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o
d
u
lar
m
u
ltil
ev
el
c
o
n
v
e
r
ter
MM
C
to
g
eth
er
with
m
o
d
u
le
p
r
ed
ictiv
e
c
o
n
tr
o
l
MPC
m
eth
o
d
f
o
r
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
with
th
e
aim
o
f
s
tab
ilizin
g
v
o
ltag
e,
i
m
p
r
o
v
i
n
g
p
o
wer
f
ac
to
r
,
a
n
d
p
r
o
v
id
i
n
g
s
u
f
f
icien
t
r
ea
ctiv
e
p
o
wer
r
eq
u
ir
e
d
b
y
th
e
g
r
id
.
T
h
e
co
n
t
r
o
l
s
y
s
tem
co
n
s
is
ts
o
f
an
o
u
ter
PI
co
n
tr
o
lle
r
an
d
a
n
in
n
er
FC
S
-
MPC
co
n
tr
o
ller
.
T
h
e
o
u
ter
PI
co
n
tr
o
ller
is
u
s
ed
to
r
ed
u
ce
s
t
atic
d
ev
iatio
n
s
i
n
c
o
n
tr
o
l
v
alu
es
an
d
to
p
r
o
v
id
e
a
r
ef
er
en
ce
v
al
u
e
f
o
r
th
e
FC
S
-
MPC
co
n
tr
o
ller
,
wh
ile
th
e
in
n
er
FC
S
-
MP
C
co
n
tr
o
ller
ca
lcu
lates
th
e
o
p
tim
al
s
witch
in
g
s
tate
f
o
r
th
e
p
u
r
p
o
s
e
o
f
r
ed
u
cin
g
th
e
s
witch
in
g
f
r
eq
u
en
cy
o
f
th
e
MM
C
.
Simu
la
tio
n
s
wer
e
ca
r
r
ied
o
u
t
b
y
MA
T
L
AB
/Si
m
u
lin
k
t
o
d
em
o
n
s
tr
ate
th
e
r
esp
o
n
s
iv
en
e
s
s
o
f
th
e
co
n
t
r
o
l
alg
o
r
ith
m
an
d
th
e
p
er
f
o
r
m
a
n
ce
o
f
D
-
STAT
C
OM
u
n
d
er
th
e
co
n
d
itio
n
s
o
f
n
o
n
-
s
in
u
s
o
id
al
an
d
u
n
s
tab
le
v
o
ltag
es.
2.
D
-
ST
A
T
CO
M
M
O
DE
L
B
A
SE
D
O
N
M
M
C
S
T
RU
CT
U
RE
2
.
1
.
D
-
ST
AT
CO
M
s
t
ruct
ur
e
ba
s
ed
o
n M
M
C
co
nv
er
t
er
s
Fig
u
r
e
1
s
h
o
ws
th
e
cir
cu
it
d
i
ag
r
am
o
f
a
n
MM
C
-
b
ased
D
-
STAT
C
OM
f
o
r
th
e
p
u
r
p
o
s
e
o
f
r
ea
ctiv
e
p
o
wer
e
x
ch
an
g
e
with
t
h
e
p
o
w
er
s
y
s
tem
.
I
n
F
ig
u
r
e
1
,
ea
ch
p
h
ase
o
f
th
e
MM
C
co
n
v
er
ter
c
o
n
s
is
ts
o
f
2
N
SMs
d
iv
id
ed
eq
u
ally
in
to
two
v
alv
e
b
r
an
ch
es.
T
h
e
MM
C
co
n
v
e
r
t
er
u
s
es
o
n
ly
o
n
e
d
c
s
o
u
r
ce
v
o
l
tag
e
at
th
e
in
p
u
t
to
g
en
er
ate
an
ac
m
u
ltil
ev
el
v
o
ltag
e
at
th
e
o
u
tp
u
t
s
id
e.
T
h
eo
r
e
tically
,
th
e
ac
v
o
ltag
e
o
f
th
e
MM
C
co
n
v
er
ter
ca
n
b
e
ex
p
a
n
d
ed
t
o
an
u
n
lim
ited
lev
el
b
y
in
c
r
ea
s
in
g
th
e
n
u
m
b
er
o
f
s
u
b
-
m
o
d
u
les
(
SMs)
in
ea
ch
p
h
ase
o
f
th
e
co
n
v
er
ter
.
As
a
r
esu
lt,
t
h
e
tr
a
n
s
f
o
r
m
er
as
well
as
t
h
e
ac
f
il
ter
s
ar
e
n
o
t
r
eq
u
ir
e
d
at
th
e
ac
s
id
e
o
f
th
e
MM
C
co
n
v
er
ter
[
1
7
]
,
[
1
8
]
.
E
ac
h
s
u
b
-
m
o
d
u
le
o
f
th
e
MM
C
co
n
v
er
t
er
co
n
s
is
ts
o
f
two
I
GB
T
s
,
S1
an
d
S2
,
as
s
h
o
w
n
in
F
ig
u
r
e
1
,
to
estab
lis
h
a
h
alf
-
b
r
id
g
e
DC
–
AC
co
n
v
er
ter
.
T
h
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
M
MC
is
o
b
tain
ed
b
y
“in
s
er
ted
”
o
r
“b
y
p
ass
ed
”
s
tates
o
f
t
h
e
SMs
in
ea
ch
p
h
ase
o
f
th
e
c
o
n
v
e
r
ter
.
