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ticle
his
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y:
R
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J
u
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1
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4
R
ev
is
ed
Oct
1
1
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2
4
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ted
Oct
2
3
,
2
0
2
4
Th
is
p
a
p
e
r
will
p
re
se
n
t
a
re
a
c
ti
v
e
p
o
we
r
c
o
n
tro
l
m
e
th
o
d
f
o
r
m
e
d
iu
m
v
o
lt
a
g
e
p
o
we
r
g
r
id
s
b
a
se
d
o
n
t
h
e
m
o
d
u
la
r
m
u
lt
il
e
v
e
l
c
o
n
v
e
rter
(M
M
C)
str
u
c
tu
re
.
I
n
p
a
rti
c
u
lar,
th
e
M
M
C
c
o
n
v
e
rter
a
p
p
li
e
s
c
o
n
tr
o
l
a
lg
o
rit
h
m
s
to
o
p
e
ra
te
a
s
a
D
-
S
TATCOM
d
e
v
ice
.
A
p
r
o
p
o
rti
o
n
a
l
–
in
teg
ra
l
(
PI
)
c
o
n
tro
l
ler
c
o
m
b
in
e
d
wit
h
a
n
imp
r
o
v
e
d
n
e
a
re
st
lev
e
l
m
o
d
u
l
a
ti
o
n
(NLM
)
m
e
th
o
d
p
e
rfo
rm
s
t
h
e
sy
ste
m
c
o
n
tro
l
p
r
o
c
e
ss
.
Th
e
p
u
r
p
o
se
is
to
c
re
a
te
sin
u
so
i
d
a
l
v
o
lt
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g
e
lev
e
ls
o
n
t
h
e
a
lt
e
rn
a
ti
n
g
c
u
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n
t
(
AC
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sid
e
to
g
e
n
e
ra
te
o
r
a
b
so
rb
re
a
c
ti
v
e
p
o
we
r
a
c
c
o
rd
in
g
to
l
o
a
d
re
q
u
irem
e
n
ts.
T
h
is
will
e
n
su
re
t
h
a
t
t
h
e
a
m
o
u
n
t
o
f
re
a
c
ti
v
e
p
o
we
r
fo
r
th
e
lo
a
d
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o
d
e
is
a
lwa
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s
with
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n
th
e
a
ll
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wa
b
le
v
a
lu
e
a
n
d
imp
ro
v
e
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o
lt
a
g
e
q
u
a
li
t
y
,
i
n
c
re
a
sin
g
t
h
e
p
o
we
r
fa
c
to
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th
e
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o
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d
.
Ve
rify
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g
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n
d
e
v
a
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a
ti
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g
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su
lt
s a
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p
e
rfo
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d
o
n
M
ATLA
B/
S
imu
li
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k
s
o
ftwa
re
.
K
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w
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r
d
s
:
C
o
m
p
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s
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r
ea
ctiv
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p
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wer
D
-
STAT
C
OM
Mo
d
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lar
m
u
ltil
ev
el
co
n
v
e
r
ter
Nea
r
est lev
el
m
o
d
u
latio
n
P
r
o
p
o
r
tio
n
al
–
in
teg
r
al
c
o
n
tr
o
ll
er
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
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-
SA
li
c
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n
se
.
C
o
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r
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s
p
o
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A
uth
o
r
:
An
T
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i H
o
ai
T
h
u
An
h
Dep
ar
tm
e
n
t
o
f
E
l
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t
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ca
l
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n
g
i
n
e
er
in
g
,
F
ac
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lt
y
o
f
E
l
ec
tr
ica
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-
E
le
ct
r
o
n
i
c
E
n
g
in
ee
r
i
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g
,
U
n
i
v
e
r
s
it
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f
T
r
a
n
s
p
o
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t
an
d
C
o
m
m
u
n
ic
ati
o
n
s
N
o.
3
C
au
Giay
,
L
a
n
g
T
h
u
o
n
g
C
o
m
m
u
n
e,
Do
n
g
Da
Dis
tr
ict,
Han
o
i,
Vietn
am
E
m
ail:
h
tan
h
.
k
td
@
u
tc.
ed
u
.
v
n
1.
I
NT
RO
D
UCT
I
O
N
Po
wer
q
u
ality
f
o
r
elec
tr
ical
eq
u
ip
m
en
t
d
ir
ec
tly
c
o
n
n
ec
ted
t
o
th
e
m
ed
iu
m
v
o
ltag
e
g
r
id
is
ess
en
tial.
Ho
wev
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,
lo
a
d
s
o
f
t
h
is
ty
p
e
a
r
e
o
f
ten
af
f
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ted
b
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m
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y
ca
u
s
es,
s
u
ch
as
p
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ase
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b
alan
ce
,
tr
an
s
ien
t
in
cid
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ts
,
o
r
s
witch
in
g
p
r
o
ce
s
s
es
in
th
e
p
o
wer
g
r
id
[
1
]
–
[
4
]
.
Am
o
n
g
th
em
,
tem
p
o
r
ar
y
v
o
ltag
e
f
lu
ctu
a
tio
n
s
ar
e
th
e
m
o
s
t
co
m
m
o
n
ca
u
s
es.
I
n
ad
d
itio
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,
t
h
e
lack
o
f
r
ea
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p
o
wer
s
u
p
p
lied
to
th
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lo
ad
also
ca
u
s
es
elec
tr
ical
eq
u
ip
m
en
t
to
o
p
e
r
ate
in
e
f
f
icien
tly
[
5
]
,
[
6
]
.
T
h
e
r
ef
o
r
e,
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
atio
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will
b
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o
m
e
n
ec
ess
ar
y
to
im
p
r
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v
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th
e
p
o
wer
f
ac
to
r
a
n
d
b
etter
v
o
ltag
e
r
eg
u
latio
n
[
7
]
.
R
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
d
ev
ices
will
s
u
p
p
lem
en
t
th
e
r
eq
u
ir
ed
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
.
T
h
e
p
ar
allel
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
s
tr
u
ctu
r
e
ad
ju
s
ts
th
e
r
ea
ctiv
e
p
o
wer
at
th
e
co
n
n
ec
tio
n
p
o
in
t
.
T
h
is
p
r
o
ce
s
s
is
d
o
n
e
b
y
c
h
a
n
g
in
g
th
e
a
m
p
litu
d
e
a
n
d
p
h
ase
an
g
le
b
etwe
en
th
e
v
o
ltag
e
o
n
t
h
e
co
m
p
en
s
atio
n
d
ev
ice
an
d
th
e
v
o
ltag
e
o
n
th
e
p
o
wer
g
r
id
[
8
]
,
[
9
]
,
s
tab
ilizin
g
th
e
v
o
ltag
e,
a
n
d
b
alan
cin
g
t
h
e
lo
ad
f
o
r
th
e
p
h
ase.
R
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
s
o
lu
tio
n
s
h
a
v
e
b
ee
n
wid
ely
r
esear
ch
ed
an
d
f
o
cu
s
ed
o
n
d
ir
ec
tio
n
s
s
u
ch
as
two
-
way
co
m
p
e
n
s
atio
n
,
f
ix
e
d
co
m
p
e
n
s
atio
n
,
o
r
f
lex
ib
le
c
o
m
p
en
s
atio
n
u
s
in
g
s
y
n
ch
r
o
n
o
u
s
c
o
m
p
en
s
ato
r
s
,
c
ap
ac
ito
r
s
,
an
d
s
tatic
v
ar
co
m
p
en
s
ato
r
(
SVC
)
[
1
0
]
–
[
1
2
]
.
T
h
er
e
h
av
e
n
o
t
b
ee
n
m
an
y
s
tu
d
ies
o
n
u
s
in
g
m
o
d
u
lar
m
u
ltil
ev
el
c
o
n
v
e
r
ter
(
M
MC
)
in
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
atio
n
to
ac
h
ie
v
e
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
ef
f
ec
ts
.
I
n
th
is
ar
ticle,
we
will
f
o
cu
s
o
n
r
esear
ch
in
g
an
im
p
r
o
v
ed
n
ea
r
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lev
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m
o
d
u
latio
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(
NL
M
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m
o
d
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latio
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m
eth
o
d
,
a
co
n
tr
o
l
s
y
s
tem
ap
p
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to
MM
C
th
at
o
p
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ates
lik
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a
D
-
STAT
C
OM
d
ev
ice
to
co
m
p
en
s
ate
r
ea
ctiv
e
p
o
wer
f
o
r
lo
a
d
n
o
d
es
o
f
m
ed
iu
m
v
o
ltag
e
p
o
wer
g
r
id
s
.
