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
(
I
J
P
E
DS)
Vo
l.
1
7
,
No
.
1
,
Ma
r
ch
20
2
6
,
p
p
.
2
6
7
~
2
81
I
SS
N:
2088
-
8
6
9
4
,
DOI
: 1
0
.
1
1
5
9
1
/ijp
ed
s
.
v
1
7
.
i
1
.
p
p
2
6
7
-
2
81
267
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
p
e
d
s
.
ia
esco
r
e.
co
m
M
o
deling
and a
na
ly
sis
of batter
y
le
ss
off
-
g
rid
pho
tov
o
ltaic with
a
da
ptive multi
-
m
o
tor
I
Wa
y
a
n Suta
y
a
1
,
I
da
Ay
u Dw
i G
iria
nta
ri
2
,
Wa
y
a
n G
ede
Aria
s
t
ina
2
,
I
Ny
o
m
a
n Sa
t
y
a
K
um
a
ra
2
1
El
e
c
t
r
o
n
i
c
S
y
s
t
e
ms
E
n
g
i
n
e
e
r
i
n
g
T
e
c
h
n
o
l
o
g
y
,
U
n
i
v
e
r
s
i
t
a
s
P
e
n
d
i
d
i
k
a
n
G
a
n
e
sh
a
,
S
i
n
g
a
r
a
j
a
,
I
n
d
o
n
e
si
a
2
El
e
c
t
r
i
c
a
l
E
n
g
i
n
e
e
r
i
n
g
,
U
n
i
v
e
r
si
t
a
s
U
d
a
y
a
n
a
,
D
e
n
p
a
sar,
I
n
d
o
n
e
si
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
1
1
,
2
0
2
5
R
ev
is
ed
Oct
2
0
,
2
0
2
5
Acc
ep
ted
Dec
1
1
,
2
0
2
5
Th
is
p
a
p
e
r
p
re
se
n
ts
a
m
o
d
e
l
o
f
a
b
a
tt
e
ry
les
s
o
ff
-
g
ri
d
p
h
o
to
v
o
l
taic
(P
V)
sy
ste
m
with
a
n
a
d
a
p
ti
v
e
m
u
lt
i
-
m
o
to
r
l
o
a
d
.
Th
is
m
o
d
e
l
is
d
e
v
e
l
o
p
e
d
a
s
a
n
e
ffo
rt
to
e
n
h
a
n
c
e
th
e
p
o
we
r
o
u
t
p
u
t
o
f
b
a
tt
e
ry
les
s
o
ff
-
g
ri
d
P
V
s
y
ste
m
s
fo
r
m
o
to
r
lo
a
d
s.
In
ste
a
d
o
f
u
si
n
g
a
sin
g
le
larg
e
-
c
a
p
a
c
it
y
m
o
t
o
r,
a
s
c
o
m
m
o
n
ly
d
o
n
e
i
n
p
re
v
io
u
s
stu
d
ies
,
t
h
e
m
o
d
e
l
d
istri
b
u
tes
th
e
l
o
a
d
i
n
to
se
v
e
r
a
l
sm
a
ll
e
r
m
o
to
rs
a
n
d
c
o
n
tro
ls
t
h
e
m
a
d
a
p
ti
v
e
ly
.
Th
is
a
p
p
ro
a
c
h
a
ll
o
ws
fo
r
b
e
tt
e
r
c
o
n
tro
l
o
f
t
h
e
to
tal
lo
a
d
imp
e
d
a
n
c
e
to
su
p
p
o
rt
m
a
x
imu
m
p
o
we
r
p
o
i
n
t
(M
P
P
)
trac
k
in
g
.
A
c
a
se
stu
d
y
in
v
o
l
v
in
g
th
re
e
t
h
re
e
-
p
h
a
se
in
d
u
c
ti
o
n
m
o
t
o
rs,
e
a
c
h
with
a
n
o
p
e
ra
ti
n
g
p
o
we
r
o
f
2
0
0
W
,
is
c
o
n
d
u
c
te
d
,
wh
e
re
t
h
e
p
o
we
r
p
ro
d
u
c
ti
o
n
o
f
th
e
p
r
o
p
o
se
d
m
o
d
e
l
is
a
n
a
ly
se
d
b
y
c
o
m
p
a
rin
g
i
t
with
t
h
e
th
e
o
re
ti
c
a
l
MPP
a
n
d
a
fix
e
d
-
lo
a
d
m
o
to
r
sy
ste
m
th
a
t
re
p
re
se
n
ts
a
si
n
g
le
larg
e
m
o
to
r.
Un
d
e
r
1
0
0
0
W/
m
²
irrad
i
a
n
c
e
a
n
d
u
sin
g
a
n
8
5
2
W
p
P
V
a
rra
y
,
th
e
p
ro
p
o
se
d
m
o
d
e
l
a
c
h
ie
v
e
s
a
p
o
we
r
o
u
t
p
u
t
o
f
8
4
2
W,
w
h
ich
c
o
rr
e
sp
o
n
d
s
to
9
8
.
8
3
%
o
f
t
h
e
MPP
.
I
n
c
o
n
tr
a
st,
th
e
sy
ste
m
with
o
u
t
t
h
is
m
o
d
e
l
o
n
ly
g
e
n
e
ra
tes
2
9
8
W
,
o
r
j
u
st
3
5
.
0
2
%
o
f
t
h
e
MPP
.
Th
e
tes
ti
n
g
p
r
o
c
e
ss
sp
a
n
s
a
5
-
se
c
o
n
d
p
e
rio
d
d
u
rin
g
t
h
e
m
o
to
r
sta
rti
n
g
sta
te.
Th
e
p
o
we
r
p
ro
d
u
c
ti
o
n
a
n
a
ly
sis
o
f
t
h
e
p
r
o
p
o
se
d
m
o
d
e
l
is
p
re
se
n
ted
i
n
g
ra
p
h
ica
l
f
o
rm
u
si
n
g
M
ATLAB/S
imu
li
n
k
.
K
ey
w
o
r
d
s
:
B
atter
y
less
Mo
d
el
Mu
lti
-
m
o
to
r
Ph
o
to
v
o
ltaic
Po
wer
p
r
o
d
u
ctio
n
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
:
I
W
ay
an
Su
tay
a
E
lectr
o
n
ic
Sy
s
tem
s
E
n
g
in
ee
r
i
n
g
T
ec
h
n
o
lo
g
y
,
Un
iv
e
r
s
itas
P
en
d
id
ik
an
Gan
esh
a
Sin
g
ar
aja,
B
ali,
I
n
d
o
n
esia
E
m
ail: w
s
u
tay
a@
u
n
d
ik
s
h
a.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
b
atter
y
less
o
f
f
-
g
r
id
p
h
o
to
v
o
ltaic
(
PV)
s
y
s
tem
is
wid
ely
r
ec
o
g
n
ized
as
a
p
r
ac
tical
ap
p
licatio
n
o
f
PV
tech
n
o
lo
g
y
,
p
ar
ticu
lar
l
y
s
u
itab
le
f
o
r
s
u
p
p
ly
in
g
p
o
wer
to
n
o
n
-
c
r
itical
lo
ad
s
,
as
d
is
cu
s
s
ed
in
s
ev
er
al
s
tu
d
ies
[
1
]
-
[
3
]
.
T
h
ese
ty
p
es
o
f
l
o
ad
s
ar
e
ch
ar
ac
ter
ized
b
y
th
eir
a
b
ilit
y
to
o
p
er
ate
o
n
l
y
wh
en
en
er
g
y
is
av
ailab
le,
with
o
u
t
r
ely
in
g
o
n
s
tr
ict
o
r
c
o
n
tin
u
o
u
s
p
o
wer
d
em
an
d
r
e
q
u
ir
em
en
ts
.
Un
lik
e
c
o
n
v
e
n
tio
n
al
lo
ad
s
th
at
m
u
s
t
r
em
ain
ac
tiv
e
b
ased
o
n
u
s
er
n
ee
d
s
,
th
ese
lo
ad
s
ar
e
o
n
ly
ac
tiv
ated
wh
en
s
u
f
f
icien
t
s
o
lar
en
er
g
y
is
av
ailab
le
to
p
o
wer
th
em
d
ir
ec
tly
.
T
h
er
ef
o
r
e,
th
e
b
atter
y
less
o
f
f
-
g
r
id
PV
s
y
s
tem
is
h
ig
h
ly
s
u
itab
le
f
o
r
f
lex
ib
le
ap
p
licatio
n
s
th
at
ca
n
ad
ap
t t
o
th
e
n
at
u
r
ally
v
ar
iab
le
av
ailab
ilit
y
o
f
r
en
ewa
b
le
en
er
g
y
.
On
e
o
f
th
e
p
r
ac
tical
ap
p
licatio
n
s
o
f
a
b
atter
y
less
PV
s
y
s
tem
is
as
a
p
o
wer
s
o
u
r
ce
f
o
r
d
r
iv
in
g
elec
tr
ic
m
o
to
r
l
o
ad
s
[
4
]
,
[
5
]
.
T
h
is
a
p
p
r
o
ac
h
is
em
p
lo
y
ed
f
o
r
v
ar
io
u
s
p
u
r
p
o
s
es,
in
clu
d
in
g
th
e
o
p
er
atio
n
o
f
h
ig
h
-
ca
p
ac
ity
wate
r
p
u
m
p
s
th
at
d
eliv
er
wate
r
in
to
r
eser
v
o
i
r
s
,
d
is
till
atio
n
p
r
o
ce
s
s
es,
an
d
o
th
er
m
ec
h
an
ical
ap
p
licatio
n
s
th
at
r
ely
o
n
m
o
to
r
-
d
r
iv
e
n
s
y
s
tem
s
.
I
n
wate
r
p
u
m
p
in
g
a
p
p
licatio
n
s
,
th
e
v
o
lu
m
e
o
f
wate
r
p
u
m
p
e
d
is
d
ir
ec
tly
d
ep
e
n
d
en
t
o
n
t
h
e
in
ten
s
ity
o
f
s
o
lar
ir
r
a
d
ian
ce
.
T
h
e
h
i
g
h
er
th
e
s
o
lar
i
n
ten
s
ity
,
th
e
g
r
ea
ter
th
e
v
o
lu
m
e
o
f
wate
r
th
at
ca
n
b
e
d
eliv
er
ed
[
6
]
.
