I
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l J
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urna
l o
f
Appl
ied P
o
wer
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ng
i
neer
ing
(
I
J
AP
E
)
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
,
p
p
.
6
3
1
~
6
3
9
I
SS
N:
2252
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7
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DOI
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p
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ia
esco
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co
m/
Effec
t
o
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DC lin
k
ca
pa
citor sho
rt
-
ci
rcuit
o
n an
inv
ert
er f
ed
induction
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tor
performa
nce
Cheik
h O
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a
a
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t
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ne
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Arbih M
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2
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1
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2
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5
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ted
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u
n
2
3
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2
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In
d
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c
ti
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m
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o
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a
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d
in
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tri
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m
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is
a
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th
a
t
m
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o
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th
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m
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to
rs
a
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c
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ll
e
d
b
y
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q
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e
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s.
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d
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stin
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ters
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th
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m
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a
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b
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m
a
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c
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to
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n
.
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h
e
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o
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tro
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m
s
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se
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fo
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in
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strial
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te
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sc
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e
n
h
a
n
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f
t
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m
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sy
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m
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lt
s
a
ffe
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t
th
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ste
m
a
s
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le.
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t
h
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p
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d
d
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o
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a
n
in
d
u
c
ti
o
n
m
o
to
r
d
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n
b
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in
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sim
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latio
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su
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th
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m
o
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r
is an
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l
y
z
e
d
a
n
d
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n
terp
re
ted
.
K
ey
w
o
r
d
s
:
B
ac
k
E
MF
DC
lin
k
ca
p
ac
ito
r
I
GB
T
I
n
d
u
ctio
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m
o
to
r
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n
v
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ter
MA
T
L
AB
/S
im
u
lin
k
Sh
o
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t
-
cir
cu
it
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
:
C
h
eik
h
Ou
d
aa
Un
ité
d
e
R
ec
h
er
ch
e
Ap
p
liq
u
é
e
au
x
E
n
e
r
g
ies R
en
o
u
v
ela
b
les,
E
au
et
E
n
v
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em
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t (
UR
A3
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)
,
FS
T
UN
d
e
No
u
ak
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tt
Ksar
C
ar
af
f
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r
C
h
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if
,
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o
u
k
c
h
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tt,
Ma
u
r
itan
ia
E
m
ail:
ch
eik
h
o
u
d
aa
4
@
g
m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
s
q
u
ir
r
el
ca
g
e
i
n
d
u
ctio
n
m
o
to
r
(
I
M)
is
wid
ely
r
ec
o
g
n
i
ze
d
as
o
n
e
o
f
th
e
m
o
s
t
co
m
m
o
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ly
u
s
ed
elec
tr
o
m
ec
h
an
ical
e
n
er
g
y
co
n
v
er
ter
in
v
ar
i
o
u
s
f
ield
s
,
in
c
lu
d
in
g
in
d
u
s
tr
y
a
n
d
tr
an
s
p
o
r
t
.
Mo
d
er
n
elec
tr
ical
d
r
iv
e
s
y
s
tem
s
ar
e
h
ig
h
ly
d
ep
en
d
en
t
o
n
th
e
c
o
n
tr
o
l
o
f
in
d
u
ctio
n
m
o
to
r
s
.
Pu
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
is
o
n
e
o
f
th
e
m
o
s
t w
ell
-
k
n
o
wn
c
o
n
tr
o
l te
ch
n
iq
u
es [
1
]
.
T
h
an
k
s
to
th
e
d
ev
elo
p
m
en
t
o
f
p
o
wer
elec
tr
o
n
ics,
th
e
co
n
t
r
o
l
m
ec
h
an
is
m
s
f
o
r
th
ese
m
o
to
r
s
h
av
e
b
ec
o
m
e
s
im
p
ler
an
d
m
o
r
e
ec
o
n
o
m
ical,
ac
h
iev
in
g
p
er
f
o
r
m
a
n
ce
s
im
ilar
to
th
at
o
f
D
C
m
o
to
r
s
.
Ho
wev
er
,
th
e
ex
ten
s
iv
e
u
tili
za
tio
n
o
f
i
n
d
u
c
tio
n
m
o
t
o
r
s
in
p
r
o
ce
s
s
au
t
o
m
atio
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h
as
r
aised
co
n
ce
r
n
s
ab
o
u
t
th
eir
r
eliab
ilit
y
u
n
d
er
d
if
f
e
r
en
t
f
au
lt
co
n
d
itio
n
s
.
Mo
to
r
s
ca
n
b
e
p
ar
t
o
f
b
asic
d
r
iv
e
s
y
s
tem
s
[
2
]
,
[
3
]
o
r
m
o
r
e
co
m
p
lex
s
y
s
tem
s
s
u
ch
as
win
d
en
er
g
y
co
n
v
er
s
io
n
s
y
s
tem
s
[
4
]
.
T
h
e
y
ca
n
b
e
p
o
wer
ed
b
y
co
n
v
en
tio
n
al
in
v
er
ter
s
o
r
m
at
r
i
x
in
v
er
ter
s
[
5
]
.
T
h
e
r
esear
c
h
co
m
m
u
n
ity
is
alwa
y
s
k
ee
n
in
i
m
p
r
o
v
i
n
g
th
e
r
eliab
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y
o
f
in
v
er
ter
f
ed
i
n
d
u
ctio
n
m
o
to
r
s
.
T
h
e
r
ef
o
r
e
,
f
au
lt a
n
al
y
s
is
r
em
ain
s
a
v
ital iss
u
e
in
th
e
d
esig
n
o
f
a
f
au
lt to
ler
a
n
t sy
s
tem
s
.
I
n
m
an
y
in
d
u
s
tr
ial
ap
p
licatio
n
s
,
in
d
u
ctio
n
m
o
to
r
s
r
u
n
at
v
ar
i
ab
le
s
p
ee
d
s
.
T
h
eir
p
o
wer
s
u
p
p
ly
co
m
es
f
r
o
m
a
co
n
v
er
s
io
n
c
h
ain
co
n
s
is
tin
g
o
f
a
r
ec
tifie
r
,
a
DC
l
in
k
,
an
d
a
n
in
v
er
te
r
;
wh
ich
r
eq
u
ir
es
a
ca
r
ef
u
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
3
1
-
639
632
atten
tio
n
to
s
tu
d
y
m
o
to
r
'
s
b
eh
av
io
r
in
th
e
p
r
esen
ce
o
f
f
au
lts
in
th
e
co
n
v
er
s
io
n
ch
ai
n
.
As
n
o
ted
in
[
6
]
-
[
1
1
]
,
th
e
two
co
m
p
o
n
e
n
ts
m
o
s
t lik
ely
t
o
b
ec
o
m
e
f
au
lty
in
elec
tr
ical
d
r
iv
es a
r
e
th
e
elec
tr
o
ly
tic
f
ilter
in
g
ca
p
ac
ito
r
s
in
th
e
DC
lin
k
an
d
th
e
p
o
wer
s
em
ico
n
d
u
ct
o
r
s
s
witch
es.
