,
±
(
1
+
2
)
}
(
1
)
Her
e,
1
is
th
e
v
o
ltag
e
ac
r
o
s
s
t
h
e
f
ir
s
t
DC
-
lin
k
(
f
r
o
m
PV1
)
,
an
d
2
is
th
e
v
o
ltag
e
th
r
o
u
g
h
t
h
e
s
ec
o
n
d
DC
-
lin
k
(
f
r
o
m
th
e
s
er
i
es
-
co
n
n
ec
ted
PV2
a
a
n
d
PV2
b
)
.
T
h
e
v
o
ltag
e
m
ag
n
itu
d
es
ar
e
s
elec
ted
s
u
ch
th
at
2
≈2
1
,
en
ab
lin
g
a
wid
e
r
an
g
e
o
f
o
u
tp
u
t
v
o
ltag
e
co
m
b
in
atio
n
s
f
r
o
m
a
co
m
p
ac
t
s
witch
in
g
s
tr
u
ctu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
u
p
er
-
tw
is
tin
g
s
lid
in
g
mo
d
e
c
o
n
tr
o
l fo
r
en
h
a
n
ce
d
p
erfo
r
ma
n
ce
o
f
…
(
C
H.
V
en
ka
t
a
A
ma
r
n
a
d
h
)
467
T
h
e
k
ey
im
p
r
o
v
em
e
n
t
o
f
th
is
to
p
o
lo
g
y
lies
in
its
ca
p
ab
ilit
y
to
s
y
n
th
esize
a
s
tair
ca
s
e
-
lik
e
AC
wav
ef
o
r
m
th
at
clo
s
ely
ap
p
r
o
x
im
ates
a
s
in
e
wav
e,
u
s
in
g
f
ewe
r
s
witch
es
co
m
p
ar
ed
to
tr
ad
itio
n
al
ca
s
ca
d
e
d
H
-
b
r
id
g
e
in
v
er
ter
s
.
T
h
is
r
ed
u
ctio
n
in
s
witch
co
u
n
t
lead
s
to
lo
wer
co
n
d
u
ctio
n
lo
s
s
es,
r
ed
u
ce
d
g
ate
d
r
iv
er
r
e
q
u
ir
e
m
en
ts
,
s
m
aller
h
ea
t
s
in
k
s
,
an
d
o
v
e
r
all
lo
wer
co
s
t a
n
d
co
m
p
lex
ity
,
with
o
u
t c
o
m
p
r
o
m
is
in
g
th
e
v
o
ltag
e
lev
el
r
eso
l
u
tio
n
o
r
wav
ef
o
r
m
q
u
ality
.
E
ac
h
s
witch
in
th
e
in
v
e
r
ter
is
ca
p
ab
le
o
f
b
id
ir
ec
tio
n
al
cu
r
r
e
n
t
co
n
d
u
ctio
n
an
d
u
n
id
ir
ec
tio
n
al
v
o
lta
g
e
b
lo
ck
in
g
,
en
s
u
r
in
g
s
af
e
o
p
er
a
tio
n
d
u
r
in
g
d
if
f
er
en
t
lo
ad
an
d
p
o
wer
f
l
o
w
co
n
d
itio
n
s
.
T
h
e
s
witch
in
g
lo
g
ic
is
d
er
iv
ed
f
r
o
m
a
p
r
e
d
ef
in
ed
s
witch
in
g
T
ab
le
2
,
wh
ic
h
m
ap
s
s
p
e
cif
ic
co
m
b
in
atio
n
s
o
f
DC
-
lin
k
v
o
ltag
es
to
d
esire
d
o
u
tp
u
t
v
o
ltag
e
lev
els.
T
h
is
d
e
ter
m
in
is
tic
s
witch
in
g
ap
p
r
o
ac
h
is
p
ar
ticu
lar
ly
c
o
m
p
atib
le
with
DM
PC
,
wh
ich
ev
alu
ates m
u
ltip
le
s
witch
in
g
s
ce
n
ar
io
s
in
r
ea
l tim
e
to
o
p
tim
i
ze
co
n
tr
o
l
p
er
f
o
r
m
an
ce
.
T
h
e
o
p
er
atio
n
o
f
th
e
in
v
er
ter
ca
n
b
e
b
r
ief
ly
ex
p
lain
ed
th
r
o
u
g
h
th
e
f
o
llo
win
g
ex
am
p
le
s
ce
n
ar
io
s
:
i)
W
h
en
th
e
o
u
tp
u
t v
o
ltag
e
n
e
ed
s
to
b
e
ze
r
o
,
s
witch
in
g
s
tate
s
ar
e
co
n
f
ig
u
r
ed
s
u
ch
th
at
n
eit
h
er
1
n
o
r
2
i
s
co
n
n
ec
ted
to
th
e
o
u
tp
u
t.
T
o
o
b
tain
=
1
,
th
e
s
witch
es
ar
e
a
r
r
a
n
g
ed
t
o
ap
p
ly
o
n
ly
th
e
f
i
r
s
t
DC
-
lin
k
v
o
ltag
e
;
ii)
Similar
ly
,
f
o
r
=
1
+
2
,
b
o
th
DC
-
lin
k
s
ar
e
co
u
p
led
in
s
er
ies
to
th
e
o
u
tp
u
t
;
an
d
iii)
Neg
ativ
e
v
o
ltag
e
lev
els ar
e
g
e
n
er
ated
b
y
r
ev
e
r
s
in
g
th
e
c
u
r
r
e
n
t p
ath
th
r
o
u
g
h
ap
p
r
o
p
r
iate
s
witch
s
elec
tio
n
s
.
T
h
is
f
lex
ib
ilit
y
in
v
o
ltag
e
s
y
n
t
h
esis
allo
ws
th
e
in
v
er
ter
to
clo
s
ely
tr
ac
k
th
e
s
in
u
s
o
id
al
r
ef
er
e
n
ce
cu
r
r
e
n
t
wav
ef
o
r
m
,
m
in
im
izin
g
th
e
T
HD
an
d
e
n
s
u
r
in
g
co
m
p
lian
ce
with
g
r
id
co
d
e
s
tan
d
ar
d
s
.