T
h
is
p
r
o
ce
s
s
r
e
q
u
ir
es
a
co
n
t
r
o
l
s
y
s
tem
ca
p
a
b
le
o
f
tr
ac
k
in
g
t
h
e
m
ax
im
u
m
p
o
wer
p
o
in
t (
MPP)
,
ty
p
ically
ac
h
iev
e
d
b
y
r
eg
u
latin
g
th
e
c
u
r
r
en
t su
p
p
lied
to
t
h
e
m
o
to
r
lo
a
d
[
7
]
.
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
:
267
-
281
268
I
n
s
ev
er
al
s
tu
d
ies,
cu
r
r
en
t
co
n
tr
o
l
to
th
e
m
o
to
r
lo
ad
is
ac
h
iev
ed
b
y
r
eg
u
latin
g
th
e
v
o
ltag
e
s
u
p
p
lied
to
th
e
m
o
to
r
.
T
h
is
v
o
ltag
e
r
e
g
u
l
atio
n
ca
n
b
e
im
p
lem
e
n
ted
u
s
in
g
two
m
ai
n
ap
p
r
o
ac
h
es:
th
e
s
in
g
le
-
s
tag
e
m
eth
o
d
an
d
th
e
two
-
s
tag
e
m
eth
o
d
.
I
n
th
e
s
in
g
le
-
s
tag
e
m
eth
o
d
,
th
e
s
y
s
tem
u
tili
ze
s
o
n
ly
an
in
v
e
r
te
r
b
lo
c
k
[
8
]
-
[
1
3
]
.
I
n
co
n
tr
ast,
th
e
two
-
s
tag
e
m
eth
o
d
em
p
lo
y
s
b
o
th
a
co
n
v
er
ter
a
n
d
an
in
v
er
ter
b
lo
c
k
in
s
eq
u
e
n
ce
[
1
4
]
-
[
1
9
]
.
T
h
e
co
n
v
er
ter
m
o
d
u
le
is
co
n
tr
o
ll
ed
u
s
in
g
p
u
ls
e
wid
th
m
o
d
u
l
atio
n
(
PW
M)
tech
n
iq
u
es,
w
h
ile
th
e
in
v
er
ter
is
r
eg
u
lated
b
ased
o
n
th
e
m
o
d
u
latio
n
in
d
e
x
[
2
0
]
.
T
h
is
co
n
t
r
o
l
s
tr
ateg
y
is
aim
ed
at
ac
h
iev
in
g
MPP
tr
ac
k
in
g
,
th
er
eb
y
o
p
tim
izin
g
th
e
en
er
g
y
u
tili
za
tio
n
f
r
o
m
t
h
e
PV sy
s
tem
.
Stu
d
ies
g
en
er
ally
r
eg
u
late
th
e
v
o
ltag
e
s
u
p
p
lied
to
m
o
to
r
lo
ad
s
to
tr
ac
k
m
ax
im
u
m
p
o
wer
,
with
co
n
tr
o
l
ap
p
lied
th
r
o
u
g
h
th
e
i
n
v
er
ter
to
m
an
ag
e
cu
r
r
e
n
t
f
lo
w
to
th
e
lo
ad
[
2
1
]
,
[
2
2
]
.
T
h
is
is
cr
u
cial
b
ec
au
s
e
m
ax
im
u
m
p
o
wer
ex
tr
ac
tio
n
d
ep
en
d
s
h
ea
v
ily
o
n
ac
h
ie
v
in
g
th
e
o
p
tim
al
c
u
r
r
en
t
lev
el.
Ho
wev
er
,
ch
allen
g
es
ar
is
e
wh
en
th
e
lo
a
d
is
an
ele
ctr
ic
m
o
to
r
,
wh
o
s
e
im
p
e
d
an
c
e
v
ar
ies
with
o
p
e
r
atin
g
c
o
n
d
i
tio
n
s
an
d
ca
n
n
o
t
b
e
tr
ea
ted
as
a
co
n
s
tan
t
r
esis
tan
ce
[
2
3
]
.
T
h
e
im
p
ed
an
ce
v
alu
e
o
f
th
e
m
o
to
r
c
h
an
g
es
d
e
p
en
d
i
n
g
o
n
its
o
p
er
atin
g
co
n
d
itio
n
.
Du
r
in
g
th
e
s
tar
tin
g
p
h
ase,
th
e
im
p
ed
a
n
ce
d
ec
r
ea
s
es
s
ig
n
if
ican
tly
co
m
p
ar
e
d
to
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
.
Similar
ly
,
wh
en
t
h
e
m
o
to
r
is
lo
a
d
ed
,
its
im
p
ed
a
n
ce
also
b
ec
o
m
es
lo
wer
.
C
o
n
v
en
tio
n
al
s
y
s
tem
s
o
f
ten
u
s
e
a
s
in
g
le
lar
g
e
m
o
to
r
o
r
m
u
ltip
le
m
o
to
r
s
co
n
n
ec
te
d
s
tatically
in
p
ar
allel,
wh
ich
m
ay
r
ed
u
ce
co
n
tr
o
l
f
lex
ib
ilit
y
.
Du
e
to
th
e
d
y
n
a
m
ic
n
atu
r
e
o
f
m
o
to
r
l
o
ad
s
[
2
4
]
,
wh
ich
d
if
f
er
s
ig
n
if
ican
tly
f
r
o
m
c
o
n
v
en
tio
n
al
r
esis
tiv
e
lo
ad
s
,
cu
r
r
en
t
c
o
n
tr
o
l
f
r
o
m
th
e
PV
p
a
n
el
th
r
o
u
g
h
v
o
ltag
e
r
e
g
u
latio
n
al
o
n
e
is
in
s
u
f
f
icien
t.
An
ad
d
itio
n
al
co
n
tr
o
l
v
a
r
iab
le
is
r
eq
u
ir
e
d
to
ac
h
ie
v
e
m
o
r
e
ef
f
icien
t
m
ax
im
u
m
p
o
wer
tr
ac
k
in
g
.
On
e
p
o
ten
tial
ap
p
r
o
ac
h
is
to
m
o
d
if
y
th
e
m
o
to
r
lo
ad
co
n
f
ig
u
r
atio
n
its
elf
b
y
r
ep
lacin
g
a
s
in
g
le
lar
g
e
m
o
to
r
o
r
m
u
ltip
le
s
tatically
co
n
n
ec
ted
m
o
to
r
s
with
an
ad
ap
tiv
e
m
u
lti
-
m
o
t
o
r
lo
a
d
.
T
h
is
allo
ws th
e
n
u
m
b
er
o
f
o
p
er
atin
g
m
o
to
r
s
to
b
e
co
n
tr
o
lled
,
m
ak
i
n
g
th
e
t
o
tal
im
p
ed
an
ce
o
f
th
e
m
o
to
r
lo
ad
s
a
v
ar
iab
le.
T
h
is
p
ap
er
p
r
esen
ts
a
p
o
wer
p
r
o
d
u
ctio
n
a
n
aly
s
is
o
f
a
m
o
d
el
o
f
a
b
atter
y
less
o
f
f
-
g
r
id
p
h
o
to
v
o
ltaic
s
y
s
tem
with
ad
ap
tiv
e
m
o
t
o
r
l
o
ad
,
wh
ich
was
d
ev
elo
p
ed
as
p
ar
t
o
f
th
e
r
esear
ch
co
n
d
u
cte
d
in
th
is
s
tu
d
y
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
aim
s
to
o
p
ti
m
ize
p
o
wer
u
tili
za
tio
n
f
r
o
m
t
h
e
PV
s
y
s
tem
b
y
ad
ju
s
tin
g
th
e
n
u
m
b
er
o
f
ac
tiv
e
m
o
to
r
s
b
ased
o
n
th
e
av
ailab
i
lity
o
f
s
o
lar
en
er
g
y
.
T
h
e
f
in
d
in
g
s
d
em
o
n
s
tr
ate
a
s
ig
n
if
ican
t
im
p
r
o
v
em
e
n
t
in
p
o
wer
o
u
tp
u
t
co
m
p
ar
ed
to
co
n
v
en
tio
n
al
ap
p
r
o
ac
h
es.
E
v
alu
atio
n
was
co
n
d
u
cted
b
y
m
ea
s
u
r
in
g
th
e
s
y
s
tem
'
s
p
o
wer
o
u
tp
u
t
at
th
e
MPP
u
n
d
er
v
ar
y
in
g
lev
els
o
f
s
o
lar
ir
r
a
d
ian
ce
.
Fo
r
co
m
p
ar
is
o
n
,
test
s
w
er
e
also
p
er
f
o
r
m
e
d
o
n
a
f
ix
ed
m
o
to
r
lo
a
d
co
n
f
i
g
u
r
atio
n
,
r
ep
r
esen
tin
g
s
y
s
tem
s
with
a
s
in
g
le
lar
g
e
m
o
to
r
o
r
m
u
ltip
le
s
tatical
ly
o
p
er
ated
m
o
to
r
s
.
T
h
is
co
m
p
a
r
is
o
n
h
ig
h
lig
h
ts
th
e
ad
v
an
tag
es
o
f
th
e
ad
ap
tiv
e
lo
a
d
m
o
d
e
l
in
en
h
an
cin
g
PV
p
o
wer
u
tili
za
tio
n
ef
f
icien
cy
.
2.
P
V
SYST
E
M
F
O
R
M
O
T
O
R
DRIVE
AP
P
L
I
C
AT
I
O
NS
Ph
o
to
v
o
ltaic
(
PV)
p
a
n
els
g
e
n
er
ate
elec
tr
ical
p
o
wer
b
ase
d
o
n
th
e
lev
el
o
f
s
o
lar
i
r
r
ad
ian
ce
th
ey
r
ec
eiv
e
[
2
5
]
,
[
2
6
]
.
E
ac
h
ir
r
ad
i
an
ce
lev
el
co
r
r
esp
o
n
d
s
to
a
s
p
ec
if
ic
m
ax
im
u
m
p
o
wer
th
at
th
e
PV
ca
n
d
eliv
er
.
T
h
is
m
ax
im
u
m
p
o
wer
ca
n
o
n
l
y
b
e
ac
h
iev
e
d
wh
en
th
e
o
u
tp
u
t
cu
r
r
en
t
an
d
v
o
ltag
e
o
f
th
e
P
V
m
ee
t
th
e
r
eq
u
ir
e
d
co
n
d
itio
n
s
.
I
f
th
e
c
u
r
r
e
n
t
d
r
aw
n
is
eith
er
lo
wer
o
r
h
ig
h
er
th
a
n
th
e
o
p
tim
al
v
alu
e,
th
e
PV
w
ill
f
ail
to
o
p
er
ate
at
its
MPP
[
2
7
]
,
[
2
8
]
.
