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q
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VFDs
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a
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e
m
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a
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li
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s
th
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a
rm
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ti
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e
th
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ffe
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ts o
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th
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rm
o
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ic
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ti
o
n
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d
c
o
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p
l
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rd
s,
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lt
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p
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rm
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se
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o
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t
t
h
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h
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rm
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t
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sp
it
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e
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ti
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tatio
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t
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e
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t
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s
f
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t
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d
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r.
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Th
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o
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d
it
i
o
n
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re
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e
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t
ty
p
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ts.
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re
se
a
rc
h
d
e
tails
th
e
e
ffe
c
ts
o
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t
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e
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flec
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sa
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s
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th
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u
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d
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ts
d
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e
t
o
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h
is.
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,
a
s
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m
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ti
c
m
e
th
o
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u
sin
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e
F
IDE
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te
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li
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A
7
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5
kW
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ted
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is
fe
d
wit
h
a
1
2
-
p
u
lse
tran
sfo
rm
e
r
is u
se
d
f
o
r
t
h
is r
e
se
a
rc
h
.
K
ey
w
o
r
d
s
:
FID
E
S
Mu
lti
-
p
u
ls
e
tr
an
s
f
o
r
m
e
r
R
eliab
ilit
y
Var
iab
le
f
r
eq
u
e
n
cy
d
r
iv
e
Vo
ltag
e
s
ag
s
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
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ing
A
uth
o
r
:
K.
Palan
is
am
y
Dep
ar
tm
en
t o
f
E
n
er
g
y
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Po
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E
lectr
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n
ics,
Sch
o
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le
ctr
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E
n
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in
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r
in
g
Vello
r
e
I
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s
titu
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o
f
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r
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6
3
2
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4
,
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d
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m
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k
p
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am
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v
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c.
in
1.
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NT
RO
D
UCT
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f
p
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q
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s
u
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ex
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t
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tio
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eq
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tr
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s
ien
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v
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tag
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ag
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[
1
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-
[
3
]
.
T
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icate
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v
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ltag
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s
ag
s
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d
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its
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s
ix
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[
4
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[
5
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.
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ically
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DC
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e
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ater
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t
d
r
o
p
s
in
ef
f
ec
tiv
e
in
d
u
ctan
ce
.
C
u
m
u
lativ
ely
,
m
ag
n
etic
s
atu
r
atio
n
in
cr
ea
s
es
SC
R
/d
io
d
e
cu
r
r
en
t
s
tr
ess
e
s
,
ca
u
s
in
g
p
r
e
m
at
u
r
e
f
a
ilu
r
es.
I
n
n
o
r
m
al
VFDs
,
ex
tr
em
e
v
o
ltag
e
u
n
b
alan
ce
s
ar
e
s
e
n
s
ed
b
y
m
ea
s
u
r
in
g
DC
lin
k
v
o
ltag
e
r
ip
p
les,
b
u
t
t
h
is
m
eth
o
d
is
in
e
f
f
ec
tiv
e
f
o
r
twelv
e
-
p
u
ls
e
co
n
n
ec
tio
n
s
.
T
h
i
s
r
esear
ch
aim
s
to
clar
if
y
th
ese
is
s
u
es a
n
d
r
ec
o
m
m
en
d
alter
n
ativ
e
s
en
s
in
g
ap
p
r
o
ac
h
e
s
to
d
esig
n
er
s
.
T
h
e
life
tim
e
o
f
ca
p
ac
ito
r
s
is
g
en
er
ally
b
ased
o
n
tem
p
er
at
u
r
e
,
o
p
er
atin
g
v
o
ltag
e
,
r
ip
p
le
c
u
r
r
en
ts
,
an
d
r
ip
p
le
f
r
eq
u
en
cies.
C
ap
ac
ito
r
lo
s
s
es
v
ar
y
d
u
e
to
d
if
f
er
en
t
o
p
er
atin
g
co
n
d
itio
n
s
o
f
th
e
in
v
er
ter
an
d
r
ec
tifie
r
.
C
ap
ac
ito
r
lo
s
s
es
an
d
h
ea
tin
g
ef
f
ec
ts
in
s
ix
-
p
u
ls
e
r
ec
tifie
r
s
d
u
e
to
u
n
b
ala
n
ce
s
an
d
p
h
ase
lo
s
s
co
n
d
itio
n
s
ar
e
d
escr
ib
ed
in
ea
r
lier
r
esear
ch
[
9
]
,
[
1
0
]
.