W
h
en
th
e
cu
r
r
en
t
h
as
t
h
e
p
o
s
itiv
e
d
ir
ec
tio
n
as
s
h
o
wn
in
Fig
u
r
es
2
(
a
)
an
d
2
(
b
)
o
r
h
as
th
e
n
eg
a
tiv
e
d
ir
ec
tio
n
as
s
h
o
wn
in
Fig
u
r
es
2
(
c
)
an
d
2
(
d
)
,
th
e
“in
s
er
ted
”
s
tate
ca
n
b
e
o
b
tain
ed
wh
en
S1
is
ON
an
d
S2
is
OFF
p
r
o
d
u
cin
g
a
v
o
lta
g
e
o
f
VSM
=
VC
=
VDC/
N
at
th
e
AC
s
id
e
o
f
SM
wh
ile
th
e
“b
y
p
ass
ed
”
s
tate
ca
n
b
e
o
b
tain
ed
wh
en
S1
is
OFF
an
d
S2
is
ON
p
r
o
d
u
cin
g
a
v
o
ltag
e
o
f
VSM
=
0
at
th
e
AC
s
id
e
o
f
SM.
2
.
2
.
O
pera
t
ing
princip
le
o
f
t
he
D
-
ST
A
T
CO
M
T
h
e
Dis
tr
ib
u
ted
Static
Sy
n
ch
r
o
n
o
u
s
C
o
m
p
en
s
ato
r
(
D
-
STAT
C
OM
)
is
a
v
o
ltag
e
s
o
u
r
ce
co
n
v
er
ter
(
VSC
)
d
esig
n
ed
to
o
p
er
ate
as
a
s
o
lid
-
s
tate
s
y
n
c
h
r
o
n
o
u
s
v
o
l
tag
e
s
o
u
r
ce
s
h
u
n
t
co
n
n
ec
ted
t
o
AC
tr
an
s
m
is
s
io
n
lin
es
f
o
r
d
y
n
am
ic
co
m
p
en
s
atio
n
an
d
r
ea
l
-
tim
e
co
n
t
r
o
l
[
1
9
]
.
Fig
u
r
e
1
s
h
o
ws
th
e
eq
u
iv
alen
t
cir
cu
it
o
f
th
e
D
-
STAT
C
OM
,
in
wh
ich
th
e
ac
ti
v
e
an
d
r
ea
ctiv
e
p
o
wer
s
ex
c
h
a
n
g
ed
at
th
e
PC
C
th
eo
r
etica
lly
ca
n
b
e
ca
lcu
lated
as
s
h
o
wn
in
(
1
)
.
1
=
1
2
;
1
=
1
(
1
−
2
c
o
s
)
(
1)
I
n
th
is
eq
u
atio
n
,
V1
an
d
V2
r
ep
r
esen
t
th
e
am
p
litu
d
es
o
f
th
e
v
o
ltag
es
at
th
e
g
r
id
a
n
d
co
n
v
er
ter
s
id
es,
r
esp
ec
tiv
ely
.
T
h
e
v
ar
iab
le
δ
is
th
e
p
h
ase
d
if
f
er
en
ce
b
etwe
en
V1
an
d
V2
,
wh
ile
XL
is
th
e
e
q
u
iv
alen
t
r
ea
ctan
ce
co
n
n
ec
tin
g
th
e
g
r
id
an
d
th
e
co
n
v
er
ter
.
D
-
STAT
C
OM
is
o
n
e
o
f
th
e
FAC
T
s
d
ev
ices
th
at
s
u
p
p
o
r
ts
r
ea
ctiv
e
p
o
wer
e
x
ch
an
g
e
with
th
e
p
o
w
er
g
r
i
d
.
(
1
)
s
h
o
ws
th
at
V1
an
d
V2
m
u
s
t
b
e
in
p
h
ase
,
m
ea
n
in
g
δ
=
0
,
allo
win
g
f
o
r
r
ea
ctiv
e
p
o
wer
ex
ch
a
n
g
e
a
t
th
e
PC
C
b
y
co
n
tr
o
llin
g
th
e
a
m
p
litu
d
es
o
f
V1
an
d
V2
.
As
a
r
esu
lt,
(
1
)
ca
n
b
e
r
ewr
itten
as in
(
2
)
.
1
=
0
;
1
=
1
(
1
−
2
)
(
2
)
Fig
u
r
e
3
s
h
o
ws
th
e
o
p
er
atin
g
p
r
in
cip
le
o
f
th
e
D
-
STAT
C
OM
f
o
r
th
e
p
u
r
p
o
s
e
o
f
r
ea
ct
iv
e
p
o
wer
ex
ch
an
g
e
.
W
h
en
V
1
>
V2
,
t
h
e
r
ea
ctiv
e
p
o
wer
Q
in
(
2
)
i
s
p
o
s
itiv
e,
r
esu
ltin
g
in
th
e
p
r
esen
ce
o
f
a
v
o
ltag
e
co
m
p
o
n
en
t
V1
2
as
s
h
o
wn
in
F
ig
u
r
e
3
(
a
)
.
I
n
th
is
ca
s
e,
th
e
D
-
STAT
C
OM
o
p
er
ates
in
th
e
in
d
u
ctiv
e
c
u
r
r
e
n
t
m
o
d
e
with
th
e
in
d
u
ctiv
e
cu
r
r
en
t
IL
b
ein
g
π/2
o
u
t
o
f
p
h
as
e
with
V1
an
d
V2
.