I
n
t
h
is
co
n
tex
t,
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
m
o
to
r
l
o
ad
b
ec
o
m
e
a
cr
itical
f
ac
to
r
in
d
eter
m
in
in
g
t
h
e
PV sy
s
tem
’
s
ab
ilit
y
to
r
ea
ch
a
n
d
m
ai
n
tain
m
ax
im
u
m
p
o
wer
p
r
o
d
u
ctio
n
[
2
9
]
.
T
h
e
PV
s
y
s
tem
as
a
s
o
u
r
ce
o
f
elec
tr
ical
en
er
g
y
is
r
ep
r
esen
t
ed
u
s
in
g
a
n
eq
u
iv
alen
t
cir
c
u
it
m
o
d
el,
as
illu
s
tr
ated
in
Fig
u
r
e
1
(
a
)
.
I
n
th
is
m
o
d
el,
th
e
PV
is
co
n
s
id
er
ed
as
a
cu
r
r
en
t
s
o
u
r
ce
.
T
h
e
MPP
th
e
PV
ca
n
d
eliv
er
is
r
ef
lecte
d
in
t
h
e
b
eh
av
io
r
o
f
th
is
eq
u
iv
alen
t
ci
r
cu
i
t.
Un
d
er
s
h
o
r
t
-
cir
cu
it
co
n
d
itio
n
s
,
as
d
escr
ib
ed
in
(
1
)
,
th
e
m
ax
im
u
m
cu
r
r
en
t
f
l
o
ws
d
ir
ec
tly
to
th
e
lo
a
d
.
I
n
co
n
tr
ast,
u
n
d
er
o
p
e
n
-
cir
cu
it
c
o
n
d
itio
n
s
,
th
e
en
tire
cu
r
r
en
t
f
lo
ws
th
r
o
u
g
h
th
e
d
i
o
d
e
co
m
p
o
n
en
t
I
D
,
ca
u
s
in
g
t
h
e
f
o
r
war
d
-
b
ias
v
o
ltag
e
to
r
e
ac
h
its
p
ea
k
v
alu
e.
C
o
n
s
eq
u
en
tly
,
th
e
ter
m
in
al
v
o
ltag
e
also
r
ea
ch
es
its
m
ax
im
u
m
lev
el,
as
s
tated
in
(
2
)
.
T
h
e
cu
r
r
en
t
o
u
t
p
u
t
f
r
o
m
th
e
PV d
u
r
in
g
ac
tiv
e
lo
ad
o
p
er
atio
n
is
s
h
o
wn
in
(
3
)
[
3
0
]
,
[
3
1
]
.
=
−
0
[
(
)
−
1
]
−
ℎ
(
1
)
=
(
0
+
1
)
(
2
)
=
−
0
(
(
+
)
−
1
)
−
(
+
ℎ
)
(
3
)
T
h
e
in
d
u
ctio
n
m
o
to
r
lo
ad
u
s
e
d
to
d
r
iv
e
th
e
p
u
m
p
ex
h
ib
its
p
o
wer
co
n
s
u
m
p
tio
n
ch
a
r
ac
ter
is
tics
th
a
t
ca
n
b
e
r
ep
r
esen
ted
u
s
in
g
a
n
e
q
u
iv
alen
t
ci
r
cu
it
m
o
d
el,
as
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
T
h
e
cu
r
r
e
n
t
f
lo
win
g
in
to
th
e
m
o
to
r
is
d
eter
m
in
e
d
b
y
th
e
o
u
tp
u
t
v
o
ltag
e
o
f
th
e
in
v
er
ter
an
d
th
e
im
p
e
d
an
ce
o
f
th
e
m
o
to
r
its
elf
.
Sev
e
r
al
s
tu
d
ies,
s
u
ch
as
th
at
co
n
d
u
cte
d
b
y
[
3
2
]
,
h
av
e
c
o
n
tr
o
lled
t
h
e
m
o
to
r
’
s
in
p
u
t
cu
r
r
e
n
t
b
y
r
eg
u
latin
g
th
e
in
v
e
r
ter
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
Mo
d
elin
g
a
n
d
a
n
a
lysi
s
o
f b
a
tt
eryless
o
ff
-
g
r
id
p
h
o
to
vo
lta
ic
w
ith
a
d
a
p
tive
mu
lti
-
mo
to
r
(
I
Wa
ya
n
S
u
t
a
ya
)
269
o
u
tp
u
t
v
o
ltag
e.
Me
an
wh
ile,
t
h
e
m
o
to
r
im
p
e
d
an
ce
is
d
ef
i
n
ed
b
y
its
r
esis
tan
ce
an
d
r
e
ac
tan
ce
,
wh
ich
ar
e
ty
p
ically
n
o
t
ac
tiv
ely
c
o
n
tr
o
l
led
b
u
t
allo
wed
to
v
ar
y
n
atu
r
ally
d
u
r
in
g
o
p
er
atio
n
.
T
h
e
m
o
to
r
r
esis
tan
ce
is
co
n
s
tan
t
an
d
ca
n
b
e
d
eter
m
i
n
ed
in
ad
v
an
ce
,
w
h
er
ea
s
th
e
r
ea
ctan
ce
d
ep
e
n
d
s
o
n
t
h
e
m
o
to
r
’
s
o
p
er
atin
g
co
n
d
itio
n
s
,
p
a
r
ticu
lar
ly
th
e
s
lip
,
wh
ich
v
a
r
ies co
n
tin
u
o
u
s
ly
d
u
r
in
g
o
p
er
atio
n
[
3
3
]
,
[
3
4
]
.
T
o
d
ate,
n
o
s
tu
d
y
h
as sp
ec
if
ically
h
ig
h
lig
h
ted
th
e
r
o
le
o
f
im
p
ed
an
ce
in
d
eter
m
i
n
in
g
th
e
m
ag
n
itu
d
e
o
f
cu
r
r
en
t
f
lo
win
g
in
to
th
e
m
o
to
r
.
T
h
is
i
n
d
icate
s
a
r
esear
ch
g
a
p
th
at
f
o
r
m
s
th
e
b
asis
f
o
r
n
o
v
elty
in
t
h
e
p
r
esen
t
s
tu
d
y
.
T
h
e
im
p
ed
an
ce
v
alu
e
r
ef
lects
th
e
o
v
e
r
all
p
e
r
f
o
r
m
an
ce
ch
ar
ac
ter
is
tics
o
f
t
h
e
m
o
to
r
lo
a
d
.
T
o
tal
im
p
ed
an
ce
p
lay
s
a
cr
u
cial
r
o
l
e
in
d
eter
m
in
in
g
th
e
s
tato
r
in
p
u
t
cu
r
r
en
t
an
d
in
f
lu
e
n
ce
s
th
e
m
o
to
r
'
s
d
y
n
am
ic
r
esp
o
n
s
e,
esp
ec
ially
d
u
r
in
g
tr
an
s
ien
t
co
n
d
itio
n
s
s
u
ch
as
s
ta
r
tu
p
o
r
lo
ad
c
h
an
g
es.
T
h
e
s
lip
v
alu
e
(
)
d
ir
ec
tly
af
f
ec
ts
th
e
m
o
to
r
im
p
ed
an
ce
mot
or
,
wh
ich
in
tu
r
n
im
p
ac
ts
b
o
t
h
th
e
cu
r
r
e
n
t
m
ag
n
itu
d
e
an
d
th
e
r
esu
ltin
g
elec
tr
o
m
ag
n
etic
to
r
q
u
e
[
3
5
]
,
[
3
6
]
.
mot
or
=
+
+
(
′
+
′
)
(
4
)
T
h
e
tr
ea
tm
en
t
o
f
th
e
lo
a
d
s
id
e
p
lay
s
a
c
r
itical
r
o
le
in
d
eter
m
in
in
g
th
e
am
o
u
n
t
o
f
p
o
wer
t
h
at
ca
n
b
e
p
r
o
d
u
ce
d
b
y
th
e
PV
p
an
el.
E
a
ch
lev
el
o
f
s
o
lar
ir
r
a
d
ian
ce
co
r
r
esp
o
n
d
s
to
a
d
i
f
f
er
en
t
MPP
.
T
o
en
s
u
r
e
th
at
th
e
PV
o
p
er
ates
at
m
ax
im
u
m
p
o
wer
u
n
d
er
v
ar
y
i
n
g
i
r
r
ad
ian
ce
co
n
d
itio
n
s
,
th
e
o
u
tp
u
t
cu
r
r
en
t
m
u
s
t
alig
n
with
t
h
e
MPP
cu
r
r
en
t,
I
mp
.
T
h
is
cu
r
r
en
t
v
alu
e
v
a
r
ies
with
ir
r
ad
ian
ce
lev
els
an
d
is
h
ig
h
ly
d
ep
en
d
e
n
t
o
n
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
co
n
n
ec
te
d
lo
ad
.
(
a)
(
b
)
Fig
u
r
e
1
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
(
a)
p
h
o
to
v
o
ltaic
s
y
s
tem
[
3
0
]
a
n
d
(
b
)
in
d
u
ctio
n
m
o
to
r
[
3
5
]
3.
M
E
T
H
O
D
T
h
e
m
o
d
el
o
f
b
atter
y
less
o
f
f
-
g
r
id
p
h
o
to
v
o
ltaic
s
y
s
tem
with
ad
ap
tiv
e
m
o
to
r
lo
ad
d
e
v
elo
p
ed
in
th
is
s
tu
d
y
is
illu
s
tr
ated
i
n
Fig
u
r
e
2
.
T
h
e
PV
ar
r
a
y
s
u
p
p
lies
elec
tr
i
ca
l
p
o
wer
b
ased
o
n
th
e
r
ec
eiv
ed
s
o
lar
ir
r
ad
ian
ce
.
I
n
th
is
m
o
d
el,
ea
c
h
m
o
to
r
is
co
n
n
ec
ted
in
p
ar
allel
with
b
o
t
h
th
e
PV
ar
r
ay
an
d
o
th
er
m
o
to
r
s
.
E
ac
h
m
o
to
r
l
o
ad
is
eq
u
ip
p
ed
with
its
o
w
n
co
n
v
er
ter
an
d
in
v
er
te
r
,
wh
ic
h
a
r
e
co
n
t
r
o
lled
b
y
a
ce
n
t
r
alize
d
co
n
tr
o
l
u
n
it.
T
h
is
co
n
tr
o
l
u
n
it
m
an
a
g
es
th
e
o
p
er
atio
n
o
f
ea
ch
m
o
to
r
d
ec
id
i
n
g
wh
eth
e
r
it
s
h
o
u
l
d
b
e
ac
t
iv
ated
o
r
n
o
t
a
n
d
d
eter
m
in
es
th
e
v
o
ltag
e
lev
el
s
u
p
p
lied
to
ea
c
h
m
o
t
o
r
lo
a
d
.
