I
nte
rna
t
io
na
l J
o
urna
l o
f
P
o
wer
E
lect
ro
nics
a
nd
Driv
e
S
y
s
t
em
s
(
I
J
P
E
DS
)
Vo
l.
1
2
,
No
.
3
,
Sep
tem
b
er
202
1
,
p
p
.
1
5
0
5
~
1
5
2
0
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/
ijp
ed
s
.
v
1
2
.i
3
.
pp
1
5
0
5
-
1
5
2
0
1505
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
Perf
o
rma
nce
imp
ro
v
ement of
d
ece
ntralized
co
ntrol
for
bidirectiona
l con
v
erte
rs in
a DC
m
icro
-
g
rid
Sey
ed
M
o
j
t
a
ba
Abba
s
i,
M
eh
di Na
f
a
r,
M
o
hs
en
Sim
a
b
De
p
a
rtme
n
t
of
El
e
c
tri
c
a
l
E
n
g
i
n
e
e
rin
g
,
M
a
rv
d
a
sh
t
Bra
n
c
h
,
Isla
m
ic
Az
a
d
Un
iv
e
rsity
,
M
a
rv
d
a
sh
t,
Ira
n
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Ma
r
3
0
,
2
0
2
1
R
ev
is
ed
J
u
l 3
,
2
0
2
1
Acc
ep
ted
J
u
l 1
4
,
2
0
2
1
In
th
is
p
a
p
e
r,
u
si
n
g
a
n
e
u
ra
l
c
o
n
t
ro
ll
e
r
a
n
d
a
g
e
n
e
ti
c
o
p
ti
m
iza
ti
o
n
a
lg
o
rit
h
m
to
c
o
n
tr
o
l
th
e
v
o
lt
a
g
e
as
we
ll
a
s,
c
o
n
tro
l
th
e
fre
q
u
e
n
c
y
of
th
e
g
r
id
a
lo
n
g
wit
h
th
e
m
a
n
a
g
e
m
e
n
t
of
th
e
re
a
c
ti
v
e
p
o
we
r
of
t
h
e
m
icro
-
g
ri
d
to
c
o
n
tro
l
th
e
o
u
tp
u
t
p
o
we
r
d
u
rin
g
islan
d
in
g
u
si
n
g
S
i
m
u
lt
a
n
e
o
u
s
b
il
a
tera
l
p
o
we
r
c
o
n
v
e
rters
with
v
o
lt
a
g
e
/
fre
q
u
e
n
c
y
d
r
o
o
p
stra
teg
y
a
n
d
o
p
ti
m
iza
ti
o
n
of
PI
c
o
e
f
ficie
n
ts
of
p
a
ra
ll
e
l
p
o
we
r
c
o
n
v
e
rters
by
g
e
n
e
ti
c
-
n
e
u
ra
l
m
icro
-
g
ri
d
a
lg
o
rit
h
m
to
su
p
p
re
ss
AC
sid
e
-
c
u
rre
n
t
flo
w
t
h
a
t
i
n
c
re
a
se
s
sta
b
il
it
y
a
n
d
im
p
ro
v
e
m
e
n
t
of
c
o
n
d
i
ti
o
n
s
fre
q
u
e
n
c
y
a
n
d
v
o
lt
a
g
e
a
re
d
isc
u
ss
e
d
.
G
iv
e
n
th
e
p
e
rf
o
rm
a
n
c
e
of
th
e
m
icro
-
g
rid
in
two
sim
u
lati
o
n
sc
e
n
a
rio
s,
n
a
m
e
ly
tra
n
siti
o
n
fro
m
on
-
g
rid
to
o
ff
-
g
ri
d
,
th
e
o
c
c
u
rre
n
c
e
of
a
ste
p
c
h
a
n
g
e
in
l
o
a
d
in
islan
d
m
o
d
e
as
we
ll
as
re
tu
rn
to
wo
rk
i
n
g
m
o
d
e
is
c
o
n
n
e
c
ted
.
Th
e
a
b
il
it
y
to
d
e
tec
t
th
e
ro
b
u
st
p
e
rfo
r
m
a
n
c
e
a
n
d
p
ro
p
e
r
p
e
rfo
rm
a
n
c
e
of
two
-
l
e
v
e
l
n
e
u
ra
l
c
o
n
tr
o
ll
e
r.
Th
e
c
o
n
tro
ll
e
r
p
e
rfo
rm
a
n
c
e
ti
m
e
wa
s
a
lso
v
e
ry
g
o
o
d
,
in
d
ica
ti
n
g
t
h
e
a
p
p
r
o
p
riate
fe
a
tu
re
s
of
th
e
m
e
th
o
d
u
se
d
to
d
e
sig
n
t
h
e
c
o
n
tro
ll
e
r,
n
a
m
e
ly
tw
o
-
lev
e
l
n
e
u
ra
l
,
g
e
n
e
ti
c
s.
Th
e
m
a
in
a
d
v
a
n
tag
e
of
t
h
is
m
e
th
o
d
is
its
sim
p
l
icity
of
d
e
sig
n
.
T
h
e
m
e
th
o
d
u
se
d
is
a
lso
e
fficie
n
t
a
n
d
re
sista
n
t
to
c
h
a
n
g
e
s
in
th
e
sy
ste
m
,
wh
ich
re
su
lt
s
fro
m
th
e
sim
u
lati
o
n
s.
K
ey
w
o
r
d
s
:
DC
m
icr
o
-
g
r
id
C
ir
cu
latin
g
cu
r
r
en
t
C
o
n
v
er
ter
Po
wer
allo
ca
tio
n
Vo
ltag
e
co
n
tr
o
l
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
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Me
h
d
i N
af
ar
Dep
ar
tm
en
t o
f
E
lectr
ical
E
n
g
i
n
ee
r
in
g
Ma
r
v
d
ash
t Bra
n
ch
I
s
lam
ic
Aza
d
Un
iv
er
s
ity
,
Ma
r
v
d
ash
t,
I
r
a
n
E
m
ail: m
n
af
ar
@
m
iau
.
ac
.
ir
1.
I
NT
RO
D
UCT
I
O
N
In
r
ec
en
t
y
ea
r
s
,
m
u
ch
atten
ti
o
n
h
as
b
ee
n
p
ai
d
to
m
icr
o
-
g
r
id
s
in
d
is
tr
ib
u
ted
n
etwo
r
k
s
an
d
th
e
p
r
esen
ce
of
th
is
tech
n
o
l
o
g
y
h
as
ch
an
g
ed
t
h
e
n
atu
r
e
of
d
is
tr
ib
u
tio
n
n
etwo
r
k
s
.
Kai
et
a
l.
[
1
]
d
ea
ls
with
v
o
ltag
e
co
n
tr
o
l
f
r
o
m
th
e
p
o
in
t
o
f
v
iew
o
f
th
e
d
is
tr
ib
u
tio
n
m
ic
r
o
-
g
r
id
o
p
er
ato
r
with
th
e
aim
o
f
m
in
i
m
izin
g
lo
s
s
es.
T
h
e
g
en
er
al
s
y
s
tem
u
n
d
er
s
tu
d
y
b
y
Xia
et
a
l.
[
2
]
is
as
f
o
llo
ws:
Sev
er
al
m
icr
o
g
r
id
s
ar
e
co
n
n
ec
ted
to
th
e
m
a
i
n
n
etwo
r
k
b
y
co
n
v
e
r
ter
s
.
Dy
n
a
m
ic
Plan
n
in
g
Alg
o
r
ith
m
is
u
s
e
d
to
ca
lcu
late
is
lan
d
v
o
ltag
e
p
r
o
f
iles
o
f
m
icr
o
-
g
r
id
co
n
n
ec
tiv
ity
to
elec
tr
ic
v
e
h
icles
in
o
r
d
er
to
im
p
r
o
v
e
v
o
ltag
e
co
n
tr
o
l
an
d
m
ax
im
ize
p
o
we
r
b
y
p
a
r
ticle
s
war
m
alg
o
r
ith
m
[
3
]
.
On
th
e
b
asis
o
f
th
e
tr
ad
itio
n
al
f
u
zz
y
PI
co
n
tr
o
ller
,
th
e
d
o
u
b
le
f
u
zz
y
PI
co
n
tr
o
ller
is
r
ea
lized
b
y
ad
d
in
g
t
h
e
s
u
b
f
u
zz
y
c
o
n
tr
o
lle
r
,
wh
ich
g
e
n
er
ates
th
e
au
x
iliar
y
co
r
r
ec
tio
n
o
f
PI
p
ar
a
m
eter
s
d
u
e
to
th
e
AC
s
id
e
v
o
ltag
e
v
ar
iatio
n
an
d
DC
s
id
e
g
iv
en
v
o
ltag
e
v
ar
iatio
n
o
f
th
e
r
ev
er
s
ib
le
th
r
ee
-
p
h
ase
PW
M
co
n
v
er
ter
[
4
]
.