Am
o
n
g
th
ese,
th
e
m
o
s
t
ty
p
ical
p
o
wer
s
em
ico
n
d
u
ct
o
r
f
au
lts
ar
e
o
p
e
n
-
cir
cu
it
a
n
d
s
h
o
r
t
-
cir
cu
it
f
au
lts
,
k
n
o
wn
r
esp
ec
tiv
el
y
as
h
ig
h
im
p
ed
a
n
ce
an
d
lo
w
im
p
ed
an
ce
f
ailu
r
es
o
f
an
I
GB
T
s
witch
.
T
h
e
f
a
u
lt p
r
o
b
a
b
ilit
y
m
en
tio
n
ed
a
b
o
v
e
h
as
alr
ea
d
y
b
ee
n
ca
lcu
lated
b
y
co
n
s
id
er
in
g
s
ev
er
al
f
ac
to
r
s
,
with
a
d
etailed
s
tu
d
y
p
r
o
v
id
e
d
in
th
e
f
o
llo
win
g
p
ap
er
s
[
1
2
]
-
[
1
4
]
.
T
h
e
r
eliab
ilit
y
ev
alu
atio
n
o
f
win
d
tu
r
b
in
e
s
y
s
tem
co
m
p
o
n
en
ts
s
h
o
ws
th
at
th
e
h
ig
h
est
f
ailu
r
e
r
a
te
o
cc
u
r
s
at
th
e
lev
el
o
f
th
e
c
o
n
v
er
ter
s
,
o
f
wh
ic
h
th
e
DC
lin
k
is
a
p
ar
t [
1
5
]
.
So
m
e
r
esear
ch
er
s
claim
th
at
s
em
ico
n
d
u
cto
r
r
eliab
ilit
y
h
a
s
s
ig
n
if
ican
tly
im
p
r
o
v
ed
.
Ho
wev
er
,
it
r
em
ain
s
a
f
ac
t
th
at
in
th
e
p
ast,
th
e
p
r
o
b
a
b
ilit
y
o
f
co
n
tr
o
l
cir
c
u
it
f
au
lts
was
5
3
.
1
%,
p
r
im
ar
il
y
d
u
e
to
th
e
lo
we
r
r
eliab
ilit
y
,
an
d
s
o
p
h
is
ticatio
n
o
f
PW
M
ch
ip
s
co
m
p
ar
ed
to
m
o
d
er
n
co
n
t
r
o
ller
tech
n
o
lo
g
y
.
T
h
u
s
,
t
h
e
r
is
k
o
f
I
GB
T
’
s
f
au
lts
h
as
b
ee
n
r
ed
u
ce
d
.
Alth
o
u
g
h
th
ese
f
au
lts
o
cc
u
r
with
in
th
e
in
v
er
ter
s
tr
u
ct
u
r
e,
th
ey
h
av
e
d
i
r
ec
t
n
eg
ativ
e
c
o
n
s
eq
u
e
n
ce
s
o
n
th
e
m
ec
h
an
ical
p
ar
ts
o
f
th
e
m
ac
h
in
e
d
u
e
t
o
th
e
v
a
r
io
u
s
f
au
lts
in
v
esti
g
ated
.
T
h
e
d
if
f
er
en
t d
e
g
r
ad
e
d
o
p
e
r
atio
n
s
o
f
th
e
m
o
to
r
d
u
e
to
t
h
ese
f
au
lts
m
ay
ca
u
s
e
h
ig
h
in
er
tia
an
d
v
ib
r
atio
n
s
lead
in
g
to
ac
ce
ler
ated
ag
in
g
o
f
th
e
m
o
to
r
'
s
m
ec
h
an
ical
co
m
p
o
n
en
ts
an
d
u
ltima
tely
r
esu
ltin
g
in
to
tal
d
eter
io
r
atio
n
.
A
r
esear
ch
s
tu
d
y
f
o
u
n
d
th
at
o
v
er
h
alf
o
f
th
e
f
ailu
r
es
in
s
witch
in
g
p
o
wer
s
u
p
p
lies
ar
e
lin
k
ed
to
f
a
u
lts
in
th
e
DC
lin
k
ca
p
ac
ito
r
.
T
h
e
f
au
lts
o
n
DC
lin
k
ca
p
ac
ito
r
s
wer
e
n
o
tifie
d
b
y
s
ev
er
al
r
e
s
ea
r
ch
er
s
in
th
eir
f
au
lt
s
tu
d
ies
;
h
o
wev
er
,
th
ey
d
id
n
o
t
in
v
esti
g
ate
th
is
p
r
o
b
lem
th
o
r
o
u
g
h
ly
.
A
r
e
v
iew
o
n
im
p
r
o
v
in
g
t
h
e
DC
lin
k
ca
p
ac
ito
r
r
eliab
ilit
y
in
p
o
wer
elec
tr
o
n
ic
s
tatic
co
n
v
e
r
ter
s
is
p
r
esen
ted
in
[
1
6
]
.
Fau
lt
m
o
d
es,
th
eir
ca
u
s
es,
an
d
ca
p
ac
ito
r
life
tim
e
m
o
d
els
ar
e
ex
p
lain
e
d
an
d
s
u
m
m
ar
ized
to
b
etter
u
n
d
er
s
tan
d
f
ailu
r
e
m
ec
h
an
is
m
s
an
d
im
p
r
o
v
e
DC
lin
k
d
esig
n
.
T
h
is
p
ap
er
em
p
h
asizes
th
e
s
ig
n
if
ican
ce
o
f
DC
lin
k
m
o
n
ito
r
i
n
g
.
A
DC
lin
k
s
h
o
r
t
-
cir
cu
it
f
au
lt
o
cc
u
r
s
d
u
e
to
a
ca
p
ac
ito
r
s
h
o
r
t
-
cir
cu
it,
o
f
ten
r
esu
ltin
g
f
r
o
m
co
n
n
ec
to
r
b
r
ea
k
ag
e
[
1
6
]
.
T
h
e
r
esu
lts
in
d
icate
t
h
at
th
e
ca
p
ac
ito
r
is
s
u
s
ce
p
tib
le
to
f
au
lts
.
An
im
p
o
r
tan
t
p
o
in
t
to
co
n
s
id
er
is
th
at
th
e
eq
u
iv
alen
t
s
er
ies
r
esi
s
t
an
ce
(
E
SR
)
o
f
th
e
ca
p
ac
ito
r
g
r
ad
u
ally
in
cr
ea
s
es
o
v
er
tim
e.
T
h
is
p
r
o
b
lem
is
n
o
t
ty
p
ically
e
n
co
u
n
ter
ed
in
c
o
n
v
en
tio
n
al
cir
cu
its
.
