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I
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148
T
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1
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p
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la
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d
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s
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ate
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d
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m
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(
MP
PT)
tech
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iq
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A
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b
ased
s
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m
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la
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esu
l
ts
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tab
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tech
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iq
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p
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2.
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RO
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L
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M
UL
AT
I
O
N
T
h
e
v
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ltag
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a
n
d
f
r
eq
u
en
c
y
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co
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in
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elec
tr
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te
m
,
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m
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in
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s
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o
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k
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in
h
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lt
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y
c
o
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d
itio
n
.
Ho
w
ev
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,
w
h
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n
a
f
a
u
lt
o
cc
u
r
s
to
th
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tili
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th
e
s
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n
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s
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t
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th
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ass
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in
th
e
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tio
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o
f
th
e
P
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.
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l
ly
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g
e
n
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d
its
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ter
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h
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e
lo
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al
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th
e
o
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n
d
m
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y
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t
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e
eq
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ip
m
en
t
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t
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n
e
l.
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h
e
I
E
E
E
s
tan
d
ar
d
9
2
9
-
2000
w
a
s
cr
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ted
to
p
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s
tr
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y
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h
f
r
eq
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en
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y
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n
d
v
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r
estrictio
n
s
th
e
d
is
tr
ib
u
tio
n
g
r
id
[3
-
4
]
.
T
ab
le
1
s
h
o
w
th
e
f
r
eq
u
e
n
c
y
an
d
v
o
ltag
e
li
m
i
ts
i
n
ten
d
ed
f
o
r
th
e
u
tili
t
y
g
r
id
.
T
ab
le
1
.
I
s
lan
d
in
g
Dete
ct
io
n
T
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m
e
o
f
Fre
q
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e
n
c
y
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d
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lta
g
e
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m
its
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th
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I
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ST
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2
9
-
2000
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me
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c
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s)
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n
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y
(
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3
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ased
m
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[
1
3
-
16]
.
C
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r
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[
1
7
-
1
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.
T
ab
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2
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mp
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e
r
r
o
-
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n
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f
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t
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i
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t
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i
b
u
t
i
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n
sy
st
e
m
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o
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e
D
i
r
e
c
t
i
n
f
l
u
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n
c
e
o
n
p
o
w
e
r
s
y
st
e
m
L
o
w
e
r
t
h
a
n
a
c
t
i
v
e
me
t
h
o
d
N
o
n
e
N
o
n
e
A
sso
c
i
a
t
e
d
i
n
v
e
r
t
e
r
I
n
f
l
u
e
n
c
e
N
o
n
e
Y
e
s
Y
e
s
N
o
n
e
N
o
n
e
T
h
e
r
e
m
o
te
m
e
th
o
d
o
f
i
s
lan
d
i
n
g
d
etec
tio
n
is
b
etter
t
h
an
lo
c
al
is
la
n
d
in
g
d
etec
tio
n
m
et
h
o
d
s
,
ex
ce
p
t
at
th
e
in
cr
ea
s
ed
co
s
t
an
d
co
m
p
le
x
it
y
[
2
0
-
23]
.
L
o
ca
l
m
e
th
o
d
s
a
r
e
m
o
r
e
p
r
ef
er
ab
le
b
ec
au
s
e
t
h
e
y
ar
e
d
ep
en
d
en
t
o
n
th
e
m
ea
s
u
r
e
m
e
n
t o
f
lo
ca
l p
ar
am
eter
s
,
f
r
ee
f
r
o
m
n
o
is
e
i
n
co
m
m
u
n
icat
io
n
,
ch
ea
p
er
etc
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
7
,
No
.
2
,
A
u
g
u
s
t
2
0
1
8
:
1
4
7
–
1
5
8
150
3
.
2
.
Sy
s
t
em
s
t
ud
y
f
o
r
is
la
nd
i
ng
det
ec
t
io
n
R
ec
o
m
m
e
n
d
ed
test
s
t
u
d
y
o
f
is
lan
d
i
n
g
d
etec
tio
n
ar
r
an
g
e
m
en
t
co
n
s
i
s
ts
o
f
an
i
n
v
er
ter
-
b
ased
DG,
p
ar
allel
R
L
C
lo
ad
a
n
d
th
e
g
r
id
r
ep
r
esen
ted
th
r
o
u
g
h
a
s
o
u
r
ce
f
o
llo
w
in
g
i
m
p
ed
an
ce
.