C
o
n
s
id
er
atio
n
o
f
DG
f
o
r
s
h
o
r
t
-
ter
m
is
lan
d
m
icr
o
-
g
r
id
s
tu
d
ies
s
ee
m
s
m
o
r
e
f
ea
s
ib
le
[
5
]
.
I
n
ad
d
itio
n
to
th
e
co
n
tr
o
l
o
f
t
h
e
v
o
ltag
e
a
n
d
f
r
eq
u
en
cy
co
n
tr
o
l
o
f
th
e
is
lan
d
ed
m
icr
o
g
r
i
d
,
it
is
also
i
m
p
o
r
tan
t
to
ca
r
ef
u
lly
an
aly
ze
th
e
d
y
n
a
m
ic
an
aly
s
is
o
f
th
e
m
icr
o
g
r
id
s
y
s
tem
th
at
d
o
m
in
ates
th
e
lo
w
f
r
eq
u
en
c
y
m
o
d
es
o
f
th
e
s
y
s
tem
lar
g
ely
af
f
ec
ted
b
y
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
in
v
er
ter
'
s
p
o
wer
s
h
ar
in
g
m
ec
h
an
is
m
[
6
]
.
T
h
i
s
u
n
it
co
n
tr
o
ls
th
e
p
er
f
o
r
m
an
ce
an
d
p
r
o
tectio
n
o
f
m
icr
o
-
g
r
i
d
s
with
r
eg
ar
d
t
o
th
e
s
tate
o
f
d
is
p
er
s
ed
p
r
o
d
u
c
tio
n
r
eso
u
r
ce
s
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
150
5
–
152
0
1506
W
an
g
et
a
l.
[
9
]
a
n
aly
ze
s
th
e
f
lo
w
p
ath
in
a
p
a
r
allel
two
-
wa
y
p
o
wer
c
o
n
v
er
te
r
s
y
s
tem
a
n
d
co
n
tr
o
ls
a
c
o
n
tr
o
l
s
tr
ateg
y
o
f
to
tal
an
d
d
i
v
er
g
e
n
t
co
n
tr
o
l.
Fo
r
asy
m
m
et
r
ic
p
o
w
er
g
r
id
co
n
d
itio
n
s
,
a
co
n
t
r
o
l
s
tr
ateg
y
is
p
r
o
p
o
s
ed
to
in
cr
ea
s
e
th
e
ab
ilit
y
to
tr
an
s
m
it
ac
tiv
e
p
o
wer
with
o
u
t
o
s
cillatin
g
cir
cu
latio
n
cu
r
r
e
n
t.
T
h
is
s
tr
ateg
y
m
ain
ly
f
o
cu
s
es
o
n
th
e
p
o
s
itiv
e
an
d
n
eg
ativ
e
co
m
p
o
n
en
ts
o
f
th
e
s
e
q
u
en
ce
,
b
u
t
d
o
es
n
o
t
co
n
s
id
er
th
e
ze
r
o
s
eq
u
en
ce
co
m
p
o
n
en
ts
th
at
ca
n
ex
is
t
a
m
o
n
g
p
ar
allel
co
n
v
er
ter
s
.
An
im
p
r
o
v
ed
s
ec
o
n
d
ar
y
d
is
tr
ib
u
tio
n
co
n
tr
o
l
m
eth
o
d
b
ased
o
n
lo
w
b
an
d
wid
th
co
m
m
u
n
icatio
n
s
y
s
tem
f
o
r
DC
v
o
ltag
e
r
ec
o
v
er
y
an
d
ass
u
r
an
ce
o
f
DC
cu
r
r
en
t
d
is
tr
ib
u
tio
n
ac
cu
r
ac
y
is
p
r
esen
ted
in
[
1
0
]
.
T
h
e
p
r
o
p
o
s
ed
co
n
t
r
o
l
m
eth
o
d
co
n
s
is
ts
m
ain
ly
o
f
th
r
ee
co
m
p
en
s
ato
r
co
n
tr
o
ller
s
p
r
o
p
o
r
tio
n
al
to
th
e
in
teg
r
al
u
s
ed
t
o
c
h
an
g
e
th
e
v
o
ltag
e
an
d
ad
j
u
s
t
th
e
s
lo
p
e
o
f
th
e
cu
r
v
e
.
T
h
e
tu
n
in
g
p
a
r
am
eter
s
(
KP,
Ki)
o
f
PI
co
n
tr
o
ller
f
o
r
a
t
h
r
ee
-
p
h
ase
v
o
ltag
e
r
e
g
u
lato
r
is
d
esig
n
ed
u
s
in
g
PS
O
alg
o
r
ith
m
in
[
1
1
]
.
T
h
e
PS
O
alg
o
r
ith
m
a
n
d
I
T
SE
as
f
itn
ess
f
u
n
ctio
n
is
in
teg
r
ated
to
f
in
d
th
e
o
p
tim
al
tu
n
in
g
b
ased
o
n
th
e
n
o
n
lin
ea
r
ity
b
eh
av
io
u
r
o
f
ea
ch
co
m
p
o
n
en
t
in
th
e
s
y
s
tem
with
o
u
t
d
ep
en
d
i
n
g
o
n
th
e
a
n
aly
tical
m
eth
o
d
f
o
r
lin
ea
r
izin
g
th
e
s
y
s
t
em
wh
ich
ca
n
n
o
t e
n
s
u
r
e
th
e
b
est co
n
tr
o
l p
er
f
o
r
m
a
n
ce
.
T
h
e
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
o
f
th
e
m
icr
o
g
r
id
ar
e
d
eter
m
in
e
d
.
W
h
en
th
e
m
icr
o
g
r
id
is
d
is
co
n
n
ec
ted
f
r
o
m
th
e
m
ain
s
an
d
o
p
er
ates
i
n
is
lan
d
m
o
d
e
,
th
e
co
n
tr
o
l
s
tr
ateg
y
m
u
s
t
b
e
c
h
an
g
e
d
to
p
r
o
v
id
e
a
r
ef
e
r
en
ce
f
o
r
f
r
eq
u
e
n
cy
a
n
d
v
o
ltag
e
[
12
]
.
A
d
r
o
o
p
c
o
n
tr
o
l
s
ch
em
e
is
g
e
n
er
ally
u
s
ed
b
y
p
ar
allelin
g
m
u
ltip
le
in
v
er
ter
s
[
13
]
in
wh
ich
th
e
v
o
ltag
e
an
d
f
r
eq
u
en
cy
o
f
ea
c
h
in
v
er
te
r
ar
e
ad
ju
s
ted
in
o
r
d
er
to
co
n
tr
o
l
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
.
B
y
way
o
f
th
e
in
d
u
s
tr
ial
d
ev
elo
p
m
en
t,
co
n
tr
o
l
o
b
ject
s
k
ee
p
g
ettin
g
m
o
r
e
co
m
p
licated
,
p
ar
ticu
la
r
ly
f
o
r
th
e
u
n
k
n
o
wn
p
a
r
am
eter
s
o
r
s
l
o
w
v
ar
iatio
n
s
in
lar
g
e
d
elay
,
tim
e
-
ch
an
g
in
g
,
n
o
n
-
lin
ea
r
c
o
m
p
licated
s
y
s
tem
s
,
with
r
an
d
o
m
in
ter
f
er
e
n
ce
o
r
d
elay
.
Ho
wev
er
,
T
h
e
Pro
p
o
r
tio
n
al
I
n
teg
r
al
De
r
iv
ativ
e
(
PID
)
co
n
tr
o
l
h
as
s
im
p
le
s
tr
u
ctu
r
e
an
d
lin
ea
r
b
e
h
av
io
r
.
Mo
r
eo
v
er
,
it
g
i
v
es
ac
ce
p
tab
l
e
p
er
f
o
r
m
a
n
ce
f
o
r
s
ev
er
al
in
d
u
s
tr
ial
ap
p
licatio
n
s
[
1
4
]
.
Am
b
r
is
h
ex
p
lain
ed
th
at
th
e
co
n
v
en
tio
n
al
tu
n
in
g
m
eth
o
d
s
h
av
e
v
er
y
lim
ited
ca
p
a
b
ilit
y
wh
ich
f
u
r
th
er
d
im
in
is
h
es
in
ca
s
e
th
e
ex
p
licit
m
ath
em
atica
l
m
o
d
el
is
n
o
t
av
ailab
le
[
1
5
]
.
An
d
er
et
a
l.
[
16
]
h
ig
h
lig
h
ts
th
e
r
o
le
o
f
p
o
we
r
elec
tr
o
n
ics
in
m
icr
o
g
r
id
s
,
esp
ec
ially
in
v
e
r
ter
v
o
ltag
e
s
o
u
r
ce
s
,
an
d
in
tr
o
d
u
ce
s
a
p
r
ec
is
e
m
eth
o
d
as
a
p
r
ec
is
e
an
d
p
r
o
v
en
ap
p
r
o
ac
h
t
o
co
n
tr
o
llin
g
m
icr
o
g
r
id
s
.