Ho
wev
er
,
it
b
ec
o
m
es
r
elev
a
n
t
wh
en
th
e
ca
p
ac
ito
r
is
u
s
ed
in
a
s
witch
in
g
cir
c
u
it,
th
e
eq
u
i
v
alen
t
s
er
ies
r
esis
tan
ce
(
E
SR
)
m
ay
in
ter
a
ct
with
th
e
s
witch
in
g
f
r
eq
u
en
cy
,
p
o
ten
tially
ca
u
s
in
g
s
el
f
-
h
ea
tin
g
th
at
ca
n
in
d
ir
ec
tly
r
esu
lt
i
n
ca
p
ac
ito
r
f
ailu
r
e.
I
n
g
e
n
er
al,
s
o
m
e
r
esea
r
ch
h
as
b
ee
n
co
n
d
u
cted
o
n
DC
lin
k
s
h
o
r
t
-
cir
c
u
it
f
au
lts
an
d
th
eir
im
p
ac
t
o
n
in
d
u
ctio
n
m
o
to
r
s
[
1
7
]
-
[
2
1
]
.
A
r
e
ce
n
t
s
tu
d
y
p
r
o
v
id
ed
a
r
ev
iew
o
f
b
o
th
i
n
ter
n
al
an
d
ex
ter
n
al
f
au
lts
in
v
a
r
io
u
s
co
m
p
o
n
en
ts
o
f
a
m
o
t
o
r
co
n
n
ec
ted
to
an
in
v
e
r
ter
.
Ho
wev
er
,
n
o
n
e
o
f
t
h
ese
s
tu
d
ies
ad
d
r
ess
ed
th
e
im
p
ac
t
o
n
th
e
th
r
ee
-
p
h
ase
r
ec
tifie
r
.
T
h
is
liter
atu
r
e
r
ev
iew
s
h
o
ws
th
at
m
o
s
t
o
f
th
e
r
esear
ch
o
n
f
au
lt
an
al
y
s
is
h
as
f
o
cu
s
ed
o
n
v
ar
iab
le
-
s
p
ee
d
in
d
u
ctio
n
m
o
to
r
s
is
r
elate
d
to
th
e
f
au
lt
an
aly
s
is
o
f
I
GB
T
s
witch
es.
Ho
wev
er
,
t
h
e
s
u
s
ce
p
tib
ilit
y
o
f
th
e
ca
p
ac
ito
r
n
ec
ess
itates
a
d
etailed
an
aly
s
is
o
f
th
e
b
eh
av
i
o
r
o
f
th
e
r
ec
tifie
r
,
in
v
er
ter
,
an
d
in
d
u
ctio
n
m
o
to
r
wh
e
n
th
is
ty
p
e
o
f
f
a
u
lt
o
cc
u
r
s
.
T
h
is
p
ap
er
p
r
esen
ts
an
an
aly
s
is
o
f
a
ca
p
ac
ito
r
s
h
o
r
t
cir
c
u
it
f
au
lt
in
t
h
e
DC
lin
k
.
A
s
im
u
latio
n
o
f
th
e
d
r
i
v
e
s
y
s
tem
'
s
b
eh
av
io
r
u
n
d
er
th
is
f
au
lt
co
n
d
itio
n
was
d
ev
elo
p
ed
to
ass
is
t
in
th
e
f
o
r
m
u
latio
n
o
f
th
e
m
ath
em
atica
l
an
aly
s
is
.
T
h
e
r
esu
lts
o
b
tain
ed
ca
n
ass
is
t
r
esear
ch
er
s
in
d
esig
n
in
g
a
n
d
en
h
an
cin
g
f
au
lt
-
to
ler
an
t
s
y
s
tem
s
,
as
well
as
in
d
ev
elo
p
in
g
o
p
tim
a
l
p
r
o
tectio
n
s
y
s
tem
d
esig
n
s
.
Un
lik
e
o
u
r
p
r
ev
io
u
s
p
ap
er
,
t
h
is
o
n
ly
d
ea
lt
with
d
if
f
er
en
t ty
p
es o
f
c
o
n
tr
o
l i
n
th
e
s
tatic
ca
s
e.
2.
DC
L
I
NK
CAP
ACI
T
O
R
SH
O
RT
-
CIRC
UI
T
F
AIL
URE
M
O
DE
L
T
h
e
s
h
o
r
t c
ir
cu
it o
f
th
e
in
ter
m
ed
iate
cir
cu
it
ca
p
ac
ito
r
cr
ea
tes
two
s
tates: a
tr
an
s
ien
t s
tate
an
d
a
s
tead
y
s
tate.
Fig
u
r
e
1
s
h
o
ws
th
e
d
iag
r
am
o
f
th
e
AC
–
DC
–
AC
in
v
er
ter
f
ee
d
in
g
a
th
r
ee
-
p
h
ase
in
d
u
c
tio
n
m
o
to
r
.
Fig
u
r
e
2
illu
s
tr
ates
an
eq
u
iv
alen
t
elec
tr
ical
cir
cu
it
o
f
a
co
n
v
er
s
io
n
ch
ain
co
n
s
is
tin
g
o
f
a
r
ec
tifie
r
,
an
in
v
er
ter
,
an
d
an
in
d
u
ctio
n
m
o
to
r
f
o
r
a
v
ar
ia
b
le
-
s
p
ee
d
ap
p
licatio
n
.
T
h
e
th
r
e
e
-
p
h
ase
v
o
ltag
es
f
r
o
m
th
e
ele
ctr
ical
n
etwo
r
k
,
Va,
Vb
,
an
d
Vc,
ar
e
co
n
v
er
ted
in
t
o
a
DC
v
o
ltag
e,
Vd
c
,
th
r
o
u
g
h
a
co
n
tr
o
lled
th
r
ee
-
p
h
ase
r
ec
tif
ier
.
T
h
e
v
o
ltag
es
in
th
e
co
n
v
er
s
io
n
ch
ai
n
,
wh
ich
co
n
s
is
t
o
f
th
e
r
ec
tifie
r
,
ar
e
g
en
er
ated
u
s
in
g
th
e
ap
p
lica
tio
n
o
f
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
,
t
h
e
in
v
er
ter
p
r
o
d
u
ce
s
n
ea
r
ly
s
in
u
s
o
id
al
o
u
tp
u
t
c
u
r
r
en
ts
,
wh
ic
h
ar
e
r
e
f
lecte
d
in
th
e
s
tato
r
cu
r
r
en
ts
o
f
t
h
e
in
d
u
ctio
n
m
o
to
r
,
as th
ey
also
ex
h
ib
it a
s
in
u
s
o
id
al
f
o
r
m
.
2
.
1
.