T
h
e
D
-
STAT
C
OM
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
p
o
we
r
g
r
id
.
W
h
en
V1
<
V
2
,
th
e
r
e
ac
tiv
e
p
o
wer
Q
in
(
2
)
is
n
eg
at
iv
e,
r
esu
ltin
g
in
th
e
p
r
esen
ce
o
f
a
v
o
ltag
e
c
o
m
p
o
n
en
t
V1
2
as
s
h
o
wn
in
F
ig
u
r
e
3
(
b
)
.
I
n
th
is
ca
s
e,
th
e
D
-
STAT
C
OM
o
p
er
ates
in
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
6
9
4
D
-
S
TATC
OM c
o
n
tr
o
l fo
r
d
is
t
r
ib
u
tio
n
g
r
id
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w
ith
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is
tr
ib
u
ted
s
o
u
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s
b
a
s
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o
n
…
(
P
h
a
m
V
iet
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h
u
o
n
g
)
427
ca
p
ac
itiv
e
cu
r
r
e
n
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m
o
d
e
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th
e
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p
ac
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r
r
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C
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e
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h
e
D
-
STAT
C
OM
r
elea
s
es
th
e
r
ea
ct
iv
e
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o
wer
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e
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o
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r
id
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W
h
en
V1
=
V2
as
s
h
o
wn
in
F
ig
u
r
e
3
(
c
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,
t
h
e
D
-
STAT
C
OM
d
o
es n
o
t e
x
ch
an
g
e
th
e
r
ea
ctiv
e
p
o
wer
with
th
e
p
o
wer
g
r
i
d
.
SM
1
SM
2
SM
N
SM
N
+
2
SM
2
N
L
o
L
o
i
HA
i
LA
i
DC
i
A
i
C
SM
1
SM
2
SM
N
SM
N
+
1
SM
N
+
2
SM
2
N
SM
1
SM
2
SM
N
SM
N
+
1
SM
N
+
2
SM
2
N
R
o
R
o
v
C
v
B
v
A
L
o
L
o
i
HB
i
LB
R
o
R
o
L
o
L
o
i
HC
i
LC
R
o
R
o
i
B
v
sA
v
sC
v
sB
V
DC
SM
S
1
S
2
V
2
I
L
v
s
b
)
c
)
X
L
M
M
C
D
-
S
T
A
T
CO
M
S
ol
a
r P
a
ne
l
s
(
PV
)
W
i
nd
T
urbi
ne
s
G
r
i
d
L
oa
d
L
oa
d
L
oa
d
a
)
+
_
SM
N
+
1
T
r
a
n
s
f
o
r
m
e
r
s
DC
/
AC
P
C
C
-
P
o
i
n
t
o
f
c
o
m
m
o
n
c
o
u
p
l
i
n
g
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
a
g
r
i
d
co
n
n
ec
ted
MM
C
-
b
as
ed
D
-
STAT
C
OM
S
1
S
2
S
1
S
2
S
1
S
2
S
1
S
2
b
)
i
i
i
i
V
DC
/
N
a
)
d
)
c
)
V
SM
V
SM
V
SM
V
SM
D
1
D
2
D
1
D
2
D
1
D
2
D
1
D
2
V
DC
/
N
V
DC
/
N
V
DC
/
N
Fig
u
r
e
2
. S
witch
in
g
o
p
er
atio
n
s
o
f
SM: (
a)
b
y
p
ass
with
p
o
s
itiv
e
cu
r
r
e
n
t,
(
b
)
in
s
er
t w
ith
p
o
s
itiv
e
cu
r
r
en
t,
(
c
)
in
s
er
t w
ith
n
eg
ativ
e
cu
r
r
e
n
t,
an
d
(
d
)
b
y
p
ass
with
n
eg
ativ
e
cu
r
r
en
t
V
1
V
2
V
12
I
L
0
V
1
V
2
V
12
I
L
0
a
)
b
)
V
1
V
2
V
12
=
0
0
c
)
I
L
=
0
Fig
u
r
e
3
.
Op
e
r
atin
g
p
r
in
cip
les
o
f
D
-
STAT
C
OM
:
(
a)
s
tate
o
f
r
ea
ctiv
e
p
o
wer
a
b
s
o
r
p
tio
n
,
(
b
)
s
tate
o
f
r
ea
ctiv
e
p
o
wer
g
en
er
atio
n
,
an
d
(
c)
s
tate
o
f
n
o
r
ea
ctiv
e
p
o
wer
ex
c
h
an
g
e
(
a)
(
b
)
(
c)
(
a)
(
b
)
(
c)
(
d
)
(
a)
(
b
)
(
c)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
425
-
4
37
428
3.
CO
NT
RO
L
SYS
T
E
M
F
O
R
D
-
ST
A
T
CO
M
3
.
1
.
M
a
t
h
m
o
del o
f
t
he
M
M
C
T
h
e
g
r
id
-
co
n
n
ec
ted
MM
C
is
s
h
o
wn
in
Fig
u
r
e
4
.
I
n
th
is
co
n
f
ig
u
r
atio
n
,
th
e
MM
C
h
as
th
r
ee
p
h
ases
with
s
ix
v
alv
e
ar
m
s
,
ea
ch
v
alv
e
ar
m
is
d
iv
id
ed
in
to
two
p
a
r
ts
,
an
u
p
p
e
r
ar
m
an
d
a
lo
wer
ar
m
,
an
d
in
ea
ch
a
r
m
th
er
e
ar
e
N
id
en
tical
SMs
co
n
n
ec
ted
in
s
er
ies
.