GA
-
PID
co
n
tr
o
ller
s
wer
e
s
im
u
lated
with
MA
T
L
AB
,
an
d
th
e
GA
o
p
tim
is
atio
n
m
et
h
o
d
u
s
ed
to
o
p
tim
is
e
th
e
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
an
d
g
ain
s
o
f
th
e
ass
o
ciate
d
PID
co
n
tr
o
ller
in
[
1
7
]
.
T
h
e
p
e
r
f
o
r
m
an
ce
o
f
th
e
GA
-
PID
in
a
DC
-
DC
b
u
ck
co
n
v
er
ter
was
in
v
esti
g
ated
b
y
s
im
u
lati
n
g
an
d
an
al
y
s
in
g
m
ax
i
m
u
m
o
v
e
r
s
h
o
o
t,
p
ea
k
tim
e,
a
n
d
s
tead
y
s
tate
tim
e
b
ased
o
n
I
SE,
I
AE
,
I
AT
E
an
d
MSE
C
r
iter
ia.
I
n
th
is
r
esear
ch
,
th
e
m
icr
o
g
r
i
d
p
r
esen
ted
in
[
18
]
h
as
b
ee
n
u
s
ed
with
s
o
m
e
ch
an
g
es
in
p
r
o
d
u
ctio
n
r
eso
u
r
ce
s
an
d
tim
es
in
o
r
d
er
to
ev
alu
ate
th
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
f
r
e
q
u
en
c
y
co
n
tr
o
l.
T
h
e
s
in
g
le
-
lin
e
d
iag
r
am
o
f
th
e
test
s
y
s
tem
,
s
h
o
win
g
th
at
ea
ch
lo
w
-
v
o
ltag
e
m
icr
o
g
r
id
is
co
n
n
ec
ted
to
th
e
m
ain
s
b
y
a
s
tatic
s
witch
;
I
t
in
clu
d
es
lo
ad
s
,
co
n
tr
o
llab
le
a
n
d
u
n
co
n
tr
o
llab
le
s
o
u
r
ce
s
as
well
as
s
to
r
ag
e
d
ev
ices
(
f
ly
w
h
ee
ls
with
b
atter
ies
)
.
An
im
p
r
o
v
ed
s
ec
o
n
d
ar
y
d
is
tr
i
b
u
tio
n
co
n
t
r
o
l
m
eth
o
d
b
ased
o
n
an
L
B
C
s
y
s
tem
is
p
r
esen
ted
f
o
r
DC
v
o
ltag
e
r
ec
o
v
er
y
an
d
ass
u
r
an
ce
o
f
th
e
ac
cu
r
ac
y
o
f
DC
cu
r
r
en
t
d
is
tr
ib
u
tio
n
.
T
h
e
p
r
o
p
o
s
ed
co
n
tr
o
l
m
eth
o
d
is
m
ain
ly
co
m
p
o
s
ed
o
f
t
h
r
ee
p
r
o
p
o
r
tio
n
al
-
in
teg
r
al
(
PI)
co
n
tr
o
ller
s
th
a
t
ar
e
u
s
ed
to
ch
a
n
g
e
t
h
e
v
o
ltag
e
an
d
ad
ju
s
t
th
e
s
lo
p
e
d
r
o
p
o
f
th
e
c
u
r
v
e
[
1
9
]
.
All
o
f
th
ese
co
n
tr
o
l
s
tr
ateg
ies
f
o
r
th
e
DC
g
r
i
d
ar
e
m
ai
n
ly
f
o
cu
s
ed
o
n
th
e
is
lan
d
ed
m
o
d
e,
n
eg
lectin
g
th
e
g
r
id
-
co
n
n
ec
ted
m
o
d
e.
A
n
ew
id
ea
th
at
ca
n
b
e
ad
d
ed
to
th
i
s
ty
p
e
o
f
P
DC
-
v
DC
2
d
r
o
o
p
co
n
tr
o
l
[
2
0
]
is
s
y
s
tem
f
r
eq
u
en
c
y
ad
a
p
tatio
n
,
wh
ich
d
e
m
an
d
s
r
e
d
esig
n
o
f
th
e
P
DC
-
v
DC
2
d
r
o
o
p
c
o
n
tr
o
l.
I
n
[
2
1
]
T
h
e
o
v
e
r
all
s
tr
u
ctu
r
e
o
f
th
e
m
icr
o
g
r
i
d
ex
am
in
e
d
in
th
i
s
m
icr
o
g
r
id
in
clu
d
es
a
p
h
o
to
v
o
ltaic
s
y
s
tem
,
f
u
el
ce
ll
a
n
d
b
atter
y
as
e
n
er
g
y
s
to
r
ag
e.
T
h
ese
d
is
tr
ib
u
ted
g
e
n
er
at
io
n
s
o
u
r
ce
s
ar
e
co
n
n
ec
ted
to
a
7
0
0
-
v
o
lt
b
u
s
v
ia
a
DC
-
to
-
DC
co
n
v
er
ter
.
T
h
e
d
ir
ec
tio
n
o
f
p
o
wer
in
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
an
d
th
e
b
atter
y
is
o
n
e
-
way
,
b
u
t
th
e
DC
-
to
-
DC
co
n
v
er
ter
o
f
th
e
b
atter
y
will
h
av
e
a
two
-
way
co
n
v
er
ter
d
u
e
to
its
f
u
n
ctio
n
o
f
en
er
g
y
s
to
r
ag
e.
R
o
s
er
o
et
a
l.
[
2
2
]
s
p
ec
if
ies
th
e
allo
ca
tio
n
o
f
ac
tiv
e
p
o
wer
a
n
d
f
r
e
q
u
en
c
y
r
eg
u
latio
n
in
th
e
d
r
o
p
-
d
o
wn
c
o
n
tr
o
l
m
eth
o
d
f
o
r
in
d
e
p
en
d
e
n
t
m
i
cr
o
g
r
id
s
u
n
d
e
r
elec
tr
ical
an
d
co
m
m
u
n
icatio
n
er
r
o
r
.
I
n
th
e
AC
m
i
cr
o
g
r
id
,
f
r
eq
u
e
n
cy
co
n
tr
o
l
is
p
er
f
o
r
m
ed
in
tellig
en
tly
b
y
th
e
p
s
o
a
lg
o
r
ith
m
u
s
in
g
f
u
zz
y
ad
ju
s
t
m
en
t
[
2
3
]
.
Sev
er
al
m
icr
o
g
r
id
s
ar
e
co
n
n
ec
ted
to
t
h
e
m
ain
n
etwo
r
k
b
y
co
n
v
er
te
r
s
in
[
2
4
]
.
T
h
e
o
u
tp
u
t
o
f
t
h
ese
co
n
v
er
te
r
s
,
wh
ich
ar
e
co
n
n
ec
ted
b
y
lin
es
with
Z
-
im
p
ed
an
c
e,
was
o
f
DC
ty
p
e,
b
u
t
th
e
m
icr
o
g
r
id
s
th
em
s
elv
es
ar
e
o
f
AC
ty
p
e
an
d
ar
e
co
n
tr
o
lle
d
b
y
Dr
o
p
c
o
n
tr
o
l
.
B
asic
s
y
s
tem
in
f
o
r
m
atio
n
s
u
ch
as
DC
lin
k
v
o
ltag
e
an
d
m
ic
r
o
g
r
id
f
r
eq
u
en
cy
is
s
en
t
to
th
e
Dr
o
o
p
co
n
tr
o
ller
.
T
h
is
s
tr
u
ctu
r
e
co
n
s
is
ts
o
f
a
b
i
p
o
lar
b
r
id
g
e
th
y
r
is
to
r
,
DC
lin
k
ca
p
ac
ito
r
,
L
s
elf
ie
f
ilter
.
T
u
n
g
ad
io
s
h
o
ws
th
at
e
x
ce
s
s
en
er
g
y
p
r
o
d
u
ce
d
b
y
th
e
p
h
o
t
o
v
o
ltaic
s
y
s
tem
is
s
to
r
e
d
in
th
e
b
atter
y
,
an
d
wh
en
th
e
p
r
o
d
u
ctio
n
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
d
ec
r
ea
s
es,
th
e
b
atter
y
will
b
e
r
esp
o
n
s
ib
le
f
o
r
p
r
o
v
id
in
g
elec
tr
ical
en
er
g
y
[
2
5
]
.
I
f
th
e
SOC
o
f
th
e
b
atter
y
is
less
th
an
a
ce
r
tain
v
alu
e,
th
e
f
u
el
c
ell
also
en
ter
s
th
e
n
etwo
r
k
an
d
th
e
task
.
2.
M
O
DE
L
I
NG
AN
D
F
O
RM
U
L
AT
I
O
N
T
h
e
o
v
e
r
all
s
tr
u
ctu
r
e
o
f
th
e
m
icr
o
-
g
r
id
in
v
esti
g
ated
in
t
h
e
p
ap
er
is
illu
s
tr
ated
in
Fig
u
r
e
1
.
I
t
co
n
tain
s
a
p
h
o
to
v
o
ltaic
s
y
s
tem
,
a
f
u
el
ce
ll
an
d
a
b
atter
y
as
a
p
o
w
er
g
en
er
atio
n
an
d
en
er
g
y
s
to
r
ag
e
s
y
s
tem
.