T
h
ese
s
tu
d
ies
also
d
is
cu
s
s
ca
p
ac
ito
r
r
i
p
p
le
c
u
r
r
e
n
t
v
a
r
iatio
n
d
u
e
to
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M
)
o
p
e
r
atio
n
o
f
th
e
in
v
er
ter
.
Pro
lo
n
g
ed
v
o
ltag
e
s
ag
s
o
f
ten
g
en
er
ate
v
o
ltag
e
u
n
b
ala
n
ce
s
,
ex
ce
p
t
f
o
r
ty
p
e
A
s
ag
s
.
Vo
ltag
e
u
n
b
alan
ce
co
n
d
itio
n
s
p
r
o
d
u
c
ed
b
y
d
if
f
er
en
t
ty
p
es
o
f
s
ag
s
tr
an
s
f
o
r
m
d
if
f
er
en
tl
y
d
ep
en
d
i
n
g
o
n
th
e
tr
a
n
s
f
o
r
m
er
ty
p
e.
I
n
twelv
e
-
p
u
ls
e
ca
s
es,
t
wo
d
if
f
er
e
n
t
tr
an
s
f
o
r
m
atio
n
s
o
cc
u
r
b
ased
o
n
th
e
co
n
s
tr
u
ctio
n
o
f
th
e
p
r
im
ar
y
an
d
s
ec
o
n
d
ar
y
win
d
in
g
s
.
T
h
is
d
i
f
f
er
en
ce
p
r
o
d
u
ce
s
a
co
n
s
id
er
a
b
le
d
if
f
er
en
ce
in
t
h
e
cu
r
r
en
t
s
tr
ess
es
b
etwe
en
th
e
t
wo
r
ec
tifie
r
c
o
m
p
o
n
en
ts
o
f
th
e
VFD.
No
n
e
o
f
t
h
e
ea
r
lier
r
e
s
ea
r
ch
h
as
an
al
y
ze
d
th
e
v
o
ltag
e
r
ef
lectio
n
in
th
e
s
ec
o
n
d
ar
y
wi
n
d
in
g
s
o
f
th
e
12
-
p
u
ls
e
tr
an
s
f
o
r
m
er
d
u
r
in
g
s
u
ch
s
a
g
s
ce
n
ar
io
s
an
d
th
e
ef
f
ec
ts
on
th
e
r
ec
tifie
r
co
m
p
o
n
en
ts
lik
e
DC
I
n
d
u
cto
r
s
an
d
ca
p
ac
ito
r
s
.
I
t
is
v
e
r
y
i
m
p
o
r
t
an
t
t
o
k
n
o
w
t
h
e
b
eh
a
v
i
o
r
d
u
r
i
n
g
s
u
c
h
c
o
n
d
i
ti
o
n
s
,
b
ec
a
u
s
e
m
o
s
t
o
f
t
h
e
VFD
m
a
n
u
f
ac
t
u
r
e
r
s
d
es
ig
n
t
h
e
c
o
n
v
er
t
er
t
o
wo
r
k
in
a
m
o
d
u
la
r
f
as
h
i
o
n
f
o
r
b
o
t
h
s
i
x
-
p
u
ls
e
o
p
e
r
ati
o
n
a
n
d
twe
lv
e
-
p
u
ls
e
o
p
e
r
at
io
n
;
h
o
we
v
e
r
,
t
h
ey
p
la
c
e
m
o
r
e
att
en
ti
o
n
p
la
ce
m
o
r
e
a
t
ten
ti
o
n
o
n
th
e
s
ix
-
p
u
ls
e
c
o
n
d
it
io
n
as
th
ese
a
r
e
t
h
e
h
i
g
h
e
r
-
v
o
l
u
m
e
p
r
o
d
u
cts
.
B
u
t
,
m
o
r
e
atte
n
ti
o
n
n
ee
d
s
to
b
e
g
i
v
e
n
d
u
r
in
g
t
h
e
1
2
p
u
ls
e
c
a
s
e
w
.
r
.
t
th
e
DC
li
n
k
d
y
n
am
ics
i
n
ca
s
e
o
f
s
a
g
s
an
d
u
n
b
ala
n
ce
ev
e
n
ts
,
as
t
h
e
r
eli
ab
i
lit
y
o
f
t
h
e
f
r
o
n
t
-
e
n
d
c
o
m
p
o
n
e
n
ts
w
i
ll
d
e
g
r
a
d
e
co
n
s
i
d
e
r
a
b
l
y
d
u
e
t
o
t
h
e
p
r
es
en
ce
o
f
t
h
e
s
ag
s
a
n
d
u
n
b
a
la
n
c
es.