Ad
d
itio
n
ally
,
th
e
s
ev
en
-
v
o
ltag
e
-
lev
el
o
u
t
p
u
t
wav
ef
o
r
m
in
h
er
en
tly
im
p
r
o
v
es
th
e
p
o
wer
q
u
ality
an
d
r
ed
u
ce
s
th
e
b
u
r
d
en
o
n
th
e
o
u
tp
u
t
f
ilter
co
m
p
o
n
en
ts
.
I
n
th
is
s
y
s
tem
,
th
e
in
v
er
ter
w
o
r
k
s
at
a
s
witch
in
g
f
r
eq
u
e
n
cy
d
eter
m
in
ed
b
y
th
e
DM
PC
alg
o
r
ith
m
,
w
h
ich
ev
al
u
ates
a
d
is
cr
ete
-
tim
e
m
o
d
el
o
f
th
e
s
y
s
tem
an
d
s
elec
ts
th
e
o
p
tim
al
s
witch
i
n
g
s
tate
at
ea
ch
s
am
p
lin
g
in
s
tan
t
.
T
h
is
ap
p
r
o
a
ch
n
ee
d
s
p
u
ls
e
-
wid
th
m
o
d
u
latio
n
(
PW
M)
,
f
u
r
th
e
r
en
h
a
n
cin
g
d
y
n
a
m
ic
r
esp
o
n
s
e
an
d
s
y
s
tem
ef
f
icien
cy
.
T
ab
le
2
.
Switch
in
g
p
atter
n
s
o
f
th
e
p
r
o
p
o
s
ed
H
-
b
r
id
g
e
m
u
ltil
ev
el
in
v
er
ter
I
n
d
e
x
S
w
i
t
c
h
i
n
g
se
q
u
e
n
c
e
S
L1
,
S
L2
S
R
1
,
S
R
2
S
a
,
s
b
1
0
,
1
0
,
1
1
,
0
−
(
1
+
2
)
2
0
,
1
1
,
0
0
,
1
2
3
0
,
1
1
,
0
1
,
0
-
1
4
1
,
0
0
,
1
0
,
1
1
5
1
,
0
0
,
1
1
,
0
−
2
6
1
,
0
1
,
0
0
,
1
(
1
+
2
)
7
1
,
0
1
,
0
1
,
0
0
3
.
3
.
G
rid
-
s
ide f
ilte
r
a
nd
inte
rf
a
ce
A
s
in
g
le
-
p
h
ase
g
r
id
c
o
n
n
ec
tio
n
is
estab
lis
h
ed
v
ia
an
L
-
f
ilte
r
,
co
n
s
is
tin
g
o
f
a
n
in
d
u
ctan
ce
an
d
a
s
er
ies
r
esi
s
tan
ce
.
T
h
is
f
ilter
at
ten
u
ates
h
ig
h
-
f
r
e
q
u
en
c
y
h
ar
m
o
n
ics
p
r
o
d
u
ce
d
b
y
in
v
e
r
ter
s
witch
in
g
an
d
h
elp
s
m
ain
tain
th
e
q
u
ality
o
f
th
e
c
u
r
r
en
t
in
jecte
d
in
to
th
e
g
r
id
,
wh
ich
is
s
m
o
o
th
an
d
s
in
u
s
o
id
al.
T
h
e
s
y
s
tem
d
o
es
n
o
t
em
p
lo
y
a
tr
an
s
f
o
r
m
er
,
m
a
k
in
g
it
a
t
r
an
s
f
o
r
m
er
less
co
n
f
i
g
u
r
atio
n
,
w
h
ich
en
h
a
n
ce
s
ef
f
i
cien
cy
an
d
r
e
d
u
ce
s
s
ize
an
d
co
s
t.
T
h
e
g
r
id
v
o
ltag
e
is
as
s
u
m
ed
to
b
e
a
k
n
o
wn
an
d
s
tab
le
s
in
u
s
o
id
al
s
o
u
r
ce
.
T
h
e
in
v
er
ter
m
u
s
t
in
ject
a
cu
r
r
en
t i
n
p
h
ase
with
t
h
is
v
o
ltag
e
to
en
s
u
r
e
u
n
ity
p
o
wer
f
ac
to
r
o
p
er
atio
n
.
4.
CO
NT
RO
L
ST
R
AT
E
G
Y
T
h
e
c
o
n
tr
o
l
t
o
p
o
l
o
g
y
i
n
t
h
e
p
r
o
p
o
s
e
d
g
r
i
d
-
c
o
n
n
ec
te
d
PV
s
y
s
te
m
is
o
r
g
a
n
i
ze
d
i
n
t
o
th
r
ee
f
u
n
c
ti
o
n
al
s
tag
es:
MPP
T
,
DC
-
li
n
k
v
o
lt
ag
e
r
e
g
u
la
ti
o
n
u
s
i
n
g
S
T
SMC
,
a
n
d
g
r
i
d
c
u
r
r
e
n
t
c
o
n
t
r
o
l
DM
PC
.
T
h
e
co
m
p
le
te
b
l
o
c
k
-
lev
el
c
o
n
t
r
o
l
f
l
o
w
,
as i
m
p
l
em
e
n
te
d
i
n
S
im
u
l
in
k
,
is
i
ll
u
s
tr
at
ed
in
Fi
g
u
r
e
2
.
I
n
th
e
f
ir
s
t
s
tag
e,
two
s
ets
o
f
PV
m
o
d
u
les
(
PV1
an
d
PV2
)
ar
e
in
d
ep
en
d
en
tly
m
o
n
ito
r
e
d
,
an
d
th
eir
m
ax
im
u
m
p
o
wer
p
o
in
ts
ar
e
tr
ac
k
ed
u
s
in
g
th
e
p
er
tu
r
b
an
d
o
b
s
er
v
e
(
P&
O)
MPPT
alg
o
r
ith
m
.
E
ac
h
PV
m
o
d
u
le
p
r
o
v
id
es
its
r
esp
ec
tiv
e
v
o
ltag
e
1
,
2
,
an
d
cu
r
r
e
n
t
1
,
2
to
th
e
MPPT
b
lo
ck
s
,
wh
ich
co
m
p
u
te
t
h
e
o
p
tim
al
r
ef
er
e
n
ce
v
o
ltag
es
1
∗
an
d
2
∗
to
ex
tr
ac
t
m
ax
im
u
m
p
o
wer
.