T
h
e
eq
u
ip
p
ed
m
o
d
e
o
f
t
h
e
DG
d
ep
en
d
s
o
n
w
h
et
h
er
t
h
e
ci
r
cu
it b
r
ea
k
er
is
clo
s
ed
o
r
n
o
t
[3
-
4]
.
T
h
e
in
v
er
ter
-
b
ased
DG
s
u
ch
a
s
p
h
o
to
v
o
ltaic
s
tr
u
ct
u
r
e
is
u
s
u
al
l
y
co
n
f
ig
u
r
e
d
w
it
h
t
h
e
MP
P
T
alg
o
r
ith
m
.
Sin
ce
i
s
la
n
d
in
g
d
etec
tio
n
ti
m
e
is
e
x
tr
e
m
el
y
s
m
a
ll,
th
e
o
u
tp
u
t
p
o
w
er
i
s
ab
le
to
m
ea
s
u
r
e
u
n
v
ar
y
in
g
th
r
o
u
g
h
t
h
e
d
etec
tio
n
.
As
a
r
es
u
lt,
b
y
a
c
o
n
s
ta
n
t
D
C
s
o
u
r
ce
f
o
llo
w
in
g
a
th
r
ee
-
p
h
ase
i
n
v
er
ter
,
th
e
DG
is
co
n
s
id
er
ed
as
a
u
n
v
ar
y
i
n
g
p
o
w
er
s
o
u
r
ce
.
Fig
u
r
e
2
s
h
o
w
s
t
h
e
is
lan
d
i
n
g
d
etec
tio
n
s
y
s
te
m
w
h
ich
co
n
s
i
s
ts
o
f
t
w
o
m
o
d
e
s
o
f
o
p
er
atio
n
s
i.e
.
,
g
r
id
-
co
n
n
ec
ted
m
o
d
e
an
d
is
lan
d
ed
m
o
d
e.
D
u
r
in
g
t
h
e
s
ta
n
d
ar
d
o
p
er
atio
n
o
r
g
r
id
-
co
n
n
ec
ted
m
o
d
e,
th
e
DG
w
i
th
i
n
t
h
e
m
icr
o
g
r
id
w
ill
b
e
o
p
er
atio
n
al
in
u
n
v
ar
y
i
n
g
c
u
r
r
en
t
co
n
tr
o
l
m
o
d
e
an
d
w
it
h
i
n
is
la
n
d
ed
m
o
d
e
,
th
e
cu
r
r
en
t
co
n
tr
o
l
ap
p
r
o
ac
h
s
w
itc
h
ed
to
v
o
ltag
e
co
n
tr
o
l
ap
p
r
o
ac
h
[
2
4
]
.
D
C
A
C
I
n
v
e
r
t
e
r
D
C
L
O
A
D
G
r
i
d
R
g
L
g
C
i
r
c
u
i
t
B
r
e
a
k
e
r
P
C
C
L
f
i
l
t
e
r
P
D
G
+
j
Q
D
G
P
G
r
i
d
+
j
Q
G
r
i
d
P
L
o
a
d
+
j
Q
L
o
a
d
D
C
A
C
I
n
v
e
r
t
e
r
D
C
L
O
A
D
G
r
i
d
R
g
L
g
C
i
r
c
u
i
t
B
r
e
a
k
e
r
P
C
C
L
f
i
l
t
e
r
P
D
G
+
j
Q
D
G
P
G
r
i
d
+
j
Q
G
r
i
d
P
L
o
a
d
+
j
Q
L
o
a
d
(
a)
Gr
id
p
er
atio
n
-
co
n
n
ec
ted
o
Mo
d
e
(
b
)
I
s
lan
d
ed
Op
er
atio
n
Mo
d
e
Fig
u
r
e
2
.
I
s
lan
d
in
g
Dete
ctio
n
Mo
d
els
E
q
u
atio
n
1
d
escr
ib
es
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
w
er
e
n
th
u
s
ia
s
tic
b
y
th
e
lo
ad
w
h
en
D
G
is
ass
o
ciate
d
to
w
ar
d
th
e
u
tili
t
y
g
r
id
in
g
r
id
-
co
n
n
ec
ted
m
o
d
e
[
2
3
-
25]
.