T
h
is
r
ese
ar
ch
c
o
n
s
i
d
e
r
s
a
7
.
5
k
W
1
2
p
u
ls
e
VF
D
t
o
v
e
r
i
f
y
th
e
a
cc
u
r
ac
y
a
n
d
e
f
f
ec
ti
v
e
n
ess
o
f
t
h
e
a
n
al
y
s
is
b
y
co
m
p
a
r
i
n
g
t
h
e
p
e
r
f
o
r
m
a
n
ce
p
r
e
d
i
c
tio
n
s
o
f
s
im
u
l
ati
o
n
s
an
d
e
x
p
er
im
en
tal
r
es
u
lts
.
T
h
e
ef
f
e
ct
o
n
th
e
DC
li
n
k
i
n
d
u
ct
o
r
c
u
r
r
e
n
ts
a
n
d
t
h
e
l
o
s
s
es
d
u
e
to
th
em
is
d
is
c
u
s
s
e
d
,
r
e
f
e
r
r
i
n
g
t
o
[
1
1
]
.
T
h
e
r
eli
a
b
ili
t
y
o
f
t
h
e
ca
p
ac
i
to
r
h
as
a
ls
o
b
ee
n
p
r
e
d
ic
te
d
b
as
ed
o
n
t
h
e
d
i
f
f
e
r
en
t
m
is
s
i
o
n
p
r
o
f
iles
[
1
2
]
,
[
1
3
]
a
n
d
t
h
r
o
u
g
h
t
h
e
F
I
DE
S
m
et
h
o
d
o
lo
g
y
[
1
4
]
.
S
o
m
e
o
f
t
h
e
ea
r
li
er
r
ese
ar
ch
w
o
r
k
[
1
5
]
-
[
2
3
]
h
as
b
ee
n
r
e
f
e
r
r
e
d
t
o
f
o
r
est
im
ati
n
g
t
h
e
f
a
ilu
r
e
r
ate
o
f
th
e
ca
p
a
cit
o
r
c
o
n
s
i
d
e
r
i
n
g
c
o
n
s
ta
n
t
a
n
d
w
ea
r
-
o
u
t
f
ail
u
r
es.
T
h
e
im
p
ac
t
o
f
t
h
e
g
r
id
i
m
b
al
an
ce
f
o
r
t
h
is
c
ase
h
as
b
e
e
n
an
al
y
z
ed
,
r
ef
er
r
i
n
g
to
t
h
e
r
ese
a
r
c
h
d
o
n
e
i
n
[
2
4
]
,
[
2
5
]
.
2.
T
W
E
L
V
E
-
P
UL
SE
VA
RIA
B
L
E
F
R
E
Q
UE
N
CY
DRI
VE
S
YST
E
M
T
welv
e
-
p
u
ls
e
r
ec
tifie
r
s
h
av
e
g
ain
ed
attr
ac
tio
n
in
th
e
p
r
ese
n
t
-
d
ay
tim
e
,
also
as
th
ey
m
ee
t
th
e
I
E
E
E
-
5
1
9
r
eq
u
ir
em
en
ts
b
ec
a
u
s
e
o
f
t
h
e
s
im
p
le
to
p
o
lo
g
ical
ad
v
a
n
ta
g
e.
T
welv
e
-
p
u
ls
e
r
ec
tifie
r
s
p
r
o
v
id
e
f
ewe
r
lo
s
s
es
an
d
r
ed
u
ce
d
co
n
tr
o
l
n
ee
d
s
,
as
n
o
ac
tiv
e
s
witch
in
g
d
ev
ices
ar
e
in
v
o
lv
ed
.
I
f
th
e
f
ield
in
s
tallatio
n
h
as
a
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
f
ac
ilit
y
,
t
h
e
o
v
er
all
c
o
s
t
o
f
th
e
twelv
e
-
p
u
ls
e
VFD
s
y
s
tem
will
b
e
th
e
s
am
e
as
th
at
o
f
th
e
s
ix
-
p
u
ls
e
VFD
s
y
s
tem
,
an
d
it
g
ets
th
e
ad
v
a
n
tag
e
o
f
m
ee
tin
g
I
E
E
E
-
5
1
9
n
ee
d
s
.