C
o
n
tr
o
l
is
ca
r
r
ied
o
u
t
b
y
ad
ju
s
tin
g
b
o
t
h
th
e
co
n
v
er
ter
an
d
i
n
v
er
ter
ass
o
ciat
ed
with
ea
ch
m
o
to
r
u
n
it.
I
n
v
ar
io
u
s
s
tu
d
ies
o
n
b
atter
y
less
PV
s
y
s
tem
s
f
o
r
p
u
m
p
o
p
e
r
atio
n
,
th
e
lo
ad
im
p
ed
an
ce
c
o
u
ld
n
o
t
b
e
ac
tiv
ely
co
n
tr
o
lled
,
as
th
e
s
y
s
tem
ty
p
ically
em
p
lo
y
ed
ei
th
er
a
s
in
g
le
lar
g
e
m
o
to
r
o
r
m
u
ltip
le
m
o
to
r
s
co
n
n
ec
ted
in
a
f
ix
e
d
co
n
f
ig
u
r
atio
n
,
ef
f
ec
tiv
ely
f
u
n
ctio
n
in
g
as
a
s
in
g
le
lar
g
e
lo
ad
[
3
7
]
,
[
3
8
]
.
I
n
co
n
tr
ast,
th
e
p
r
o
p
o
s
ed
m
o
d
el
in
t
h
is
s
tu
d
y
allo
ws
th
e
eq
u
iv
alen
t
i
m
p
ed
a
n
ce
to
b
e
ad
ju
s
ted
,
r
esem
b
lin
g
th
e
b
eh
av
io
r
o
f
a
r
h
eo
s
tat.
T
h
is
is
m
a
d
e
p
o
s
s
ib
le
th
r
o
u
g
h
th
e
u
s
e
o
f
an
ad
ap
ti
v
e
m
u
lti
-
m
o
to
r
lo
ad
,
wh
er
e
th
e
to
tal
lo
ad
ca
n
b
e
in
cr
ea
s
ed
b
y
ac
tiv
atin
g
ad
d
itio
n
al
m
o
to
r
s
.
(
PV
=
mot
o
r
)
(5
)
(
PV
⋅
PV
=
√
3
⋅
ph
⋅
ph
⋅
c
os
θ
)
(
6
)
(
mot
or
=
√
3
⋅
ph
2
mot
or
⋅
c
os
θ
)
(
7
)
m
o
t
o
r
=
(
∑
1
+
′
+
(
+
′
)
=
1
)
−
1
(
8
)
T
h
e
p
o
wer
g
en
e
r
ated
b
y
th
e
PV
p
an
el
is
ca
lcu
lated
b
ased
o
n
th
e
r
elatio
n
s
h
ip
d
escr
ib
ed
in
(
5
)
-
(
7
)
wh
er
e
mot
or
r
ep
r
esen
ts
th
e
im
p
e
d
a
n
ce
o
f
t
h
e
m
o
t
o
r
[
3
9
]
.
T
h
is
ap
p
r
o
ac
h
lim
its
th
e
s
y
s
tem
'
s
f
lex
ib
ilit
y
in
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
:
267
-
281
270
ad
ap
tin
g
to
v
a
r
iatio
n
s
in
s
o
lar
ir
r
ad
ian
ce
.
T
h
e
p
r
o
p
o
s
ed
ad
a
p
tiv
e
m
u
lti
-
m
o
to
r
m
o
d
el
ca
lcu
l
ates
th
e
PV
o
u
tp
u
t
cu
r
r
en
t
as
th
e
s
u
m
o
f
th
e
in
d
i
v
id
u
al
cu
r
r
e
n
ts
d
r
awn
b
y
ea
c
h
m
o
to
r
,
wh
e
r
e
ea
ch
m
o
to
r
o
p
er
ates
with
its
o
wn
v
o
ltag
e
an
d
im
p
ed
a
n
ce
ch
ar
ac
ter
is
tics
.
B
y
in
d
ep
en
d
en
tly
co
n
tr
o
llin
g
th
e
v
o
ltag
e
f
o
r
ea
ch
m
o
to
r
an
d
s
elec
tiv
ely
ac
tiv
atin
g
o
r
d
ea
cti
v
atin
g
m
o
to
r
s
as
n
ee
d
ed
,
th
e
s
y
s
tem
ca
n
d
y
n
am
ically
a
d
ju
s
t
its
to
tal
eq
u
iv
alen
t
im
p
ed
an
ce
,
as
f
o
r
m
u
lated
in
(
9
)
.
As
a
r
esu
lt,
p
o
wer
p
r
o
d
u
ctio
n
ca
n
m
o
r
e
clo
s
ely
ap
p
r
o
ac
h
th
e
MPP
u
n
d
e
r
v
ar
y
in
g
ir
r
ad
ian
ce
co
n
d
itio
n
s
.
T
h
e
p
r
o
p
o
s
ed
an
d
test
ed
m
o
d
el
is
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
e
m
u
lti
-
m
o
to
r
lo
ad
in
th
is
co
n
f
ig
u
r
atio
n
is
r
ep
r
esen
ted
u
s
in
g
th
r
ee
th
r
ee
-
p
h
ase
m
o
to
r
s
.
As
th
e
s
y
s
tem
im
p
lem
en
ts
a
two
-
s
tag
e
p
o
wer
co
n
v
er
s
io
n
ar
ch
itectu
r
e,
th
e
r
eg
u
latio
n
o
f
elec
tr
ical
p
o
wer
co
n
s
u
m
p
ti
o
n
f
o
r
ea
c
h
m
o
t
o
r
is
ac
h
ie
v
e
d
th
r
o
u
g
h
b
o
t
h
th
e
co
n
v
er
ter
a
n
d
in
v
e
r
ter
m
o
d
u
l
es.
T
h
e
co
n
v
er
ter
m
o
d
u
le
p
r
o
v
id
es
a
DC
o
u
tp
u
t
v
o
ltag
e,
wh
ile
th
e
in
v
er
ter
m
o
d
u
le
g
en
er
ates a
th
r
ee
-
p
h
as
e
AC
o
u
tp
u
t v
o
ltag
e
.
T
h
e
m
o
d
el
d
e
v
elo
p
ed
in
t
h
is
s
tu
d
y
was
s
im
u
lated
a
n
d
te
s
ted
u
s
in
g
MA
T
L
AB
,
as
illu
s
tr
ated
in
Fig
u
r
e
3
.
T
o
r
ep
r
esen
t
t
h
e
m
u
lti
-
m
o
to
r
lo
a
d
,
th
r
ee
th
r
ee
-
p
h
a
s
e
in
d
u
ctio
n
m
o
to
r
s
wer
e
u
s
e
d
,
ea
ch
r
ated
at
2
0
0
W
.
E
ac
h
m
o
to
r
is
eq
u
ip
p
ed
with
its
o
wn
co
n
v
er
ter
an
d
in
v
er
ter
cir
cu
itr
y
,
all
co
n
n
ec
t
ed
to
a
ce
n
tr
alize
d
co
n
tr
o
l
u
n
it.
T
h
is
co
n
tr
o
l
u
n
i
t
d
eter
m
in
es
wh
ich
m
o
to
r
s
s
h
o
u
ld
b
e
ac
tiv
ated
b
y
r
eg
u
latin
g
th
eir
r
esp
ec
tiv
e
co
n
v
er
ter
s
an
d
i
n
v
er
ter
s
.
Ad
d
itio
n
ally
,
th
e
co
n
tr
o
l
u
n
it
m
o
n
ito
r
s
th
e
PV
o
u
tp
u
t
cu
r
r
en
t
an
d
im
p
lem
en
ts
th
e
Per
tu
r
b
an
d
Ob
s
er
v
e
(
P&
O)
m
eth
o
d
to
tr
ac
k
th
e
MPP [
4
0
]
,
[
4
1
]
.
Fig
u
r
e
2
.
A
m
o
d
el
o
f
a
b
atter
y
less
o
f
f
-
g
r
id
PV sy
s
tem
with
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
lo
a
d
d
e
v
e
lo
p
ed
in
t
h
is
s
tu
d
y
Fig
u
r
e
3
.
Desig
n
a
n
d
test
in
g
o
f
a
m
o
d
el
o
f
a
b
atter
y
less
o
f
f
-
g
r
id
PV sy
s
tem
with
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
l
o
ad
d
ev
elo
p
e
d
in
th
is
s
tu
d
y
u
s
in
g
MA
T
L
AB
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
Mo
d
elin
g
a
n
d
a
n
a
lysi
s
o
f b
a
tt
eryless
o
ff
-
g
r
id
p
h
o
to
vo
lta
ic
w
ith
a
d
a
p
tive
mu
lti
-
mo
to
r
(
I
Wa
ya
n
S
u
t
a
ya
)
271
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
I
n
th
e
test
in
g
an
d
a
n
aly
s
is
p
r
o
ce
s
s
o
f
th
e
d
ev
el
o
p
ed
m
o
d
el
,
a
PV
ar
r
ay
with
a
ca
p
ac
ity
o
f
8
5
2
W
p
was
u
s
ed
.
Fig
u
r
e
4
(
a
)
p
r
esen
ts
th
e
MPP
cu
r
v
e
o
f
th
e
PV
u
n
d
er
v
ar
io
u
s
lev
els
o
f
s
o
lar
ir
r
ad
ia
n
ce
.
T
h
e
m
ax
im
u
m
p
o
wer
o
u
tp
u
t
o
f
8
5
2
W
was
ac
h
iev
ed
wh
e
n
th
e
s
o
lar
p
an
el
r
ec
eiv
ed
an
ir
r
ad
ia
n
ce
o
f
1
0
0
0
W
/m
²,
with
an
o
u
tp
u
t
cu
r
r
en
t
o
f
7
.
3
5
A.
U
n
d
er
th
is
co
n
d
itio
n
,
th
e
PV
o
u
tp
u
t
v
o
ltag
e
a
d
ju
s
ted
to
a
p
p
r
o
x
im
ately
1
1
6
V.
Me
an
wh
ile,
Fig
u
r
e
4
(
b
)
s
h
o
ws
th
e
cu
r
r
en
t
-
v
o
ltag
e
(
I
–
V)
ch
ar
ac
ter
is
tics
,
illu
s
tr
atin
g
h
o
w
th
e
PV
v
o
ltag
e
v
ar
ies with
ch
a
n
g
es in
th
e
o
u
tp
u
t c
u
r
r
en
t.