SMs
ar
e
s
er
ies
co
n
n
ec
ted
with
o
n
e
in
d
u
cto
r
(
L
o
)
an
d
o
n
e
r
esis
to
r
(
R
o
)
.
T
h
e
in
d
u
ct
o
r
L
o
lim
its
th
e
s
h
o
r
t
-
cir
cu
it
cu
r
r
e
n
t
o
f
an
MM
C
an
d
r
em
o
v
es
th
e
h
ig
h
-
f
r
eq
u
e
n
cy
h
ar
m
o
n
ics o
f
th
e
cu
r
r
en
t a
r
m
[
20
]
.
T
h
e
r
esis
to
r
R
o
r
ep
r
esen
ts
th
e
p
o
wer
l
o
s
s
es with
in
ea
ch
ar
m
.
v
HA
L
o
v
LA
v
HB
v
LB
v
HC
v
LC
V
DC
/
2
V
DC
/
2
0
M
M
C
L
o
L
o
L
o
L
o
L
o
R
o
R
o
R
o
R
o
R
o
R
o
i
LA
v
A
v
B
v
C
i
HA
i
LB
i
HB
i
LC
i
HC
L
L
L
R
R
R
v
sA
v
sB
v
sC
SM
1
SM
2
SM
N
N
S
u
bm
odu
l
e
i
vB
i
vA
i
vC
i
A
i
C
i
B
Fig
u
r
e
4
.
Stru
ctu
r
e
th
e
th
r
ee
-
p
h
ase
o
f
th
e
MM
C
o
n
t
h
e
DC
/AC
s
id
e
T
h
e
SM'
s
co
n
f
ig
u
r
atio
n
is
a
h
alf
-
b
r
id
g
e
co
n
v
er
ter
with
t
h
e
o
p
e
r
atin
g
m
o
d
e
s
h
o
wn
in
Fig
u
r
e
2
.
Du
r
in
g
o
p
er
atio
n
,
ea
c
h
SM
p
r
o
v
id
es
an
o
u
tp
u
t
v
o
ltag
e
o
f
0
o
r
vC
b
ased
o
n
t
h
e
s
t
ates
o
f
S1
an
d
S2
.
Sp
ec
if
ically
,
Fig
u
r
e
2
(
a)
s
h
o
w
s
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
S
M
as
vC
,
at
wh
ich
p
o
in
t
S1
=
ON
an
d
S2
=
OFF.
Fig
u
r
e
2
(
c
)
s
h
o
ws
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
t
h
e
SM
as
0
,
at
w
h
ich
p
o
in
t
S1
=
OFF
an
d
S2
=
ON.
T
h
ese
SMs
o
p
er
ate
b
ased
o
n
co
n
tr
o
l
c
o
m
m
an
d
s
f
r
o
m
th
e
m
icr
o
p
r
o
ce
s
s
o
r
s
y
s
tem
.
I
n
o
n
e
o
p
er
atin
g
cy
cle,
th
e
m
icr
o
p
r
o
ce
s
s
o
r
co
m
m
an
d
s
al
way
s
en
s
u
r
e
t
h
at
o
n
ly
N
SMs
ar
e
s
witch
ed
o
n
(
with
an
o
u
tp
u
t
v
o
ltag
e
o
f
vC
)
to
cr
ea
te
a
s
tep
p
ed
v
o
ltag
e
o
f
N+
1
at
th
e
o
u
tp
u
t
o
f
th
e
MM
C
.
B
ased
o
n
th
e
law
s
o
f
cu
r
r
en
t,
th
e
m
ath
em
atica
l
eq
u
atio
n
s
d
escr
ib
in
g
th
e
o
p
er
a
tio
n
o
f
p
h
ase
x
(
x
=
A,
B
,
C
)
i
n
th
e
MM
C
ar
e
r
ep
r
esen
te
d
as
(
3
)
-
(
5
)
.
2
−
−
−
+
+
−
=
0
(
3
)
−
2
+
+
+
+
+
−
=
0
(
4
)
=
−
2
+
;
=
2
+
(
5
)
W
h
er
e:
i
Hx
an
d
i
Lx
ar
e
th
e
cu
r
r
en
ts
in
ea
ch
ar
m
(
u
p
p
e
r
ar
m
an
d
lo
wer
ar
m
)
;
i
vx
is
th
e
cir
cu
latin
g
cu
r
r
en
t
in
ea
c
h
p
h
ase.
i
vx
d
o
e
s
n
o
t
af
f
ec
t
th
e
q
u
ality
o
f
t
h
e
alter
n
atin
g
cu
r
r
en
t,
b
u
t
i
vx
will
ca
u
s
e
p
o
wer
lo
s
s
in
s
id
e
th
e
MM
C
[
2
1
].
T
h
er
ef
o
r
e
,
wh
en
th
e
MM
C
is
wo
r
k
in
g
,
it
is
d
esira
b
le
th
at
i
vx
alw
ay
s
h
as
th
e
s
m
alle
s
t
v
alu
e
;
th
is
is
d
if
f
icu
lt to
ac
h
ie
v
e
b
y
c
o
n
v
e
n
tio
n
al
m
ea
n
s
.