T
h
e
m
ain
g
o
al
is
to
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
6
3
-
1
4
7
2
1464
im
p
r
o
v
e
th
e
p
o
wer
f
ac
to
r
a
n
d
s
tab
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th
e
v
o
ltag
e
at
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h
e
lo
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o
d
e.
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h
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MM
C
m
u
lti
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lev
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co
n
v
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ter
h
as
o
u
ts
tan
d
in
g
a
d
v
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tag
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c
o
m
p
ar
ed
to
o
t
h
er
m
u
lti
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lev
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co
n
v
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ter
s
b
ec
au
s
e
it
h
as
a
s
im
p
l
e
s
tr
u
ctu
r
e
an
d
ca
n
wo
r
k
with
h
ig
h
v
o
ltag
e
r
an
g
e
s
an
d
h
ig
h
p
o
wer
[
1
3
]
.
T
h
e
MM
C
s
tr
u
ctu
r
e
is
v
er
y
s
u
itab
le
f
o
r
c
o
r
r
ec
t
p
o
we
r
co
m
p
en
s
atio
n
f
o
r
m
ed
iu
m
v
o
ltag
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lo
ad
s
to
ad
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s
t
th
e
am
o
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n
t
o
f
r
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ctiv
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p
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wer
s
h
o
r
tag
e
o
r
ex
ce
s
s
;
th
is
i
s
esp
ec
ially
im
p
o
r
tan
t
wh
en
en
s
u
r
in
g
th
e
p
er
f
o
r
m
an
ce
o
f
h
ig
h
-
ca
p
ac
ity
m
o
to
r
s
[
1
4
]
.
I
n
th
i
s
p
ap
er
,
th
e
co
n
tr
o
l
p
r
o
ce
s
s
f
o
r
D
-
STAT
C
OM
is
b
ased
o
n
th
e
p
r
o
p
o
r
tio
n
al
–
i
n
teg
r
al
(
PI)
co
n
t
r
o
l
m
eth
o
d
co
m
b
in
ed
with
th
e
im
p
r
o
v
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d
NL
M
m
o
d
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latio
n
m
eth
o
d
.
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m
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im
p
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o
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d
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n
ap
p
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to
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.
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h
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s
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u
latio
n
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s
ed
s
y
s
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m
e
d
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M
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/
Simu
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o
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e
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th
e
alg
o
r
ith
m
'
s
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f
ec
tiv
en
ess
.
2.
M
O
DE
L
O
F
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T
CO
M
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D
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H
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M
M
C
ST
R
UCTUR
E
2
.
1
.
M
M
C
co
nv
er
t
er
s
t
ruct
ure
T
h
e
m
o
d
u
lar
m
u
ltil
ev
el
co
n
v
e
r
ter
ca
n
m
ee
t
th
e
c
o
n
v
er
s
io
n
r
eq
u
ir
em
en
ts
with
lar
g
e
v
o
ltag
e
an
d
h
ig
h
p
o
wer
[
1
5
]
,
[
1
6
]
.
MM
C
h
as
th
e
ad
v
a
n
tag
e
o
f
p
o
wer
r
an
g
e
ex
p
an
s
io
n
a
n
d
s
im
p
le
co
n
f
ig
u
r
atio
n
[
1
7
]
,
a
n
d
it
ca
n
g
en
er
ate
an
y
d
esire
d
v
o
ltag
e
lev
el
with
g
o
o
d
h
ar
m
o
n
i
c
q
u
ality
.
On
ly
o
n
e
d
ir
ec
t
cu
r
r
en
t
(
DC
)
v
o
ltag
e
s
o
u
r
ce
is
u
s
ed
at
th
e
i
n
p
u
t
w
ith
o
u
t
tr
an
s
f
o
r
m
er
s
an
d
f
ilter
s
,
m
ak
in
g
th
e
s
tr
u
ctu
r
e
co
m
p
a
ct
an
d
ec
o
n
o
m
ical
[
1
8
]
.
T
h
e
s
tr
u
ctu
r
e
o
f
D
-
STAT
C
OM
b
ased
o
n
MM
C
i
s
s
h
o
wn
in
Fig
u
r
e
1
.
I
n
wh
ich
,
F
ig
u
r
e
1
(
a
)
is
th
e
p
o
we
r
cir
cu
it
s
tr
u
ctu
r
e
o
f
D
-
STAT
C
OM
b
ased
o
n
MM
C
an
d
F
ig
u
r
e
1
(
b
)
is
th
e
d
iag
r
am
o
f
D
-
STAT
C
O
M
r
ep
lace
m
en
t in
t
h
e
g
r
id
co
n
n
e
ctio
n
m
o
d
el.
SM
1
SM
2
SM
N
SM
N
+
1
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
Ha
v
La
+
_
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
u
A
R
f
L
f
R
f
L
f
R
f
L
f
u
C
u
B
V
DC
SM
S
1
S
2
V
2
I
L
V
1
a
)
b
)
X
L
MMC
N
o
d
e
o
f
th
e
e
l
e
c
tr
i
c
a
l
s
y
s
te
m
i
Fig
u
r
e
1
.
Sch
em
atic
d
iag
r
am
o
f
D
-
STAT
C
OM
b
ased
o
n
M
MC c
o
n
n
ec
t g
r
id
(
a)
p
o
wer
cir
cu
it st
r
u
ctu
r
e
o
f
D
-
STAT
C
OM
b
ased
o
n
MM
C
an
d
(
b
)
alter
n
ativ
e
d
iag
r
am
o
f
D
-
STAT
C
OM
in
g
r
id
co
n
n
ec
tio
n
m
o
d
el
I
n
th
is
d
iag
r
am
,
ea
ch
p
h
ase
o
f
th
e
MM
C
co
m
p
r
is
es
two
b
r
an
ch
es
with
th
e
s
am
e
n
u
m
b
e
r
o
f
o
f
s
u
b
m
o
d
u
les
(
SMs
)
co
n
n
ec
te
d
in
s
er
ies.
T
h
e
alter
n
atin
g
cu
r
r
en
t
(
AC
)
v
o
ltag
e
o
n
ea
ch
p
h
ase
is
tak
en
at
th
e
m
id
p
o
in
t
b
etwe
en
th
e
two
r
e
ac
to
r
s
o
f
ea
c
h
b
r
an
c
h
;
th
e
r
esis
to
r
in
ea
c
h
b
r
an
ch
lim
its
ex
ter
n
al
s
h
o
c
k
cu
r
r
en
ts
in
to
th
e
MM
C
[
1
9
]
.
T
h
e
MM
C
's D
C
in
p
u
t v
o
ltag
e
is
s
u
p
p
lied
b
y
a
s
in
g
le
v
o
ltag
e
d
ir
ec
t c
u
r
r
en
t
(
)
s
o
u
r
ce
.
E
ac
h
SM
will
s
witch
at
d
if
f
er
en
t
tim
es
f
r
o
m
co
n
tr
o
l
co
m
m
an
d
s
s
o
th
e
co
n
v
er
te
r
ca
n
ac
h
iev
e
h
ig
h
ef
f
icien
cy
an
d
r
ed
u
ce
h
ar
m
o
n
ic
d
is
to
r
tio
n
[
2
0
]
.
T
h
e
n
u
m
b
e
r
o
f
SMs
o
f
th
e
MM
C
co
n
v
er
ter
d
ep
e
n
d
s
o
n
th
e
v
o
ltag
e
lev
el
r
eq
u
i
r
em
en
ts
o
n
th
e
AC
s
id
e.
T
h
eo
r
etica
lly
,
th
e
n
u
m
b
er
o
f
SMs
ca
n
b
e
in
c
r
e
ased
in
d
ef
in
itely
t
o
m
ee
t a
n
y
r
eq
u
ir
em
e
n
t f
o
r
o
u
tp
u
t v
o
ltag
e
lev
el
o
n
th
e
AC
s
id
e
[
2
1
]
.
T
h
e
s
p
ec
if
ic
wo
r
k
i
n
g
s
tates o
f
SM
d
ep
en
d
o
n
th
e
s
tate
o
f
v
al
v
es
1
,
an
d
2
an
d
th
e
d
ir
ec
tio
n
o
f
th
e
c
u
r
r
e
n
t.
W
h
en
th
e
c
u
r
r
en
t
i
in
th
e
cir
cu
it
h
as
a
p
o
s
itiv
e
d
ir
ec
tio
n
,
v
al
v
e
1
is
ON
an
d
v
alv
e
2
is
OFF,
th
e
v
o
lta
g
e
o
n
th
e
AC
s
id
e
o
f
th
e
SM
is
=
=
/
.