T
h
ese
r
ef
er
en
ce
v
o
ltag
es
ar
e
c
o
m
p
ar
ed
with
ac
tu
al
v
o
ltag
es to
p
r
o
d
u
c
e
er
r
o
r
s
ig
n
als f
o
r
th
e
v
o
ltag
e
co
n
tr
o
l stag
e.
T
h
e
to
tal
MPP
r
e
f
er
en
ce
p
o
we
r
is
(
2
)
.
T
h
is
p
o
wer
is
u
s
ed
to
c
o
m
p
u
te
th
e
id
ea
l
p
ea
k
g
r
id
c
u
r
r
en
t
u
n
d
er
u
n
ity
p
o
wer
f
ac
to
r
co
n
d
itio
n
s
(
3
)
.
∗
=
1
∗
+
2
∗
(
2
)
̂
=
2
∗
̂
(
3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
464
-
479
468
T
h
e
s
ec
o
n
d
s
tag
e
in
co
r
p
o
r
at
es
th
e
STSMC,
wh
ich
r
ep
la
ce
s
th
e
co
n
v
e
n
tio
n
al
PI
c
o
n
t
r
o
ller
.
T
h
e
STSMC
r
ec
eiv
es
th
e
to
tal
D
C
-
lin
k
v
o
ltag
e
er
r
o
r
=
∗
−
an
d
th
e
p
r
e
v
io
u
s
er
r
o
r
v
alu
e
,
to
g
en
er
ate
a
co
n
tr
o
l
o
u
t
p
u
t
(
)
.
T
h
is
co
n
tr
o
l
s
ig
n
al
r
eg
u
lates
th
e
p
ea
k
r
e
f
er
en
ce
v
al
u
e
o
f
g
r
id
c
u
r
r
en
t
̂
g
.
T
h
e
ac
tu
al
in
s
tan
tan
eo
u
s
r
ef
e
r
en
ce
cu
r
r
en
t
∗
is
th
e
n
g
en
er
ated
u
s
in
g
̂
g
an
d
th
e
g
r
id
v
o
ltag
e
with
t
h
e
h
e
lp
o
f
a
p
h
ase
-
lo
ck
ed
lo
o
p
(
PLL
)
to
en
s
u
r
e
s
y
n
ch
r
o
n
izatio
n
with
g
r
id
.
T
h
e
co
m
b
in
ed
DC
-
lin
k
v
o
ltag
e
er
r
o
r
is
c
o
m
p
u
te
d
as
(
4
)
.
A
s
lid
in
g
s
u
r
f
ac
e
is
d
e
f
in
ed
as
(
5
)
.
I
t
d
y
n
am
ically
a
d
ju
s
ts
th
e
r
ef
er
e
n
ce
cu
r
r
e
n
t a
m
p
litu
d
e
in
(
6
)
.
(
)
=
(
1
+
2
)
−
1
∗
+
2
∗
)
(
4
)
(
)
=
(
)
+
∫
(
)
(
5
)
̂
=
̂
+
(
)
(
6
)
T
h
is
co
r
r
ec
ted
am
p
litu
d
e
is
u
s
ed
to
g
en
er
ate
th
e
in
s
tan
tan
e
o
u
s
s
in
u
s
o
id
al
r
ef
er
e
n
ce
cu
r
r
en
t
∗
(
)
,
en
s
u
r
in
g
s
tab
le
p
o
wer
tr
an
s
f
er
a
n
d
DC
-
lin
k
r
eg
u
latio
n
.
I
n
th
e
th
i
r
d
s
tag
e,
th
e
DM
PC
co
n
tr
o
ller
u
ti
lizes
th
e
r
ef
er
en
ce
cu
r
r
en
t
∗
,
m
ea
s
u
r
ed
g
r
id
cu
r
r
en
t
,
an
d
p
r
e
d
icted
v
alu
es
̂
g
,
1
,
2
f
r
o
m
a
d
is
cr
ete
p
r
ed
ictio
n
m
o
d
el.
T
h
e
co
n
tr
o
ller
ev
alu
ates
a
co
s
t
f
u
n
ctio
n
o
v
er
all
f
ea
s
ib
le
s
witch
in
g
s
tates
to
s
elec
t
th
e
o
p
tim
al
co
n
tr
o
l
s
ig
n
als
th
at
m
in
im
ize
cu
r
r
e
n
t
an
d
v
o
ltag
e
tr
ac
k
in
g
er
r
o
r
s
.
T
h
ese
o
p
tim
al
s
tates
ar
e
u
s
ed
to
d
r
iv
e
s
witch
in
g
d
e
v
ices
o
f
H
-
b
r
id
g
e
in
v
e
r
ter
(
SL1
,
SL2
,
SR
1
,
SR
2
,
Sa,
Sb
)
,
en
ab
lin
g
s
ev
en
-
lev
el
v
o
ltag
e
s
y
n
th
esis
f
o
r
g
r
id
co
n
n
ec
tio
n
.
A
co
s
t f
u
n
ctio
n
is
ev
alu
ate
d
(
7
)
.
=
|
∗
−
(
+
1
)
|
+
(
|
1
∗
−
1
(
+
1
)
|
+
|
2
∗
−
2
(
+
1
)
|
)
(
7
)
T
h
e
s
witch
in
g
s
tate
th
at
r
ed
u
ce
s
th
e
co
s
t
f
u
n
ctio
n
is
s
elec
ted
as
th
e
o
p
tim
al
ch
o
ice
b
y
t
h
e
DM
PC
co
n
tr
o
ller
.
B
ased
o
n
th
is
s
el
ec
tio
n
,
th
e
co
r
r
esp
o
n
d
in
g
s
witch
in
g
p
atter
n
is
r
etr
iev
ed
f
r
o
m
th
e
in
v
er
ter
’
s
p
r
ed
ef
in
e
d
s
witch
in
g
tab
le
an
d
u
s
ed
to
g
e
n
er
ate
th
e
g
atin
g
p
u
ls
es f
o
r
in
v
er
ter
s
witch
es.
T
o
en
h
an
ce
p
r
ed
ictio
n
ac
cu
r
ac
y
,
th
e
s
y
s
tem
also
in
c
o
r
p
o
r
ates
a
d
e
d
icate
d
p
r
ed
icti
o
n
b
lo
ck
th
at
esti
m
ates
f
u
tu
r
e
v
alu
es
o
f
k
ey
s
tate
v
ar
iab
les
s
u
ch
as
g
r
i
d
c
u
r
r
en
t
an
d
PV
v
o
ltag
es
u
s
in
g
c
u
r
r
en
t
o
p
er
atin
g
co
n
d
itio
n
s
.