T
h
e
cir
cu
latin
g
cu
r
r
en
t in
th
e
cir
cu
it
in
(
6
)
.
=
+
2
(
6
)
B
y
ca
lcu
latin
g
b
ased
o
n
(
3
)
-
(
6
)
,
we
ca
n
d
e
d
u
ce
(
7
)
an
d
(
8
)
,
wh
ich
r
ep
r
esen
t
th
e
p
h
ase
cu
r
r
en
t
a
n
d
lo
o
p
cu
r
r
en
t in
th
e
cir
cu
it.
=
−
(
+
2
)
+
2
+
−
+
2
+
2
+
2
(
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
D
-
S
TATC
OM c
o
n
tr
o
l fo
r
d
is
t
r
ib
u
tio
n
g
r
id
s
w
ith
d
is
tr
ib
u
ted
s
o
u
r
ce
s
b
a
s
ed
o
n
…
(
P
h
a
m
V
iet
P
h
u
o
n
g
)
429
=
−
−
1
2
(
+
)
+
1
2
(
8
)
W
h
en
in
s
er
tin
g
o
r
o
m
itti
n
g
S
Ms
ac
co
r
d
in
g
to
th
e
co
n
tr
o
l
la
w,
a
v
o
ltag
e
is
g
e
n
er
ated
o
n
e
ac
h
b
r
an
c
h
.
T
h
e
s
p
ec
if
ic
n
u
m
b
er
o
f
SMs
in
s
er
ted
f
o
r
th
e
u
p
p
e
r
an
d
l
o
wer
b
r
an
c
h
es
b
ased
o
n
th
e
c
o
n
t
r
o
l
law
will
b
e
n
Hx
an
d
n
Lx
,
r
esp
ec
tiv
ely
,
an
d
th
e
co
r
r
esp
o
n
d
in
g
v
o
ltag
e
v
alu
es
g
en
er
ated
in
th
is
ca
s
e
ar
e
v
Hx
an
d
v
Lx
.
W
h
en
th
e
co
n
tr
o
l
law
af
f
ec
ts
th
e
SMs
to
ch
an
g
e
t
h
e
n
u
m
b
er
o
f
SMs,
th
e
ca
p
ac
ito
r
v
o
ltag
e
v
alu
e
o
f
th
e
SMs
ch
an
g
es
d
ep
en
d
i
n
g
o
n
th
e
d
ir
ec
tio
n
o
f
th
e
cu
r
r
en
t
i
n
ea
ch
b
r
an
ch
.
W
h
en
th
e
v
o
ltag
es
o
n
t
h
e
ca
p
ac
ito
r
s
ar
e
b
alan
ce
d
,
th
e
v
o
ltag
e
o
n
ea
c
h
ca
p
ac
ito
r
is
ap
p
r
o
x
im
ately
eq
u
al
to
v
mx
/N
(
m
=
H,
L),
wh
er
e
v
mx
is
th
e
t
o
tal
ca
p
ac
ito
r
v
o
ltag
e
o
f
ea
ch
v
al
v
e
b
r
a
n
ch
.
T
h
en
,
th
e
b
r
an
c
h
v
o
ltag
e
is
ex
p
r
ess
ed
b
y
(
9
).
=
(
9
)
E
x
p
r
ess
es a
to
tal
ca
p
ac
ito
r
(
1
0
)
:
=
=
(
1
0
)
Her
e
,
th
e
v
alu
e
o
f
th
e
ca
p
ac
it
o
r
in
o
n
e
wo
r
k
in
g
cy
cle
is
C
m
.
W
h
en
r
ep
lacin
g
i
Hx
an
d
i
Lx
f
r
o
m
(
5
)
,
(
6
)
in
to
(
10
)
,
we
ca
n
d
ed
u
ce
th
e
e
q
u
atio
n
r
elatin
g
th
e
ca
p
ac
ito
r
v
o
ltag
e
o
n
ea
ch
b
r
an
c
h
,
alo
n
g
with
th
e
n
u
m
b
e
r
o
f
SM
in
s
er
ted
an
d
th
e
c
u
r
r
en
t
i
vx
,
as (
1
1
)
an
d
(
1
2
).
=
−
2
+
(
1
1
)
=
2
+
(
1
2
)
3
.
2
.
T
he
o
pera
t
ing
princip
le
o
f
M
M
C
is
ba
s
e
d o
n t
he
F
CS
-
M
P
C
co
ntr
o
l a
lg
o
rit
hm
T
h
is
s
ec
tio
n
will
p
r
esen
t
th
e
o
p
er
atio
n
o
f
th
e
MM
C
b
ased
o
n
th
e
FC
S
-
MP
C
co
n
tr
o
l
alg
o
r
ith
m
.
T
h
e
p
r
o
ce
s
s
is
p
er
f
o
r
m
ed
b
ased
o
n
p
r
ed
ictin
g
th
e
AC
cu
r
r
en
t
v
alu
e
o
f
th
e
MM
C
at
a
f
u
tu
r
e
ti
m
e
ac
co
r
d
i
n
g
to
th
e
m
o
d
el
at
th
e
p
r
esen
t
tim
e.
T
h
en
,
o
p
tim
ize
th
e
co
s
t
f
u
n
ctio
n
to
s
elec
t
th
e
b
est
v
alv
e
o
n
/o
f
f
s
tate
in
o
n
e
o
p
er
atin
g
cy
cle
o
f
t
h
e
MM
C
.