íü
ïï
ïï
ïï
ïï
ïï
ïï
ïï
ïï
ìý
ïï
ïï
ïï
ïï
æö
ïï
÷
ç
ïï
÷
ç
÷
ïï
ç
èø
ïï
îþ
P
C
C
G
2
P
C
C
L
o
a
d
D
G
G
r
i
d
2
L
o
a
d
D
G
G
r
i
d
P
C
C
V
=
V
V
P
=
P
+
Δ
P
=
3
R
1
Q
=
Q
+
Δ
Q
=
3
V
-
ω
C
ωL
(
1
)
T
h
e
r
eso
n
an
t f
r
eq
u
e
n
c
y
(
f
LC
)
an
d
q
u
alit
y
f
ac
to
r
(
Q
f
)
o
f
p
ar
allel
R
L
C
lo
ad
ar
e
d
ef
in
ed
lik
e
:
LC
1
f=
2
π
L
C
(
2
)
f
C
Q
=
R
L
(
3
)
I
s
la
n
d
ed
m
o
d
e
in
cid
en
tal
f
r
o
m
eq
.
(
1
)
th
at
if
th
e
ac
tiv
e
p
o
w
er
d
is
p
ar
it
y
(
∆P
)
=P
Load
-
P
DG
=P
Grid
is
n
o
t
id
en
tica
l
to
ze
r
o
.
T
h
e
P
C
C
v
o
lta
g
e
r
eso
l
v
e
d
r
o
p
o
r
r
ai
s
e
it
d
o
es
n
o
t
d
ep
en
d
s
o
n
D
G
o
p
er
ates
o
n
u
n
it
y
p
o
w
er
f
ac
to
r
o
r
n
o
t.
T
h
e
q
u
a
n
tit
y
o
f
v
o
ltag
e
d
iv
er
g
e
n
ce
d
ep
en
d
s
u
p
o
n
o
n
th
e
a
s
s
e
s
s
m
e
n
t
o
f
∆P
.
I
f
t
h
e
ac
t
iv
e
p
o
w
er
o
r
ien
tatio
n
o
f
t
h
e
DG
i
s
s
et
to
b
e
co
n
s
tan
t,
∆P
ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
[
2
4
-
25]
:
(
)
æö
÷
ç
÷
ç
÷
ç
÷
ç
÷
ç
èø
DG
2
1
Δ
P
=
P
-
1
1+
ΔV
(
4
)
w
h
er
e,
∆V
r
ep
r
esen
ts
th
e
v
o
lta
g
e
d
is
p
ar
it
y
a
n
d
it c
an
b
e
ex
p
r
ess
ed
as:
P
C
C
.
i
P
C
C
P
C
C
V
-
V
Δ
V
=
V
(
5
)
w
h
er
e
V
PCC
an
d
V
P
CC.
i
d
escr
ib
es
th
e
P
C
C
v
o
lta
g
e
b
ef
o
r
e
an
d
af
ter
is
la
n
d
in
g
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
A
n
E
n
h
a
n
ce
d
C
o
n
tr
o
l S
tr
a
teg
y
fo
r
th
e
S
ta
b
le
Op
era
tio
n
o
f
Dis
tr
ib
u
ted
Gen
era
tio
n
.
.
.
(
Ya
tin
d
r
a
Go
p
a
l
)
151
4.
P
RO
P
O
SE
D
T
E
CH
NI
Q
U
E
T
h
r
ee
-
p
h
ase
t
w
o
-
s
tag
e
g
r
id
-
c
o
n
n
ec
ted
i
n
v
er
ter
is
co
llect
ed
o
f
t
w
o
co
n
v
er
s
io
n
s
ta
g
es,
th
e
f
ir
s
t
-
s
tag
e
is
D
C
-
DC
b
o
o
s
t c
o
n
v
er
ter
i.e
.
u
s
ed
to
b
o
o
s
t t
h
e
P
V
s
ec
tio
n
o
u
tp
u
t
v
o
lta
g
e
a
n
d
o
r
g
a
n
ize
t
h
e
P
V
v
o
lta
g
e
w
h
ic
h
r
eg
u
late
s
t
h
e
o
p
er
atio
n
o
f
a
m
o
d
u
le
at
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
(
MP
P
)
.