T
h
ese
d
is
tr
ib
u
ted
g
en
er
atio
n
s
o
u
r
c
es
ar
e
co
n
n
ec
ted
to
th
e
7
0
0
-
v
o
lt
b
u
s
v
ia
th
e
DC
-
to
-
DC
co
n
v
er
ter
.
T
h
e
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
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f d
ec
en
tr
a
liz
ed
co
n
tr
o
l fo
r
b
id
ir
ec
tio
n
a
l c
o
n
ve
r
ters
… (
S
ey
ed
Mo
jta
b
a
A
b
b
a
s
i
)
1507
d
ir
ec
tio
n
ality
o
f
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
is
o
n
e
-
way
,
b
u
t
th
e
DC
-
to
-
DC
b
atter
y
co
n
v
er
ter
h
av
e
a
b
i
-
d
ir
ec
tio
n
al
co
n
v
e
r
ter
d
u
e
to
its
en
er
g
y
s
av
in
g
f
u
n
ctio
n
.
T
h
e
ex
tr
a
en
er
g
y
g
en
er
ated
b
y
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
is
s
to
r
ed
in
th
e
b
atter
y
,
an
d
w
h
en
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
o
u
tp
u
t
is
r
ed
u
ce
d
,
th
e
b
atter
y
will
h
av
e
th
e
p
o
wer
to
s
u
p
p
ly
elec
tr
icity
.
I
f
th
e
b
atter
y
SOC
is
lo
wer
th
an
th
e
s
p
ec
if
ied
am
o
u
n
t,
th
e
f
u
el
ce
ll
co
n
n
ec
ted
to
g
r
id
a
n
d
will
h
av
e
t
h
e
task
o
f
r
ec
h
ar
g
in
g
th
e
b
atter
y
an
d
s
u
p
p
ly
in
g
p
ar
t
o
f
t
h
e
lo
a
d
.
T
h
e
D
C
to
AC
co
n
v
er
te
r
co
n
n
ec
ts
th
e
v
o
ltag
e
p
r
o
d
u
ce
d
in
th
e
DC
b
u
s
to
th
e
AC
g
r
id
o
r
lo
ad
s
.
Fig
u
r
e
1
.
T
h
e
m
icr
o
-
g
r
id
s
tu
d
i
ed
3.
CO
NT
RO
L
M
E
T
H
O
D
I
n
th
e
f
o
llo
win
g
,
th
e
co
n
tr
o
l
m
eth
o
d
is
d
escr
ib
ed
to
s
u
p
p
r
e
s
s
th
e
cir
cu
latio
n
cu
r
r
en
t
b
y
a
p
p
r
o
p
r
iately
d
eter
m
in
in
g
th
e
t
r
an
s
v
er
s
e
p
o
les
o
f
th
e
co
n
tr
o
l
co
n
v
er
s
io
n
at
a
s
tab
le
p
o
in
t.
I
t
s
h
o
u
ld
b
e
n
o
ted
th
at
wh
e
n
co
n
n
ec
ted
t
o
th
e
g
r
id
,
m
ai
n
tain
in
g
th
e
p
r
o
p
er
v
o
ltag
e
an
d
f
r
eq
u
en
cy
p
r
o
f
iles
an
d
its
s
tab
ilit
y
is
p
r
o
v
id
e
d
b
y
th
e
m
ain
g
r
id
.
Acc
o
r
d
in
g
l
y
,
t
h
e
in
v
er
ter
s
in
th
e
m
icr
o
-
g
r
id
ar
e
co
n
tr
o
lled
in
s
u
ch
a
way
th
at
th
e
ac
tiv
e
an
d
r
ea
ctiv
e
p
o
wer
ar
e
in
jecte
d
in
to
th
e
m
icr
o
-
g
r
id
b
y
DGs.
T
h
e
o
u
tlin
e
o
f
th
e
p
r
o
p
o
s
ed
co
n
tr
o
l
is
p
r
esen
te
d
i
n
th
e
f
o
llo
win
g
Fig
u
r
e
2
.
B
ase
o
n
Fig
u
r
e
2
,
T
h
e
c
u
r
r
en
t
an
d
v
o
ltag
e
o
f
th
e
t
h
r
ee
-
p
h
ase
g
r
id
ar
e
t
h
en
co
n
v
er
t
ed
to
d
q
co
m
p
o
n
en
ts
an
d
co
m
p
ar
ed
w
ith
th
e
r
ef
er
en
ce
v
alu
es
o
b
tai
n
ed
f
r
o
m
th
e
r
ef
e
r
en
ce
an
d
r
ea
ctiv
e
p
o
wer
.
T
h
e
d
if
f
er
en
ce
b
e
twee
n
th
e
m
is
m
in
im
ized
b
y
a
PI
co
n
tr
o
ller
;
th
e
co
n
tr
o
ller
o
u
tp
u
t,
af
ter
s
witch
in
g
to
th
r
ee
-
p
h
ase
m
o
d
e
an
d
p
ass
in
g
th
r
o
u
g
h
a
p
u
ls
e
wav
e
g
en
er
at
o
r
,
p
r
o
v
i
d
es
th
e
co
n
tr
o
l
s
ig
n
als
n
ee
d
ed
to
c
o
n
tr
o
l
th
e
in
v
er
ter
.
So
,
th
e
in
v
er
ter
with
t
h
e
p
u
ls
es
p
r
o
v
i
d
ed
d
u
r
i
n
g
a
s
p
ec
if
ic
p
r
o
ce
s
s
f
o
r
ce
s
th
e
ex
is
tin
g
DGs
to
f
o
llo
w
th
eir
o
u
tp
u
t
p
o
wer
,
th
e
P
ref
an
d
Q
ref
v
alu
es.
Fig
u
r
e
2
.
T
h
e
co
n
tr
o
l f
r
a
m
ewo
r
k
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
150
5
–
152
0
1508
I
n
d
is
co
n
n
ec
tio
n
m
o
d
e,
s
in
ce
r
ef
er
en
ce
v
alu
es
f
o
r
th
e
v
o
lta
g
e
r
an
g
e
a
n
d
f
r
eq
u
en
cy
ar
e
n
o
t
p
r
o
v
i
d
ed
th
r
o
u
g
h
th
e
g
r
id
,
it
is
th
er
e
f
o
r
e
n
ec
ess
ar
y
to
co
n
tr
o
l
th
e
DG
s
to
r
ec
o
n
s
tr
u
ct
th
ese
v
al
u
es,
wh
ich
is
to
ac
t
as
a
s
y
n
ch
r
o
n
o
u
s
g
en
er
at
o
r
o
n
th
e
g
r
id
.
T
h
e
b
asis
o
f
f
r
eq
u
en
cy
a
n
d
v
o
ltag
e
co
n
tr
o
l in
co
n
v
en
ti
o
n
al
p
o
wer
s
y
s
tem
s
is
o
f
ten
p
r
o
v
id
ed
b
y
s
ev
er
al
c
o
n
tr
o
l
lo
o
p
s
,
wh
ich
will
b
e
b
r
i
ef
ly
in
tr
o
d
u
ce
d
in
th
e
f
o
llo
win
g
.
T
h
e
f
ir
s
t
co
n
tr
o
l
lo
o
p
is
b
ased
o
n
th
e
d
r
o
p
-
o
f
f
ch
ar
ac
ter
is
tic
o
f
th
e
s
y
n
ch
r
o
n
o
u
s
g
en
er
ato
r
s
;
th
is
is
ca
lled
p
r
im
ar
y
co
n
tr
o
l.
T
h
is
co
n
tr
o
l
lo
o
p
is
m
o
u
n
ted
o
n
s
y
n
ch
r
o
n
o
u
s
g
en
e
r
ato
r
s
.
T
h
e
b
a
s
is
o
f
th
e
o
p
er
atio
n
o
f
th
is
co
n
tr
o
l
lo
o
p
is
s
h
o
wn
in
Fig
u
r
e
3
(
a)
an
d
Fig
u
r
e
3
(
b
)
.
(
a)
(
b
)
Fig
u
r
e
3
.
I
n
itial c
o
n
tr
o
l
b
y
d
r
o
o
p
ch
ar
ac
te
r
is
tic
f
o
r
(
a)
,
v
o
lta
g
e
an
d
(
b
)
f
r
eq
u
en
cy
a
d
ju
s
tm
en
t
Acc
o
r
d
in
g
to
th
e
Fig
u
r
es
3
(
a)
,
3
(
b
)
,
if
th
e
r
ea
l
an
d
im
a
g
in
ar
y
p
o
wer
d
ep
ar
t
f
r
o
m
th
e
n
o
m
in
al
v
alu
es,
th
e
f
r
eq
u
en
cy
a
n
d
v
o
ltag
e
also
s
h
if
t
with
th
e
p
o
wer
ch
an
g
es.