T
o
d
o
th
is
,
th
e
f
ir
s
t
s
tep
is
to
c
o
n
s
tr
u
ct
a
d
is
cr
ete
-
tim
e
m
o
d
el
to
p
r
ed
ict
o
n
e
s
tep
f
o
r
war
d
o
f
th
e
c
o
n
tr
o
llab
le
v
ar
iab
les
o
f
th
e
MM
C
co
n
v
er
t
er
.
Nex
t
is
estab
lis
h
es
a
co
s
t
f
u
n
ctio
n
ass
o
ciate
d
with
a
p
r
ed
ef
in
e
d
co
n
t
r
o
l
o
b
je
ctiv
e.
Fin
ally
,
ev
alu
ate
th
e
co
s
t
f
u
n
ctio
n
f
o
r
all
s
witch
in
g
s
tates
in
o
n
e
cy
cle
o
f
th
e
MM
C
,
th
er
eb
y
s
elec
tin
g
th
e
o
p
tim
al
s
witch
in
g
s
tate
in
ter
m
s
o
f
q
u
ality
f
o
r
th
e
alter
n
atin
g
cu
r
r
en
t
o
f
th
e
MM
C
.
T
h
e
s
tep
s
ar
e
s
h
o
wn
in
Fig
u
r
e
5
(
a
)
[2
2
]
.
I
n
wh
ich
i
(
k
)
is
th
e
co
n
tr
o
l
v
ar
iab
le,
i
(
k
+1
)
is
th
e
p
r
ed
icted
v
alu
e
o
f
i(
k
)
in
th
e
n
ex
t
cy
cle
,
ir
ef
(
k
+1
)
is
th
e
r
ef
er
en
ce
v
al
u
e
o
f
i(
k
+1
)
,
S(k
)
ar
e
th
e
o
p
tim
ized
I
GB
T
v
alv
e
o
n
/o
f
f
s
tates.
T
h
e
cu
r
r
en
t c
o
n
tr
o
l p
r
o
ce
s
s
b
y
th
e
FC
S
-
MPC
s
tr
ateg
y
is
s
h
o
wn
in
d
etail
in
Fig
u
r
e
5
(
b
)
.
I
n
th
er
e,
th
e
o
u
tp
u
t
AC
cu
r
r
e
n
t
will
b
e
co
n
tr
o
lled
clo
s
ely
to
th
e
r
ef
e
r
en
ce
v
alu
e.
Acc
o
r
d
in
g
to
[
1
3
]
,
in
a
s
in
g
le
-
p
h
ase
(
n
+1
)
le
v
el
MM
C
,
th
e
to
tal
p
o
s
s
ib
le
s
wi
tch
in
g
s
tates a
r
e:
=
2
=
2
!
!
(
2
−
)
!
(
1
3
)
(
a)
(
b
)
Fig
u
r
e
5
.
MPC
co
n
tr
o
ller
f
o
r
MM
C
:
(
a)
MPC
co
n
tr
o
l m
eth
o
d
s
tr
u
ctu
r
e
f
o
r
MM
C
an
d
(
b
)
a
lg
o
r
ith
m
o
f
p
r
e
d
ictiv
e
co
n
tr
o
l f
o
r
cu
r
r
en
t A
C
Fro
m
(
13
)
,
we
ca
n
d
ed
u
ce
th
at
in
th
e
th
r
ee
p
h
ases
o
f
th
e
MM
C
,
th
er
e
will
b
e
N
3
s
w
itc
h
in
g
s
tates.
T
h
e
FC
S
-
MPC
co
n
tr
o
l
p
r
o
ce
s
s
will
ca
lcu
late
th
e
co
s
t
f
u
n
cti
o
n
to
d
eter
m
in
e
th
e
o
p
tim
al
s
witch
in
g
s
tate
at
a
f
u
tu
r
e
tim
e
to
ap
p
ly
to
th
e
MM
C
.
T
o
d
o
th
is
,
(
1
2
)
m
u
s
t
b
e
d
is
cr
etize
d
u
s
in
g
th
e
E
u
ler
m
eth
o
d
.
Ass
u
m
in
g
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
425
-
4
37
430
s
am
p
lin
g
p
er
io
d
o
f
th
e
s
y
s
te
m
is
T
s
,
wh
en
d
is
cr
etizin
g
(
1
2
)
,
we
g
et
th
e
d
is
cr
ete
-
tim
e
m
o
d
el
o
f
th
e
MM
C
o
u
tp
u
t c
u
r
r
en
t a
s
(
1
4
).
(
+
1
)
=
.
(
)
+
.
[
(
+
1
)
−
(
+
1
)
−
2
(
+
1
)
.
]
(
1
4
)
I
n
wh
ich
:
(
+
1
)
=
1
6
∑
(
(
+
1
)
−
(
+
1
)
)
=
,
,
;
=
+
2
−
(
+
2
)
+
2
;
=
+
2
;
=
−
(
)
=
[
(
)
(
)
(
)
]
(
)
=
[
(
)
(
)
(
)
]
(
)
=
[
(
)
(
)
(
)
]
W
e
s
ee
th
at,
to
im
p
lem
e
n
t
FC
S
-
MP
C
ac
co
r
d
in
g
t
o
(
1
4
)
,
we
m
u
s
t
m
ea
s
u
r
e
th
e
cu
r
r
en
t
i
x
(
t)
an
d
th
e
v
alu
es
v
Hx
(
k)
an
d
v
Lx
(
k
)
in
ea
c
h
b
r
an
c
h
,
th
en
e
x
tr
ap
o
late
th
e
m
to
th
e
v
alu
es
v
Hx
(
k+1
)
a
n
d
v
Lx
(
k+1
)
b
y
E
u
ler
'
s
m
eth
o
d
[
2
3
].