T
h
e
r
eg
u
lated
v
o
lta
g
e
o
f
DC
-
D
C
b
o
o
s
t
co
n
v
er
ter
is
atte
n
d
ed
to
th
e
D
C
li
n
k
,
w
h
ic
h
is
a
n
i
n
p
u
t
o
f
t
h
e
DC
-
AC
i
n
v
er
ter
.
T
h
e
DC
-
AC
i
n
v
er
ter
s
u
itab
le
f
o
r
m
ain
tain
i
n
g
th
e
DC
li
n
k
v
o
ltag
e
an
d
co
n
t
r
o
l
th
e
o
u
tp
u
t
cu
r
r
en
t.
P
L
L
in
te
n
d
ed
f
o
r
A
C
p
o
w
er
o
u
tp
u
t
o
f
th
e
in
v
er
ter
is
s
y
n
c
h
r
o
n
ized
w
it
h
th
e
g
r
id
a
n
d
is
la
n
d
in
g
d
etec
t
io
n
p
u
r
p
o
s
e
w
h
en
g
r
id
f
r
eq
u
e
n
c
y
an
d
v
o
lta
g
e
i
s
b
elo
w
an
d
ab
o
v
e
I
E
E
E
s
tan
d
ar
d
s
li
m
its
.
T
h
e
ex
p
lan
at
io
n
o
f
p
r
o
p
o
s
ed
tech
n
iq
u
e
is
ca
teg
o
r
ized
in
f
o
llo
w
i
n
g
i.e
.
m
o
d
eli
n
g
o
f
P
V
m
o
d
u
le,
m
ax
i
m
u
m
p
o
w
er
p
o
in
t
tr
ac
k
i
n
g
(
P
&
O)
,
a
d
esig
n
o
f
b
o
o
s
t
co
n
v
er
ter
an
d
in
v
er
ter
co
n
tr
o
l s
tr
ateg
y
.
4
.
1
.
M
o
delin
g
o
f
P
V
m
o
du
le
A
p
h
o
to
v
o
ltaic
m
o
d
u
le
is
cr
ea
ted
b
y
co
n
ce
r
n
i
n
g
m
an
y
s
o
lar
ce
lls
in
s
er
ies
a
n
d
p
ar
allel,
it
c
o
n
s
is
ts
o
f
a
cu
r
r
en
t so
u
r
ce
,
a
d
io
d
e,
an
d
s
er
ies
-
p
ar
allel
ar
r
an
g
e
m
en
t r
es
is
to
r
s
as see
n
f
r
o
m
Fi
g
u
r
e
3
.
I
P
V
I
d
I
s
h
R
s
h
V
d
R
s
I
V
Fig
u
r
e
3
.
E
q
u
iv
ale
n
t
cir
cu
it o
f
s
in
g
le
d
io
d
e
P
V
m
o
d
u
l
e
T
h
e
ch
ar
ac
ter
is
tic
eq
u
atio
n
f
o
r
a
p
h
o
to
v
o
ltaic
ce
ll is
s
p
ec
i
f
ie
d
b
y
[
2
6
-
29
]
:
(
)
éù
æö
÷
ç
êú
÷
ç
÷
êú
ç
÷
ç
èø
êú
ëû
Ss
P
V
,
n
1
0
n
t
h
s
h
V
+
R
I
V
+
R
I
G
I
=
I
+
K
Δ
T
-
I
e
x
p
-
1
-
G
V
a
R
(
6)
w
h
er
e,
V
th
æö
÷
ç
÷
ç
÷
ç
èø
s
N
K
T
q
in
d
icate
s
t
h
e
t
h
er
m
al
v
o
ltag
e
o
f
t
h
e
PV
ar
r
an
g
e
m
en
t
,
K
r
ep
r
esen
t
s
B
o
ltz
m
a
n
n
co
n
s
tan
t
(
1
.
3
8
0
6
5
0
3
*
1
0
-
23
J
/K)
,
a
r
ep
r
esen
ts
id
ea
lit
y
f
ac
to
r
g
e
n
er
all
y
p
r
ef
er
r
ed
i
n
t
h
e
r
an
g
e
1
≤
ɑ
≤
1
.