T
h
is
s
tate
is
ca
lled
th
e
SM
-
i
n
s
er
ted
s
tate.
On
th
e
co
n
tr
a
r
y
,
if
v
alv
e
1
is
OFF
an
d
v
alv
e
2
is
ON,
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
n
tr
o
l to
co
mp
en
s
a
te
r
ea
cti
ve
p
o
w
er a
t m
ed
iu
m
vo
lta
g
e
lo
a
d
n
o
d
es to
.
.
.
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
1465
v
o
ltag
e
o
n
th
e
AC
s
id
e
o
f
th
e
SM
is
=
0
.
T
h
is
s
tate
is
ca
lled
th
e
SM
b
y
p
ass
s
tate.
W
h
en
th
e
c
u
r
r
en
t
in
th
e
cir
cu
it
h
as
a
n
eg
ativ
e
d
ir
ec
tio
n
.
I
n
th
is
ca
s
e,
th
e
in
s
er
te
d
s
tate
also
o
cc
u
r
s
wh
en
v
alv
e
1
is
ON
an
d
2
is
OFF;
T
h
e
b
y
p
ass
s
tate
also
o
cc
u
r
s
wh
en
v
alv
e
1
is
OFF,
an
d
v
alv
e
2
is
ON.
2
.
2
.
T
he
o
pera
t
io
n o
f
M
M
C
f
o
llo
ws t
he
im
pro
v
ed
NL
M
m
o
d
ula
t
io
n m
et
ho
d
T
h
e
im
p
r
o
v
ed
NL
M
m
eth
o
d
is
u
s
ed
to
g
en
er
ate
th
e
n
u
m
b
er
o
f
lev
els
o
f
th
e
o
u
tp
u
t
v
o
lt
ag
e
o
f
t
h
e
MM
C
as
2
+
1
[
2
2
]
.
Fig
u
r
e
2
illu
s
tr
ates th
e
o
p
er
atin
g
p
r
in
cip
le
o
f
th
e
im
p
r
o
v
ed
NL
M
m
eth
o
d
. T
h
is
m
eth
o
d
is
u
s
ed
to
m
o
d
u
late
f
o
r
MM
C
co
n
v
er
ter
with
1
0
SMs
p
er
v
alv
e
b
r
an
ch
a
n
d
ap
p
lied
in
th
e
D
-
STAT
C
O
M
m
o
d
el
[
2
2
]
.
V
V
DC
V
C
V
DC
/
2
V
C
/
2
0
0
-
V
DC
/
2
V
C
/
4
T
/
2
T
/
2
t
t
t
1
t
2
t
3
Fig
u
r
e
2
.
Prin
cip
le
o
f
th
e
im
p
r
o
v
ed
NL
M
m
eth
o
d
T
h
e
d
iag
r
am
in
F
ig
u
r
e
2
u
s
es two
s
in
e
wav
es
an
d
to
m
ak
e
th
e
s
et
s
ig
n
als an
d
ar
e
cr
ea
ted
as
(
2
)
.
Nex
t,
th
e
s
tep
wav
es
an
d
will
b
e
cr
ea
ted
b
y
th
e
r
o
u
n
d
in
g
f
u
n
ctio
n
an
d
ar
e
d
eter
m
i
n
e
d
as
(
3
)
.
T
h
en
,
we
ca
n
s
y
n
th
esize
th
e
s
in
e
wav
e
s
et
an
d
th
e
s
tep
p
e
d
wav
e
at
th
e
AC
o
u
tp
u
t
in
Fig
u
r
e
2
,
eq
u
iv
alen
t to
(
4
)
a
n
d
(
5
)
.
Deta
ils
o
f
th
e
p
r
o
ce
s
s
es a
r
e
ex
p
lain
ed
as f
o
llo
ws:
T
h
e
r
o
u
n
d
f
u
n
c
t
i
o
n
d
e
t
e
r
m
i
n
i
n
g
t
h
e
n
u
m
b
e
r
o
f
S
M
s
i
n
s
e
r
t
e
d
d
u
r
i
n
g
t
h
e
w
o
r
k
i
n
g
c
y
c
l
e
i
s
e
x
p
r
e
s
s
e
d
a
s
(
1
)
:
{
=
0
.
25
{
2
[
1
−
(
)
]
}
=
0
.
25
{
2
[
1
+
(
)
]
}
(
1
)
T
h
e
r
o
u
n
d
f
u
n
ctio
n
0
.
25
(
)
m
ea
n
s
th
at
th
e
v
alu
e
is
r
o
u
n
d
ed
to
th
e
n
ea
r
est
in
teg
er
v
alu
e
d
ep
e
n
d
in
g
o
n
th
e
d
ec
im
al
p
ar
t
o
f
.
I
f
th
e
d
ec
im
al
p
ar
t
o
f
is
m
o
r
e
s
ig
n
if
ican
t
th
an
0
.
2
5
,
th
en
is
r
o
u
n
d
ed
u
p
to
th
e
n
ex
t
s
p
ec
if
ied
v
alu
e;
o
th
er
wis
e,
is
r
o
u
n
d
ed
d
o
wn
to
th
e
p
r
ev
i
o
u
s
ly
d
eter
m
in
ed
v
al
u
e.
T
h
e
im
p
r
o
v
ed
NL
M
m
eth
o
d
an
aly
s
is
co
n
s
id
er
s
two
tim
e
p
er
io
d
s
f
r
o
m
1
to
2
,
f
r
o
m
2
to
3
in
Fig
u
r
e
3
.
T
h
e
f
ir
s
t
ca
s
e
is
th
e
p
er
io
d
f
r
o
m
1
to
2
.
Su
p
p
o
s
e
=
,
th
e
s
et
v
alu
e
o
f
b
r
a
n
ch
v
o
ltag
e
an
d
AC
o
u
tp
u
t
v
o
lta
g
e
at
1
is
d
eter
m
in
ed
ac
c
o
r
d
in
g
to
(
2
)
:
{
=
(
+
0
.
25
)
=
[
(
−
−
1
)
+
0
.
75
]
=
(
−
0
.
5
+
0
.
25
)
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
6
3
-
1
4
7
2
1466
Acc
o
r
d
in
g
to
t
h
e
r
o
u
n
d
in
g
f
u
n
ctio
n
,
th
e
s
tep
wav
ef
o
r
m
o
f
t
h
e
b
r
an
c
h
v
o
ltag
e
a
n
d
AC
v
o
l
tag
e
in
th
e
f
ir
s
t c
ase
is
d
eter
m
in
ed
as (
3
)
:
{
=
=
(
−
)
=
(
−
0
.
5
)
(
3
)
T
h
e
s
e
c
o
n
d
c
a
s
e
i
s
f
r
o
m
2
t
o
3
.
T
h
e
s
e
t
v
a
l
u
e
o
f
t
h
e
b
r
a
n
c
h
v
o
l
tag
e
a
n
d
A
C
v
o
l
t
a
g
e
a
t
2
i
s
d
e
t
e
r
m
i
n
e
d
b
y
(
4
)
.
{
=
[
(
−
1
)
+
0
.
75
]
=
[
(
−
)
+
0
.
25
]
=
(
−
0
.
5
−
0
.
25
)
(
4
)
T
h
e
s
tep
p
ed
wav
e
f
o
r
m
o
f
th
e
b
r
an
ch
v
o
ltag
e
a
n
d
AC
v
o
ltag
e,
in
th
is
ca
s
e,
is
d
eter
m
in
ed
:
{
=
=
(
−
+
1
)
=
(
−
0
.
5
−
0
.
5
)
(
5
)
C
o
m
p
ar
in
g
(
3
)
an
d
(
5
)
,
it
ca
n
b
e
s
ee
n
th
at
th
e
s
tep
s
ize
in
i
s
0
.
5
.
T
h
e
m
o
s
t
s
ig
n
if
ican
t
d
ev
iatio
n
b
etwe
en
an
d
ap
p
ea
r
s
d
u
r
in
g
s
tep
ch
an
g
e
(
1
,
2
an
d
3
)
.
C
o
m
p
a
r
in
g
i
n
(
3
)
,
(
4
)
,
a
n
d
(
5
)
,
w
e
s
e
e
th
a
t
t
h
e
m
a
x
i
m
u
m
d
e
v
i
a
t
i
o
n
i
s
0
.
2
5
.
T
h
i
s
p
r
o
c
e
s
s
w
i
ll
c
a
u
s
e
t
h
e
o
u
t
p
u
t
v
o
l
t
a
g
e
t
o
h
a
v
e
s
e
v
e
r
a
l
l
e
v
e
l
s
o
f
2
+
1
,
as sh
o
wn
in
Fig
u
r
e
4
.