Ana
ly
s
is
o
f
t
he
elec
t
ric
a
l net
wo
rk
a
nd
f
a
ults o
n t
he
r
ec
t
if
ier
s
ide
T
h
is
f
au
lt
ca
u
s
es
th
e
D
C
l
in
k
ca
p
ac
ito
r
to
s
h
o
r
t
-
cir
cu
it
th
e
r
ec
tifie
r
'
s
o
u
tp
u
t
v
o
ltag
e,
wh
ich
in
tu
r
n
s
h
o
r
t
-
cir
cu
its
th
e
elec
tr
ical
n
e
two
r
k
p
h
ases
.
T
o
clar
if
y
t
h
is
p
h
en
o
m
en
o
n
,
Fig
u
r
e
3
is
p
r
o
v
id
ed
.
I
t
d
ep
icts
a
s
im
p
lifie
d
cir
cu
it
r
ep
r
esen
tin
g
th
e
is
s
u
e
[
2
2
]
.
L
et
u
s
f
o
cu
s
o
n
th
e
r
ec
tifie
r
s
id
e
an
d
t
h
e
ele
ctr
ical
n
etwo
r
k
.
I
n
Fig
u
r
e
3
,
th
e
s
witch
K
is
p
lac
ed
in
p
ar
allel
with
th
e
f
ilter
c
ap
ac
ito
r
,
w
h
ile
th
e
DC
v
o
ltag
e
s
o
u
r
ce
s
u
p
p
lies
a
v
o
ltag
e
th
at
ch
ar
g
es
th
e
ca
p
ac
ito
r
.
Ud
c
s
er
v
es
as
a
s
im
p
lifie
d
m
o
d
el
o
f
th
e
o
u
tp
u
t
f
r
o
m
th
e
th
r
ee
-
p
h
ase
r
ec
tifie
r
im
p
lem
en
ted
in
th
e
s
im
u
latio
n
s
etu
p
o
f
th
e
elec
tr
i
ca
l
d
r
iv
e
s
y
s
tem
.
At
tim
e
t
=
0
,
p
r
i
o
r
to
cl
o
s
in
g
s
witch
K,
th
e
v
o
ltag
e
p
r
esen
t a
cr
o
s
s
th
e
ca
p
ac
ito
r
is
as (
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
ffect
o
f D
C
lin
k
ca
p
a
cito
r
s
h
o
r
t
-
circu
it o
n
a
n
in
ve
r
ter fed
i
n
d
u
ctio
n
mo
to
r
p
erfo
r
ma
n
ce
(
C
h
eikh
Ou
d
a
a
)
633
U
(
t
=
0
)
=
U
DC
(
1
)
I
n
o
th
er
wo
r
d
s
,
th
e
f
ilter
ca
p
a
cito
r
v
o
ltag
e
is
eq
u
al
to
th
e
r
e
ctif
ier
'
s
o
u
tp
u
t
DC
v
o
ltag
e.
T
h
er
ef
o
r
e
,
wh
en
th
e
ca
p
ac
ito
r
v
o
ltag
e
is
eq
u
al
to
,
th
e
cu
r
r
e
n
t is ze
r
o
.
(
=
0
)
=
0
(
2
)
I
n
th
e
v
ar
ia
b
le
s
p
ee
d
s
y
s
tem
d
esig
n
,
th
e
p
r
esen
ce
o
f
a
s
in
g
le
ca
p
ac
ito
r
at
th
e
DC
-
lin
k
lev
el
im
p
lies
th
at
n
o
ad
d
itio
n
al
d
ev
ice
is
av
ailab
le
to
lim
it
o
r
s
to
p
th
e
s
u
d
d
en
ch
a
n
g
e
in
cu
r
r
en
t.
C
o
n
s
eq
u
en
tly
,
at
t=0
,
wh
en
th
e
s
witch
K
is
clo
s
ed
,
th
e
ca
p
ac
ito
r
is
s
h
o
r
t
-
ci
r
cu
it
ed
.
Giv
en
th
at
th
e
r
esis
tan
ce
is
n
ea
r
ly
ze
r
o
,
th
e
s
o
u
r
ce
cu
r
r
en
t in
cr
ea
s
es e
x
p
o
n
en
tially
.
i
c
(
t
=
0
)
=
U
R
⁄
(
3
)
Sin
ce
R
ten
d
s
to
ze
r
o
,
(
3
)
b
ec
o
m
es
(
4
)
.
i
c
(
t
=
0
)
=
∞
(
4
)
Af
ter
clo
s
in
g
s
witch
K,
th
e
cir
cu
it o
p
er
ates u
n
d
er
th
e
s
am
e
c
o
n
d
itio
n
s
as a
n
R
C
cir
cu
it,
th
e
n
as (
5
)
.
i
=
A
e
(
t
RC
⁄
)
(
5
)
Her
e
,
A
r
ep
r
esen
ts
a
co
n
s
tan
t
,
R
C
=
τ
i
s
th
e
tim
e
co
n
s
tan
t,
an
d
t is th
e
tim
e
.
Af
ter
clo
s
in
g
th
e
s
witch
K,
t
h
e
r
esis
tan
ce
R
ap
p
r
o
ac
h
es
z
er
o
.
I
f
R
=
0
,
th
e
cir
cu
it
p
r
o
d
u
ce
s
an
ex
tr
em
ely
lar
g
e
c
u
r
r
en
t
th
at
t
h
eo
r
etica
lly
ten
d
s
to
war
d
i
n
f
i
n
ity
.
As
a
r
esu
lt,
if
th
e
ap
p
r
o
p
r
iate
f
u
s
es
ar
e
n
o
t
s
elec
ted
,
th
is
f
au
lt m
ay
lead
to
s
ig
n
if
ican
t d
am
ag
e
to
th
e
r
ec
tifie
r
ap
p
r
o
p
r
iately
r
ate
d
.
Fig
u
r
e
1
.
Simu
latio
n
co
n
f
ig
u
r
atio
n
Fig
u
r
e
2
.
E
q
u
iv
alen
t e
lectr
ical
cir
cu
it o
f
a
MA
S c
o
u
p
led
with
a
s
tatic
co
n
v
er
ter
Fig
u
r
e
3
.
Simp
lifie
d
d
iag
r
am
o
f
an
e
q
u
iv
alen
t
cir
cu
it f
o
r
a
ca
p
ac
ito
r
s
h
o
r
t
-
cir
cu
it f
au
lt
C
D1
D2
D3
D4
D5
D6
K1
K2
K3
K4
K5
K6
M
M
3
~
U
V
W
L
a
b
c
R
e
ct
i
f
i
e
r
I
n
v
e
r
t
e
r
Load
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
9
2
I
n
t J Ap
p
l Po
wer
E
n
g
,
Vo
l.
14
,
No
.
3
,
Sep
tem
b
er
20
25
:
6
3
1
-
639
634
2
.
2
.
F
a
ult
a
na
ly
s
is
o
n t
he
inv
er
t
er
a
nd
ind
uct
io
n m
o
t
o
r
s
ides
W
e
will
n
o
w
an
aly
ze
th
e
in
v
e
r
ter
an
d
th
e
in
d
u
ctio
n
m
o
to
r
s
ec
tio
n
s
.