T
h
e
cu
r
r
en
t
v
alu
e
in
(
1
4
)
will
b
e
o
p
tim
ized
b
y
th
e
co
s
t
f
u
n
ctio
n
(
1
5
)
to
d
eter
m
in
e
th
e
s
witch
in
g
s
tate
s
u
itab
le
f
o
r
th
e
o
p
tim
ize
d
AC
s
id
e
cu
r
r
e
n
t.
T
h
en
th
e
c
u
r
r
en
t
o
u
tp
u
t
o
f
th
e
MM
C
at
t
h
e
cu
r
r
en
t
m
o
m
en
t
will st
ick
to
its
r
ef
er
en
ce
v
alu
e.
=
|
_
(
+
1
)
−
(
+
1
)
|
(
1
5
)
W
h
er
e
i
x
-
ref
is
th
e
r
ef
er
en
ce
o
f
p
h
ase’
s
cu
r
r
e
n
t
an
d
i
x
(
t+T
s
)
o
b
tain
ed
f
r
o
m
(
1
4
)
is
th
e
n
ex
t
-
s
tep
p
r
ed
icted
cu
r
r
en
t.
T
h
e
s
am
p
le
p
e
r
io
d
is
s
m
all
en
o
u
g
h
t
o
_
(
+
1
)
≈
_
(
)
,
an
d
(
1
5
)
r
ewr
ites
as (
1
6
).
=
|
_
(
)
−
(
+
1
)
|
(
1
6
)
I
n
th
eo
r
y
,
th
e
m
in
i
m
u
m
v
al
u
e
o
f
th
e
co
s
t
f
u
n
ctio
n
(
1
6
)
s
h
o
u
ld
b
e
0
.
Ho
wev
e
r
,
in
p
r
ac
tice,
th
is
v
alu
e
is
o
n
ly
ap
p
r
o
x
im
ately
0
an
d
is
u
s
ed
to
s
elec
t
th
e
s
w
itch
in
g
s
tate
o
f
th
e
MM
C
to
g
en
er
ate
th
e
d
esire
d
AC
cu
r
r
en
t,
w
h
ich
is
th
e
b
est
p
o
s
s
ib
le
v
alu
e
o
f
th
e
c
o
n
tr
o
l
o
b
jec
tiv
e.
T
h
is
p
r
o
c
ess
is
r
ep
ea
ted
m
an
y
tim
es
d
u
r
in
g
th
e
o
p
er
atio
n
o
f
th
e
MM
C
an
d
is
d
escr
ib
ed
b
y
t
h
e
alg
o
r
ith
m
f
lo
wch
ar
t a
s
s
h
o
wn
in
Fig
u
r
e
6
.
C
a
l
c
u
l
a
t
e
i
x
(
k
+
1
)
b
a
s
e
d
o
n
t
h
e
e
q
u
a
t
i
o
n
(
13
)
C
a
l
c
u
l
a
t
e
t
h
e
c
o
s
t
f
u
n
c
t
i
o
n
J
j
b
a
s
e
d
o
n
t
h
e
e
q
u
a
t
i
o
n
(
15
)
S
e
l
e
c
t
s
t
a
t
e
o
p
t
i
m
i
z
e
d
v
a
l
v
e
s
w
i
t
c
h
S
ux
=
S
ux
(
k
)
v
à J
m
i
n
=
J
x
P
e
r
f
o
r
m
s
w
i
t
c
h
i
n
g
v
a
l
v
e
s
S
ux
No
Y
e
s
Y
e
s
No
Si
gnal
m
e
as
ur
e
d
i
x
(
k
)
,
v
jH
(
k
)
,
v
jL
(
k
)
f
r
om
M
M
C
i
x
re
f
(
k
)
J
j
<
J
m
i
n
?
Fig
u
r
e
6
.
Flo
wch
ar
t
o
f
th
e
MPC
alg
o
r
ith
m
to
ap
p
ly
to
MM
C
3
.
3
.
Co
ntr
o
l st
ruct
ure
o
f
D
-
ST
A
T
CO
M
s
y
s
t
em
Sin
ce
th
e
D
-
STAT
C
OM
s
y
s
t
em
o
n
ly
co
m
p
e
n
s
ates
r
ea
ctiv
e
p
o
wer
,
i
n
th
is
co
n
tr
o
l
m
o
d
el,
ac
tiv
e
p
o
wer
will
n
o
t
b
e
ex
c
h
an
g
e
d
with
th
e
g
r
id
a
n
d
will
al
way
s
b
e
co
n
tr
o
lled
to
0
.
T
h
er
ef
o
r
e,
in
th
e
D
-
STAT
C
OM
co
n
tr
o
l
s
y
s
tem
,
th
e
co
n
tr
o
l
cir
cu
it
is
o
n
ly
d
e
s
ig
n
ed
to
g
en
er
ate
o
r
ab
s
o
r
b
r
ea
ctiv
e
p
o
wer
to
ex
ch
an
g
e
with
th
e
g
r
i
d
[
2
4
].