5
,
q
in
d
icate
s
elec
tr
o
n
ch
ar
g
e
(
1
.
6
0
2
1
7
6
4
6
*
1
0
-
19
C
)
.
4
.
2
.
M
a
x
i
m
u
m
po
w
er
po
int
t
ra
c
kin
g
P
er
tu
r
b
an
d
o
b
s
er
v
e
(
P
&
O)
al
g
o
r
ith
m
is
ex
te
n
s
iv
e
l
y
u
s
ed
in
MPPT
b
ec
au
s
e
o
f
th
eir
s
i
m
p
l
e
s
tr
u
ctu
r
e
an
d
r
ea
l
-
ti
m
e
i
m
p
le
m
en
tatio
n
is
ea
s
y
.
B
y
t
h
e
h
elp
o
f
MP
PT
co
n
tr
o
ller
,
p
r
o
d
u
ce
d
u
ty
c
y
cle
to
tr
ig
g
er
t
h
e
b
o
o
s
t
co
n
v
er
ter
s
w
itc
h
[
3
0
-
3
1
]
.
T
h
e
m
at
h
e
m
a
tical
i
ll
u
s
tr
atio
n
o
f
P
&
O
al
g
o
r
ith
m
[
3
2
]
is
g
iv
e
n
as
f
o
llo
w
s
P
V
P
V
P
V
d
P
P
(
k
)
-
P
(
k
-
1
)
(
k
)
=
d
V
V
(
k
)
-
V
(
k
-
1
)
(7
)
T
h
e
o
p
er
atin
g
p
o
in
t
is
p
er
tu
r
b
ed
f
r
o
m
ti
m
e
to
ti
m
e
b
y
s
h
i
f
ti
n
g
th
e
v
o
ltag
e
in
P
V
s
y
s
te
m
.
T
h
e
w
o
r
k
i
n
g
v
o
lta
g
e
o
f
P
V
s
ec
tio
n
is
d
is
co
n
ce
r
ted
b
y
a
s
m
all
r
i
s
e
an
d
th
e
co
n
s
eq
u
e
n
tial
c
h
an
g
e
in
p
o
w
er
(
∆P
)
.
I
f
∆P
is
p
o
s
iti
v
e,
t
h
e
w
o
r
k
in
g
p
o
in
t
r
ea
ch
ed
s
e
c
u
r
e
to
MP
P
.
I
f
∆P
is
n
e
g
ati
v
e,
t
h
e
o
p
er
atin
g
p
o
in
t
h
a
s
m
o
v
ed
d
is
tan
t
f
r
o
m
t
h
e
MP
P
an
d
d
ir
e
ctio
n
o
f
p
er
tu
r
b
atio
n
e
n
co
u
r
ag
ed
in
v
er
ted
r
ev
er
s
e
to
w
ar
d
s
M
P
P
[
3
2
-
3
3
]
.
4
.
3
.
Desig
n o
f
bo
o
s
t
co
nv
er
t
er
T
h
e
b
o
o
s
t
co
n
v
er
ter
is
s
tep
u
p
th
e
v
al
u
e
o
f
i
n
p
u
t
D
C
v
o
lt
ag
e
an
d
g
iv
e
s
b
y
an
o
u
tp
u
t.
T
h
e
m
ai
n
co
m
p
o
n
e
n
t
s
o
f
a
b
o
o
s
t
co
n
v
er
ter
ar
e
an
in
d
u
cto
r
,
a
d
io
d
e,
a
ca
p
ac
ito
r
an
d
h
ig
h
-
f
r
eq
u
en
c
y
I
GB
T
s
w
itc
h
[
3
4
-
3
5
]
.
I
n
th
is
p
ap
er
,
th
e
d
u
t
y
c
y
c
le
o
f
co
n
v
er
ter
s
w
itc
h
is
g
en
er
ated
f
r
o
m
MP
P
T
tech
n
i
q
u
e
an
d
o
p
er
atin
g
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
at
h
ig
h
t
o
g
en
er
ate
m
ax
i
m
u
m
p
o
w
er
.