I
n
a
twelv
e
-
p
u
ls
e
v
ar
iab
le
f
r
e
q
u
en
c
y
d
r
iv
e
s
y
s
tem
s
h
o
wn
in
Fig
u
r
e
1
,
th
e
in
p
u
t
cu
r
r
en
t
will
h
av
e
h
ar
m
o
n
ic
c
o
m
p
o
n
en
ts
at
1
1
,
1
3
,
23,
25,
35,
3
7
th
m
u
ltip
les
o
f
f
u
n
d
a
m
en
tal
f
r
eq
u
en
cy
,
wh
er
ein
f
o
r
a
s
ix
-
p
u
ls
e
v
ar
iab
le
f
r
eq
u
en
cy
d
r
iv
e
,
in
a
d
d
itio
n
to
th
is
,
5
,
7,
17,
1
9
,
29,
3
1
s
t
m
u
ltip
les
ar
e
also
p
r
esen
t.
T
o
ac
h
iev
e
a
twelv
e
-
p
u
ls
e
f
u
n
ctio
n
i
n
a
v
ar
ia
b
le
f
r
eq
u
en
cy
d
r
iv
e
,
m
o
s
t
o
f
th
e
m
an
u
f
ac
tu
r
e
r
s
u
s
e
co
n
v
en
tio
n
al
s
ix
-
p
u
ls
e
d
r
iv
es
an
d
co
n
n
ec
t
th
e
DC
s
id
e
o
f
t
h
e
r
ec
tifie
r
p
o
r
tio
n
in
p
ar
allel
,
as
s
h
o
w
n
in
Fig
u
r
e
1
.
Ultim
ately
,
in
th
e
twelv
e
-
p
u
ls
e
d
r
iv
es,
t
h
e
DC
lin
k
ca
p
ac
it
o
r
s
will
ex
p
e
r
ien
c
e
r
ed
u
ce
d
r
ip
p
le
cu
r
r
en
ts
co
m
p
a
r
ed
to
s
ix
-
p
u
ls
e
d
r
iv
es.
T
h
is
is
b
ec
au
s
e
th
e
r
ip
p
le
v
o
ltag
e
p
r
e
s
en
t in
th
e
DC
lin
k
is
les
s
in
m
ag
n
itu
d
e
,
an
d
th
e
r
ip
p
le
f
r
eq
u
e
n
cy
o
f
th
e
DC
lin
k
v
o
ltag
e
is
6
0
0
H
z,
wh
er
e
th
e
s
ix
-
p
u
ls
e
d
r
iv
e
will
s
ee
3
0
0
Hz.
T
h
ese
f
ac
to
r
s
will
g
en
er
ally
r
e
d
u
ce
th
e
l
o
s
s
in
th
e
ca
p
ac
ito
r
s
.
B
u
t
th
e
d
io
d
e/SC
R
b
r
id
g
es
an
d
th
e
in
d
u
cto
r
will
ex
p
er
ien
ce
s
im
ilar
cu
r
r
en
t
co
n
d
u
ctio
n
as
th
at
o
f
th
e
s
ix
-
p
u
ls
e
r
ec
tifie
r
ca
s
e
,
with
th
e
p
h
ase
s
h
if
t
in
th
e
cu
r
r
e
n
ts
.
B
ec
au
s
e
o
f
th
i
s
p
h
en
o
m
e
n
o
n
,
t
h
e
s
tr
ess
es
in
th
e
DC
lin
k
co
m
p
o
n
en
ts
ar
e
n
o
t
ex
ac
tly
th
e
s
am
e
as
th
o
s
e
o
f
th
e
s
ix
-
p
u
ls
e
ca
s
e.
T
h
e
u
s
e
o
f
in
ter
p
h
ase
r
ea
cto
r
s
ca
n
r
ed
u
ce
t
h
is
ef
f
ec
t.
B
u
t
th
e
d
esig
n
is
m
o
r
e
ex
p
en
s
iv
e
,
an
d
m
an
y
d
r
iv
e
m
an
u
f
ac
tu
r
e
r
s
d
o
n
o
t
p
r
ef
er
th
is
o
p
tio
n
,
a
n
d
th
e
m
o
d
u
lar
ity
in
th
e
d
esig
n
will
b
e
lo
s
t
.
No
n
e
o
f
th
e
ea
r
lier
r
esear
ch
h
as
an
aly
ze
d
th
e
s
tr
ess
es
in
th
e
DC
lin
k
co
m
p
o
n
en
ts
o
f
twelv
e
-
p
u
ls
e
r
ec
tifie
r
s
in
d
etail.
T
h
e
v
o
ltag
e
r
ef
lecte
d
o
n
th
e
DC
s
id
e
o
f
th
e
VFD
will
b
e
d
ir
ec
tly
im
p
ac
ted
b
y
two
p
ar
am
eter
s
.