T
h
e
p
r
im
ar
y
co
n
t
r
o
l
lo
o
p
lim
its
th
e
f
r
eq
u
e
n
cy
an
d
v
o
ltag
e
Dr
o
o
p
ca
u
s
ed
b
y
th
e
lo
ad
c
h
an
g
e
to
a
ce
r
tain
v
alu
e
a
n
d
p
r
ev
en
ts
i
ts
co
n
tin
u
o
u
s
lo
s
s
an
d
in
s
tab
ilit
y
.
T
h
is
is
illu
s
tr
a
ted
in
th
e
Fig
u
r
e
4
an
d
F
ig
u
r
e
5
.
B
u
t
th
e
d
is
ad
v
an
tag
e
o
f
th
is
co
n
tr
o
l
lo
o
p
is
th
at
it
is
u
n
ab
le
to
r
et
u
r
n
v
o
ltag
e
an
d
f
r
e
q
u
en
c
y
to
n
o
m
in
al
v
alu
es.
An
d
it
is
n
ec
ess
ar
y
to
u
s
e
a
co
m
p
lem
en
tar
y
o
r
s
ec
o
n
d
ar
y
co
n
tr
o
l
lo
o
p
.
A
s
ec
o
n
d
a
r
y
c
o
n
tr
o
l
lo
o
p
is
u
s
ed
in
o
r
d
er
to
ze
r
o
th
e
er
r
o
r
in
th
e
v
o
ltag
e
o
r
f
r
e
q
u
en
c
y
p
r
o
f
ile
a
s
s
h
o
wn
in
th
e
Fig
u
r
e
4
.
T
h
e
v
alu
e
o
f
p
er
s
is
ten
t
f
r
eq
u
en
c
y
er
r
o
r
is
o
f
ten
s
et
to
ze
r
o
b
y
a
class
ical
PI
co
n
tr
o
ller
.
Fig
u
r
e
4
.
Fre
q
u
en
cy
d
r
o
o
p
r
estricte
d
b
y
p
r
im
ar
y
c
o
n
tr
o
l
Fig
u
r
e
5
.
Seco
n
d
ar
y
co
n
tr
o
l f
r
am
ewo
r
k
W
h
en
d
is
co
n
n
ec
ted
f
r
o
m
t
h
e
m
ain
g
r
id
,
th
ey
e
n
ab
le
th
e
m
icr
o
-
g
r
i
d
to
im
p
le
m
en
t
p
r
i
m
ar
y
an
d
s
ec
o
n
d
ar
y
c
o
n
tr
o
l
m
eth
o
d
s
b
y
ap
p
ly
in
g
th
e
VSI
co
n
tr
o
l
m
et
h
o
d
,
w
h
ich
is
s
till
b
ased
o
n
th
e
ac
tiv
e
p
r
esen
ce
o
f
elec
tr
o
n
ic
p
o
wer
elem
en
ts
.
T
h
e
g
en
er
al
s
tr
u
ctu
r
e
o
f
th
is
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
6
.
Acc
o
r
d
in
g
to
th
is
m
eth
o
d
,
o
n
e
o
r
m
o
r
e
DGs
ar
e
r
esp
o
n
s
ib
le
f
o
r
s
tab
ilizin
g
th
e
m
icr
o
-
g
r
id
f
r
eq
u
en
cy
an
d
v
o
ltag
e
o
r
,
in
o
th
e
r
wo
r
d
s
,
ap
p
ly
in
g
o
n
e
o
r
m
o
r
e
DGs
to
th
e
V
SI
m
eth
o
d
an
d
co
n
tr
o
llin
g
th
e
o
th
er
DGs
f
o
r
s
u
p
p
ly
i
n
g
lo
ca
l
m
ic
ro
-
g
r
i
d
lo
ad
s
.
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
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f d
ec
en
tr
a
liz
ed
co
n
tr
o
l fo
r
b
id
ir
ec
tio
n
a
l c
o
n
ve
r
ters
… (
S
ey
ed
Mo
jta
b
a
A
b
b
a
s
i
)
1509
Fig
u
r
e
6
.
C
o
n
tr
o
l f
r
am
ew
o
r
k
4.
ARTI
F
I
CI
AL
N
E
URA
L
NE
T
WO
RK
B
ased
o
n
th
e
s
tr
u
ctu
r
e
o
f
th
e
s
e
n
etwo
r
k
s
a
n
d
h
o
w
t
o
in
te
g
r
ate
th
e
p
r
o
ce
s
s
in
g
elem
en
ts
,
th
er
e
ar
e
s
ev
er
al
im
p
o
r
tan
t
an
d
im
p
o
r
tan
t
ap
p
licatio
n
s
s
u
ch
as
m
in
d
m
o
d
elin
g
,
f
in
an
cial
m
o
d
elin
g
,
tim
e
s
er
ies
p
r
ed
ictio
n
,
co
n
tr
o
l
s
y
s
tem
s
a
n
d
o
p
tim
izatio
n
f
o
r
it.
T
o
a
p
p
ly
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
s
to
th
e
p
r
o
ce
s
s
es
m
en
tio
n
ed
ab
o
v
e,
we
n
ee
d
t
o
co
n
s
id
er
a
m
ath
em
atica
l
m
o
d
el
o
f
th
em
.
A
s
im
p
le
m
at
h
em
atica
l
m
o
d
el
to
an
aly
ze
its
b
eh
av
io
r
is
s
h
o
w
n
Fig
u
r
e
7
.
B
ased
o
n
Fig
u
r
e
7
,
T
h
e
X,
W
,
an
d
,
f
(net)
v
ec
t
o
r
s
ar
e
th
e
in
p
u
t
v
ec
to
r
s
an
d
weig
h
ts
,
th
e
b
ias
v
alu
e,
an
d
th
e
f
u
n
ctio
n
in
te
n
d
ed
f
o
r
t
h
e
n
eu
r
o
n
,
r
esp
ec
tiv
ely
.
T
h
e
o
u
tp
u
t
o
f
th
is
m
o
d
el
will b
e
in
ac
c
o
r
d
an
ce
with
th
e
eq
u
atio
n
g
iv
e
n
in
(
1
)
.
(
)
=
(
∑
(
)
+
0
=
1
)
.
(
1
)
T
h
e
ad
v
an
tag
e
o
f
n
o
n
l
in
ea
r
f
u
n
ctio
n
s
o
v
e
r
lin
ea
r
f
u
n
ctio
n
s
i
s
in
u
p
d
atin
g
weig
h
ts
an
d
tr
ain
in
g
,
a
n
d
m
ak
es
th
e
s
y
s
tem
n
o
t su
b
ject
to
s
u
d
d
e
n
c
h
an
g
es.
Fig
u
r
e
7
.
Ma
th
e
m
atica
l m
o
d
el
in
g
o
f
a
ty
p
e
o
f
ar
tific
ial
n
e
u
r
a
l n
etwo
r
k
s
.
5.
E
L
E
M
E
N
T
A
L
M
O
D
E
L
I
N
G
5
.
1
.
M
o
delin
g
t
he
ph
o
t
o
v
o
lt
a
ic
sy
s
t
em
T
h
e
elec
tr
ical
m
o
d
el
o
f
a
p
h
o
t
o
v
o
ltaic
ce
ll
is
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
m
o
d
el
in
clu
d
es
a
r
ev
er
s
e
d
io
d
e
an
d
a
p
a
r
allel
cu
r
r
en
t
s
o
u
r
ce
.
An
d
b
o
th
s
er
ies an
d
p
ar
allel
r
e
s
is
to
r
s
s
im
u
late
s
y
s
tem
lo
s
s
e
s
.
=
ℎ
−
[
(
(
+
)
)
−
1
]
(
2
)
ℎ
=
[
+
1
(
−
)
]
1000
(
3
)
=
(
)
3
(
(
1
−
1
)
)
(
4
)
W
h
er
e
I
s
th
e
ce
ll
s
atu
r
atio
n
cu
r
r
en
t,
N
p
an
d
N
s
n
u
m
b
er
o
f
s
er
ies
an
d
p
ar
allel
ar
r
ay
s
,
V
pv
o
u
tp
u
t
v
o
ltag
e
o
f
s
o
lar
s
y
s
tem
,
q
ele
ctr
o
n
ch
a
r
g
e,
k
B
o
ltzam
an
co
n
s
tan
t,
I
rs
an
d
I
sc
r
ev
e
r
s
e
s
atu
r
atio
n
cu
r
r
en
t
an
d
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
150
5
–
152
0
1510
s
h
o
r
t
cir
cu
it,
E
g
s
ilico
n
f
is
s
io
n
en
er
g
y
,
k
1
c
o
ef
f
icien
t
T
h
e
t
em
p
er
atu
r
e
d
ep
en
d
en
ce
an
d
λ
ar
e
th
e
am
o
u
n
t
o
f
r
ad
iatio
n
.
T
h
e
s
o
lar
s
y
s
tem
u
n
d
er
c
o
n
s
id
er
atio
n
is
5
0
k
W
an
d
co
n
s
is
ts
o
f
3
3
p
ar
allel
m
o
d
u
les
an
d
5
s
er
ies
m
o
d
u
les.