R
ep
r
esen
tat
io
n
c
ir
cu
it
d
iag
r
a
m
o
f
b
o
o
s
t
co
n
v
er
ter
as
d
ep
icted
in
Fig
u
r
e
4
.
T
h
e
eq
u
atio
n
s
f
o
r
an
in
d
u
cto
r
(
L
)
,
a
ca
p
ac
it
o
r
(
C
)
a
n
d
Du
t
y
c
y
cle
(
D)
ar
e
g
iv
e
n
by
[
34]
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
7
,
No
.
2
,
A
u
g
u
s
t
2
0
1
8
:
1
4
7
–
1
5
8
152
i
i
n
L
i
L
D
S
B
1
C
V
c
i
c
V
i
n
V
o
u
t
Fig
u
r
e
4
.
C
ir
cu
it
d
ia
g
r
a
m
f
o
r
b
o
o
s
t c
o
n
v
er
ter
in
L
V
D
T
L=
Δi
;
0
0
VD
C=
Δ
V
R
f
;
o
u
t
i
n
out
V
-
V
D=
V
h
er
e,
∆i
L
in
d
icate
s
in
d
u
cto
r
r
ip
p
le
cu
r
r
en
t
an
d
∆V
0
in
d
icate
s
ca
p
ac
ito
r
v
o
ltag
e
r
ip
p
le,
T
i
s
th
e
ti
m
e
p
er
io
d
(
s
ec
)
.
4
.
4
.
I
nv
er
t
er
c
o
ntr
o
l st
ra
t
e
g
y
T
h
e
co
n
tr
o
l
s
y
s
te
m
o
f
a
n
in
v
er
ter
is
b
ased
o
n
P
L
L
f
o
r
d
eter
m
in
a
tio
n
o
f
f
r
eq
u
e
n
c
y
a
n
d
v
o
ltag
e
to
is
lan
d
i
n
g
d
etec
tio
n
.
P
L
L
co
n
s
is
ts
o
f
t
w
o
lo
o
p
s
i.e
.
an
o
u
ter
l
o
o
p
s
ch
e
m
i
n
g
t
h
e
DC
li
n
k
v
o
ltag
e
an
d
an
in
n
er
lo
o
p
s
ch
e
m
i
n
g
t
h
e
ac
ti
v
e
(
I
d
)
an
d
r
ea
ctiv
e
(
I
q
)
o
r
th
o
g
o
n
al
cu
r
r
en
t
co
m
p
o
n
e
n
ts
.
T
h
e
o
r
ien
t
atio
n
s
etti
n
g
f
o
r
th
e
I
d
co
m
p
o
n
e
n
t
is
d
eter
m
i
n
ed
b
y
a
n
ex
ter
n
al
v
o
ltag
e
co
n
tr
o
ller
at
th
e
s
a
m
e
ti
m
e
as
th
e
v
alu
e
o
f
th
e
I
q
co
m
p
o
n
e
n
t
is
s
et
to
ze
r
o
to
k
ee
p
u
p
u
n
it
y
p
o
w
er
f
ac
to
r
.
T
h
e
o
u
tp
u
t
p
o
w
er
o
f
th
r
e
e
-
p
h
a
s
e
i
n
v
er
ter
i
s
co
o
r
d
in
ated
th
r
o
u
g
h
g
r
id
u
s
in
g
a
P
L
L
.
P
L
L
i
s
d
esi
g
n
ed
f
o
r
th
e
m
ai
n
l
y
d
eter
m
i
n
atio
n
o
f
t
h
e
f
r
eq
u
e
n
c
y
a
n
d
an
g
le
o
r
ien
ta
tio
n
at
t
h
e
P
C
C
,
it
co
n
s
is
ts
o
f
f
o
u
r
co
m
p
o
n
en
t
s
i.
e.
C
lar
k
’
s
tr
a
n
s
f
o
r
m
atio
n
,
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
,
P
I
r
eg
u
lat
o
r
an
d
an
in
te
g
r
ato
r
.
d
q
0
to
ab
c
tr
an
s
f
o
r
m
atio
n
i
s
ca
lled
C
lar
k
’
s
tr
an
s
f
o
r
m
atio
n
an
d
ab
c
to
d
q
0
tr
an
s
f
o
r
m
a
ti
o
n
is
ca
lled
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
.