T
h
is
f
ee
d
f
o
r
war
d
p
r
ed
ictio
n
im
p
r
o
v
es
t
h
e
c
o
n
tr
o
ller
’
s
r
e
s
p
o
n
s
iv
en
ess
an
d
co
n
tr
i
b
u
tes
to
b
etter
d
y
n
am
ic
s
tab
ilit
y
,
esp
ec
ially
u
n
d
er
f
lu
ctu
atin
g
s
o
lar
ir
r
a
d
ian
ce
a
n
d
tem
p
er
at
u
r
e
c
o
n
d
itio
n
s
.
B
y
s
witch
in
g
th
e
PI
co
n
t
r
o
ller
with
th
e
STSMC in
th
e
v
o
ltag
e
r
eg
u
latio
n
s
tag
e,
th
e
p
r
o
p
o
s
ed
c
o
n
tr
o
l
s
y
s
tem
ac
h
iev
es
f
aster
tr
an
s
ien
t
r
esp
o
n
s
e,
h
i
g
h
er
r
o
b
u
s
tn
ess
to
d
is
tu
r
b
an
ce
s
,
an
d
m
o
r
e
ac
cu
r
ate
v
o
ltag
e
tr
ac
k
in
g
.
T
h
ese
en
h
an
ce
m
en
ts
lead
to
im
p
r
o
v
ed
q
u
ality
in
th
e
r
ef
er
en
ce
c
u
r
r
e
n
t
s
ig
n
al,
r
esu
l
tin
g
in
s
ig
n
i
f
ican
tly
r
ed
u
ce
d
T
HD
in
th
e
g
r
i
d
cu
r
r
en
t
an
d
o
v
er
all
b
etter
p
o
wer
q
u
ality
in
th
e
g
r
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ab
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Fig
u
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3
D
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i
n
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c
a
p
a
c
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t
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r
s
C
1
a
n
d
C
2
-
47
I
n
d
u
c
t
a
n
c
e
Lf
2
5
R
e
si
st
a
n
c
e
R
f
2
10
F
i
l
t
e
r
R
f
a
n
d
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f
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G
r
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S
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C
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a
i
n
1
λ3
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7
S
TSM
C
G
a
i
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2
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.
9
1
5.
M
E
T
H
O
D
T
h
e
STSMC
is
a
p
o
wer
f
u
l
co
n
tr
o
l
m
eth
o
d
d
esig
n
ed
to
h
a
n
d
l
e
s
y
s
tem
s
with
u
n
ce
r
tain
ties
a
n
d
ex
ter
n
al
d
is
tu
r
b
an
ce
s
wh
ile
en
s
u
r
in
g
s
tr
o
n
g
s
tab
ilit
y
.
T
r
ad
itio
n
al
s
lid
in
g
m
o
d
e
co
n
tr
o
l
wo
r
k
s
b
y
f
o
r
cin
g
th
e
s
y
s
tem
’
s
b
eh
av
io
r
o
n
to
a
s
p
ec
ial
s
u
r
f
ac
e
ca
lled
a
s
l
id
in
g
s
u
r
f
ac
e
an
d
k
ee
p
in
g
it
th
er
e,
wh
ich
m
ak
es
th
e
s
y
s
tem
r
o
b
u
s
t.
Ho
wev
er
,
th
is
tr
ad
itio
n
al
m
eth
o
d
o
f
te
n
ca
u
s
es
a
p
r
o
b
lem
c
alled
ch
atter
in
g
-
r
a
p
id
,
u
n
wa
n
ted
s
witch
in
g
in
th
e
co
n
tr
o
l sig
n
al
th
at
ca
n
h
ar
m
m
ec
h
an
ical
p
a
r
ts
an
d
r
ed
u
ce
p
er
f
o
r
m
an
ce
.
STSMC so
lv
es th
is
b
y
u
s
in
g
a
s
ec
o
n
d
-
o
r
d
er
s
lid
in
g
m
o
d
e
tech
n
iq
u
e
t
h
at
p
r
o
d
u
ce
s
s
m
o
o
th
,
co
n
tin
u
o
u
s
co
n
tr
o
l
ac
tio
n
,
g
r
ea
tly
r
e
d
u
cin
g
o
r
elim
in
atin
g
ch
atter
in
g
wh
ile
m
ain
tain
i
n
g
t
h
e
r
o
b
u
s
tn
ess
o
f
th
e
s
y
s
tem
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
Fig
u
r
e
3
.
C
o
n
tr
o
l stru
ctu
r
e
o
f
t
h
e
STSMC
STSMC
ac
h
iev
es
r
o
b
u
s
t
co
n
tr
o
l
b
y
r
e
g
u
latin
g
b
o
th
th
e
s
lid
in
g
v
ar
iab
le
an
d
its
r
ate
o
f
ch
a
n
g
e,
en
ab
lin
g
th
e
s
y
s
tem
to
r
ea
ch
th
e
d
esire
d
s
tate
q
u
ick
ly
an
d
ac
cu
r
atel
y
with
in
a
f
in
ite
tim
e.
T
h
e
c
o
n
tr
o
ller
em
p
lo
y
s
a
s
p
ec
ial
co
n
tr
o
l
law
co
m
p
o
s
ed
o
f
two
p
ar
ts
:
o
n
e
th
at
d
ep
en
d
s
o
n
th
e
m
ag
n
itu
d
e
o
f
th
e
er
r
o
r
,
an
d
a
n
o
th
er
th
at
ad
ju
s
ts
b
ased
o
n
th
e
er
r
o
r
’
s
d
i
r
ec
tio
n
.
T
h
is
d
esig
n
e
n
s
u
r
es th
e
s
y
s
tem
r
em
ain
s
s
tab
le
ev
e
n
i
n
th
e
o
cc
u
r
r
e
n
ce
o
f
u
n
ce
r
tain
ties
an
d
ex
te
r
n
al
d
is
tu
r
b
an
ce
s
,
wh
ile
p
r
o
v
id
i
n
g
s
m
o
o
th
co
n
tr
o
l
an
d
s
tr
o
n
g
r
o
b
u
s
tn
ess
.