All so
lar
s
y
s
tem
p
ar
am
eter
s
ar
e
tak
en
f
r
o
m
[
5
]
.
Fig
u
r
e
8
.
Mo
d
el
o
f
a
p
h
o
to
v
o
ltaic
ce
ll
5
.
2
.
E
nerg
y
s
t
o
ra
g
e
s
y
s
t
em
T
h
e
b
atter
y
m
o
d
el
in
th
is
s
tu
d
y
is
a
c
o
n
tr
o
llab
le
v
o
ltag
e
s
o
u
r
ce
with
a
s
er
ies
r
esis
to
r
as
p
r
esen
ted
in
[
5
]
.
T
h
e
f
o
llo
win
g
eq
u
atio
n
s
a
r
e
p
r
esen
ted
in
th
is
s
tu
d
y
f
o
r
b
atter
y
m
o
d
elin
g
.
=
0
−
−
∫
+
∗
(
∫
)
(
5
)
=
−
(
6
)
=
100
(
1
+
∫
)
(
7
)
W
h
er
e
E
0
is
th
e
o
p
en
cir
cu
it
v
o
ltag
e,
Qb
th
e
b
atter
y
ca
p
ac
i
ty
,
K
th
e
p
o
la
r
izin
g
v
o
ltag
e,
B
is
th
e
ex
p
o
n
en
tial
ca
p
ac
ity
,
an
d
A
is
th
e
ex
p
o
n
en
tial v
o
ltag
e.
5
.
3
.
F
uel c
ell
Fu
el
ce
lls
ar
e
a
n
ew
tech
n
o
lo
g
y
f
o
r
th
e
p
r
o
d
u
ctio
n
o
f
el
ec
tr
icity
th
at
p
r
o
d
u
ce
s
elec
tr
icity
d
ir
ec
tly
f
r
o
m
th
e
co
m
b
i
n
atio
n
o
f
f
u
el
a
n
d
o
x
i
d
izer
.
T
h
e
co
n
s
tan
t v
o
ltag
e
p
r
o
d
u
ce
d
b
y
t
h
e
f
u
el
ce
ll c
an
b
e
o
b
tain
ed
b
y
:
=
0
(
0
+
2
(
2
2
0
.
5
2
)
)
−
(
8
)
2
=
1
1
+
[
2
]
(
9
)
2
=
1
2
(
1
0
)
2
=
1
2
1
+
2
[
1
2
−
]
(
1
1
)
2
=
1
2
1
+
2
[
2
]
(
1
2
)
wh
er
e
E
0
is
th
e
s
tan
d
ar
d
ce
ll
v
o
ltag
e,
N0
is
th
e
ce
ll
n
u
m
b
er
,
r
is
th
e
g
as
co
n
s
tan
t,
f
is
th
e
Far
ad
ay
co
n
s
tan
t,
r
is
th
e
s
tack
r
esis
tan
ce
,
T
is
th
e
ce
ll
tem
p
er
atu
r
e
p
H
2
,
p
O
2
a
n
d
p
H2
O
h
y
d
r
o
g
en
p
r
ess
u
r
e,
o
x
y
g
e
n
an
d
wate
r
v
ap
o
r
.
T
h
e
d
y
n
am
ic
m
o
d
el
o
f
SOFC
i
s
p
r
esen
ted
b
y
th
e
f
o
ll
o
win
g
r
elatio
n
s
h
ip
s
in
t
h
e
p
ap
er
.
6.
CO
NT
RO
L
O
N
CO
M
P
O
NE
NT
6
.
1
.
P
ho
t
o
v
o
lt
a
ic
s
y
s
t
em
c
o
ntr
ol
T
h
e
DC
-
to
-
DC
co
n
v
er
ter
will
b
e
r
esp
o
n
s
ib
le
f
o
r
c
o
n
tr
o
llin
g
th
e
p
h
o
to
v
o
ltaic
s
y
s
tem
.
T
h
is
co
n
v
er
ter
is
r
esp
o
n
s
ib
le
f
o
r
in
cr
ea
s
in
g
t
h
e
v
o
ltag
e
p
r
o
d
u
ce
d
b
y
th
e
P
V
an
d
o
b
tain
in
g
m
ax
im
u
m
p
o
wer
f
r
o
m
th
e
PV.
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
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f d
ec
en
tr
a
liz
ed
co
n
tr
o
l fo
r
b
id
ir
ec
tio
n
a
l c
o
n
ve
r
ters
… (
S
ey
ed
Mo
jta
b
a
A
b
b
a
s
i
)
1511
T
h
e
m
eth
o
d
,
s
h
o
r
tly
k
n
o
wn
a
s
th
e
d
is
tu
r
b
a
n
ce
m
eth
o
d
,
is
a
co
m
m
o
n
a
n
d
wid
ely
u
s
ed
m
eth
o
d
i
n
m
a
x
im
u
m
p
o
wer
tr
ac
k
in
g
alg
o
r
ith
m
s
.
T
h
is
m
eth
o
d
is
ess
en
tially
a
tr
ial
-
an
d
-
er
r
o
r
m
et
h
o
d
a
n
d
d
o
es
n
o
t
r
eq
u
ir
e
tem
p
er
atu
r
e
an
d
r
ad
iatio
n
s
en
s
o
r
s
an
d
ce
ll
ch
ar
ac
ter
is
tic
cu
r
v
es.
T
h
e
p
h
o
to
v
o
ltaic
co
n
tr
o
ll
er
s
lig
h
tly
ch
an
g
e
s
th
e
b
ase
v
alu
e
o
f
th
e
in
v
er
te
r
o
u
tp
u
t
an
d
o
b
s
er
v
es
th
e
ac
tu
al
o
u
tp
u
t
p
o
wer
v
alu
e.
I
f
t
h
e
o
u
tp
u
t
p
o
wer
is
in
cr
ea
s
ed
,
th
is
ch
an
g
e
will c
o
n
tin
u
e.
T
h
e
f
lo
wch
ar
t
o
f
th
is
m
eth
o
d
is
s
h
o
wn
in
Fig
u
r
e
9
.
Fig
u
r
e
9
.
P&
O
f
lo
wc
h
ar
t
6
.
2
.
B
a
t
t
er
y
(
ener
g
y
s
t
o
ra
g
e
)
co
n
t
ro
l
T
h
e
b
atter
y
is
c
o
n
n
ec
te
d
to
t
h
e
7
0
0
-
v
o
lt
b
u
s
v
ia
a
DC
-
to
-
DC
co
n
v
er
ter
.
T
h
e
p
r
im
ar
y
t
ask
o
f
th
e
b
atter
y
is
to
s
av
e
t
h
e
ex
t
r
a
p
o
wer
g
en
e
r
ated
b
y
th
e
p
h
o
to
v
o
l
taic
s
y
s
tem
u
n
til
th
e
p
o
we
r
o
u
tp
u
t
f
r
o
m
t
h
e
PV
is
lo
w
o
r
a
lar
g
e
l
o
ad
is
f
ed
i
n
to
th
e
m
icr
o
-
g
r
id
to
s
u
p
p
ly
th
e
m
icr
o
-
g
r
i
d
.
I
n
ad
d
itio
n
,
th
e
b
a
tter
y
is
r
esp
o
n
s
ib
le
f
o
r
m
ain
tain
in
g
th
e
DC
lin
k
v
o
ltag
e
co
n
s
tan
t.
T
h
e
SOFC
c
o
n
tr
o
l
b
lo
c
k
d
iag
r
a
m
in
Fig
u
r
e
1
0
also
d
escr
ib
es
th
e
s
tep
s
.
I
f
th
e
p
o
wer
g
en
er
at
io
n
b
y
th
e
PV is lo
w
o
r
th
e
lo
ad
is
in
cr
e
ased
s
o
th
at
th
e
PV
a
lo
n
e
ca
n
n
o
t su
p
p
ly
it,
th
e
b
atter
y
will
h
a
v
e
th
e
m
a
in
task
o
f
p
o
wer
s
u
p
p
ly
.
I
f
t
h
e
b
atter
y
ch
ar
g
e
is
less
th
an
2
0
%,
d
is
ch
ar
g
in
g
th
e
b
atter
y
f
u
r
th
e
r
r
ed
u
ce
s
th
e
lif
e
o
f
th
e
b
atter
y
.
I
n
th
is
ca
s
e,
th
e
f
u
el
ce
ll
ca
n
en
ter
th
e
g
r
id
an
d
s
u
p
p
ly
th
e
ch
ar
g
e
as we
ll a
s
ch
ar
g
e
t
h
e
b
atter
y
.
Fig
u
r
e
1
0
.
SOFC
co
n
tr
o
l b
lo
c
k
d
iag
r
am
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
150
5
–
152
0
1512
6
.
3
.
DC
-
to
-
DC
co
nv
er
t
er
c
o
ntr
o
l
B
o
o
s
t c
o
n
v
er
ter
p
u
ls
es a
r
e
p
r
o
d
u
ce
d
ac
co
r
d
in
g
to
th
e
p
r
o
p
o
s
ed
P&
O
m
eth
o
d
.