2
.
3
.
M
o
del o
f
D
-
ST
AT
CO
M
is
ba
s
ed
o
n M
M
C
D
-
STAT
C
OM
is
b
ased
o
n
M
MC
co
n
v
er
ter
s
c
o
n
n
ec
ted
in
p
ar
allel
to
th
e
d
is
tr
ib
u
tio
n
g
r
i
d
an
d
ca
n
ad
ap
t
to
h
ig
h
ly
v
a
r
iab
le
p
o
we
r
s
o
u
r
ce
s
[
2
3
]
,
[
2
4
]
.
T
h
is
d
ev
i
ce
wo
r
k
s
lik
e
a
v
o
ltag
e
s
o
u
r
ce
to
p
r
o
d
u
ce
an
AC
o
u
tp
u
t
v
o
ltag
e
f
r
o
m
a
DC
v
o
ltag
e
s
o
u
r
ce
[
2
5
]
.
W
h
en
p
e
r
f
o
r
m
in
g
c
o
n
tr
o
l
f
o
r
MM
C
a
s
a
D
-
STAT
C
OM
d
ev
ice,
th
is
s
y
s
tem
ad
ju
s
ts
th
e
v
o
ltag
e
o
r
p
o
wer
at
t
h
e
in
s
talled
lo
ca
tio
n
b
y
c
h
an
g
i
n
g
th
e
a
m
p
litu
d
e
an
d
p
h
ase
an
g
le
b
etwe
en
th
e
v
o
ltag
e
o
n
D
-
STAT
C
OM
an
d
th
e
v
o
lta
g
e
o
n
th
e
g
r
id
n
o
d
e.
T
h
en
,
t
h
e
cu
r
r
en
t
p
ass
in
g
th
r
o
u
g
h
D
-
STAT
C
OM
ca
n
b
e
s
lo
wer
o
r
f
aster
th
an
th
e
u
p
s
tr
ea
m
v
o
ltag
e,
b
r
in
g
in
g
th
e
v
o
l
tag
e
at
th
e
n
o
d
e
to
its
r
ated
v
alu
e
an
d
co
m
p
en
s
atin
g
f
o
r
th
e
am
o
u
n
t
o
f
r
e
ac
tiv
e
p
o
wer
as
r
eq
u
ir
ed
.
T
h
e
ce
n
tr
al
p
ar
t
o
f
D
-
STAT
C
OM
is
th
e
MM
C
co
n
v
er
ter
,
wh
ich
co
n
v
er
ts
th
e
v
o
ltag
e
s
o
u
r
ce
f
r
o
m
DC
to
AC
an
d
v
ice
v
er
s
a
th
r
o
u
g
h
c
o
n
tr
o
l
laws.
T
h
e
s
p
ec
ial
f
ea
tu
r
e
o
f
th
is
c
o
n
f
ig
u
r
a
tio
n
is
th
e
q
u
ick
r
esp
o
n
s
e
to
g
en
er
ate
o
r
a
b
s
o
r
b
r
ea
ctiv
e
p
o
wer
to
co
n
tr
o
l
th
e
f
lo
w
o
f
r
ea
ctiv
e
p
o
wer
at
t
h
e
co
m
p
en
s
ated
n
o
d
e,
p
r
ev
e
n
tin
g
f
lick
er
in
g
o
f
t
h
e
p
o
wer
g
r
i
d
[
2
6
]
.
3.
T
H
E
O
P
E
R
AT
I
O
N
O
F
D
-
ST
AT
CO
M
I
S B
A
SE
D
O
N
M
M
C
3
.
1
.
Co
nn
ec
t
io
n
D
-
ST
AT
C
O
M
wit
h po
wer
s
y
s
t
em
no
de
Fig
u
r
e
1
(
b
)
s
h
o
ws
th
e
D
-
STA
T
C
OM
d
iag
r
am
u
s
in
g
a
n
M
MC
co
n
v
er
ter
p
a
r
allel
to
th
e
p
o
wer
g
r
id
.
On
e
en
d
o
f
D
-
STAT
C
OM
is
co
n
n
ec
ted
to
th
e
s
ec
o
n
d
ar
y
s
id
e
o
f
th
e
tr
an
s
f
o
r
m
e
r
(
wh
en
y
o
u
wan
t
to
r
aise
th
e
v
o
ltag
e
v
alu
e
t
o
th
e
ap
p
r
o
p
r
iat
e
v
o
ltag
e
lev
el)
,
an
d
th
e
o
th
er
is
co
n
n
ec
ted
to
a
DC
en
er
g
y
s
to
r
ag
e
d
e
v
ice.
T
h
is
s
y
s
tem
is
o
f
ten
p
lace
d
at
th
e
n
o
d
e
to
s
u
p
p
ly
p
o
wer
to
th
e
l
o
ad
,
lim
itin
g
h
ar
m
o
n
ics
in
lar
g
e
-
ca
p
ac
ity
m
o
to
r
s
an
d
m
etallu
r
g
ical
tech
n
o
lo
g
y
.
I
t
is
also
p
lace
d
in
b
u
ild
in
g
s
to
r
ed
u
ce
s
ig
n
al
d
is
to
r
tio
n
an
d
en
h
an
ce
elec
tr
ical
eq
u
ip
m
en
t'
s
p
o
wer
q
u
ality
an
d
o
p
er
atio
n
al
r
eliab
ilit
y
[
2
5
]
.
3
.
2
.
M
o
delin
g
t
he
M
M
C
co
n
v
er
t
er
in re
a
ct
iv
e
po
wer
c
o
mp
ens
a
t
io
n m
o
de
T
h
e
co
n
v
er
ter
m
o
d
el
f
o
r
g
r
id
co
n
n
ec
tio
n
,
as
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
,
in
clu
d
es
an
MM
C
co
n
v
er
ter
to
co
n
v
er
t
elec
tr
icity
f
r
o
m
DC
to
AC
;
R
f
an
d
L
f
ar
e
t
h
e
r
esis
tan
ce
an
d
in
d
u
ctan
ce
b
etwe
e
n
th
e
MM
C
cir
cu
it
b
o
ar
d
a
n
d
th
e
g
r
id
,
(
=
A
,
B
,
C
)
is
d
en
o
ted
as
g
r
id
v
o
ltag
e,
is
th
e
o
u
tp
u
t v
o
ltag
e
o
f
th
e
cir
cu
it
b
r
ea
k
er
,
v
ex
is
th
e
in
ter
n
al
elec
tr
o
m
o
tiv
e
f
o
r
c
e
o
f
th
e
cir
c
u
it
b
r
ea
k
er
,
is
th
e
o
u
tp
u
t
c
u
r
r
e
n
t
o
f
th
e
MM
C
.
I
t
h
as
th
e
d
ir
ec
tio
n
f
r
o
m
MM
C
to
th
e
g
r
id
.
W
h
en
s
en
d
in
g
en
er
g
y
to
th
e
g
r
id
,
MM
C
wo
r
k
s
in
i
n
v
er
ter
m
o
d
e
an
d
tr
an
s
f
er
s
en
er
g
y
f
r
o
m
th
e
DC
cir
cu
it to
th
e
g
r
id
.
Ap
p
ly
in
g
Kir
h
o
f
f
'
s
law
to
th
e
cir
cu
it,
th
e
eq
u
atio
n
c
o
n
n
ec
tin
g
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
th
e
elem
en
ts
o
f
th
e
MM
C
is
as (
6
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
n
tr
o
l to
co
mp
en
s
a
te
r
ea
cti
ve
p
o
w
er a
t m
ed
iu
m
vo
lta
g
e
lo
a
d
n
o
d
es to
.
.
.
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
1467
{
=
−
2
−
2
=
−
2
−
2
=
−
2
−
2
(
6
)
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
o
u
tp
u
t
v
o
ltag
e
an
d
th
e
g
r
id
v
o
ltag
e
th
r
o
u
g
h
th
e
r
esis
tan
ce
an
d
in
d
u
ctan
ce
o
f
th
e
g
r
id
is
wr
itten
as (
7
)
:
{
=
+
+
=
+
+
=
+
+
(
7
)
Fro
m
(
6
)
an
d
(
7
)
,
it is
d
ed
u
ce
d
:
{
=
+
(
+
2
)
+
(
+
2
)
=
+
(
+
2
)
+
(
+
2
)
=
+
(
+
2
)
+
(
+
2
)
(
8
)
Set
=
+
2
,
=
+
2
in
(
8
)
is
r
ewr
itten
as (
9
)
.