(
a)
(
b
)
Fig
u
r
e
4
.
Po
wer
p
r
o
d
u
ctio
n
g
r
ap
h
s
: (
a)
p
o
wer
o
u
t
p
u
t v
e
r
s
u
s
v
o
ltag
e
an
d
(
b
)
cu
r
r
en
t o
u
tp
u
t
f
r
o
m
th
e
PV
v
er
s
u
s
v
o
ltag
e
at
th
e
PV te
r
m
i
n
al
4
.
1
.
P
V
po
wer
o
utput
a
nd
mo
t
o
r
lo
a
d c
o
ns
um
ptio
n r
esu
l
t
s
T
h
e
s
im
u
latio
n
test
r
esu
lts
o
f
PV
p
o
wer
p
r
o
d
u
ctio
n
an
d
m
o
to
r
p
o
wer
co
n
s
u
m
p
tio
n
,
alo
n
g
with
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
m
o
to
r
lo
a
d
s
,
ar
e
p
r
esen
te
d
in
th
e
f
o
r
m
o
f
g
r
a
p
h
s
.
T
h
ese
g
r
ap
h
s
d
is
p
lay
th
e
cu
r
r
en
t
d
r
awn
b
y
ea
ch
m
o
to
r
lo
a
d
.
Oscill
atio
n
s
in
th
e
c
u
r
r
en
t
ar
e
o
b
s
er
v
ed
as
th
e
m
o
t
o
r
s
r
ea
ch
th
eir
s
tea
d
y
-
s
tate
co
n
d
itio
n
,
wh
ich
is
ca
u
s
ed
b
y
th
e
o
s
cillatin
g
elec
tr
o
m
ag
n
etic
f
o
r
ce
g
e
n
er
ated
b
y
t
h
e
m
o
to
r
s
th
at
o
p
p
o
s
es
th
e
in
co
m
in
g
cu
r
r
en
t.
D
u
r
in
g
t
h
e
s
tar
tin
g
c
o
n
d
itio
n
,
th
e
m
o
t
o
r
s
h
av
e
n
o
t
y
et
r
ea
ch
e
d
th
eir
m
a
x
im
u
m
s
p
ee
d
,
r
esu
ltin
g
in
a
r
elativ
ely
s
m
all
b
ac
k
elec
tr
o
m
o
tiv
e
f
o
r
ce
(
E
MF)
[
2
3
]
.
Fro
m
th
e
test
r
esu
lt
g
r
ap
h
s
,
th
e
tim
e
r
eq
u
ir
ed
b
y
ea
ch
m
o
to
r
to
r
ea
ch
s
tead
y
-
s
tate
co
n
d
itio
n
s
ca
n
b
e
clea
r
ly
o
b
s
er
v
ed
.
4
.
1
.
1
.
I
rr
a
dia
nce
o
f
1
0
0
0
W/m
²
wit
h
a
da
ptiv
e
m
ulti
-
m
o
t
o
r
lo
a
d
T
h
e
cu
r
r
en
t
c
o
n
s
u
m
p
tio
n
g
r
ap
h
u
n
d
er
an
ir
r
ad
ian
ce
co
n
d
itio
n
o
f
1
0
0
0
W
/m
²
is
s
h
o
wn
in
F
ig
u
r
e
5
.
I
n
Fig
u
r
e
5
(
a
)
,
th
e
cu
r
r
en
t
d
r
aw
n
b
y
Mo
to
r
1
d
u
r
in
g
th
e
in
itial
s
tar
tin
g
co
n
d
itio
n
is
r
ec
o
r
d
ed
at
7
.
3
A.
W
ith
in
ap
p
r
o
x
im
ately
0
.
7
s
ec
o
n
d
s
,
M
o
to
r
1
r
ea
ch
es
its
s
tead
y
-
s
tate
co
n
d
itio
n
,
r
esu
ltin
g
in
a
s
ig
n
if
ican
t
r
ed
u
ctio
n
in
cu
r
r
en
t
to
1
.
9
A.
Af
ter
Mo
to
r
1
r
ea
ch
es
s
tead
y
s
tate,
Mo
t
o
r
2
is
ac
tiv
ated
.
T
h
e
s
tar
tin
g
cu
r
r
en
t
d
r
awn
b
y
Mo
to
r
2
is
5
.
5
A,
an
d
it
r
ea
c
h
es
a
s
tead
y
-
s
tate
c
o
n
d
itio
n
i
n
ab
o
u
t
0
.
9
s
ec
o
n
d
s
,
as
p
r
ese
n
ted
in
Fig
u
r
e
5
(
b
)
.
Nex
t,
in
Fig
u
r
e
5
(
c
)
,
M
o
to
r
3
is
tu
r
n
ed
o
n
with
a
s
tar
tin
g
cu
r
r
en
t
o
f
4
A
an
d
r
ea
ch
es
a
s
tead
y
-
s
tate
co
n
d
itio
n
with
in
1
.
2
5
s
ec
o
n
d
s
.
On
ce
all
th
r
ee
m
o
to
r
s
h
av
e
r
ea
ch
e
d
s
t
ea
d
y
-
s
tate
o
p
e
r
atio
n
,
ea
ch
d
r
a
ws
ap
p
r
o
x
im
ately
th
e
s
am
e
cu
r
r
en
t,
ar
o
u
n
d
1
.
8
A.
T
h
e
to
tal
tim
e
r
eq
u
i
r
ed
to
r
ea
ch
s
tead
y
-
s
tate
co
n
d
itio
n
s
f
o
r
th
e
en
tire
s
y
s
tem
is
2
.
8
5
s
ec
o
n
d
s
.
T
h
is
v
alu
e
is
o
b
tain
ed
b
y
m
ea
s
u
r
i
n
g
th
e
p
ea
k
c
u
r
r
e
n
t
co
n
s
u
m
p
tio
n
d
u
r
in
g
t
h
e
s
tar
tin
g
p
r
o
ce
s
s
u
n
til
all
th
r
ee
m
o
to
r
s
r
ea
ch
s
tead
y
-
s
tate.
B
ased
o
n
Fig
u
r
e
5
(
d
)
,
th
e
to
tal
cu
r
r
en
t
d
r
awn
w
h
en
all
th
r
ee
m
o
to
r
s
ar
e
in
s
tead
y
-
s
tate
o
p
er
atio
n
is
7
.
4
7
A.
T
h
is
v
alu
e
is
v
er
y
cl
o
s
e
to
th
e
cu
r
r
e
n
t a
t th
e
MPP,
wh
ich
is
7
.
3
5
A.
T
h
e
p
o
wer
c
o
n
s
u
m
p
tio
n
g
r
ap
h
o
f
th
e
m
o
t
o
r
l
o
ad
s
u
n
d
er
1
0
0
0
W
/m
²
ir
r
ad
ian
ce
is
s
h
o
wn
i
n
Fig
u
r
e
6
.
I
n
Fig
u
r
e
6
(
a)
,
th
e
p
o
wer
co
n
s
u
m
ed
b
y
Mo
to
r
1
d
u
r
in
g
th
e
s
tar
tin
g
co
n
d
itio
n
r
ea
c
h
es
8
4
7
W
o
v
er
a
p
er
i
o
d
o
f
0
.
7
s
ec
o
n
d
s
.
Af
ter
r
ea
ch
in
g
s
tead
y
-
s
tate,
th
e
p
o
we
r
co
n
s
u
m
p
tio
n
o
f
Mo
to
r
1
d
r
o
p
s
s
ig
n
if
i
ca
n
tly
to
ar
o
u
n
d
2
0
0
W
.
On
ce
Mo
to
r
1
is
in
s
tead
y
-
s
tate,
Mo
to
r
2
is
th
e
n
ac
tiv
ate
d
,
as
p
r
esen
ted
in
Fig
u
r
e
6
(
b
)
,
co
n
s
u
m
in
g
6
5
0
W
f
o
r
ap
p
r
o
x
im
ately
0
.
9
s
ec
o
n
d
s
b
ef
o
r
e
s
tab
ilizin
g
.
Su
b
s
eq
u
en
tly
,
in
Fig
u
r
e
6
(
c
)
,
Mo
to
r
3
is
s
wi
tch
ed
o
n
,
d
r
awin
g
5
0
0
W
d
u
r
in
g
its
s
tar
tin
g
p
h
ase
an
d
r
e
q
u
ir
in
g
ab
o
u
t
1
.
2
5
s
ec
o
n
d
s
to
r
ea
c
h
s
tead
y
-
s
tate.
Ov
er
all,
th
e
g
r
ap
h
illu
s
tr
ates
th
e
p
o
wer
co
n
s
u
m
p
tio
n
c
h
ar
ac
ter
is
tics
o
f
e
ac
h
m
o
to
r
f
r
o
m
t
h
e
s
tar
tin
g
p
h
ase
to
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
.
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
:
267
-
281
272
T
h
e
t
o
t
a
l
t
i
m
e
r
e
q
u
i
r
e
d
t
o
r
e
ac
h
t
h
e
s
t
e
a
d
y
-
s
ta
t
e
c
o
n
d
it
i
o
n
is
2
.
8
5
s
e
c
o
n
d
s
.
T
h
e
p
o
w
e
r
p
r
o
d
u
c
e
d
b
y
t
h
e
P
V
s
y
s
t
e
m
t
o
b
r
i
n
g
t
h
e
t
h
r
e
e
m
o
t
o
r
s
i
n
t
o
s
t
e
a
d
y
-
s
ta
t
e
o
p
e
r
a
ti
o
n
i
s
8
4
2
W
,
as
s
h
o
w
n
i
n
F
i
g
u
r
e
6
(
d
)
.
T
h
i
s
p
o
w
e
r
l
e
v
e
l
i
s
a
l
r
e
a
d
y
v
e
r
y
c
l
o
s
e
t
o
t
h
e
M
P
P
,
w
h
i
c
h
is
8
5
2
W
.
T
h
i
s
i
n
d
i
c
a
t
es
t
h
a
t
t
h
e
PV
s
y
s
t
e
m
o
p
e
r
a
t
e
s
e
f
f
i
c
ie
n
t
l
y
,
d
e
l
i
v
e
r
i
n
g
n
e
a
r
l
y
m
a
x
i
m
u
m
a
v
a
i
l
a
b
l
e
p
o
w
e
r
d
u
r
i
n
g
t
h
e
s
t
e
a
d
y
-
s
t
a
t
e
c
o
n
d
i
t
i
o
n
o
f
t
h
e
m
u
l
ti
-
m
o
t
o
r
l
o
a
d
.
(
a)
(
b
)
(
c)
(
d
)
F
i
g
u
r
e
5
.