B
o
o
s
t c
o
n
v
e
r
ter
p
u
ls
es
ar
e
in
jecte
d
u
s
in
g
th
e
b
lo
c
k
d
iag
r
am
m
eth
o
d
ab
o
v
e.
An
e
x
am
p
le
o
f
a
p
h
o
to
v
o
ltaic
s
y
s
tem
is
lis
ted
in
th
e
b
lo
ck
d
ia
g
r
am
.
T
h
e
f
o
llo
win
g
Fig
u
r
e
1
1
s
h
o
ws th
e
DC
-
to
-
DC
co
n
v
er
ter
.
Fig
u
r
e
1
1
.
DC
-
to
-
DC
co
n
v
er
te
r
co
n
tr
o
l b
lo
ck
d
iag
r
am
6
.
4
.
P
rinciples
o
f
L
a
nd
C
des
ig
n
a
pp
ro
pria
t
e
t
o
prev
ent
c
irc
ula
t
io
n
T
h
e
co
n
v
e
r
ter
d
esig
n
f
o
r
th
e
p
u
r
p
o
s
e
o
f
h
av
in
g
a
s
tab
le
p
o
le
in
v
o
lv
es
co
r
r
ec
tly
s
elec
tin
g
th
e
v
alu
es
o
f
th
e
i
n
d
u
cto
r
s
an
d
ca
p
ac
ito
r
s
.
T
h
e
d
esig
n
p
r
esen
ted
b
elo
w
is
b
ased
o
n
c
o
n
s
tan
t
in
p
u
t
v
o
ltag
e
an
d
o
u
tp
u
t
v
o
ltag
e
wh
ic
h
also
c
o
n
f
ir
m
s
th
e
v
a
r
iab
le
in
p
u
t
v
o
ltag
e
an
d
co
n
s
tan
t
o
u
tp
u
t
v
o
ltag
e,
s
o
th
e
f
o
llo
win
g
:
T
r
an
s
f
o
r
m
e
r
d
esig
n
in
d
icato
r
s
ar
e
co
v
er
ed
:
s
elec
tiv
e
L
1
d
e
p
en
d
s
o
n
th
e
m
ax
im
u
m
n
u
m
b
e
r
o
f
cu
r
r
en
t
r
i
p
p
les
i
1
,
in
th
e
s
tead
y
s
tate,
th
e
p
ea
k
-
to
-
p
ea
k
i
1
C
u
r
r
en
t
ch
a
n
g
es d
u
r
in
g
th
e
tim
e
th
e
s
witch
is
clo
s
ed
f
o
llo
ws:
1
=
1
(
−
)
.
T
h
e
v
o
ltag
e
at
ter
m
in
al
L
1
is
th
e
s
am
e
d
u
r
in
g
b
o
t
h
th
e
o
n
an
d
o
f
f
s
witch
es
an
d
th
e
f
s
s
witch
in
g
f
r
eq
u
e
n
cy
d
ep
en
d
s
o
n
t
h
e
in
te
n
d
ed
u
s
e,
s
o
in
ea
c
h
o
p
er
atin
g
co
n
d
itio
n
th
e
L
1
in
d
u
ctan
ce
v
alu
e
is
d
eter
m
in
ed
b
ased
o
n
th
e
m
ax
im
u
m
v
alu
e.
W
h
en
th
e
s
witch
i
s
o
n
,
th
e
ca
p
ac
ito
r
C
0
s
tar
ts
ch
ar
g
in
g
to
r
ep
lace
it
wh
en
th
e
s
witch
is
o
f
f
,
an
d
th
e
ca
p
ac
it
o
r
C
0
m
u
s
t
s
elec
t
th
e
v
o
ltag
e
r
ip
p
les
th
at
ca
n
b
e
ca
lcu
lated
f
r
o
m
th
e
f
o
llo
win
g
f
o
r
m
u
la:
=
=
8
×
×
.
W
h
ich
d
elta
i
0
ca
n
b
e
ca
lcu
lat
ed
f
r
o
m
E
q
u
atio
n
d
elta
i
1
+
d
e
lta
i
2
an
d
d
elta
i
2
f
r
o
m
th
e
f
o
ll
o
win
g
f
o
r
m
u
la:
2
=
2
(
−
)
.
B
y
p
u
ttin
g
in
e
q
u
atio
n
d
elta
i
0
we
h
av
e:
=
(
1
+
2
)
[
1
8
×
]
.
6
.
5
.
Select
t
he
v
a
lues
o
f
C
n
a
nd
L
2
T
h
e
p
u
r
p
o
s
e
is
to
o
b
tain
a
p
o
l
y
n
o
m
ial
r
esp
o
n
s
e
with
th
e
least
n
u
m
b
er
o
f
o
s
cillatio
n
s
,
ele
v
atio
n
s
,
an
d
also
th
e
lo
west s
itti
n
g
tim
e.
I
n
o
r
d
er
to
av
o
id
th
e
in
h
e
r
en
t e
f
f
ec
ts
o
f
m
in
im
u
m
p
h
ase,
a
weig
h
ted
co
s
t f
u
n
ctio
n
is
d
ef
in
ed
as:
=
∑
(
∗
−
[
]
)
2
=
=
1
.
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
694
P
erfo
r
ma
n
ce
imp
r
o
ve
men
t o
f d
ec
en
tr
a
liz
ed
co
n
tr
o
l fo
r
b
id
ir
ec
tio
n
a
l c
o
n
ve
r
ters
… (
S
ey
ed
Mo
jta
b
a
A
b
b
a
s
i
)
1513
W
h
ile
V
*
0
th
e
o
u
t
p
u
t v
o
ltag
e
v
alu
e
is
id
ea
l,
V
0
[
n
T
n
]
,
n
th
e
f
aith
f
u
l
s
am
p
le
o
f
v
o
ltag
e
r
esp
o
n
s
e
d
u
e
to
d
u
ty
c
y
cle
v
ar
iatio
n
s
is
also
th
e
n
u
m
b
er
o
f
all
s
am
p
les.
T
h
e
v
alu
es
f
o
r
t
h
e
weig
h
tin
g
f
ac
to
r
ar
e
ca
r
ef
u
lly
ad
ju
s
ted
,
w=
1
,
as
f
o
r
V
0
[
n
T
n
]
>V
0
[
0
]
an
d
w=
0
.
9
8
5
f
o
r
th
e
r
est
o
f
th
e
s
tates.
T
h
ese
v
alu
es
ar
e
s
elec
ted
in
s
u
ch
a
way
th
at
th
e
d
if
f
e
r
en
ce
e
x
p
r
ess
ed
b
y
t
h
e
m
in
im
u
m
p
h
ase
is
m
in
im
ized
(
d
u
e
to
th
e
tr
an
s
ien
t
v
o
ltag
e
r
esp
o
n
s
e)
C
n
an
d
L
2
th
e
v
alu
e
s
will
b
e
o
b
tain
ed
if
th
e
m
in
i
m
u
m
v
alu
e
is
estab
lis
h
ed
.
T
o
h
av
e
a
ch
o
ice
L
2
it
is
n
ec
ess
ar
y
to
co
n
s
id
er
C
0
a
r
eset
f
r
o
m
th
e
eq
u
atio
n
ab
o
v
e.
Sin
ce
L
1
an
d
L
2
b
o
th
v
alu
es
will
h
av
e
an
ef
f
ec
t
o
n
th
e
v
alu
es
d
elta
i
1
an
d
d
elta
i
2
th
er
ef
o
r
e
C
0
th
e
v
alu
e
is
u
p
d
ated
an
d
ca
n
b
e
r
e
-
u
s
ed
ag
ain
,
th
is
p
r
o
ce
s
s
co
n
tin
u
es u
n
til it r
ea
c
h
es th
e
l
o
west p
o
s
s
ib
le
v
alu
es
an
d
E
t
h
e
d
ef
in
e
d
r
an
g
e.
6
.
6
.
Circ
uit
f
lo
w
co
ntr
o
l
L
in
ea
r
r
esis
tan
ce
b
etwe
en
b
id
ir
ec
tio
n
al
p
o
wer
c
o
n
v
e
r
ter
s
f
o
r
p
ar
allel
b
id
ir
ec
tio
n
al
p
o
wer
co
n
v
er
ter
s
is
th
e
in
p
u
t
an
d
o
u
tp
u
t
th
at
s
h
o
ws
th
e
co
lo
r
e
d
s
ec
tio
n
s
o
f
th
e
cir
cu
latin
g
p
ath
s
b
etwe
en
th
e
b
id
ir
ec
tio
n
al
p
o
wer
co
n
v
er
ter
s
,
as sh
o
wn
b
elo
w.