T
h
is
p
r
o
ce
s
s
will
b
e
d
o
n
e
b
y
co
m
p
ar
in
g
th
e
MM
C
o
u
tp
u
t
v
o
ltag
e
v
alu
e
a
n
d
th
e
g
r
id
v
o
ltag
e
ac
co
r
d
in
g
t
o
(
1
7
).
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
D
-
S
TATC
OM c
o
n
tr
o
l fo
r
d
is
t
r
ib
u
tio
n
g
r
id
s
w
ith
d
is
tr
ib
u
ted
s
o
u
r
ce
s
b
a
s
ed
o
n
…
(
P
h
a
m
V
iet
P
h
u
o
n
g
)
431
=
+
(
1
7
)
Her
e
V
is
m
ea
s
u
r
ed
f
r
o
m
th
e
s
y
s
tem
to
co
m
p
ar
e
with
its
r
ef
er
en
ce
v
alu
e
V
ref
,
Xs
is
th
e
to
tal
im
p
ed
an
ce
o
f
th
e
s
y
s
tem
.
T
h
e
r
ea
ctiv
e
cu
r
r
en
t
I
is
alwa
y
s
ad
ju
s
ted
with
in
th
e
r
an
g
e
(
-
I
Max
,
I
Max
).
If
V
<
V
ref
,
th
e
co
n
tr
o
ller
will
in
cr
ea
s
e
th
e
v
o
ltag
e
V
to
th
e
v
alu
e
V
ref
,
an
d
if
V
>
V
ref
,
th
e
c
o
n
tr
o
lle
r
will
d
ec
r
ea
s
e
th
e
v
o
ltag
e
V
t
o
th
e
v
alu
e
V
ref
.
T
h
e
u
ltima
te
g
o
al
o
f
th
ese
two
c
ases
is
to
en
s
u
r
e
th
at
th
e
v
alu
e
V
is
eq
u
al
to
V
ref
an
d
is
s
h
o
wn
as sh
o
wn
in
th
e
F
ig
u
r
e
7
[
2
4
].
V
-
I
m
ax
I
m
a
x
0
X
s
V
r
e
f
I
Fig
u
r
e
7
.
V
-
I
ch
ar
ac
ter
is
tics
o
f
D
-
STAT
C
OM
T
h
is
m
ak
es
th
e
r
ea
ctiv
e
p
o
wer
at
th
e
g
r
id
n
o
d
e
alwa
y
s
m
ain
t
ain
ed
at
th
e
d
esire
d
v
alu
e.
T
h
e
r
ef
o
r
e,
t
o
d
esig
n
a
co
n
tr
o
ller
to
co
m
p
en
s
ate
f
o
r
r
ea
ctiv
e
p
o
wer
,
it
is
n
ec
ess
ar
y
to
d
esig
n
a
DC
v
o
lta
g
e
co
n
tr
o
ller
[
2
5
].
Fro
m
th
e
D
-
STAT
C
OM
s
y
s
te
m
in
Fig
u
r
e
4
,
we
ca
n
d
ed
u
ce
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
DC
v
o
ltag
e
an
d
th
e
AC
p
o
wer
in
th
e
f
o
r
m
o
f
(
1
8
)
an
d
(
1
9
)
.
2
=
3
2
=
(
1
8
)
=
3
2
1
(
1
9
)
T
h
e
co
n
tr
o
l
s
y
s
tem
o
f
D
-
STA
T
C
OM
is
d
esig
n
ed
b
ased
o
n
t
h
e
MM
C
co
n
v
er
ter
s
h
o
wn
in
Fig
u
r
e
8
,
wh
ich
co
n
s
is
ts
o
f
two
co
n
tr
o
l lo
o
p
s
to
co
n
tr
o
l
th
e
s
tab
le
DC
v
o
ltag
e
an
d
a
co
n
tr
o
l
lo
o
p
t
o
co
n
tr
o
l
th
e
r
ea
cti
v
e
p
o
wer
e
x
ch
an
g
ed
with
th
e
g
r
id
ac
co
r
d
in
g
to
(
1
9
).
T
h
e
F
C
S
-
MP
C
co
n
tr
o
l
s
tag
e
is
u
s
ed
in
t
h
is
m
o
d
el
to
r
ep
lace
th
e
p
u
ls
e
m
o
d
u
latio
n
s
tag
es.
i
DC
MM
C
S
(
k
)
V
DC
C
a
l
c
u
l
a
t
e
p
o
w
e
r
Q
a
c
c
o
r
d
i
n
g
t
o
e
q
u
a
t
i
o
n
(
18
)
PI
PI
dq
/
ab
c
abc
/
dq
F
C
S
-
M
P
C
P
L
L
i
d
i
q
u
d
u
q
Q
V
D
C
r
e
f
Q
r
e
f
S
(
k
)
i
A
,
B
,
C
v
A
,
B
,
C
R
L
R
L
R
L
i
A
i
B
i
C
+
+
_
+
_
PI
+
_
PI
L
L
_
i
d
V
ol
t
age
c
on
t
r
ol
l
e
r
C
u
r
r
e
n
t
C
on
t
r
ol
l
e
r
i
q
u
d
u
q
v
A
v
B
v
C
+
+
+
+
+
_
P
ow
e
r
C
on
t
r
ol
l
e
r
G
r
i
d
Fig
u
r
e
8
.
Stru
ctu
r
e
d
iag
r
am
o
f
th
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