{
=
+
+
=
+
+
=
+
+
(
9
)
In
(
9
)
is
f
o
r
co
n
tr
o
ller
d
esig
n
p
u
r
p
o
s
es
if
th
e
MM
C
is
ap
p
lied
an
d
c
o
n
n
ec
te
d
to
th
e
p
o
wer
g
r
id
to
co
m
p
en
s
ate
f
o
r
r
ea
ctiv
e
p
o
w
er
.
Use
th
e
tr
an
s
f
o
r
m
atio
n
s
o
f
co
o
r
d
in
ates
to
0
co
o
r
d
in
ate
s
th
r
o
u
g
h
PAR
K
co
o
r
d
in
ate
tr
an
s
f
o
r
m
ati
o
n
s
lik
e
in
(
1
0
)
:
{
=
−
+
−
+
=
−
−
−
+
(
1
0
)
Activ
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
ar
e
r
ep
r
esen
ted
b
y
(
1
1
)
:
{
=
3
2
{
.
∗
}
=
3
2
(
+
)
=
3
2
{
.
∗
}
=
3
2
(
−
+
)
(
11
)
T
h
e
r
elatio
n
s
h
ip
o
f
p
o
wer
b
ala
n
ce
b
etwe
en
AC
in
p
u
t a
n
d
DC
o
u
tp
u
t is wr
itten
as
(
1
2
)
:
=
3
2
(
.
+
.
)
=
.
(
1
2
)
wh
er
e
an
d
ar
e
th
e
v
o
ltag
e
a
n
d
cu
r
r
e
n
t o
n
th
e
DC
s
id
e.
3
.
3
.
Rea
c
t
iv
e
po
wer
co
m
pens
a
t
io
n principl
e
o
f
D
-
ST
AT
CO
M
Activ
e
p
o
wer
an
d
r
ea
ctiv
e
p
o
wer
at
th
e
p
o
wer
s
y
s
tem
n
o
d
e
in
Fig
u
r
e
1
(
a
)
ar
e
s
h
o
wn
in
(
1
3
)
.
1
=
1
2
;
1
=
1
(
1
−
2
c
o
s
)
(1
3
)
I
n
wh
ich
1
an
d
1
ar
e
th
e
v
o
ltag
e
am
p
litu
d
e
an
d
p
h
ase
an
g
le
at
th
e
p
o
wer
s
y
s
tem
n
o
d
e;
2
an
d
2
ar
e
th
e
v
o
ltag
e
am
p
litu
d
e
a
n
d
p
h
ase
an
g
le
o
f
D
-
STAT
C
OM
;
δ
is
th
e
p
h
ase
d
if
f
er
e
n
ce
an
g
le
b
etw
ee
n
th
e
g
r
id
a
n
d
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
6
3
-
1
4
7
2
1468
co
m
p
en
s
ato
r
;
is
th
e
r
ea
ctan
ce
b
etwe
en
th
e
g
r
id
a
n
d
th
e
c
o
m
p
en
s
ato
r
.
Fr
o
m
(
1
3
)
,
it
is
s
ee
n
th
at
r
ea
ctiv
e
p
o
wer
ca
n
b
e
a
d
ju
s
ted
b
y
ad
ju
s
tin
g
th
e
am
p
litu
d
e
o
f
th
e
AC
v
o
ltag
e
o
r
th
e
p
h
ase
an
g
le
s
o
th
at
D
-
STAT
C
OM
ca
n
ch
an
g
e
th
e
ab
s
o
r
p
tio
n
o
r
em
is
s
io
n
o
f
r
ea
c
tiv
e
p
o
wer
.
T
h
e
d
esire
o
f
D
-
STAT
C
OM
i
s
o
n
ly
to
p
r
o
v
id
e
o
r
c
o
n
s
u
m
e
r
ea
ctiv
e
p
o
wer
.
I
f
y
o
u
a
d
ju
s
t
th
e
p
h
ase
an
g
le,
it
will
af
f
ec
t
th
e
cu
r
r
en
t
o
f
ac
tiv
e
p
o
wer
e
x
ch
an
g
e.
T
h
er
ef
o
r
e,
th
e
r
ea
ctiv
e
p
o
wer
is
ad
ju
s
ted
b
y
co
n
tr
o
llin
g
t
h
e
p
h
ase
d
if
f
er
en
ce
an
g
le
o
f
t
h
e
p
h
ases
o
f
1
an
d
2
to
ze
r
o
an
d
s
im
u
ltan
e
o
u
s
ly
ad
ju
s
tin
g
th
e
v
o
ltag
e
am
p
litu
d
e
o
f
2
.
T
h
en
,
in
th
e
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
o
p
er
atin
g
m
o
d
e,
2
is
in
p
h
ase
with
1
(
δ
=
0
)
; a
t th
e
v
o
ltag
e
n
o
d
e,
o
n
l
y
r
ea
ctiv
e
p
o
wer
tr
an
s
m
its
in
(
1
3
)
b
ec
o
m
es (
1
4
)
.
1
=
0
;
1
=
1
(
1
−
2
)
(
1
4
)
Fro
m
(
1
4
)
,
we
s
ee
th
at
r
ea
ctiv
e
p
o
wer
Q
is
p
r
o
p
o
r
tio
n
al
to
(
1
−
2
)
.
I
f
1
>
2
,
th
en
>
0
e
x
is
ts
a
v
o
ltag
e
co
m
p
o
n
en
t
12
,
co
r
r
esp
o
n
d
in
g
to
th
e
in
d
u
ctan
ce
cu
r
r
e
n
t
I
L
b
ein
g
o
u
t
o
f
p
h
ase
with
1
an
d
2
at
an
an
g
le
/
2
.
T
h
en
,
D
-
STAT
C
OM
a
b
s
o
r
b
s
r
ea
ctiv
e
p
o
wer
.
I
f
1
<
2
,
th
en
Q
<
0
,
th
e
v
o
ltag
e
c
o
m
p
o
n
en
t
12
ex
is
ts
,
co
r
r
esp
o
n
d
in
g
to
th
e
I
C
ca
p
ac
itiv
e
cu
r
r
en
t
b
ein
g
in
p
h
ase
with
an
an
g
le
π
/2
;
th
e
g
r
id
will
r
ec
eiv
e
r
ea
ctiv
e
p
o
wer
f
r
o
m
th
e
co
m
p
en
s
ato
r
.
T
h
en
,
D
-
STAT
C
OM
g
en
er
ates
r
ea
ctiv
e
p
o
we
r
f
o
r
th
e
g
r
id
.
I
f
1
=
2
,
th
en
Q
=
0
,
MM
C
d
o
es n
o
t a
b
s
o
r
b
o
r
em
it r
ea
ctiv
e
p
o
wer
.
4.
CO
NT
RO
L
SYS
T
E
M
F
O
R
ST
A
T
CO
M
T
h
e
co
n
tr
o
l
d
esig
n
o
f
th
e
MM
C
co
n
v
er
ter
in
D
-
STAT
C
OM
in
th
is
s
ec
tio
n
m
u
s
t
ad
d
r
ess
is
s
u
es
s
u
ch
as
a
p
p
ly
in
g
th
e
D
-
STAT
C
OM
co
n
tr
o
l
s
tr
u
ctu
r
e
b
ased
o
n
N
L
M
m
o
d
u
latio
n
f
o
r
MM
C
,
u
s
i
n
g
lo
o
p
s
to
co
n
tr
o
l
th
e
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
to
b
e
co
m
p
e
n
s
ated
in
th
e
co
o
r
d
in
ate
s
y
s
tem
to
ac
h
iev
e
th
e
r
eq
u
ir
em
e
n
ts
f
o
r
th
e
p
o
wer
v
alu
e
to
b
e
co
m
p
e
n
s
ated
.
T
h
e
d
esig
n
p
r
o
ce
s
s
m
u
s
t
en
s
u
r
e
in
s
tan
tan
eo
u
s
co
n
tr
o
l
o
f
r
ea
ctiv
e
p
o
wer
m
o
b
ilis
ed
ac
co
r
d
in
g
to
th
e
s
et
am
o
u
n
t.
T
h
e
s
et
v
alu
e
o
f
r
ea
c
tiv
e
p
o
wer
is
ca
lcu
lated
in
s
tan
tan
eo
u
s
ly
f
r
o
m
th
e
d
if
f
er
en
ce
b
etwe
en
th
e
v
o
lta
g
e
v
alu
e
at
th
e
elec
tr
ical
s
y
s
tem
co
n
n
ec
tio
n
p
o
in
t
an
d
th
e
d
esire
d
r
ef
er
e
n
ce
v
o
ltag
e
at
th
e
o
u
tp
u
t
o
f
th
e
M
MC.