T
h
e
elec
tr
o
m
o
tiv
e
f
o
r
ce
(
E
MF)
is
r
ep
r
esen
ted
as
a
s
in
u
s
o
id
al
v
o
ltag
e
s
o
u
r
ce
,
an
d
th
e
m
o
to
r
win
d
in
g
s
ar
e
m
o
d
eled
u
s
in
g
a
s
er
ies
co
m
b
in
atio
n
o
f
r
esis
tan
ce
an
d
in
d
u
ctan
ce
f
o
r
ea
ch
o
f
th
e
t
h
r
ee
p
h
ases
.
T
h
e
I
GB
T
s
f
u
n
ctio
n
as
s
witch
e
s
,
eith
er
co
n
n
ec
tin
g
o
r
d
is
co
n
n
ec
tin
g
th
e
DC
-
lin
k
f
r
o
m
th
e
in
d
u
ctio
n
m
o
to
r
,
a
s
illu
s
tr
ated
in
Fig
u
r
e
2
.
Fo
r
in
s
tan
ce
,
in
a
s
tate
wh
er
e
I
GB
T
s
K1
,
K4
,
an
d
K
6
ar
e
c
o
n
d
u
ctin
g
(
clo
s
ed
)
wh
ile
K2
,
K3
,
an
d
K5
ar
e
n
o
t
co
n
d
u
ctin
g
(
o
p
en
)
,
Fig
u
r
e
4
p
r
esen
ts
a
s
im
p
lifie
d
cir
cu
it d
ep
ictin
g
t
h
e
f
au
lt o
n
t
h
e
in
v
er
ter
an
d
i
n
d
u
ctio
n
m
o
t
o
r
s
id
e
[
2
3
]
,
[
2
4
]
.
At
th
is
m
o
m
en
t,
th
e
p
h
ase
-
A
cu
r
r
en
t
e
q
u
als
th
e
co
m
b
in
ed
cu
r
r
en
ts
o
f
p
h
ase
-
B
an
d
p
h
a
s
e
-
C
.
T
h
is
co
n
d
itio
n
is
s
h
o
wn
i
n
(
6
)
.
i
a
=
i
b
+
i
c
(
6
)
Sin
ce
th
e
cu
r
r
en
t
f
lo
ws
f
r
o
m
p
h
ase
-
A,
wh
ich
is
co
n
n
ec
te
d
to
th
e
p
o
s
itiv
e
ter
m
in
al
o
f
th
e
DC
-
lin
k
.
T
h
e
v
o
ltag
e
eq
u
atio
n
f
o
r
th
e
p
h
ase
A
is
g
iv
en
in
(
7
)
.
U
a0
=
U
z
+
E
ba
(
7
)
W
h
er
e
U
ao
is
p
h
ase
-
A
v
o
ltag
e
r
elativ
e
to
g
r
o
u
n
d
,
U
z
is
t
h
e
lin
e
im
p
ed
an
ce
v
o
ltag
e
d
r
o
p
,
an
d
E
ba
is
th
e
in
d
u
ctio
n
m
o
to
r
E
MF
r
etu
r
n
f
o
r
p
h
ase
-
A.
So
,
(
7
)
b
ec
o
m
es
(
8
)
.
U
a0
=
R
.
i
+
L
(
di
dt
⁄
)
+
E
ba
(
8
)
Af
ter
th
e
s
h
o
r
t
cir
c
u
it
at
DC
b
u
s
th
e
v
o
ltag
e
at
th
e
in
v
er
te
r
o
u
tp
u
t
will
b
ec
o
m
e
ze
r
o
as
in
d
i
ca
ted
in
[
2
5
]
.
As
a
r
esu
lt,
(
8
)
b
ec
o
m
es
(
9
)
.
−
E
ba
=
R
.
i
+
L
(
di
dt
⁄
)
(
9
)
At
th
e
m
o
m
en
t (
t =
0
)
,
th
e
cu
r
r
en
t e
x
p
r
ess
io
n
is
g
iv
en
b
y
(
1
0
)
.
i
r
(
t
=
0
−
1
)
=
i
l
(
t
=
0
−
1
)
=
(
E
ba
−
U
DC
)
R
(
1
0
)
Sin
ce
th
e
cir
cu
it
co
n
tain
s
an
in
d
u
ctan
ce
L
,
it
o
p
p
o
s
es
s
u
d
d
e
n
ch
an
g
es
in
cu
r
r
e
n
t,
p
r
ev
en
ti
n
g
it
f
r
o
m
v
ar
y
in
g
in
s
tan
tan
eo
u
s
ly
.
Ho
wev
er
,
th
e
cu
r
r
en
t w
ill f
o
llo
w
t
h
e
s
p
ec
if
i
c
s
o
lu
tio
n
g
iv
e
n
as (
1
1
)
an
d
(
1
2
)
.
i
r
(
t
=
0
−
1
)
=
i
l
(
t
=
0
−
1
)
=
E
ba
R
(
1
1
)
i
=
(
E
ba
R
⁄
)
(
1
−
e
t
τ
)
(
1
2
)
T
h
e
tr
an
s
ien
t
s
h
o
r
t
-
cir
c
u
it
cu
r
r
en
t
d
ec
r
ea
s
es
in
d
ef
in
itely
d
u
e
to
t
h
e
p
r
esen
ce
o
f
t
h
e
win
d
i
n
g
r
esis
to
r
R
.
T
h
e
tim
e
c
o
n
s
tan
t
τ
\
tau
τ
d
eter
m
in
es
th
e
d
u
r
atio
n
r
eq
u
ir
ed
to
elim
in
ate
th
e
tr
a
n
s
ien
t
ef
f
ec
ts
o
f
t
h
e
s
tato
r
cu
r
r
en
t.
I
n
s
tead
y
-
s
tate
o
p
e
r
at
io
n
,
th
e
v
o
ltag
e
ap
p
lied
to
th
e
m
o
to
r
d
r
o
p
s
to
ze
r
o
,
lea
d
in
g
to
an
im
m
e
d
iate
s
h
u
td
o
wn
o
f
th
e
in
d
u
ctio
n
m
o
t
o
r
.
Fig
u
r
e
4
.
Fau
lt e
q
u
iv
alen
t c
ir
c
u
it o
n
th
e
i
n
v
er
ter
a
n
d
th
e
in
d
u
ctio
n
m
o
t
o
r
s
id
e
u
n
d
er
DC
-
lin
k
ca
p
ac
ito
r
K
L
1
2
L
1
2
L
1
2
C
D1
D2
D3
R
R
R
Ea
Eb
Ec
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
ffect
o
f D
C
lin
k
ca
p
a
cito
r
s
h
o
r
t
-
circu
it o
n
a
n
in
ve
r
ter fed
i
n
d
u
ctio
n
mo
to
r
p
erfo
r
ma
n
ce
(
C
h
eikh
Ou
d
a
a
)
635
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
m
o
to
r
is
p
o
wer
e
d
b
y
a
t
wo
-
lev
el
in
v
er
ter
a
n
d
co
n
tr
o
ll
ed
b
y
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
.