C
u
r
r
e
n
t
f
l
o
w
t
o
m
o
t
o
r
l
o
a
d
s
u
n
d
e
r
1
,
0
0
0
W
/
m
²
i
r
r
a
d
i
a
n
c
e
:
(
a
)
c
u
r
r
e
n
t
f
l
o
w
i
n
g
t
o
M
o
t
o
r
1
l
o
a
d
,
(
b
)
c
u
r
r
e
n
t
f
l
o
w
i
n
g
t
o
M
o
t
o
r
2
l
o
a
d
,
(
c
)
c
u
r
r
e
n
t
f
l
o
w
i
n
g
t
o
M
o
t
o
r
3
l
o
a
d
,
a
n
d
(
d
)
t
o
t
a
l
c
u
r
r
e
n
t
o
u
t
p
u
t
f
r
o
m
t
h
e
P
V
(
a)
(
b
)
(
c)
(
d
)
F
i
g
u
r
e
6
.
P
o
w
e
r
c
o
n
s
u
m
p
t
i
o
n
b
y
m
o
t
o
r
l
o
a
d
s
u
n
d
e
r
1
0
0
0
W
/
m
²
i
r
r
a
d
i
a
n
c
e
:
(
a
)
p
o
w
e
r
c
o
n
s
u
m
e
d
b
y
M
o
t
o
r
1
l
o
a
d
,
(
b
)
p
o
w
e
r
c
o
n
s
u
m
e
d
b
y
M
o
t
o
r
2
l
o
a
d
,
(
c
)
p
o
w
e
r
c
o
n
s
u
m
e
d
b
y
M
o
t
o
r
3
l
o
a
d
,
a
n
d
(
d
)
p
o
w
e
r
p
r
o
d
u
c
e
d
b
y
PV
T
h
e
m
o
to
r
s
p
ee
d
g
r
a
p
h
,
u
s
ed
as
an
in
d
icato
r
o
f
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
o
f
th
e
m
o
to
r
lo
ad
s
u
n
d
er
1
0
0
0
W
/m
²
ir
r
ad
ian
ce
,
is
s
h
o
wn
in
Fig
u
r
e
7
.
T
h
e
m
a
x
im
u
m
m
o
to
r
s
p
ee
d
o
f
1
5
0
0
r
p
m
i
s
ac
h
iev
ed
at
s
tead
y
-
s
tate.
T
h
is
s
p
ee
d
also
s
er
v
es
as
an
in
d
icato
r
th
at
th
e
m
o
to
r
h
as
r
ea
ch
e
d
its
s
tead
y
o
p
er
atin
g
co
n
d
itio
n
.
I
n
Fig
u
r
e
7
(
a
)
,
Mo
t
o
r
1
tak
es
0
.
7
s
ec
o
n
d
s
to
r
ea
ch
s
tead
y
-
s
tate.
I
n
Fig
u
r
e
7
(
b
)
,
Mo
to
r
2
r
e
q
u
ir
es
0
.
9
s
ec
o
n
d
s
,
wh
ile
in
Fig
u
r
e
7
(
c)
,
Mo
to
r
3
tak
es
1
.
2
5
s
ec
o
n
d
s
t
o
r
ea
ch
s
tead
y
-
s
tate.
Fig
u
r
e
7
(
d
)
s
h
o
w
s
th
e
v
o
ltag
e
at
th
e
PV te
r
m
in
al.
4
.
1
.
2
.
I
rr
a
dia
nce
o
f
9
0
0
W/
m
²
wit
h a
da
ptiv
e
m
ulti
-
m
o
t
o
r
m
o
del
W
h
en
th
e
PV r
ec
eiv
es ir
r
ad
ian
ce
o
f
9
0
0
W
/m
²,
Mo
to
r
1
is
ac
tiv
ated
f
ir
s
t u
n
til it r
ea
ch
es st
ea
d
y
-
s
tate.
T
h
e
cu
r
r
en
t
f
l
o
win
g
to
Mo
to
r
1
d
u
r
in
g
th
e
tr
a
n
s
itio
n
to
s
te
ad
y
-
s
tate
is
s
h
o
wn
in
Fig
u
r
e
8
(
a)
.
I
t
ca
n
b
e
s
ee
n
th
at
a
cu
r
r
en
t
o
f
6
.
8
A
f
l
o
ws
to
Mo
to
r
1
f
o
r
0
.
8
s
ec
o
n
d
s
.
Af
ter
th
at,
Mo
t
o
r
1
r
ea
c
h
es
s
tead
y
-
s
tate
an
d
d
r
aws
a
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
Mo
d
elin
g
a
n
d
a
n
a
lysi
s
o
f b
a
tt
eryless
o
ff
-
g
r
id
p
h
o
to
vo
lta
ic
w
ith
a
d
a
p
tive
mu
lti
-
mo
to
r
(
I
Wa
ya
n
S
u
t
a
ya
)
273
s
m
aller
cu
r
r
en
t o
f
1
.
8
A.
Nex
t
,
as sh
o
wn
in
Fig
u
r
e
8
(
b
)
,
Mo
to
r
2
is
ac
tiv
ated
,
d
r
awin
g
a
cu
r
r
en
t o
f
4
.
9
A
f
o
r
1
s
ec
o
n
d
.
Su
b
s
eq
u
en
tly
,
in
Fig
u
r
e
8
(
c
)
,
M
o
to
r
3
is
tu
r
n
e
d
o
n
,
d
r
awin
g
3
.
2
A
a
n
d
r
eq
u
ir
in
g
2
.
5
s
ec
o
n
d
s
to
r
ea
ch
s
tead
y
-
s
tate.
T
h
e
g
r
ap
h
o
f
th
e
cu
r
r
en
t
o
u
tp
u
t
f
r
o
m
th
e
PV is sh
o
wn
in
Fig
u
r
e
8
(
d
)
.
T
h
e
to
tal
tim
e
r
eq
u
ir
ed
f
o
r
a
ll
m
o
to
r
s
to
r
ea
c
h
s
tead
y
-
s
tate
is
4
.
3
s
ec
o
n
d
s
.
T
h
e
cu
r
r
en
t
d
r
awn
t
o
b
r
in
g
t
h
e
th
r
ee
m
o
t
o
r
s
in
to
s
tead
y
-
s
tate
o
p
e
r
atio
n
is
6
.
7
A,
a
s
s
h
o
wn
in
Fig
u
r
e
8
(
d
)
.
T
h
is
c
u
r
r
en
t v
alu
e
is
v
er
y
clo
s
e
to
th
e
MPP c
u
r
r
en
t,
wh
i
ch
is
6
.
6
2
A.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
7
.
I
r
r
ad
ia
n
ce
o
f
1
0
0
0
W
/m
²
with
PW
M
3
0
an
d
m
o
d
u
latio
n
in
d
e
x
0
.
8
5
: (
a)
Mo
to
r
1
s
p
ee
d
r
ea
c
h
in
g
s
tead
y
-
s
tate,
(
b
)
Mo
to
r
2
s
p
ee
d
r
ea
ch
in
g
s
tead
y
-
s
tate,
(
c)
M
o
to
r
3
s
p
ee
d
r
ea
ch
i
n
g
s
tead
y
-
s
tate,
an
d
(
d
)
v
o
ltag
e
at
th
e
PV te
r
m
in
al
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
8
.
C
u
r
r
e
n
t f
lo
w
to
m
o
t
o
r
lo
ad
s
u
n
d
er
9
0
0
W
/m
²
ir
r
ad
ian
ce
with
ad
ap
tiv
e
m
u
lti
-
m
o
t
o
r
co
n
f
ig
u
r
atio
n
:
(
a)
cu
r
r
en
t in
Mo
t
o
r
1
,
(
b
)
cu
r
r
en
t in
Mo
to
r
2
,
(
c
)
cu
r
r
en
t in
Mo
to
r
3
,
(
d
)
t
o
tal
cu
r
r
e
n
t f
r
o
m
th
e
PV
T
h
e
p
o
wer
co
n
s
u
m
p
tio
n
o
f
th
e
m
o
to
r
l
o
ad
s
u
n
d
er
a
n
ir
r
a
d
ian
ce
lev
el
o
f
9
0
0
W
/m
²
is
illu
s
tr
ated
in
Fig
u
r
e
9
.
As
s
h
o
w
n
in
Fig
u
r
e
9
(
a)
,
Mo
to
r
1
co
n
s
u
m
es
7
6
1
W
d
u
r
in
g
th
e
s
tar
tin
g
-
s
tate
co
n
d
itio
n
,
wh
ich
last
s
f
o
r
ap
p
r
o
x
im
atel
y
0
.
8
s
ec
o
n
d
s
.
Af
ter
r
ea
ch
in
g
s
tead
y
-
s
tate,
its
p
o
wer
co
n
s
u
m
p
tio
n
d
ec
r
ea
s
es
s
ig
n
if
ican
tly
to
2
0
0
W
.
Un
d
er
th
is
co
n
d
itio
n
,
Mo
to
r
2
is
th
en
ac
tiv
ated
,
d
r
awin
g
5
6
2
W
f
o
r
ab
o
u
t
1
s
e
co
n
d
,
as
s
h
o
wn
in
Fig
u
r
e
9
(
b
)
.
Su
b
s
eq
u
en
tly
,
M
o
to
r
3
is
s
witch
ed
o
n
an
d
co
n
s
u
m
es
3
6
0
W
d
u
r
in
g
its
s
tar
tin
g
-
s
tate
co
n
d
itio
n
.
Mo
to
r
3
r
eq
u
ir
es
ap
p
r
o
x
im
ately
2
.
5
s
ec
o
n
d
s
to
r
ea
c
h
s
tead
y
-
s
tate,
as
d
ep
icted
in
Fig
u
r
e
9
(
c
)
.
T
h
e
t
o
tal
m
ax
im
u
m
p
o
wer
th
at
ca
n
b
e
p
r
o
d
u
ce
d
,
7
6
0
W
,
is
p
r
esen
ted
i
n
Fig
u
r
e
9
(
d
)
.
T
h
e
av
e
r
ag
e
p
o
wer
g
e
n
er
ate
d
b
y
th
e
PV
s
y
s
tem
to
b
r
in
g
th
e
th
r
ee
m
o
t
o
r
l
o
ad
s
to
s
tead
y
-
s
tate
co
n
d
itio
n
is
7
6
0
W
.
Me
an
wh
i
le,
th
e
MPP
o
f
th
e
PV
u
n
d
e
r
an
ir
r
a
d
ian
ce
lev
el
o
f
9
0
0
W
/m
²
is
7
6
5
W
.