Fro
m
th
e
an
aly
s
is
o
f
th
e
p
r
in
cip
le
o
f
r
ea
ctiv
e
p
o
wer
co
m
p
en
s
atio
n
ab
o
v
e,
in
th
e
ac
tiv
e
p
o
wer
co
n
tr
o
l
s
y
s
tem
,
th
e
ac
tiv
e
p
o
wer
is
alwa
y
s
co
n
tr
o
lled
to
ze
r
o
,
m
ea
n
in
g
th
e
co
n
tr
o
ller
will
n
o
t e
x
ch
a
n
g
e
ac
tiv
e
p
o
wer
with
th
e
g
r
id
.
T
h
en
,
i
n
th
e
co
n
t
r
o
l
s
y
s
tem
,
o
n
ly
th
e
co
n
tr
o
l c
ir
cu
it e
m
its
o
r
ab
s
o
r
b
s
r
ea
ctiv
e
p
o
we
r
;
th
e
p
r
o
ce
s
s
o
f
ab
s
o
r
b
in
g
an
d
g
en
e
r
atin
g
r
e
ac
tiv
e
p
o
wer
d
ep
e
n
d
s
o
n
c
o
m
p
ar
in
g
th
e
v
o
ltag
e
v
alu
e
o
f
t
h
e
o
u
t
p
u
t v
o
ltag
e
an
d
th
e
g
r
i
d
v
o
ltag
e
.
as
an
aly
ze
d
in
(
1
5
)
.
=
+
(1
5
)
I
n
wh
ich
:
is
th
e
p
o
s
itiv
e
s
eq
u
en
ce
v
o
ltag
e;
is
th
e
r
ea
ctiv
e
c
u
r
r
en
t
(
>
0
is
th
e
in
d
u
ctiv
e
cu
r
r
en
t,
<
0
is
th
e
ca
p
ac
itiv
e
cu
r
r
en
t)
;
i
s
s
lo
p
e
r
esis
tan
ce
.
T
h
e
v
o
lta
g
e
v
alu
e
is
alwa
y
s
m
ea
s
u
r
ed
f
r
o
m
th
e
s
y
s
tem
an
d
co
m
p
ar
e
d
with
t
h
e
s
et
v
o
ltag
e
.
T
h
e
r
ea
ctiv
e
cu
r
r
en
t
will
b
e
a
d
ju
s
ted
with
in
th
e
cu
r
r
e
n
t
v
al
u
e
r
an
g
e
(
−
,
)
wh
en
V
<
,
an
d
th
e
co
n
tr
o
ller
will
in
cr
ea
s
e
th
e
v
o
ltag
e
to
th
e
v
alu
e.
O
n
th
e
co
n
tr
ar
y
,
wh
en
V
>
,
th
e
co
n
tr
o
ller
will
ad
ju
s
t
th
e
s
y
s
tem
u
n
til
=
.
T
h
er
ef
o
r
e,
a
DC
-
s
id
e
v
o
ltag
e
co
n
tr
o
ller
is
n
ec
ess
ar
y
to
d
esig
n
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
.
T
h
e
r
elatio
n
s
h
ip
b
etwe
en
DC
v
o
ltag
e
an
d
AC
ac
tiv
e
p
o
wer
is
in
th
e
f
o
r
m
(
1
6
)
an
d
(
1
7
)
:
2
=
3
2
=
(1
6
)
=
3
2
1
(1
7
)
Fig
u
r
e
3
is
th
e
co
n
tr
o
l
s
y
s
tem
s
tr
u
ctu
r
e
d
ia
g
r
am
f
o
r
D
-
STA
T
C
OM
.
T
h
e
s
y
s
tem
in
clu
d
es
t
wo
co
n
t
r
o
l
lo
o
p
s
:
an
ex
ter
n
al
co
n
tr
o
l
lo
o
p
to
co
n
tr
o
l
DC
v
o
ltag
e
an
d
r
ea
ctiv
e
p
o
wer
;
th
e
o
u
tp
u
t
o
f
th
e
r
ea
ctiv
e
p
o
wer
co
n
tr
o
ller
is
if
c
u
r
r
e
n
t,
wh
ic
h
is
th
e
cu
r
r
en
t
p
er
p
e
n
d
icu
lar
to
a
v
o
ltag
e
th
at
c
o
n
tr
o
ls
th
e
r
e
ac
tiv
e
p
o
wer
f
lo
w.
T
h
e
o
u
tp
u
t
o
f
th
e
DC
v
o
ltag
e
r
eg
u
lato
r
is
th
e
i
dref
c
u
r
r
e
n
t,
w
h
ich
is
th
e
cu
r
r
e
n
t
in
p
h
ase
with
th
e
v
o
ltag
e
th
at
co
n
tr
o
ls
th
e
ac
tiv
e
p
o
wer
f
lo
w
.
An
in
ter
n
al
co
n
tr
o
l lo
o
p
is
u
s
ed
to
co
n
tr
o
l th
e
cu
r
r
e
n
t b
ased
o
n
th
e
p
ar
am
eter
s
p
r
o
v
id
e
d
b
y
th
e
ex
ter
n
al
co
n
tr
o
ller
af
ter
p
er
f
o
r
m
in
g
co
n
tr
o
l
s
ig
n
als.
T
h
e
co
n
tr
o
ller
o
u
tp
u
t v
alu
e
is
th
e
am
o
u
n
t
o
f
s
ettin
g
n
ec
ess
ar
y
to
p
u
t
i
n
to
th
e
m
o
d
u
latio
n
s
tag
e
t
o
d
e
ter
m
in
e
th
e
v
al
v
e
s
witch
in
g
s
tate
o
f
th
e
MM
C
.
C
o
m
p
ar
ed
to
v
o
ltag
e
s
o
u
r
ce
c
o
n
v
er
ter
(
VSC
)
co
m
p
en
s
atio
n
s
tr
u
ctu
r
es,
th
is
s
tr
u
ctu
r
e
is
s
im
p
le
to
im
p
lem
e
n
t
b
ec
au
s
e
it u
s
es lin
ea
r
PI
r
eg
u
l
ato
r
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
n
tr
o
l to
co
mp
en
s
a
te
r
ea
cti
ve
p
o
w
er a
t m
ed
iu
m
vo
lta
g
e
lo
a
d
n
o
d
es to
.
.
.
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
1469
i
DC
M
M
C
S
(
k
)
V
DC
C
al
c
u
l
at
e
p
ow
e
r
Q
ac
c
or
d
i
n
g t
o
(
14
)
PI
PI
dq
/
ab
c
abc
/
dq
I
m
p
l
e
m
e
n
t
i
n
g
t
h
e
N
L
M
m
od
u
l
at
i
on
s
t
r
at
e
gy
f
i
gu
r
e
3
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
u
A
,
B
,
C
R
f
L
f
R
f
L
f
R
f
L
f
i
A
i
B
i
C
+
+
_
+
_
PI
+
_
PI
L
L
_
i
d
V
ol
t
age
c
on
t
r
ol
C
u
r
r
e
n
t
c
on
t
r
ol
i
q
u
d
u
q
v
A
v
B
v
C
+
+
+
+
+
_
P
ow
e
r
c
on
t
r
ol
ω
s
N
o
d
e
o
f
t
h
e
e
l
e
c
t
r
i
c
a
l
s
y
s
t
e
m
θ
u
A
u
B
u
C
Fig
u
r
e
3
.
Stru
ctu
r
e
d
iag
r
am
o
f
D
-
STAT
C
OM
co
n
tr
o
l
s
y
s
tem
b
ased
o
n
MM
C
co
n
t
r
o
ller
5.
SI
M
UL
A
T
I
O
N
A
ND
E
V
AL
UAT
E
T
H
E
R
E
S
UL
T
S
Simu
latio
n
p
ar
am
eter
s
f
o
r
t
h
e
MM
C
co
n
tr
o
l sy
s
tem
ar
e
s
h
o
wn
in
T
ab
le
1
.
Fig
u
r
e
4
s
h
o
ws th
e
r
esu
lts
o
f
th
e
MM
C
s
witch
'
s
A
C
o
u
t
p
u
t
cu
r
r
e
n
t
an
d
v
o
ltag
e
wh
en
o
p
er
atin
g
in
r
ea
ctiv
e
p
o
wer
c
o
m
p
en
s
atio
n
m
o
d
e
,
in
wh
ich
Fig
u
r
e
4
(
a)
is
th
e
cu
r
r
en
t
r
esu
lt
o
n
th
r
ee
p
h
ases
o
n
th
e
AC
s
id
e,
Fig
u
r
e
4
(
b
)
is
th
e
v
o
ltag
e
r
esu
lt
o
n
th
r
ee
p
h
ases
o
n
th
e
AC
s
id
e
.