Simu
latio
n
r
esu
lts
will
b
e
p
r
e
s
en
ted
in
MA
T
L
AB
Simu
lin
k
f
o
r
th
e
h
ea
lth
y
ca
s
e
a
n
d
f
a
u
lty
ca
s
e
in
th
e
DC
lin
k
ca
p
ac
ito
r
.
T
h
e
m
o
to
r
p
ar
a
m
eter
s
ar
e
s
h
o
wn
in
T
a
b
le
1.
3
.
1
.
Sim
ula
t
i
o
n r
esu
lt
s
:
hea
lt
hy
ca
s
e
a
nd
dis
cus
s
io
ns
T
h
e
in
d
u
ctio
n
m
o
to
r
is
co
n
n
ec
ted
to
th
e
in
v
er
te
r
o
u
tp
u
t v
ia
t
h
r
ee
p
h
ases
,
an
d
t
h
e
s
am
p
lin
g
f
r
eq
u
e
n
cy
is
2
k
Hz.
T
h
e
av
er
ag
e
v
o
ltag
e
o
f
th
e
th
r
ee
-
p
h
ase
r
ec
tifie
r
o
u
t
p
u
t is g
iv
en
as
in
(
1
3
)
.
U
DC
=
3
√
3
π
V
m
(
1
3
)
W
h
er
e
m
ax
im
u
m
v
o
ltag
e
.
T
h
e
m
o
t
o
r
was
r
u
n
n
i
n
g
at
s
tead
y
s
tate
b
ef
o
r
e
th
e
f
a
u
lt
o
cc
u
r
r
ed
,
as
s
h
o
wn
b
y
th
e
wav
ef
o
r
m
s
in
Fig
u
r
e
5
.
T
h
e
m
o
to
r
s
tar
ts
u
p
a
n
d
r
ea
c
h
es its
r
ated
s
p
ee
d
in
a
v
e
r
y
s
h
o
r
t tim
e
(
0
.
0
5
s
)
.
T
ab
le
1
.
Par
am
eter
s
o
f
th
e
I
M
S
.
L.
D
e
scri
p
t
i
o
n
V
a
l
u
e
(
u
n
i
t
)
1
P
o
w
e
r
s
u
p
p
l
y
4
0
0
V
2
R
a
t
e
d
p
o
w
e
r
4
k
W
3
R
a
t
e
d
s
p
e
e
d
1
4
3
0
R
P
M
4
S
t
a
t
o
r
r
e
s
i
st
a
n
c
e
0
.
0
3
5
1
3
Ω
5
R
o
t
o
r
r
e
si
s
t
a
n
c
e
0
.
0
3
4
8
8
Ω
6
S
t
a
t
o
r
c
y
c
l
i
c
i
n
d
u
c
t
a
n
c
e
0
.
0
4
5
8
6
Ω
7
R
o
t
o
r
c
y
c
l
i
c
i
n
d
u
c
t
a
n
c
e
0
.
0
4
5
8
6
Ω
8
M
u
t
u
a
l
i
n
d
u
c
t
a
n
c
e
1
.
3
5
2
Ω
9
p
o
l
e
s
p
a
i
r
s
n
u
mb
e
r
2
10
M
o
me
n
t
o
f
i
n
e
r
t
i
a
0
.
0
4
0
4
k
g
.
m
2
11
C
o
e
f
f
i
c
i
e
n
t
o
f
v
i
s
c
o
u
s
f
r
i
c
t
i
o
n
r
a
d
-
1
s
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
5
.
MA
S p
er
f
o
r
m
a
n
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n
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itio
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r
r
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s
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n
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to
r
q
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e
3
.
2
.
Sim
ula
t
i
o
n r
esu
lt
s
:
f
a
ulty
ca
s
e
a
nd
dis
cus
s
io
ns
T
h
e
f
au
lty
ca
s
e
in
Fig
u
r
e
6
,
p
r
esen
ted
as
a
s
h
o
r
t
cir
c
u
it
,
ca
n
in
p
r
ac
tice
b
e
lin
k
ed
to
o
v
er
cu
r
r
en
ts
an
d
th
er
m
al
s
tr
ess
es
o
f
th
e
DC
b
u
s
ca
p
ac
ito
r
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T
h
is
f
au
lty
ca
s
e
c
an
b
e
a
s
er
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s
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r
o
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MA
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i
s
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n
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h
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h
e
g
r
ea
ter
th
e
in
e
r
tia,
th
e
lo
n
g
er
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d
u
r
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n
o
f
b
ac
k
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MF
g
en
er
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n
.
T
h
ese
co
u
n
ter
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tr
o
m
o
tiv
e
f
o
r
ce
s
d
im
in
is
h
an
d
ca
n
ce
l
with
th
e
in
v
er
te
r
o
u
t
p
u
t
v
o
lta
g
es,
cr
ea
tin
g
tr
an
s
ien
t
cu
r
r
en
ts
o
f
s
ig
n
if
ican
t
am
p
lit
u
d
e,
o
v
e
r
cu
r
r
e
n
t
an
d
th
er
m
al
s
tr
ess
.
I
n
d
u
ctio
n
m
o
to
r
s
tato
r
p
h
ase
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r
r
en
ts
at
t
=
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1
:
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e
tr
an
s
ien
t
cu
r
r
en
ts
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e
co
n
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er
ab
ly
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ig
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d
th
en
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r
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e
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ch
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ze
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alu
e.
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h
e
v
o
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e
cu
r
v
e
at
t
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1
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e
v
o
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alu
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ec
r
ea
s
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er
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ly
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ch
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g
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v
al
u
e
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en
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ili
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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2
I
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14
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3
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Sep
tem
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20
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:
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3
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636
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o
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s
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it
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u
r
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h
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ee
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was
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ee
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g
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ad
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ally
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ec
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h
en
s
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ilis
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T
h
e
elec
tr
o
m
ag
n
etic
to
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q
u
e
c
u
r
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e
:
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h
en
th
e
f
au
lt
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r
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at
t
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ad
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ec
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d
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ilis
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r
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n
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t
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h
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e
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etec
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ty
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a
u
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ich
ar
e
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o
s
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ib
le
in
r
ea
l
ca
s
es,
ar
e
th
r
o
u
g
h
th
e
m
ea
s
u
r
e
o
f
th
e
DC
b
u
s
v
o
ltag
e
lev
el.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
MA
S p
er
f
o
r
m
a
n
ce
u
n
d
er
h
ea
lth
y
co
n
d
itio
n
s
(
DC
lin
k
f
au
lt):
(
a)
cu
r
r
en
ts
,
(
b
)
v
o
ltag
e,
(
c)
s
p
ee
d
,
a
n
d
(
d
)
to
r
q
u
e
4.