W
h
en
th
e
s
witc
h
in
g
s
tatu
s
o
f
two
-
way
p
o
wer
co
n
v
er
te
r
s
is
d
if
f
er
en
t,
th
er
e
is
a
v
o
ltag
e
Dr
o
o
p
b
etwe
en
t
h
e
two
-
way
p
o
wer
co
n
v
er
ter
s
,
th
en
a
cir
c
u
latin
g
c
u
r
r
en
t
is
g
en
er
ated
alo
n
g
th
e
p
ath
if
th
e
s
y
s
tem
Dr
o
o
p
is
lo
w.
T
h
e
h
ig
h
s
witch
p
ath
is
o
n
an
d
th
e
lo
w
s
witch
p
ath
in
p
h
ase
(
a)
o
f
th
e
f
ir
s
t
two
way
p
o
wer
co
n
v
er
ter
is
o
f
f
,
wh
ile
th
e
h
ig
h
s
witch
p
ath
is
o
f
f
an
d
th
e
l
o
w
s
witch
p
ath
in
p
h
ase
(
a)
o
f
th
e
s
ec
o
n
d
two
way
p
o
wer
co
n
v
er
ter
is
o
n
.
T
h
en
a
cir
cu
lar
f
lo
w
p
ath
is
f
o
r
m
ed
th
at
is
in
d
icate
d
b
y
th
e
ar
r
o
w
an
d
ca
n
b
e
d
er
iv
ed
i
n
an
eq
u
iv
ale
n
t
cir
cu
it.
B
ased
o
n
th
e
ab
o
v
e
an
aly
s
is
,
an
ad
d
itio
n
al
ze
r
o
ax
is
is
in
tr
o
d
u
ce
d
wh
ich
m
ain
l
y
co
m
p
r
is
es
asy
m
m
etr
ic
co
m
p
o
n
e
n
ts
.
C
ir
cu
la
tio
n
f
lo
w
an
aly
s
is
,
cir
c
u
latin
g
f
lo
w
p
ath
s
a
n
d
th
e
eq
u
iv
alen
t c
ir
cu
it
o
f
a
p
air
o
f
B
P
C
ar
e
s
h
o
wn
in
Fig
u
r
e
1
2
.
Fig
u
r
e
1
2
.
T
h
e
cir
c
u
latio
n
f
lo
w
is
f
o
r
m
ed
b
etwe
en
th
e
p
h
ases
an
d
its
eq
u
iv
alen
t c
ir
cu
it
T
h
e
n
ew
p
o
wer
s
y
s
tem
r
eq
u
ir
es
in
cr
ea
s
ed
in
tellig
en
ce
an
d
f
lex
ib
ilit
y
in
co
n
tr
o
l
an
d
o
p
tim
izatio
n
to
en
s
u
r
e
lo
a
d
b
alan
cin
g
an
d
p
r
o
d
u
ctio
n
ca
p
a
b
ilit
ies
in
th
e
e
v
en
t
o
f
d
is
tu
r
b
an
ce
s
.
T
h
ese
c
o
m
m
o
n
ch
a
n
g
es
a
n
d
u
n
ce
r
tain
ties
in
a
p
o
wer
g
r
id
eq
u
ip
p
e
d
with
a
class
ic
co
n
tr
o
ller
ar
e
n
o
t
ab
le
to
c
o
n
tr
o
l
th
e
g
r
id
in
th
e
r
ig
h
t
d
ir
ec
tio
n
.
T
h
e
r
ef
o
r
e
,
in
th
is
p
ap
er
,
u
s
in
g
t
h
e
o
n
lin
e
in
tell
ig
en
t
n
eu
r
al
s
y
s
tem
an
d
its
in
teg
r
atio
n
w
ith
th
e
g
en
etic
alg
o
r
ith
m
is
u
s
ed
to
o
p
tim
ize
an
d
tu
n
e
th
e
PI
co
n
tr
o
ller
co
ef
f
icien
ts
.
T
h
e
r
e
ar
e
s
ev
er
al
m
eth
o
d
s
to
o
b
tain
th
e
b
est
PI
c
o
n
tr
o
ller
p
er
f
o
r
m
an
ce
a
n
d
to
d
eter
m
in
e
th
e
co
n
tr
o
ller
-
r
elate
d
c
o
ef
f
i
cien
ts
in
p
r
ac
tice,
we’
v
e
u
s
ed
th
e
n
eu
r
o
to
o
p
tim
ize
.
Neu
r
al
Gen
etic
Alg
o
r
ith
m
is
a
m
eth
o
d
o
f
o
p
tim
izatio
n
t
h
at
o
p
e
r
ates
o
n
th
e
p
r
in
cip
le
o
f
s
u
r
v
iv
al
m
o
s
t a
p
p
r
o
p
r
iate
in
liv
i
n
g
th
in
g
s
.
7.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
m
icr
o
-
g
r
id
u
n
d
er
s
tu
d
y
in
g
in
clu
d
es
a
p
h
o
to
v
o
ltaic
s
y
s
t
em
with
a
ca
p
ac
ity
o
f
5
0
k
W
,
a
f
u
el
ce
ll
with
a
ca
p
ac
ity
o
f
1
0
0
k
W
an
d
a
b
atter
y
with
th
e
ca
p
ac
it
y
o
f
Ah
2
5
0
.
T
h
e
am
o
u
n
t
o
f
s
u
n
lig
h
t
an
d
b
atter
y
SOC
v
ar
ied
in
th
ese
two
ca
s
e
s
tu
d
ies
an
d
th
e
p
er
f
o
r
m
a
n
c
e
o
f
th
e
co
n
tr
o
l
s
y
s
tem
f
o
r
v
o
ltag
e
co
n
tr
o
l
was
ev
alu
ated
.
T
h
e
g
en
e
r
al
s
tr
u
ctu
r
e
o
f
th
e
s
tu
d
ied
m
icr
o
-
g
r
i
d
is
s
h
o
wn
in
Fig
u
r
e
1
3
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
694
I
n
t J
Po
w
E
lec
&
Dr
i
Sy
s
t
,
Vo
l.
12
,
No
.
3
,
Sep
tem
b
er
2
0
2
1
:
150
5
–
152
0
1514
Fig
u
r
e
1
3
.
Ov
er
all
s
tr
u
ctu
r
e
o
f
th
e
s
tu
d
ied
m
icr
o
-
g
r
i
d
T
o
ev
alu
ate
th
e
e
f
f
icien
cy
o
f
th
e
d
esig
n
ed
g
e
n
etic
n
eu
r
al
m
o
d
el,
th
e
two
d
atasets
ar
e
s
elec
ted
f
r
o
m
r
ea
l
an
d
tr
ain
in
g
d
ata
as
tes
t
d
ata
an
d
co
m
p
ar
ed
.
T
h
ey
ar
e
also
p
lo
tted
in
th
e
f
o
r
m
o
f
two
d
atasets
.
C
o
m
p
ar
is
o
n
o
f
r
ea
l
a
n
d
m
ic
r
o
-
g
r
i
d
d
ata
s
h
o
ws
th
at
th
e
tr
ain
in
g
p
r
o
ce
s
s
h
as
b
ee
n
p
er
f
o
r
m
ed
with
g
r
ea
t
ac
cu
r
ac
y
a
n
d
th
at
th
e
n
e
u
r
al
h
as
well
r
ec
o
n
s
tr
u
cted
th
e
s
y
s
tem
b
eh
av
i
o
r
.
I
t
is
im
p
o
r
ta
n
t
t
o
r
em
em
b
er
th
at
8
0
%
o
f
th
e
d
ata
ar
e
u
s
ed
f
o
r
t
r
ain
in
g
,
1
0
%
f
o
r
test
in
g
a
n
d
th
e
o
t
h
er
1
0
%
f
o
r
v
alid
at
io
n
.
B
ased
o
n
t
h
e
in
f
o
r
m
atio
n
g
iv
e
n
,
Fig
u
r
e
1
4
i
n
d
icate
s
th
e
d
eg
r
ee
o
f
c
o
n
f
o
r
m
ity
o
f
th
e
d
ata
with
th
e
p
r
ed
i
cted
v
alu
es.
Fig
u
r
e
1
4
.
R
eg
r
ess
io
n
cu
r
v
e
Fig
u
r
e
1
5
,
cu
r
v
e
s
h
o
ws
th
e
ex
ten
t
to
wh
ich
th
e
d
ata
ar
e
co
n
s
is
ten
t
w
ith
th
e
p
r
ed
icted
v
alu
es.
As
ca
n
b
e
s
ee
n
,
it
is
v
er
y
well
ad
ap
te
d
.
T
h
e
Fig
u
r
e
1
5
s
h
o
ws
th
e
p
er
f
o
r
m
a
n
ce
o
f
t
h
e
n
eu
r
al
n
etw
o
r
k
f
o
r
d
ata
d
u
r
in
g
th
e
tr
ain
in
g
,
v
e
r
if
icatio
n
a
n
d
t
esti
n
g
p
r
o
ce
s
s
,
wh
ich
r
ea
ch
e
d
its
ac
ce
p
tab
le
r
esp
o
n
s
es
af
ter
ap
p
r
o
x
im
ately
4
0
0
r
o
u
n
d
s
an
d
th
e
s
lo
p
e
d
ec
r
ea
s
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.