T
h
e
r
esu
lts
s
h
o
w
t
h
at
th
e
cu
r
r
en
t
an
d
v
o
ltag
e
h
a
v
e
a
s
tan
d
a
r
d
s
in
u
s
o
id
al
s
h
ap
e
,
ab
n
o
r
m
al
tr
an
s
ien
t
p
h
e
n
o
m
e
n
a
d
o
n
o
t
a
p
p
ea
r
in
th
e
s
in
e
wav
e
o
f
cu
r
r
e
n
t
a
n
d
v
o
lta
g
e
wh
en
th
e
MM
C
o
p
er
ates
in
n
o
r
m
al
m
o
d
e
.
Fig
u
r
e
5
s
h
o
ws
th
e
r
ea
ctiv
e
p
o
wer
r
esp
o
n
s
e
o
f
th
e
p
o
wer
s
y
s
tem
at
th
e
s
u
r
v
ey
tim
e
f
r
o
m
0
t
o
0
.
3
s
; th
e
co
m
p
en
s
at
ed
r
ea
ctiv
e
p
o
wer
alwa
y
s
tr
ac
k
s
to
th
e
s
et
v
alu
e
af
ter
0
.
0
3
s
,
th
is
is
a
v
er
y
s
m
all
tim
e
in
ter
v
al
s
h
o
win
g
v
er
y
q
u
ick
r
esp
o
n
s
e
o
f
th
e
c
o
n
tr
o
ller
to
s
tab
ilize
th
e
r
ea
ctiv
e
p
o
wer
v
alu
e
as
r
eq
u
i
r
ed
.
B
ec
au
s
e
MM
C
o
p
er
ates
in
r
ea
ctiv
e
p
o
wer
co
m
p
e
n
s
atio
n
m
o
d
e,
t
h
e
ac
tiv
e
p
o
wer
s
u
p
p
lied
to
th
e
g
r
id
is
alwa
y
s
ze
r
o
ac
co
r
d
in
g
to
a
p
r
eset
am
o
u
n
t.
Fig
u
r
e
6
s
h
o
ws
th
e
d
-
a
xis
an
d
q
-
a
xis
cu
r
r
en
t
i
n
th
e
dq
co
o
r
d
in
ate
s
y
s
tem
.
T
h
e
v
alu
es o
f
th
ese
two
cu
r
r
en
ts
will c
o
r
r
esp
o
n
d
to
th
e
am
o
u
n
t
o
f
ac
tiv
e
p
o
we
r
a
n
d
r
ea
ctiv
e
p
o
wer
o
f
th
e
s
y
s
tem
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
p
o
wer
o
f
th
e
t
r
ac
k
in
g
ef
f
ec
t
is
s
et
to
0
,
s
o
th
e
d
-
a
xi
s
cu
r
r
en
t
also
h
as
a
co
r
r
esp
o
n
d
in
g
v
alu
e
o
f
0
.
T
h
e
q
-
a
xis
c
u
r
r
e
n
t
h
as
a
n
e
g
ativ
e
v
alu
e
co
r
r
esp
o
n
d
in
g
to
t
h
e
v
alu
e
o
f
r
ea
ctiv
e
p
o
wer
p
u
m
p
e
d
to
th
e
g
r
id
.
W
h
en
u
s
in
g
MM
C
to
co
m
p
en
s
a
te
r
ea
ctiv
e
p
o
wer
f
o
r
th
e
p
o
w
er
s
y
s
tem
,
it
b
r
in
g
s
ce
r
tain
ef
f
ec
ts
o
n
th
e
s
tab
ilit
y
o
f
th
e
co
m
p
e
n
s
ated
p
o
wer
s
y
s
tem
,
s
u
ch
as
a
wid
e
r
ea
ctiv
e
p
o
wer
ad
ju
s
tm
en
t
r
an
g
e
an
d
q
u
ick
r
esp
o
n
s
e
to
g
en
er
ate
p
o
wer
.
r
ea
ctan
ce
t
o
co
n
tr
o
l
th
e
r
ea
ctiv
e
p
o
wer
f
lo
w
at
th
e
co
m
p
e
n
s
ated
n
o
d
e;
DC
p
o
we
r
v
alu
e
is
alwa
y
s
s
tab
le
ar
o
u
n
d
th
e
r
ated
v
alu
e
in
n
o
r
m
al
o
p
er
atin
g
m
o
d
e;
ca
n
p
r
ev
en
t
g
r
id
f
lu
ctu
atio
n
s
ca
u
s
ed
b
y
a
s
h
o
r
t
ag
e
o
f
r
ea
ctiv
e
p
o
wer
,
th
er
eb
y
im
p
r
o
v
in
g
th
e
s
tab
ilit
y
an
d
p
o
wer
q
u
ality
o
f
th
e
d
is
tr
ib
u
tio
n
g
r
id
.
I
n
p
a
r
ticu
lar
,
it
s
tab
ilize
s
th
e
v
o
ltag
e
v
alu
e
o
f
th
e
lo
ad
with
in
th
e
allo
wab
le
lim
it
to
im
p
r
o
v
e
th
e
life
an
d
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
m
ac
h
in
e
.
I
n
r
ea
ctiv
e
p
o
w
er
co
m
p
e
n
s
atio
n
m
o
d
e,
MM
C
'
s
p
ar
am
eter
s
an
d
tech
n
ical
in
d
icato
r
s
ar
e
g
u
ar
a
n
teed
s
tab
le
th
r
o
u
g
h
o
u
t th
e
wo
r
k
in
g
p
r
o
ce
s
s
.
T
ab
le
1.
Simu
latio
n
p
ar
am
eter
s
f
o
r
th
e
MM
C
co
n
tr
o
l sy
s
tem
S
i
mu
l
a
t
i
o
n
p
a
r
a
m
e
t
e
r
s
S
y
mb
o
l
V
a
l
u
e
Lo
a
d
r
e
si
s
t
a
n
c
e
70
Ω
Lo
a
d
i
n
d
u
c
t
a
n
c
e
5
.
1
0
-
3
H
B
r
a
n
c
h
r
e
s
i
st
o
r
s
0
,
5
Ω
B
r
a
n
c
h
i
n
d
u
c
t
a
n
c
e
4
,
2
.
1
0
-
3
H
C
a
p
a
c
i
t
o
r
p
e
r
S
M
1
0
0
F
D
C
v
o
l
t
a
g
e
6
0
0
0
V
N
u
mb
e
r
o
f
S
M
s
p
e
r
b
r
a
n
c
h
1
3
S
M
V
o
l
t
a
g
e
a
c
r
o
ss c
a
p
a
c
i
t
o
r
1
0
0
0
V
F
u
n
d
a
m
e
n
t
a
l
f
r
e
q
u
e
n
c
y
50
Hz
N
LM
m
o
d
u
l
a
t
i
o
n
f
r
e
q
u
e
n
c
y
3
0
0
Hz
M
o
d
u
l
a
t
i
o
n
c
o
e
f
f
i
c
i
e
n
t
0
.
9
5
S
y
st
e
m c
a
p
a
c
i
t
y
5
0
0
k
V
A
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
2
,
Ap
r
il
20
25
:
1
4
6
3
-
1
4
7
2
1470
(
a)
(
b
)
Fig
u
r
e
4
.
C
u
r
r
e
n
t a
n
d
v
o
ltag
e
r
esp
o
n
s
es
o
f
D
-
STAT
C
OM
wh
en
co
n
n
ec
ted
to
th
e
p
o
wer
s
y
s
tem
n
o
d
e
in
(
a)
cu
r
r
en
t o
u
tp
u
t a
n
d
(
b
)
v
o
ltag
e
o
u
tp
u
t
x
10
5
0
0
.
1
0
.
3
T
i
m
es
(
s
)
0
.
2
3
4
2
5
1
0
R
e
a
c
t
i
v
e
p
o
w
e
r
Q
(
V
a
r
)
V
a
l
u
e
o
f
r
ef
er
en
c
e
Q
V
a
l
u
e
o
f
a
c
t
u
a
l
Q
Fig
u
r
e
5
.
R
esp
o
n
s
e
o
f
r
ea
ctiv
e
p
o
wer
wh
e
n
MM
C
co
m
p
en
s
a
tes r
ea
ctiv
e
p
o
wer
0
0
.
1
0
.
3
T
i
m
es
(
s
)
0
.
2
C
u
r
r
e
n
t
(
A
)
-
50
0
-
100
-
150
-
200
Fig
u
r
e
6
.