CO
NCLU
SI
O
N
T
h
is
p
ap
er
h
ig
h
lig
h
ts
th
e
im
p
ac
t
o
f
a
s
h
o
r
t
-
ci
r
cu
it
at
th
e
in
ter
m
ed
iate
ca
p
ac
ito
r
cir
c
u
it.
I
t
also
h
ig
h
lig
h
ts
th
e
s
en
s
itiv
e
co
m
p
o
n
en
ts
o
f
a
s
y
s
tem
wh
o
s
e
f
ailu
r
e
ca
n
b
e
f
atal
to
th
e
s
y
s
tem
.
I
n
ad
d
itio
n
,
it
s
h
o
ws
th
e
elec
tr
ical
an
d
m
ec
h
an
ical
b
eh
av
io
u
r
o
f
a
co
m
p
lete
elec
tr
ic
d
r
iv
e
s
y
s
tem
co
n
s
is
tin
g
o
f
an
in
d
u
ctio
n
m
o
to
r
f
ed
b
y
a
v
ar
ia
b
le
-
s
p
ee
d
s
y
s
te
m
(
a
r
ec
tifie
r
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a
DC
lin
k
an
d
a
n
in
v
e
r
ter
)
.
T
h
e
th
eo
r
y
a
n
d
m
ath
em
atica
l
an
aly
s
is
p
r
esen
ted
h
av
e
b
ee
n
v
e
r
if
ie
d
b
y
s
im
u
latio
n
s
.
T
h
is
wo
r
k
h
as
en
ab
led
u
s
to
g
ath
er
in
f
o
r
m
atio
n
o
n
th
e
b
eh
av
io
u
r
o
f
th
e
r
ec
tifie
r
,
i
n
v
er
ter
an
d
in
d
u
ctio
n
m
o
to
r
d
u
r
in
g
a
s
h
o
r
t
-
cir
c
u
it
f
a
u
lt
o
f
th
e
DC
lin
k
ca
p
ac
ito
r
.
A
d
etailed
an
aly
s
is
ce
r
tain
ly
c
o
n
tr
ib
u
tes
to
th
e
d
iag
n
o
s
is
an
d
d
esig
n
o
f
r
o
b
u
s
t
f
au
lt
-
to
ler
a
n
t
s
y
s
tem
s
,
as
well
as
to
th
e
im
p
r
o
v
em
en
t
o
f
f
a
u
lt
d
etec
tio
n
tech
n
iq
u
es.
I
n
f
ac
t,
it
ca
n
b
e
s
aid
t
h
at
th
e
ef
f
ec
t
o
n
th
e
s
y
s
tem
at
th
e
m
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en
t
th
e
f
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lt
ap
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r
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co
m
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y
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ad
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al
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ee
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ef
o
r
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ilis
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[
2
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.
RE
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NC
E
S
[
1
]
J.
D
.
P
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,
D
.
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M
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[
2
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A
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in
e
in
1
9
9
4
,
a
n
d
late
r
e
a
rn
e
d
h
is
P
h
.
D.
in
El
e
c
tri
c
a
l
En
g
in
e
e
rin
g
fr
o
m
M
o
h
a
m
m
e
d
V
Un
iv
e
rsity
(UM
5
R)
in
Ra
b
a
t,
M
o
r
o
c
c
o
,
in
2
0
1
9
.
He
is
c
u
rre
n
tl
y
se
rv
in
g
a
s
a
lec
tu
re
r
a
ss
istan
t
a
t
th
e
Hig
h
e
r
T
e
c
h
n
o
l
o
g
ica
l
I
n
stit
u
te
o
f
R
o
ss
o
.
His
re
se
a
rc
h
in
tere
sts
fo
c
u
s
o
n
e
lec
tri
c
a
l
n
e
two
r
k
s,
p
o
we
r
sy
ste
m
s,
e
n
e
rg
y
e
fficie
n
c
y
,
a
n
d
a
u
to
m
a
ti
c
c
o
n
tr
o
l.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
e
th
m
a
n
e
isse
lem
a
rb
ih
1
9
6
6
@g
m
a
il
.
c
o
m
.
Mo
h
a
m
e
d
A
m
in
e
K
h
e
li
f
wa
s
b
o
r
n
i
n
M
il
ian
a
,
Ai
n
-
De
fla,
Al
g
e
ria,
in
1
9
9
1
.
He
re
c
e
iv
e
d
h
is
B
a
c
h
e
lo
r
a
n
d
M
a
ste
r
d
e
g
re
e
s
fro
m
th
e
Un
iv
e
rsity
Dj
il
a
li
Bo
u
n
a
a
m
a
,
Alg
e
ria
in
2
0
1
3
a
n
d
2
0
1
5
,
re
sp
e
c
ti
v
e
ly
.
He
is
c
u
rre
n
tl
y
wo
r
k
in
g
fo
r
h
is
P
h
.
D.
d
e
g
re
e
a
t
UST
O
-
M
B,
Alg
e
ria.
His
re
se
a
rc
h
in
tere
sts
i
n
c
lu
d
e
p
o
we
r
c
o
n
v
e
rsio
n
,
e
lec
t
ric
m
a
c
h
in
e
s
,
d
ri
v
e
s
,
a
n
d
to
lera
n
c
e
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
k
.
a
m
in
e
.
h
@li
v
e
.
fr
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ap
p
l Po
wer
E
n
g
I
SS
N:
2252
-
8
7
9
2
E
ffect
o
f D
C
lin
k
ca
p
a
cito
r
s
h
o
r
t
-
circu
it o
n
a
n
in
ve
r
ter fed
i
n
d
u
ctio
n
mo
to
r
p
erfo
r
ma
n
ce
(
C
h
eikh
Ou
d
a
a
)
639
Ahm
e
d
M
o
h
a
m
e
d
Y
a
h
y
a
s
in
c
e
2
0
1
7
,
h
e
h
a
s
h
e
l
d
t
h
e
p
o
sit
io
n
o
f
As
so
c
iate
P
ro
fe
ss
o
r
in
t
h
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De
p
a
rtme
n
t
o
f
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h
y
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s
a
t
th
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Un
i
v
e
rsity
o
f
N
o
u
a
k
c
h
o
tt
in
M
a
u
rit
a
n
ia.
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e
a
rn
e
d
h
is
a
d
v
a
n
c
e
d
stu
d
ies
d
i
p
lo
m
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i
n
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o
lar
E
n
e
rg
y
i
n
2
0
0
5
fro
m
Ch
e
ik
h
A
n
ta
Dio
p
Un
iv
e
rsity
i
n
Da
k
a
r,
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e
n
e
g
a
l,
a
n
d
c
o
m
p
lete
d
h
is
P
h
.