I
n
th
is
wo
r
k
,
an
im
p
r
o
v
e
d
co
n
tr
o
l
s
tr
ateg
y
is
u
s
ed
f
o
r
a
n
o
v
el
H
-
b
r
id
g
e
M
L
I
.
T
h
e
k
e
y
en
h
an
ce
m
en
t
lie
s
in
r
ep
lacin
g
th
e
co
n
v
en
tio
n
al
PI
co
n
tr
o
ller
u
s
e
d
f
o
r
DC
-
lin
k
v
o
ltag
e
r
eg
u
latio
n
with
th
e
STSMC,
o
v
er
co
m
in
g
lim
itatio
n
s
s
u
ch
as sl
o
w
d
y
n
am
ic
r
esp
o
n
s
e
a
n
d
lack
o
f
r
o
b
u
s
tn
ess
.
T
h
e
STSMC
s
tr
u
ctu
r
e
is
d
ev
e
lo
p
ed
in
s
im
u
latio
n
,
as
s
h
o
wn
in
Fig
u
r
e
3
m
o
d
el
d
iag
r
am
.
I
t
r
ec
eiv
es
DC
-
lin
k
v
o
ltag
e
er
r
o
r
(
)
,
wh
ich
r
ep
r
esen
ts
th
e
d
ev
iatio
n
b
etwe
en
r
ef
er
en
ce
v
o
ltag
e
an
d
th
e
ac
t
u
al
ag
g
r
eg
ated
PV
v
o
ltag
e.
T
h
e
co
n
tr
o
ller
s
tr
u
ctu
r
e
in
clu
d
es
two
m
ain
co
n
tr
o
l
ter
m
s
:
th
e
s
u
p
er
-
twis
tin
g
ter
m
an
d
th
e
in
teg
r
ato
r
-
b
ased
co
r
r
ec
tio
n
.
T
h
e
u
p
p
er
p
ath
o
f
th
e
d
iag
r
am
c
o
m
p
u
tes th
e
f
ir
s
t c
o
n
tr
o
l c
o
m
p
o
n
en
t b
ased
o
n
th
e
s
q
u
ar
e
r
o
o
t
o
f
th
e
ab
s
o
lu
te
er
r
o
r
m
u
ltip
lied
b
y
its
s
ig
n
.
T
h
is
ter
m
is
th
en
s
ca
led
b
y
th
e
g
ain
−
₃
=
−
0
.
7
an
d
u
s
ed
to
d
r
iv
e
a
f
ast
co
r
r
ec
ti
v
e
ac
tio
n
f
o
r
th
e
tr
ac
k
i
n
g
e
r
r
o
r
.
T
h
e
lo
wer
p
ath
r
ep
r
esen
ts
th
e
s
ec
o
n
d
-
o
r
d
er
co
r
r
ec
tio
n
,
wh
e
r
e
th
e
er
r
o
r
is
m
u
ltip
lied
b
y
a
g
ain
₄
=
0
.
91
an
d
th
en
in
teg
r
ated
o
v
e
r
tim
e
to
p
r
o
v
id
e
s
m
o
o
th
an
d
s
tab
le
r
eg
u
latio
n
.
T
h
e
s
u
m
o
f
t
h
ese
two
co
n
tr
o
l
s
ig
n
als
f
o
r
m
s
th
e
f
in
al
c
o
n
tr
o
l
ac
tio
n
(
)
,
wh
ich
d
y
n
a
m
ically
ad
ju
s
ts
p
ea
k
v
alu
e
o
f
r
ef
e
r
en
ce
g
r
id
cu
r
r
en
t.
T
h
is
v
alu
e
is
p
ass
ed
to
DM
PC
b
lo
ck
,
wh
ich
u
s
es
it
to
co
m
p
u
te
th
e
co
n
v
er
tin
g
m
o
v
em
en
ts
o
f
th
e
H
-
b
r
id
g
e
in
v
er
ter
.
T
h
e
in
teg
r
a
tio
n
o
f
STSMC
en
h
an
ce
s
s
y
s
tem
’
s
ca
p
ab
ilit
y
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
464
-
479
470
r
ejec
t d
is
tu
r
b
an
ce
s
an
d
ac
c
u
r
a
tely
tr
ac
k
v
o
ltag
e
r
ef
er
en
ce
s
,
ev
en
u
n
d
er
r
a
p
id
ly
ch
a
n
g
in
g
s
o
lar
co
n
d
itio
n
s
s
u
ch
as
f
lu
ctu
atio
n
s
in
ir
r
a
d
ian
ce
a
n
d
tem
p
e
r
atu
r
e.
U
n
lik
e
tr
ad
iti
o
n
al
co
n
v
er
ter
s
th
at
r
ely
o
n
li
n
ea
r
er
r
o
r
c
o
r
r
ec
tio
n
an
d
f
ix
ed
g
ain
tu
n
i
n
g
,
STSMC
o
f
f
er
s
n
o
n
lin
ea
r
,
r
o
b
u
s
t
co
n
tr
o
l
with
f
in
ite
-
tim
e
co
n
v
e
r
g
e
n
ce
,
m
ak
in
g
it
well
-
s
u
ited
f
o
r
p
o
wer
elec
tr
o
n
ic
a
p
p
licatio
n
s
.
I
n
th
is
p
r
o
ject,
im
p
lem
en
tin
g
STSMC
s
ig
n
if
ican
tly
im
p
r
o
v
es
th
e
d
y
n
am
ic
p
er
f
o
r
m
an
ce
o
f
DC
-
lin
k
v
o
ltag
e
r
eg
u
latio
n
.
As
a
r
e
s
u
lt,
th
e
q
u
ality
o
f
th
e
g
e
n
er
at
ed
r
ef
er
e
n
ce
cu
r
r
en
t
is
en
h
an
ce
d
,
lead
in
g
to
lo
we
r
T
HD
in
th
e
g
r
id
cu
r
r
en
t
an
d
b
etter
o
v
er
all
p
o
wer
q
u
ality
o
n
th
e
g
r
id
s
id
e.
T
h
e
co
n
tr
o
l
g
ain
s
f
o
r
STSMC
we
r
e
ca
r
ef
u
lly
tu
n
ed
th
r
o
u
g
h
s
im
u
latio
n
to
en
s
u
r
e
s
tab
ilit
y
a
n
d
a
f
ast
d
y
n
a
m
ic
r
esp
o
n
s
e.