T
h
is
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
:
267
-
281
274
in
d
icate
s
th
at
th
e
p
o
wer
p
r
o
d
u
ce
d
b
y
th
e
PV
is
v
er
y
cl
o
s
e
to
its
m
ax
im
u
m
p
o
wer
p
o
in
t,
d
em
o
n
s
tr
atin
g
th
at
th
e
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
lo
ad
m
o
d
el
o
p
er
ates e
f
f
icien
tly
an
d
o
p
tim
ally
in
u
tili
zin
g
th
e
av
ai
lab
le
p
o
wer
.
T
h
e
g
r
ap
h
illu
s
tr
atin
g
th
e
s
p
ee
d
o
f
ea
ch
m
o
to
r
lo
ad
is
s
h
o
wn
in
Fig
u
r
e
1
0
.
T
h
e
m
o
to
r
s
p
ee
d
g
r
ap
h
s
er
v
es
as
an
in
d
icato
r
o
f
wh
e
n
ea
ch
m
o
to
r
r
ea
c
h
es
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
.
Stead
y
-
s
tat
e
is
ac
h
iev
ed
wh
en
th
e
m
o
to
r
r
ea
c
h
es
a
s
p
ee
d
o
f
1
5
0
0
r
p
m
.
T
h
e
f
ig
u
r
e
d
is
p
lay
s
th
e
s
p
ee
d
p
r
o
f
ile
o
f
ea
c
h
m
o
to
r
as
it
a
p
p
r
o
a
ch
es
s
tead
y
-
s
tate.
R
esp
ec
tiv
ely
,
Fi
g
u
r
es
1
0
(
a
)
-
1
0
(
c)
s
h
o
w
th
e
a
b
ilit
y
o
f
Mo
to
r
1
,
M
o
to
r
2
,
a
n
d
Mo
to
r
3
t
o
r
ea
ch
s
tead
y
-
s
tate
co
n
d
itio
n
s
with
in
0
.
8
s
,
1
.
0
s
,
an
d
1
.
5
s
.
Me
an
wh
ile,
Fig
u
r
e
1
0
(
d
)
p
r
esen
ts
th
e
o
u
t
p
u
t
v
o
ltag
e
o
f
th
e
PV sy
s
tem
.
(
a)
(
b
)
(
d
)
(
d
)
Fig
u
r
e
9
.
Po
wer
c
o
n
s
u
m
p
tio
n
b
y
m
o
t
o
r
lo
ad
s
u
n
d
er
9
0
0
W
/m
²
ir
r
ad
ian
ce
: (
a)
p
o
wer
co
n
s
u
m
ed
b
y
Mo
to
r
1
lo
ad
,
(
b
)
p
o
we
r
co
n
s
u
m
e
d
b
y
Mo
to
r
2
lo
a
d
,
(
c
)
p
o
we
r
co
n
s
u
m
ed
b
y
Mo
to
r
3
lo
ad
,
an
d
(
d
)
to
tal
p
o
wer
p
r
o
d
u
ce
d
b
y
th
e
PV
(
a)
(
b
)
(
c)
(
b
)
Fig
u
r
e
1
0
.
Mo
to
r
l
o
ad
s
p
ee
d
u
n
d
er
9
0
0
W
/m
²
ir
r
ad
ia
n
ce
: (
a)
s
p
ee
d
o
f
Mo
t
o
r
1
l
o
ad
,
(
b
)
s
p
e
ed
o
f
Mo
t
o
r
2
lo
ad
,
(
c)
s
p
ee
d
o
f
Mo
to
r
3
lo
a
d
,
an
d
(
d
)
PV o
u
tp
u
t
v
o
ltag
e
4
.
1
.
3
.
I
rr
a
dia
nce
o
f
1
0
0
0
W/
m
²
wit
h f
ix
ed
m
ulti
-
m
o
t
o
r
c
o
nfig
ura
t
io
n
As a
co
m
p
ar
is
o
n
to
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
lo
ad
m
o
d
el
d
ev
elo
p
ed
i
n
th
is
s
tu
d
y
,
a
test
was
also
co
n
d
u
cted
u
s
in
g
a
f
i
x
ed
m
u
lti
-
m
o
to
r
co
n
f
i
g
u
r
atio
n
with
th
e
s
am
e
l
o
ad
.
T
h
is
ty
p
e
o
f
lo
a
d
s
er
v
es
as
a
r
ep
r
esen
tatio
n
o
f
th
e
s
tu
d
y
p
r
esen
ted
in
[
4
]
,
[
5
]
.
I
n
th
is
s
ce
n
ar
io
,
th
e
th
r
ee
m
o
to
r
lo
a
d
s
wer
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
6
9
4
Mo
d
elin
g
a
n
d
a
n
a
lysi
s
o
f b
a
tt
eryless
o
ff
-
g
r
id
p
h
o
to
vo
lta
ic
w
ith
a
d
a
p
tive
mu
lti
-
mo
to
r
(
I
Wa
ya
n
S
u
t
a
ya
)
275
co
n
n
ec
ted
in
a
f
ix
ed
m
an
n
e
r
with
o
u
t
em
p
lo
y
in
g
an
a
d
ap
tiv
e
co
n
tr
o
l
s
y
s
tem
.
T
h
is
co
n
f
ig
u
r
atio
n
ca
n
also
b
e
co
n
s
id
er
ed
as a
r
e
p
r
esen
tatio
n
o
f
a
s
in
g
le
lar
g
e
m
o
to
r
with
an
eq
u
iv
alen
t to
tal
p
o
wer
r
atin
g
.
Fig
u
r
e
1
1
illu
s
tr
ates
th
e
cu
r
r
e
n
t
co
n
s
u
m
p
tio
n
o
f
ea
ch
m
o
to
r
an
d
th
e
to
tal
c
u
r
r
en
t
o
u
tp
u
t
f
r
o
m
th
e
PV
u
n
d
er
th
e
f
ix
ed
co
n
f
ig
u
r
atio
n
.
Fig
u
r
es 1
1
(
a)
–
11
(
c
)
illu
s
tr
ate
th
at
Mo
to
r
s
1
,
2
,
a
n
d
3
c
o
n
s
u
m
e
th
e
s
am
e
cu
r
r
en
t
o
f
2
.
5
9
A.
Fig
u
r
e
1
1
(
d
)
illu
s
tr
ates th
at
th
e
to
tal
cu
r
r
en
t d
r
awn
b
y
th
e
th
r
ee
m
o
to
r
s
is
7
.
7
7
A,
wh
er
ea
s
th
e
id
ea
l
cu
r
r
en
t
r
e
q
u
ir
e
d
f
o
r
th
e
PV
to
o
p
er
ate
at
its
m
ax
im
u
m
p
o
wer
p
o
in
t
(
MPP)
is
7
.
3
5
A
.
T
h
is
d
is
cr
ep
an
cy
in
d
icate
s
th
at
th
e
PV sy
s
tem
is
n
o
t o
p
er
atin
g
at
its
m
ax
im
u
m
p
o
wer
p
o
in
t,
lead
i
n
g
to
s
u
b
o
p
tim
al
u
tili
za
tio
n
o
f
th
e
av
ailab
le
p
o
wer
.
As a
r
esu
lt,
th
e
o
v
er
all
ef
f
icien
cy
o
f
th
e
PV sy
s
tem
in
th
is
co
n
f
ig
u
r
ati
o
n
is
r
ed
u
ce
d
.
Fig
u
r
es
1
2
(
a)
-
1
2
(
c)
illu
s
tr
at
e
th
at
ea
ch
m
o
to
r
co
n
s
u
m
es
9
9
W
,
r
esu
ltin
g
in
a
to
tal
p
o
wer
co
n
s
u
m
p
tio
n
o
f
2
9
8
W
,
as
p
r
esen
ted
in
Fig
u
r
e
1
2
(
d
)
.
T
h
is
v
alu
e
is
s
ig
n
if
ican
tly
lo
wer
t
h
an
th
e
m
ax
im
u
m
ca
p
ac
ity
o
f
t
h
e
PV,
wh
ich
is
c
ap
ab
le
o
f
d
eliv
er
in
g
u
p
to
8
5
2
W
at
th
e
MPP.
Du
r
in
g
th
e
5
-
s
ec
o
n
d
s
im
u
latio
n
,
all
m
o
to
r
s
r
em
ain
ed
in
th
e
s
tar
tin
g
co
n
d
itio
n
,
an
d
n
o
n
e
o
f
th
em
r
ea
ch
ed
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
.
T
h
is
o
u
tco
m
e
in
d
icate
s
th
at
th
e
f
ix
ed
m
u
lti
-
m
o
to
r
co
n
f
ig
u
r
atio
n
is
u
n
ab
le
to
u
tili
ze
th
e
av
aila
b
le
p
o
wer
f
r
o
m
th
e
PV e
f
f
ec
tiv
ely
,
r
esu
ltin
g
in
in
ef
f
icien
t o
v
er
all
s
y
s
tem
p
e
r
f
o
r
m
an
ce
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
1
.
C
u
r
r
en
t f
l
o
w
to
m
o
to
r
lo
ad
s
u
n
d
er
1
,
0
0
0
W
/m
²
ir
r
ad
ian
ce
with
s
tatically
co
n
n
ec
ted
m
o
to
r
l
o
ad
s
:
(
a)
cu
r
r
en
t in
Mo
t
o
r
1
,
(
b
)
cu
r
r
en
t in
Mo
to
r
2
,
(
c
)
cu
r
r
en
t in
Mo
to
r
3
,
a
n
d
(
d
)
to
tal
c
u
r
r
e
n
t
f
r
o
m
th
e
PV
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
2
.
I
r
r
a
d
ian
ce
o
f
1
0
0
0
W
/m
²
with
s
tatical
ly
co
n
n
ec
te
d
m
o
to
r
lo
ad
s
(
a)
p
o
wer
c
o
n
s
u
m
ed
b
y
Mo
to
r
1
lo
ad
,
(
b
)
p
o
we
r
co
n
s
u
m
e
d
b
y
Mo
to
r
2
lo
a
d
,
(
c
)
p
o
we
r
co
n
s
u
m
ed
b
y
Mo
to
r
3
lo
ad
,
an
d
(
d
)
to
tal
p
o
wer
p
r
o
d
u
ce
d
b
y
th
e
PV
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
:
267
-
281
276
T
h
e
m
o
to
r
s
p
ee
d
r
esu
ltin
g
f
r
o
m
th
e
f
ix
ed
m
u
lti
-
m
o
to
r
co
n
f
ig
u
r
atio
n
,
u
s
ed
as
a
co
m
p
ar
is
o
n
to
th
e
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
lo
ad
m
o
d
el,
is
s
h
o
wn
in
Fig
u
r
e
1
3
.