D.
i
n
2
0
1
2
a
t
t
h
e
sa
m
e
u
n
i
v
e
rsity
,
sp
e
c
ializin
g
in
so
lar
e
n
e
rg
y
,
m
a
t
e
rials,
a
n
d
sy
ste
m
s.
He
h
a
s
a
u
th
o
re
d
a
n
d
c
o
-
a
u
th
o
re
d
m
o
re
th
a
n
2
0
tec
h
n
ica
l
p
a
p
e
rs
p
u
b
li
s
h
e
d
in
in
tern
a
ti
o
n
a
l
jo
u
rn
a
ls
a
n
d
c
o
n
fe
re
n
c
e
s,
a
s
we
ll
a
s
c
o
n
tri
b
u
ted
to
two
b
o
o
k
c
h
a
p
ters
.
His
p
r
o
fe
ss
io
n
a
l
b
a
c
k
g
ro
u
n
d
i
n
c
lu
d
e
s
b
r
o
a
d
e
x
p
e
rien
c
e
i
n
e
lec
tri
c
a
l
e
n
e
rg
y
,
p
a
rti
c
u
larly
i
n
re
n
e
wa
b
le
e
n
e
rg
y
.
He
h
a
s
c
o
ll
a
b
o
ra
ted
with
n
u
m
e
ro
u
s
c
o
m
p
a
n
ies
a
n
d
p
u
b
li
c
i
n
stit
u
ti
o
n
s
,
g
a
i
n
in
g
e
x
ten
siv
e
e
x
p
e
rti
se
in
c
o
n
d
u
c
ti
n
g
fe
a
sib
il
it
y
st
u
d
ies
fo
r
p
r
o
jec
ts
su
c
h
a
s
p
h
o
to
v
o
lt
a
i
c
p
o
we
r
p
la
n
ts,
wi
n
d
fa
rm
s,
s
o
l
a
r
p
u
b
li
c
li
g
h
ti
n
g
sy
ste
m
s,
m
e
a
su
re
m
e
n
t
sta
ti
o
n
s,
m
e
d
i
u
m
a
n
d
l
o
w
-
v
o
lt
a
g
e
n
e
two
r
k
s,
ice
p
ro
d
u
c
ti
o
n
u
n
it
s,
a
n
d
se
a
wa
ter
d
e
sa
li
n
a
ti
o
n
fa
c
il
it
ies
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
b
i
y
a
h
2
0
0
1
@
y
a
h
o
o
.
fr
.
Be
n
d
ia
b
d
e
l
la
h
Az
e
d
d
in
e
is
a
n
IEE
E
m
e
m
b
e
r,
Al
g
e
ria.
He
e
a
rn
e
d
h
is
Ba
c
h
e
l
o
r
o
f
En
g
i
n
e
e
rin
g
d
e
g
re
e
with
h
o
n
o
rs
in
1
9
8
0
a
n
d
h
is
P
h
.
D.
in
1
9
8
5
,
b
o
t
h
fr
o
m
t
h
e
Un
i
v
e
rsity
o
f
S
h
e
ffield
,
En
g
lan
d
.
He
is
c
u
rre
n
tl
y
a
P
ro
fe
ss
o
r
a
n
d
re
se
a
rc
h
e
r
i
n
t
h
e
F
a
c
u
lt
y
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
a
t
th
e
Un
i
v
e
rsity
o
f
S
c
ien
c
e
a
n
d
Tec
h
n
o
l
o
g
y
o
f
Ora
n
(UST
O
-
M
B),
Alg
e
ria,
wh
e
re
h
e
a
lso
se
rv
e
s
a
s
Dire
c
to
r
o
f
th
e
El
e
c
tri
c
a
l
Driv
e
s
De
v
e
lo
p
m
e
n
t
Lab
o
ra
t
o
ry
(LDE
E)
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
m
o
d
e
li
n
g
a
n
d
a
n
a
ly
sis
o
f
e
lec
tri
c
a
l
m
a
c
h
in
e
s
a
n
d
d
ri
v
e
s,
c
o
n
tro
l
o
f
e
lec
tri
c
a
l
m
a
c
h
in
e
s
a
n
d
c
o
n
v
e
rters
,
a
s
we
ll
a
s
fa
u
lt
d
iag
n
o
sis
a
n
d
fa
u
lt
-
t
o
lera
n
t
o
p
e
ra
ti
o
n
o
f
e
lec
tri
c
a
l
d
riv
e
s.
He
c
a
n
b
e
c
o
n
ta
c
ted
a
t
e
m
a
il
:
b
e
n
d
iaz
z
@y
a
h
o
o
.
fr
.
Abd
e
l
K
a
d
e
r
M
a
h
m
o
u
d
wa
s
b
o
r
n
in
Ale
g
,
M
a
u
rit
a
n
ia
in
1
9
6
0
.
He
re
c
e
iv
e
d
h
i
s
M
a
ste
r
d
e
g
re
e
o
f
S
c
ien
c
e
s
in
P
o
we
r
S
tatio
n
s
i
n
1
9
8
8
a
n
d
h
is
P
h
.
D.
d
e
g
re
e
in
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
fr
o
m
th
e
Tec
h
n
ica
l
Un
iv
e
rsity
o
f
Tas
h
k
e
n
t
i
n
Uz
b
e
k
istan
,
in
1
9
9
1
.
Th
e
n
h
e
re
c
e
iv
e
d
h
is
se
c
o
n
d
d
o
c
t
o
ra
l
d
e
g
r
e
e
in
re
n
e
wa
b
le
e
n
e
rg
y
fr
o
m
t
h
e
Un
iv
e
rsity
o
f
Ch
e
ik
h
A
n
ta
Dio
p
(UCA
D),
Da
k
a
r,
S
e
n
e
g
a
l,
i
n
2
0
0
8
.
Cu
rre
n
tl
y
,
h
e
is
in
c
h
a
rg
e
o
f
th
e
Ap
p
li
e
d
Re
se
a
rc
h
Lab
o
ra
to
r
y
o
f
Re
n
e
wa
b
le
E
n
e
rg
y
(LRAER).
He
is
th
e
a
u
th
o
r
a
n
d
c
o
-
a
u
th
o
r
o
f
m
o
re
t
h
a
n
3
0
sc
ien
ti
fic
p
a
p
e
rs
.
Th
e
ir
c
u
rre
n
t
p
r
o
jec
t
is
‘
Co
m
p
a
riso
n
b
e
twe
e
n
th
e
d
iffere
n
t
n
u
m
e
rica
l
m
o
d
e
ls
a
n
d
d
e
term
in
a
ti
o
n
o
f
p
a
ra
m
e
ters
c
h
a
ra
c
teristics
p
h
y
sic
a
l
m
a
teria
l
s
’
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
n
a
k
a
d
e
r@y
a
h
o
o
.
fr
.
Evaluation Warning : The document was created with Spire.PDF for Python.