T
h
ese
tr
an
s
f
o
r
m
atio
n
s
i
n
th
e
P
L
L
m
eth
o
d
w
il
l
g
e
n
er
ate
a
t
h
r
ee
-
p
h
ase
b
a
lan
ce
d
w
av
e
f
o
r
m
th
r
o
u
g
h
a
1
2
0
o
p
h
ase
s
h
i
f
t
w
h
i
ch
ca
n
b
e
g
iv
e
n
a
s
i
n
p
u
t
to
th
e
in
v
er
ter
.
P
I
r
eg
u
lato
r
s
ar
e
u
s
e
d
f
o
r
s
ch
e
m
i
n
g
t
h
e
er
r
o
r
s
in
th
e
o
u
tp
u
t
o
f
th
e
g
r
id
f
r
eq
u
en
c
y
an
d
g
r
id
v
o
ltag
e
m
ag
n
it
u
d
e.
C
lar
k
’
s
an
d
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
eq
u
atio
n
ar
e
g
i
v
e
n
b
elo
w
:
C
lar
k
’
s
tr
a
n
s
f
o
r
m
atio
n
:
[
]
éù
êú
êú
éù
êú
êú
êú
êú
êú
êú
êú
êú
êú
êú
ëû
êú
êú
ëû
d
q
a
b
c
0
2
2
1
s
i
n
(
ω
t
)
c
o
s
(
ω
t
)
3
3
3
V
2
π
2
π
1
V
=
s
i
n
(
ω
t
-
)
c
o
s
(
ω
t
-
)
V
V
V
3
3
3
V
2
π
2
π
1
s
i
n
(
ω
t
+
)
c
o
s
(
ω
t
+
)
3
3
3
(8
)
P
ar
k
’
s
tr
an
s
f
o
r
m
atio
n
:
éù
êú
êú
éù
êú
êú
êú
éù
êú
êú
êú
ëû
êú
êú
êú
êú
ëû
êú
êú
ëû
a
b
d
q
0
c
s
i
n
(
ω
t
)
c
o
s
(
ω
t
)
1
V
2
π
2
π
V
=
s
i
n
(
ω
t
-
)
c
o
s
(
ω
t
-
)
1
V
V
V
33
V
2
π
2
π
s
i
n
(
ω
t
+
)
c
o
s
(
ω
t
+
)
1
33
(9
)
W
h
er
e,
V
a
,
V
b
,
V
c
ar
e
th
e
co
n
s
ta
n
t
q
u
a
n
tit
y
a
n
d
V
d
,
V
q
,
V
0
ar
e
s
tip
u
lated
q
u
an
t
it
y
o
f
th
r
ee
-
p
h
ase
v
o
ltag
e.
T
h
e
b
lo
ck
d
iag
r
a
m
o
f
i
n
v
er
ter
co
n
tr
o
l
f
o
r
p
r
o
j
ec
ted
is
lan
d
in
g
d
etec
tio
n
p
r
o
ce
s
s
is
s
p
ec
if
ie
d
in
Fi
g
u
r
e
5
.
I
t
in
clu
d
es
th
r
ee
-
p
h
a
s
e
r
ea
ctiv
e
c
u
r
r
en
t
co
m
p
o
n
en
ts
,
o
u
ter
v
o
ltag
e
lo
o
p
in
ten
d
ed
f
o
r
p
o
w
er
co
n
tr
o
l
a
n
d
in
n
er
lo
o
p
in
te
n
d
ed
f
o
r
g
r
id
v
o
ltag
e
co
n
tr
o
l
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
A
P
E
I
SS
N:
2252
-
8792
A
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ates
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it
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∆P
(
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=
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Load
-
P
DG
).
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h
u
s
,
th
e
v
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d
is
s
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m
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f
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s
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et
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ta
n
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is
p
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it
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ca
n
b
e
ex
p
r
ess
ed
as f
o
llo
w
s
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2252
-
8792
IJ
A
P
E
Vo
l.
7
,
No
.