T
h
e
o
u
tp
u
t
o
f
t
h
is
co
n
tr
o
ller
d
y
n
a
m
ically
ad
ju
s
ts
r
ef
er
en
ce
cu
r
r
en
t
b
ased
o
n
th
e
v
o
ltag
e
er
r
o
r
,
en
ab
lin
g
th
e
s
y
s
tem
to
q
u
ick
l
y
r
esp
o
n
d
t
o
s
u
d
d
e
n
d
is
tu
r
b
a
n
c
es o
r
ch
an
g
es in
o
p
er
atin
g
co
n
d
itio
n
s
.
6.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
o
ass
ess
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
STSMC
co
m
b
i
n
ed
with
DM
PC
in
a
g
r
id
-
co
n
n
ec
ted
PV
s
y
s
tem
,
ex
ten
s
iv
e
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
u
s
in
g
MA
T
L
AB
/Si
m
u
lin
k
as
d
is
p
lay
ed
in
Fig
u
r
e
4
.
T
h
e
ev
alu
atio
n
s
ce
n
ar
i
o
s
in
clu
d
e
d
ch
an
g
es
i
n
s
o
lar
i
r
r
ad
ian
ce
a
n
d
tem
p
e
r
atu
r
e
to
a
n
aly
ze
th
e
s
y
s
tem
’
s
d
y
n
am
ic
b
eh
av
io
r
,
v
o
ltag
e
s
tab
ilit
y
,
p
o
wer
h
ar
v
esti
n
g
ca
p
a
b
ilit
y
,
an
d
h
ar
m
o
n
ic
c
h
ar
ac
ter
is
tics
.
T
h
e
p
r
im
ar
y
g
o
al
was
to
d
em
o
n
s
tr
ate
th
at
r
ep
lacin
g
th
e
co
n
v
en
tio
n
al
PI
c
o
n
tr
o
ller
wit
h
STSMC
en
h
an
ce
s
th
e
r
o
b
u
s
t
n
ess
,
r
esp
o
n
s
e
tim
e,
an
d
p
o
wer
q
u
ality
o
f
th
e
s
y
s
tem
.
E
ac
h
s
im
u
latio
n
ca
s
e
s
tu
d
ie
s
a
d
if
f
er
en
t
d
is
tu
r
b
a
n
ce
s
ce
n
ar
io
,
an
d
t
h
e
s
y
s
tem
'
s
b
eh
av
io
r
is
an
aly
ze
d
th
r
o
u
g
h
v
o
ltag
e,
p
o
wer
,
cu
r
r
en
t,
a
n
d
T
HD
r
esp
o
n
s
es.
Fig
u
r
e
4
.
S
im
u
latio
n
m
o
d
el
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
6
.
1
.
Ca
s
e
1
:
Su
dd
en
v
a
ria
t
io
n in so
la
r
irra
dia
nce
o
f
P
V1
Fig
u
r
e
5
illu
s
tr
ates
th
e
s
y
s
tem
r
esp
o
n
s
e
wh
en
th
e
ir
r
ad
ian
ce
o
f
PV1
is
ab
r
u
p
tly
r
ed
u
ce
d
f
r
o
m
1
0
0
0
W
/m
²
to
6
0
0
W
/m
².
T
h
e
r
ef
er
e
n
ce
v
o
ltag
e
a
n
d
p
o
wer
v
alu
es
ad
ju
s
t
to
th
e
n
ew
ir
r
a
d
ian
ce
,
a
n
d
th
e
ac
tu
al
o
u
t
p
u
t
ac
cu
r
ately
f
o
llo
ws
th
ese
r
ef
e
r
en
ce
s
.
T
h
e
p
r
o
p
o
s
ed
STSM
C
d
em
o
n
s
tr
ates
r
ap
id
tr
ac
k
i
n
g
with
n
eg
lig
ib
le
o
v
er
s
h
o
o
t,
in
co
n
tr
ast
to
co
n
v
en
tio
n
al
PI
co
n
t
r
o
ller
s
th
at
ty
p
ically
ex
h
ib
it
lag
an
d
o
s
cillato
r
y
b
eh
a
v
io
r
u
n
d
er
s
u
ch
co
n
d
itio
n
s
.
T
h
is
co
n
f
ir
m
s
th
e
ef
f
ec
tiv
en
ess
o
f
STSMC
in
h
an
d
lin
g
ab
r
u
p
t
en
v
ir
o
n
m
en
tal
v
a
r
iatio
n
s
,
en
s
u
r
in
g
s
tab
le
v
o
ltag
e
r
eg
u
latio
n
an
d
co
n
tin
u
o
u
s
p
o
wer
in
je
ctio
n
in
to
th
e
g
r
id
.
6
.
2
.
Ca
s
e
2
:
Ste
p
v
a
ri
a
t
io
n i
n so
la
r
irra
dia
nce
o
f
P
V2
a
a
nd
P
V2
b
Fig
u
r
es
6
an
d
7
s
h
o
w
th
e
im
p
ac
t
o
f
s
tep
c
h
an
g
es
in
ir
r
ad
ia
n
ce
o
n
PV2
a
an
d
PV2
b
.
W
h
en
ir
r
ad
ian
ce
d
r
o
p
s
in
PV2
a,
th
e
co
m
b
in
ed
s
er
ies
-
co
n
n
ec
ted
v
o
ltag
e
r
is
es
wh
ile
p
o
wer
o
u
tp
u
t
d
ec
r
ea
s
e
s
.
Similar
ly
,
PV2
b
ex
h
ib
its
co
r
r
esp
o
n
d
in
g
v
o
lta
g
e
an
d
p
o
wer
ad
j
u
s
tm
en
ts
.
T
h
e
STSMC
m
ain
tain
s
s
m
o
o
th
tr
an
s
itio
n
s
with
m
in
im
al
r
ip
p
le,
wh
ile
a
v
o
id
in
g
d
is
tu
r
b
an
ce
p
r
o
p
ag
atio
n
to
PV1
d
esp
ite
th
e
s
h
ar
ed
DC
-
lin
k
.