R
esp
o
n
s
es o
f
c
u
r
r
en
t
o
n
th
e
d
-
ax
is
an
d
q
-
a
x
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
C
o
n
tr
o
l to
co
mp
en
s
a
te
r
ea
cti
ve
p
o
w
er a
t m
ed
iu
m
vo
lta
g
e
lo
a
d
n
o
d
es to
.
.
.
(
Tr
a
n
Hu
n
g
C
u
o
n
g
)
1471
6.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
as
ch
o
s
en
th
e
N
L
M
m
o
d
u
latio
n
m
eth
o
d
a
n
d
t
h
e
o
p
er
atin
g
s
tr
u
ctu
r
e
o
f
D
-
STAT
C
OM
b
ased
o
n
MM
C
to
co
m
p
en
s
at
e
f
o
r
r
ea
ctiv
e
p
o
wer
.
I
s
s
u
es
r
eg
ar
d
in
g
o
p
er
atin
g
p
r
in
ci
p
les
an
d
r
ea
ctiv
e
p
o
wer
co
n
tr
o
l
p
r
in
cip
les
b
ased
o
n
MM
C
co
n
v
er
ter
s
ar
e
an
aly
s
e
d
,
ev
alu
ated
,
a
n
d
d
esig
n
ed
.
S
im
u
latio
n
r
esu
lts
o
f
D
-
STAT
C
OM
's
o
p
er
atio
n
s
h
a
v
e
b
ee
n
p
r
esen
ted
a
n
d
o
b
jecti
v
ely
ev
al
u
ated
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
cu
r
r
en
t
an
d
v
o
ltag
e
o
f
D
-
STAT
C
OM
ar
e
s
tab
le
an
d
o
f
q
u
ality
,
wh
ich
en
s
u
r
es
th
e
T
HD
in
d
ex
an
d
co
n
tr
o
l
r
eq
u
ir
em
e
n
ts
.
At
th
e
s
am
e
tim
e,
th
e
r
esu
lts
also
r
ef
lect
th
e
p
er
f
o
r
m
a
n
ce
q
u
ality
o
f
t
h
e
M
MC
co
n
v
er
ter
b
ased
o
n
th
e
ap
p
licatio
n
o
f
NL
M
m
o
d
u
latio
n
m
eth
o
d
s
to
th
e
PI
c
o
n
tr
o
l
alg
o
r
ith
m
p
r
o
p
o
s
ed
f
o
r
th
e
s
y
s
tem
's
co
n
tr
o
l
s
tr
u
ctu
r
e.
Fro
m
th
e
r
e,
we
s
ee
th
at
it
is
p
o
s
s
ib
le
to
f
lex
ib
ly
co
n
tr
o
l
th
e
am
o
u
n
t
o
f
r
ea
ctiv
e
p
o
wer
at
th
e
p
o
we
r
g
r
id
n
o
d
e
to
e
n
s
u
r
e
t
h
e
n
ec
es
s
ar
y
am
o
u
n
t
o
f
p
o
wer
a
n
d
th
a
t
th
e
n
o
d
e
v
o
ltag
e
d
o
es
n
o
t
e
x
ce
ed
th
e
allo
wab
le
v
alu
e
ac
co
r
d
in
g
to
ac
tu
al
o
p
er
atin
g
r
eg
u
latio
n
s
.
ec
o
n
o
m
ics o
f
th
e
p
o
wer
s
y
s
tem
.
RE
F
E
R
E
NC
E
S
[
1
]
B
.
S
i
n
g
h
,
A
.
C
h
a
n
d
r
a
,
a
n
d
K
.
A
l
‐
H
a
d
d
a
d
,
P
o
w
e
r
q
u
a
l
i
t
y
p
r
o
b
l
e
m
s
a
n
d
m
i
t
i
g
a
t
i
o
n
t
e
c
h
n
i
q
u
e
s
.
W
i
l
e
y
,
2
0
1
5
,
d
o
i
:
1
0
.
1
0
0
2
/
9
7
8
1
1
1
8
9
2
2
0
6
4
.
[
2
]
A
.
N
g
u
y
e
n
e
t
a
l
.
,
“
H
i
g
h
P
V
p
e
n
e
t
r
a
t
i
o
n
i
mp
a
c
t
s
o
n
f
i
v
e
l
o
c
a
l
d
i
st
r
i
b
u
t
i
o
n
n
e
t
w
o
r
k
s
u
si
n
g
h
i
g
h
r
e
so
l
u
t
i
o
n
s
o
l
a
r
r
e
so
u
r
c
e
a
ssessm
e
n
t
w
i
t
h
s
k
y
i
m
a
g
e
r
a
n
d
q
u
a
si
-
st
e
a
d
y
s
t
a
t
e
d
i
st
r
i
b
u
t
i
o
n
sy
s
t
e
m
si
mu
l
a
t
i
o
n
s,
”
S
o
l
a
r
E
n
e
r
g
y
,
v
o
l
.
1
3
2
,
p
p
.
2
2
1
–
2
3
5
,
J
u
l
.
2
0
1
6
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
so
l
e
n
e
r
.
2
0
1
6
.
0
3
.
0
1
9
.
[
3
]
R
.
J
a
y
a
k
r
i
s
h
n
a
n
a
n
d
V
.
S
r
u
t
h
y
,
“
F
a
u
l
t
r
i
d
e
t
h
r
o
u
g
h
a
u
g
m
e
n
t
a
t
i
o
n
o
f
m
i
c
r
o
g
r
i
d
,
”
i
n
2
0
1
5
I
n
t
e
r
n
a
t
i
o
n
a
l
C
o
n
f
e
r
e
n
c
e
o
n
T
e
c
h
n
o
l
o
g
i
c
a
l
A
d
v
a
n
c
e
m
e
n
t
s
i
n
P
o
w
e
r
a
n
d
E
n
e
r
g
y
(
T
A
P
E
n
e
r
g
y
)
,
J
u
n
.
2
0
1
5
,
p
p
.
3
5
7
–
3
6
2
,
d
o
i
:
1
0
.
1
1
0
9
/
T
A
P
E
N
E
R
G
Y
.
2
0
1
5
.
7
2
2
9
6
4
5
.
[
4
]
O
.
M
r
e
h
e
l
a
n
d
A
.
A
.
I
ssa,
“
V
o
l
t
a
g
e
i
mb
a
l
a
n
c
e
i
n
v
e
s
t
i
g
a
t
i
o
n
i
n
r
e
s
i
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t
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re
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h
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g
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h
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d
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t
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tri
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a
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g
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t
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h
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.
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tere
sts
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p
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p
la
n
t
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two
rk
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m
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c
ti
n
g
m
a
teria
ls
a
n
d
a
p
p
li
c
a
ti
o
n
s;
re
n
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rg
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,
sim
u
latio
n
,
a
n
d
m
o
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li
n
g
o
f
in
v
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rter
sy
ste
m
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
tu
n
g
n
n
@tlu
.
e
d
u
.
v
n
.
An
Th
i
H
o
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re
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h
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n
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r
(1
9
9
7
),
M
.
Sc
.
(
2
0
0
2
)
d
e
g
re
e
s
i
n
in
d
u
strial
a
u
t
o
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a
ti
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e
n
g
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n
e
e
rin
g
fro
m
Ha
n
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U
n
iv
e
rsit
y
o
f
S
c
i
e
n
c
e
a
n
d
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d
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o
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d
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h
.
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.
d
e
g
re
e
i
n
2
0
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fro
m
U
n
iv
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o
f
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s
p
o
rt
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n
d
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o
m
m
u
n
ica
ti
o
n
s
(UTC)
.
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w,
sh
e
is
a
lec
tu
re
r
o
f
F
a
c
u
lt
y
o
f
El
e
c
tri
c
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l
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n
d
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tro
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ic
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n
g
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n
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rin
g
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n
d
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r
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rsity
o
f
Tran
sp
o
rt
a
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m
m
u
n
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ti
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n
s
(UTC).
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r
c
u
rre
n
t
in
tere
sts
in
c
lu
d
e
p
o
we
r
e
lec
tro
n
ic
c
o
n
v
e
rters
,
e
lec
tri
c
m
o
to
r
d
ri
v
e
,
sa
v
i
n
g
e
n
e
rg
y
so
l
u
ti
o
n
s
a
p
p
li
e
d
fo
r
i
n
d
u
stry
a
n
d
tran
sp
o
rtati
o
n
.
S
h
e
c
a
n
b
e
c
o
n
tac
t
e
d
a
t
e
m
a
il
:
h
tan
h
.
k
td
@
u
tc.ed
u
.
v
n
.
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