2
,
A
u
g
u
s
t
2
0
1
8
:
1
4
7
–
1
5
8
154
(
)
2
1
1
1
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÷
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D
=
-
÷
ç
÷
ç
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+D
èø
DG
PP
V
(
15
)
an
d
∆V
ca
n
b
e
ex
p
r
ess
ed
as
*
-
D=
P
C
C
P
C
C
P
C
C
VV
V
V
Si
m
i
lar
l
y
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it
ca
n
b
e
s
ee
n
f
r
o
m
E
q
u
atio
n
(
1
2
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at
t
h
e
a
m
o
u
n
t
o
f
d
is
p
ar
it
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i
n
t
h
e
f
r
eq
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e
n
c
y
d
ep
en
d
s
o
n
th
e
s
ig
n
i
f
ica
n
ce
o
f
b
o
th
ac
tiv
e
a
n
d
r
ea
ctiv
e
p
o
w
er
d
is
p
ar
it
y
p
r
ev
io
u
s
l
y
is
la
n
d
i
n
g
o
cc
u
r
s
.
I
f
t
h
e
D
G
o
p
er
ates
at
a
u
n
it
y
p
o
w
er
f
a
cto
r
an
d
th
er
e
is
r
ej
ec
tio
n
a
ctiv
e
p
o
w
er
d
is
p
ar
it
y
t
h
r
o
u
g
h
o
u
t
i
s
la
n
d
in
g
,
t
h
e
r
ea
ctiv
e
p
o
w
er
d
iv
er
g
e
n
ce
∆
Q
(
∆Q
=
Q
L
oad
-
Q
DG
)
ca
n
b
e
w
r
itte
n
in
e
x
p
r
ess
io
n
s
o
f
t
h
e
f
r
eq
u
en
c
y
d
is
p
ar
it
y
as f
o
llo
w
s
:
2
2
2
3
1
2
(
)
æö
÷
ç
÷
D
=
-
ç
÷
ç
÷
ç
p
+
D
èø
P
C
C
V
f
Q
f
L
f
f
(
16
)
an
d
∆f
ca
n
b
e
ex
p
r
es
s
ed
as
*
D
=
-
f
f
f
SP
W
M
is
i
m
p
l
e
m
e
n
ted
to
esta
b
lis
h
t
h
e
o
n
-
o
f
f
s
i
g
n
a
ls
o
f
in
v
e
r
ter
s
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e
s
.
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h
is
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te
g
o
r
y
o
f
in
ter
f
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e
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n
o
r
g
an
ize
t
h
e
DG
ac
ti
v
e
a
n
d
r
ea
ctiv
e
p
o
w
er
o
u
tp
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t.
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
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O
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I
n
th
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s
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tio
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h
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ted
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eth
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tio
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d
esig
n
ed
f
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th
e
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p
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f
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m
.
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ch
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i
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g
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n
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itio
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t
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k
er
o
n
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h
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tili
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itio
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.
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he
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ted
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in
g
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tio
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w
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h
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ased
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ter
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te
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me
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1
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r
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T
h
e
am
o
u
n
t
o
f
o
u
tp
u
t
p
o
w
er
g
en
er
ate
b
y
P
V
m
o
d
u
le
d
ep
en
d
s
o
n
o
p
er
atin
g
v
o
ltag
e
o
f
th
e
ar
r
ay
.
T
h
e
o
u
tp
u
t v
o
lta
g
e
a
n
d
cu
r
r
en
t o
f
t
h
e
MP
PT
b
ased
P
V
s
tr
u
ctu
r
e
d
ev
o
id
o
f
b
o
o
s
t sh
o
w
n
i
n
Fi
g
u
r
e
6
.
T
h
e
g
en
er
ated
d
u
t
y
c
y
cle
f
r
o
m
th
e
MP
P
T
alg
o
r
ith
m
w
id
t
h
o
f
t
h
e
p
u
ls
e
i
s
m
o
d
i
f
ied
ac
co
r
d
in
g
to
d
esire
d
o
u
tp
u
t,
g
en
er
ated
o
u
t
p
u
t
d
u
t
y
c
y
cle
p
u
ls
e
th
r
o
u
g
h
MP
PT
w
h
ic
h
g
iv
e
s
to
co
n
v
er
ter
s
w
itc
h
i
s
s
h
o
w
n
in
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Evaluation Warning : The document was created with Spire.PDF for Python.