T
h
is
h
ig
h
lig
h
ts
th
e
co
n
tr
o
ller
’
s
ca
p
ab
ilit
y
t
o
is
o
l
ate
an
d
s
tab
ilize
th
e
o
p
er
atio
n
o
f
m
u
ltip
le
PV
m
o
d
u
les
u
n
d
er
p
a
r
tial
s
h
a
d
in
g
co
n
d
itio
n
s
,
en
s
u
r
in
g
in
d
ep
en
d
en
t m
ax
im
u
m
p
o
wer
p
o
in
t tr
a
ck
in
g
f
o
r
ea
ch
DC
-
lin
k
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
u
p
er
-
tw
is
tin
g
s
lid
in
g
mo
d
e
c
o
n
tr
o
l fo
r
en
h
a
n
ce
d
p
erfo
r
ma
n
ce
o
f
…
(
C
H.
V
en
ka
t
a
A
ma
r
n
a
d
h
)
471
Fig
u
r
e
5
.
Simu
latio
n
r
esu
lts
o
f
ca
s
e
1
Fig
u
r
e
6
.
Var
iatio
n
o
f
s
tep
i
n
i
r
r
ad
ian
ce
o
f
PV2
a
Fig
u
r
e
7
.
Step
c
h
an
g
e
i
n
s
o
lar
ir
r
ad
ian
ce
o
f
PV2
b
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
464
-
479
472
6
.
3
.
Ca
s
e
3
:
Su
dd
en
v
a
ria
t
io
n in t
em
pera
t
ure
o
f
P
V1
I
n
Fig
u
r
e
8
,
th
e
tem
p
e
r
atu
r
e
o
f
PV1
is
in
cr
ea
s
ed
f
r
o
m
2
5
°C
to
3
5
°
C
at
t
=
0
.
4
s
.
T
h
e
r
is
e
in
tem
p
er
atu
r
e
ca
u
s
es
a
d
r
o
p
in
r
ef
er
en
ce
v
o
ltag
e
an
d
p
o
wer
,
wh
ich
th
e
STSMC
-
co
n
tr
o
lled
s
y
s
tem
tr
ac
k
s
with
h
ig
h
ac
cu
r
ac
y
.
Un
lik
e
PI
co
n
tr
o
ller
s
th
at
o
f
ten
r
esu
lt
in
o
s
cillatio
n
s
o
r
d
elay
ed
co
n
v
er
g
en
ce
u
n
d
e
r
th
er
m
al
d
is
tu
r
b
an
ce
s
,
th
e
STSMC
m
ain
tain
s
a
s
tab
le
r
esp
o
n
s
e
with
o
u
t
r
ip
p
le.
T
h
is
d
em
o
n
s
tr
ates
its
r
o
b
u
s
tn
ess
ag
ain
s
t
n
o
n
lin
ea
r
tem
p
er
atu
r
e
ef
f
ec
ts
an
d
its
ab
ilit
y
to
p
r
eser
v
e
v
o
lt
ag
e
s
tab
ilit
y
u
n
d
er
th
er
m
al
s
tr
ess
.
6
.
4
.
Ca
s
e
4
:
Su
dd
en
t
em
pera
t
ure
v
a
ria
t
io
n o
f
P
V2
a
Fig
u
r
e
9
s
h
o
ws
th
e
r
esp
o
n
s
e
wh
en
PV2
a
ex
p
er
ien
ce
s
a
s
u
d
d
en
tem
p
er
at
u
r
e
in
cr
ea
s
e.
T
h
e
r
ef
er
en
c
e
p
o
wer
d
ec
r
ea
s
es
an
d
th
e
v
o
lta
g
e
s
lig
h
tly
in
cr
ea
s
es
d
u
e
t
o
th
e
th
er
m
al
ef
f
ec
t.
T
h
e
STSMC
ef
f
ec
tiv
ely
tr
ac
k
s
th
ese
ch
an
g
es
with
s
m
o
o
th
an
d
s
tab
le
tr
an
s
itio
n
s
.
T
h
e
ab
s
en
ce
o
f
o
s
cillatio
n
s
o
r
d
elay
e
d
s
ettlin
g
em
p
h
asizes
th
e
im
p
r
o
v
ed
d
is
tu
r
b
a
n
ce
r
eje
ctio
n
o
f
STSMC
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
co
n
tr
o
ller
s
,
th
e
r
eb
y
v
alid
atin
g
its
s
u
itab
ilit
y
f
o
r
m
ain
tain
in
g
s
y
s
tem
s
tab
ilit
y
d
u
r
in
g
ab
r
u
p
t e
n
v
ir
o
n
m
en
tal
f
l
u
ctu
atio
n
s
.
Fig
u
r
e
8
.
Simu
latio
n
r
esu
lts
o
f
ca
s
e
3
Fig
u
r
e
9
.
Simu
latio
n
r
esu
lts
o
f
ca
s
e
4
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
S
u
p
er
-
tw
is
tin
g
s
lid
in
g
mo
d
e
c
o
n
tr
o
l fo
r
en
h
a
n
ce
d
p
erfo
r
ma
n
ce
o
f
…
(
C
H.
V
en
ka
t
a
A
ma
r
n
a
d
h
)
473
6
.
5
.
Ca
s
e
5
:
Sim
ulta
neo
us
v
a
ria
t
io
n in irr
a
dia
nce
a
nd
t
em
pera
t
ure
o
f
P
V
1
Fig
u
r
e
1
0
d
em
o
n
s
tr
ates
a
co
m
p
o
u
n
d
d
is
tu
r
b
an
ce
w
h
er
e
b
o
t
h
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e
o
f
PV1
ar
e
v
ar
ied
s
im
u
ltan
e
o
u
s
ly
.
T
h
is
r
e
s
u
lts
in
a
s
h
ar
p
d
r
o
p
in
o
u
tp
u
t
p
o
wer
a
n
d
a
m
o
d
er
ate
v
o
ltag
e
ch
an
g
e.
Desp
ite
th
e
co
m
b
in
ed
n
o
n
lin
ea
r
d
is
tu
r
b
an
ce
s
,
th
e
STSMC
ef
f
icien
tly
s
tab
ilizes
b
o
th
v
o
ltag
e
a
n
d
p
o
wer
with
m
in
im
al
d
ev
iatio
n
f
r
o
m
r
ef
er
e
n
ce
v
al
u
es.