B
ased
o
n
th
e
s
im
u
latio
n
r
esu
lts
,
th
e
m
ax
im
u
m
s
p
ee
d
ac
h
iev
ed
b
y
ea
ch
m
o
to
r
was
o
n
ly
5
0
0
r
p
m
,
as
illu
s
tr
ated
i
n
Fig
u
r
es
1
3
(
a
)
–
1
3
(
c)
,
wh
ich
is
s
ig
n
if
ican
tly
lo
wer
th
an
th
e
ex
p
ec
ted
s
tead
y
-
s
tate
s
p
ee
d
o
f
1
5
0
0
r
p
m
.
T
h
is
i
n
d
i
ca
tes
th
at
th
e
m
o
to
r
s
f
ailed
t
o
r
ea
ch
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
d
u
r
in
g
th
e
s
im
u
latio
n
p
er
io
d
.
Fig
u
r
e
1
3
(
d
)
s
h
o
ws th
e
PV o
u
tp
u
t v
o
ltag
e,
wh
ich
is
n
o
tab
ly
lo
w.
T
h
is
v
o
ltag
e
d
r
o
p
was
ca
u
s
ed
b
y
th
e
h
ig
h
cu
r
r
en
t
d
r
aw
n
s
im
u
ltan
eo
u
s
ly
b
y
all
th
r
ee
m
o
to
r
s
.
T
h
e
to
tal
cu
r
r
en
t
ex
ce
ed
ed
th
e
o
p
tim
al
cu
r
r
en
t
at
th
e
MPP,
p
r
ev
e
n
tin
g
th
e
PV
f
r
o
m
o
p
er
atin
g
e
f
f
icien
tl
y
.
As
a
r
esu
lt,
th
e
s
y
s
tem
’
s
o
v
er
all
ef
f
icien
cy
wa
s
s
ig
n
if
ican
tly
r
ed
u
ce
d
[
4
2
]
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
3
.
I
r
r
a
d
ian
ce
o
f
1
0
0
0
W
/m
²
with
s
tatical
ly
co
n
n
ec
te
d
m
o
to
r
:
(
a)
s
p
ee
d
o
f
Mo
t
o
r
1
,
(
b
)
s
p
ee
d
o
f
Mo
t
o
r
2
,
(
c)
s
p
ee
d
o
f
Mo
t
o
r
3
,
an
d
(
d
)
o
u
tp
u
t v
o
ltag
e
at
th
e
PV te
r
m
in
al
4
.
2
.
Ana
ly
s
is
o
f
t
est
da
t
a
re
s
ults
T
ab
le
1
p
r
o
v
id
es
r
ef
er
e
n
ce
v
al
u
es
f
o
r
PV
p
o
wer
o
u
tp
u
t
at
th
e
m
ax
im
u
m
p
o
we
r
p
o
in
t
u
n
d
e
r
d
if
f
e
r
en
t
lev
els
o
f
s
o
lar
ir
r
a
d
ian
ce
.
Fo
r
th
e
PV
m
o
d
u
le
u
s
ed
in
t
h
is
s
tu
d
y
,
r
ated
at
8
5
2
W
p
,
th
e
s
y
s
tem
d
eliv
er
s
8
5
2
W
o
f
p
o
wer
u
n
d
e
r
an
ir
r
ad
ian
ce
o
f
1
0
0
0
W
/m
²,
ass
u
m
in
g
a
lo
a
d
cu
r
r
e
n
t o
f
7
.
5
A.
At
9
0
0
W
/m
²,
th
e
PV p
r
o
d
u
ce
s
7
6
5
W
wh
en
th
e
lo
ad
d
r
aws
7
A
o
f
cu
r
r
e
n
t,
a
n
d
s
o
f
o
r
th
f
o
r
o
th
er
ir
r
ad
ian
c
e
lev
els.
T
h
e
d
ata
i
n
th
is
tab
le
s
er
v
e
as
a
r
ef
er
en
ce
f
o
r
ev
alu
atin
g
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
m
o
d
el
o
f
a
b
atter
y
less
o
f
f
-
g
r
i
d
PV
s
y
s
tem
with
ad
ap
tiv
e
m
u
lti
-
m
o
to
r
lo
a
d
d
e
v
elo
p
ed
in
t
h
is
s
tu
d
y
.
T
h
e
m
ea
s
u
r
em
en
t
r
esu
lts
f
r
o
m
th
e
o
v
er
all
p
o
wer
p
r
o
d
u
cti
o
n
test
u
s
in
g
th
e
m
o
d
el
o
f
a
b
atter
y
less
o
f
f
-
g
r
id
PV
s
y
s
tem
with
a
d
a
p
tiv
e
m
u
lti
-
m
o
to
r
lo
ad
ar
e
p
r
esen
ted
in
T
ab
le
2
.
Fo
r
th
e
p
o
wer
p
r
o
d
u
ctio
n
an
aly
s
is
u
n
d
er
a
n
ir
r
a
d
ian
ce
l
ev
el
o
f
1
0
0
0
W
/m
²,
th
e
PV
p
r
o
d
u
ce
d
an
a
v
er
ag
e
p
o
wer
o
u
t
p
u
t
o
f
8
4
2
W
.
T
h
is
v
alu
e
r
ep
r
esen
ts
th
e
av
e
r
ag
e
p
o
wer
r
eq
u
ir
ed
d
u
r
in
g
th
e
o
p
er
atio
n
to
b
r
in
g
th
e
t
h
r
ee
m
o
to
r
s
to
s
tead
y
-
s
tate
co
n
d
itio
n
s
.
W
h
en
all
th
r
e
e
m
o
to
r
s
wer
e
in
th
e
s
tar
tin
g
co
n
d
itio
n
,
Mo
to
r
1
r
ec
ei
v
ed
p
o
w
er
(
Pm
1
)
o
f
8
4
7
W
,
Mo
to
r
2
(
Pm
2
)
r
ec
eiv
ed
6
4
3
W
,
an
d
Mo
to
r
3
(
Pm
3
)
r
ec
eiv
ed
4
4
0
W
.
I
t
is
n
o
ted
th
at
ea
c
h
m
o
to
r
co
n
s
u
m
es
2
0
0
W
wh
en
o
p
e
r
atin
g
in
a
s
tead
y
s
tate.
B
ased
o
n
th
e
5
-
s
ec
o
n
d
test
d
u
r
atio
n
,
Mo
to
r
1
r
ea
ch
ed
s
tead
y
s
tate
i
n
0
.
7
s
ec
o
n
d
s
,
wh
ile
Mo
to
r
2
an
d
Mo
to
r
3
r
eq
u
ir
ed
0
.
9
s
ec
o
n
d
s
an
d
1
.
2
5
s
ec
o
n
d
s
,
r
esp
ec
tiv
e
ly
.
T
h
e
n
e
x
t
a
n
a
l
y
s
i
s
f
o
c
u
s
e
s
o
n
t
h
e
m
e
a
s
u
r
e
m
e
n
t
r
e
s
u
l
t
s
u
n
d
e
r
a
n
i
r
r
a
d
i
a
n
c
e
l
e
v
e
l
o
f
9
0
0
W
/
m
²
.
T
h
e
p
o
w
e
r
g
e
n
e
r
a
t
e
d
b
y
t
h
e
P
V
(
P
p
v
)
w
a
s
7
6
5
W
.
D
u
r
i
n
g
t
h
e
5
-
s
e
c
o
n
d
t
e
s
t
d
u
r
a
t
i
o
n
,
a
l
l
m
o
t
o
r
l
o
a
d
s
w
e
r
e
a
b
l
e
t
o
r
e
a
c
h
t
h
e
s
t
e
a
d
y
-
s
t
a
t
e
c
o
n
d
i
t
i
o
n
.
I
n
t
h
i
s
s
t
r
a
t
e
g
y
,
M
o
t
o
r
1
w
a
s
s
e
t
t
o
c
o
n
s
u
m
e
7
6
5
W
o
f
p
o
w
e
r
,
w
h
i
l
e
t
h
e
s
u
b
s
e
q
u
e
n
t
m
o
t
o
r
l
o
a
d
s
c
o
n
s
u
m
e
d
5
6
2
W
a
n
d
3
6
0
W
,
r
e
s
p
e
c
t
i
v
e
l
y
.
E
a
c
h
m
o
t
o
r
c
o
n
s
u
m
e
s
2
0
0
W
w
h
e
n
o
p
e
r
a
t
i
n
g
i
n
a
s
t
e
a
d
y
s
t
a
t
e
.
T
h
e
t
o
t
a
l
t
i
m
e
r
e
q
u
i
r
e
d
f
o
r
a
l
l
m
o
t
o
r
s
t
o
r
e
a
c
h
t
h
e
s
t
e
a
d
y
-
s
t
a
t
e
c
o
n
d
i
t
i
o
n
w
a
s
3
.
3
s
e
c
o
n
d
s
.
At
th
e
lo
west
ir
r
ad
ian
ce
lev
el
o
f
4
0
0
W
/m
²,
th
e
PV
s
y
s
tem
was
ab
le
to
g
en
e
r
ate
2
0
0
W
o
f
p
o
we
r
.
Un
d
er
th
is
co
n
d
itio
n
,
th
e
s
y
s
t
em
co
u
ld
o
n
ly
o
p
er
ate
a
s
in
g
l
e
m
o
to
r
lo
a
d
.
T
h
e
s
y
s
tem
m
a
n
ag
ed
to
r
e
g
u
late
th
e
p
o
wer
co
n
s
u
m
p
tio
n
o
f
Mo
to
r
1
d
u
r
in
g
th
e
s
tar
tin
g
s
tate
b
y
s
u
p
p
ly
in
g
it
with
2
0
0
W
eq
u
i
v
alen
t
to
th
e
p
o
wer
ty
p
ically
co
n
s
u
m
ed
in
th
e
s
tead
y
-
s
tate
co
n
d
itio
n
.
Ho
wev
e
r
,
in
th
is
ca
s
e,
th
e
p
o
wer
was
co
n
tr
o
lled
s
o
th
at
Mo
to
r
1
co
n
s
u
m
ed
2
0
0
W
f
r
o
m
th
e
b
eg
i
n
n
in
g
o
f
th
e
s
tar
t
in
g
s
tate.
As
a
r
esu
lt,
Mo
to
r
1
was
ab
le
to
r
ea
ch
s
tead
y
s
tate
with
in
5
s
ec
o
n
d
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.