T
h
e
r
a
p
id
an
d
ac
cu
r
ate
r
eg
u
latio
n
ac
h
iev
ed
u
n
d
er
w
o
r
s
t
-
ca
s
e
o
p
er
atin
g
co
n
d
itio
n
s
c
o
n
f
ir
m
s
t
h
e
s
u
p
e
r
io
r
ad
a
p
tab
ilit
y
o
f
STSMC
to
r
ea
l
-
wo
r
ld
s
ce
n
ar
io
s
w
h
er
e
m
u
l
tip
le
en
v
ir
o
n
m
en
tal
p
ar
am
eter
s
f
lu
ctu
ate
c
o
n
cu
r
r
e
n
tly
.
Fig
u
r
e
1
0
.
Step
v
ar
iatio
n
in
ir
r
ad
ian
ce
an
d
tem
p
er
atu
r
e
o
f
PV1
6
.
6
.
Ca
s
e
6
:
Neg
a
t
iv
e
ra
m
p
cha
ng
e
in irr
a
dia
nce
o
f
P
V1
Fig
u
r
e
1
1
p
r
esen
ts
th
e
ef
f
ec
t
o
f
a
g
r
a
d
u
al
r
ed
u
ctio
n
in
PV
1
ir
r
ad
ian
ce
f
o
llo
win
g
a
n
eg
a
tiv
e
r
am
p
f
u
n
ctio
n
.
T
h
e
STSMC
s
u
cc
ess
f
u
lly
m
an
a
g
es
th
is
n
o
n
lin
ea
r
a
n
d
s
lo
w
tr
an
s
itio
n
b
y
m
ain
tain
in
g
ac
cu
r
ate
v
o
ltag
e
an
d
p
o
wer
tr
ac
k
in
g
with
o
u
t
l
ag
o
r
o
s
cillatio
n
s
.
I
n
co
n
tr
ast,
PI
co
n
tr
o
ller
s
ty
p
ically
ex
h
ib
it
d
elay
ed
tr
ac
k
in
g
u
n
d
er
s
u
ch
c
o
n
d
itio
n
s
.
T
h
is
r
esu
lt
d
em
o
n
s
tr
ates
th
e
ad
ap
tab
ilit
y
o
f
STSMC
f
o
r
h
an
d
lin
g
r
ea
l
-
life
s
ce
n
ar
io
s
s
u
ch
as c
lo
u
d
m
o
v
em
e
n
t a
n
d
p
ar
tial sh
ad
in
g
,
w
h
er
e
ir
r
a
d
ian
ce
ch
an
g
es g
r
ad
u
ally
r
ath
er
th
a
n
ab
r
u
p
tly
.
6
.
7
.
Ca
s
e
7
:
I
m
pa
ct
o
f
s
t
ep
c
ha
ng
es in so
la
r
irra
dia
nce
o
n t
he
g
rid c
urre
nt
Fig
u
r
e
1
2
illu
s
tr
ates
th
e
s
y
s
tem
p
er
f
o
r
m
a
n
ce
in
ter
m
s
o
f
g
r
id
cu
r
r
e
n
t,
g
r
id
v
o
ltag
e,
an
d
m
u
ltil
ev
el
in
v
er
ter
o
u
tp
u
t
wav
ef
o
r
m
d
u
r
i
n
g
s
tep
ir
r
ad
ian
ce
c
h
an
g
es.
T
h
e
ac
tu
al
g
r
i
d
cu
r
r
en
t
cl
o
s
ely
f
o
llo
ws
th
e
r
ef
er
en
c
e,
ev
en
u
n
d
er
d
is
tu
r
b
a
n
ce
s
,
an
d
r
em
ain
s
well
s
y
n
ch
r
o
n
ized
wi
th
th
e
g
r
id
v
o
ltag
e,
en
s
u
r
i
n
g
o
p
er
atio
n
at
n
ea
r
ly
u
n
ity
p
o
wer
f
ac
to
r
.
T
h
e
s
ev
en
-
lev
el
o
u
tp
u
t
wav
ef
o
r
m
o
f
th
e
p
r
o
p
o
s
ed
in
v
e
r
ter
is
clea
r
ly
v
is
i
b
le,
d
em
o
n
s
tr
atin
g
r
ed
u
ce
d
h
ar
m
o
n
ic
co
n
ten
t
an
d
b
etter
s
in
u
s
o
id
al
ap
p
r
o
x
im
atio
n
co
m
p
ar
e
d
to
co
n
v
en
tio
n
al
to
p
o
lo
g
ies.
T
h
is
co
n
f
ir
m
s
th
e
c
o
m
b
i
n
ed
ef
f
ec
tiv
en
ess
o
f
STSMC
an
d
DM
PC
in
en
s
u
r
in
g
r
eliab
le
g
r
i
d
s
y
n
ch
r
o
n
izatio
n
a
n
d
im
p
r
o
v
e
d
wav
ef
o
r
m
q
u
ality
.
6
.
8
.
Ca
s
e
8
:
P
o
wer
t
ra
c
k
ing
un
der
m
ultiple d
is
t
urba
nce
s
Fig
u
r
e
1
3
co
m
p
ar
es
th
e
r
e
f
er
en
ce
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP
)
,
ex
tr
ac
ted
p
o
wer
,
a
n
d
d
eliv
er
ed
o
u
tp
u
t
p
o
wer
u
n
d
e
r
a
s
eq
u
e
n
c
e
o
f
ir
r
ad
ian
ce
a
n
d
tem
p
er
atu
r
e
d
is
tu
r
b
an
ce
s
.
T
h
e
e
x
tr
ac
ted
an
d
o
u
tp
u
t
p
o
wer
co
n
s
is
ten
tly
tr
ac
k
th
e
r
ef
er
e
n
ce
v
alu
es,
d
em
o
n
s
tr
atin
g
th
e
ab
ilit
y
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
s
ch
em
e
to
s
u
s
tain
m
ax
im
u
m
p
o
wer
e
x
tr
ac
tio
n
an
d
ef
f
icie
n
t
en
er
g
y
tr
a
n
s
f
er
u
n
d
e
r
d
y
n
am
ic
c
o
n
d
itio
n
s
.
T
h
is
v
alid
ates
th
e
co
o
r
d
in
atio
n
b
etwe
en
STSMC
an
d
DM
PC
,
wh
er
e
th
e
STSMC
en
s
u
r
es
s
tab
le
v
o
ltag
e
r
eg
u
l
atio
n
wh
ile
DM
PC
g
u
ar
an
tee
s
ac
cu
r
ate
cu
r
r
e
n
t tr
a
ck
in
g
an
d
g
r
i
d
in
jectio
n
.
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