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
6
9
4
I
mp
a
ct
a
n
d
r
elia
b
ilit
y
a
n
a
lysi
s
o
f v
o
lta
g
e
s
a
g
s
in
a
mu
lti
-
p
u
l
s
e
tr
a
n
s
fo
r
mer
…
(
R
.
Go
va
r
th
a
n
a
n
)
125
f
ir
s
t
o
n
e
is
th
e
v
o
ltag
e
tr
a
n
s
f
o
r
m
atio
n
in
t
h
e
s
ec
o
n
d
a
r
y
win
d
i
n
g
s
.
T
h
e
s
ec
o
n
d
o
n
e
is
th
e
v
o
lt
ag
e
v
ar
iatio
n
in
th
e
tr
an
s
f
o
r
m
atio
n
d
u
e
t
o
th
e
v
o
ltag
e
s
ag
s
an
d
th
eir
t
y
p
e.
T
h
e
f
o
llo
win
g
two
s
ec
tio
n
s
d
escr
ib
e
th
e
s
am
e.
Fig
u
r
e
1
.
T
welv
e
-
p
u
ls
e
v
ar
ia
b
le
f
r
eq
u
e
n
cy
d
r
iv
e
3.
VO
L
T
AG
E
T
R
ANSF
O
R
M
AT
I
O
N
I
N
DIFF
E
RE
N
T
T
YP
E
S
O
F
T
RA
NSFO
R
M
E
R
S
T
h
e
tr
an
s
f
o
r
m
e
r
ty
p
es
ar
e
class
if
ied
in
to
th
r
ee
ca
teg
o
r
ies.
Du
r
in
g
th
e
p
r
e
-
f
au
lt
v
o
ltag
es
an
d
d
u
r
in
g
th
e
f
au
lt
co
n
d
itio
n
s
,
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
atio
n
will
b
e
d
if
f
e
r
en
t
with
r
esp
ec
t
to
d
i
f
f
er
en
t
t
y
p
e
s
o
f
tr
an
s
f
o
r
m
er
s
in
ter
m
s
o
f
m
ag
n
itu
d
e
an
d
p
h
ase
-
an
g
le.
T
h
is
is
g
ettin
g
r
o
tate
d
with
o
u
t
an
y
in
f
lu
en
ce
o
n
th
e
eq
u
ip
m
en
t.
Su
ch
p
h
aso
r
r
o
tatio
n
ca
n
b
e
s
ee
n
as
a
s
h
if
t
in
th
e
ze
r
o
p
o
in
t
o
n
th
e
tim
e
ax
is
,
w
h
ich
,
o
f
co
u
r
s
e
,
h
as
n
o
in
f
lu
e
n
ce
o
n
th
e
eq
u
ip
m
en
t
b
e
h
av
io
r
.
T
h
e
th
r
ee
d
if
f
e
r
en
t
ty
p
es
o
f
t
r
an
s
f
o
r
m
er
s
an
d
th
eir
t
r
an
s
f
o
r
m
ati
o
n
ar
e
as
ex
p
lain
ed
b
elo
w,
r
ef
er
e
n
cin
g
[
3
]
.
−
T
y
p
e
1
:
T
r
a
n
s
f
o
r
m
er
s
th
at
d
o
n
o
t
ch
an
g
e
a
n
y
th
in
g
to
th
e
v
o
l
tag
es.
Her
e,
th
e
s
ec
o
n
d
ar
y
v
o
l
tag
es
ar
e
eq
u
al
to
th
e
p
r
im
ar
y
v
o
ltag
es.
T
h
is
is
p
o
s
s
ib
le
with
o
n
ly
a
s
tar
-
s
tar
(
Yy
)
tr
a
n
s
f
o
r
m
er
with
s
tar
p
o
in
ts
g
r
o
u
n
d
ed
.
T
h
e
f
o
llo
win
g
is
th
e
v
o
ltag
e
t
r
an
s
f
o
r
m
atio
n
m
atr
ix
o
f
ty
p
e
1
t
r
an
s
f
o
r
m
er
.
1
=
[
1
0
0
0
1
0
0
0
1
]
(
1
)
−
T
y
p
e
2
:
T
r
an
s
f
o
r
m
er
th
at
ca
n
r
em
o
v
e
th
e
ze
r
o
-
s
eq
u
en
ce
c
o
m
p
o
n
e
n
t.
T
h
e
s
ec
o
n
d
ar
y
v
o
lta
g
es
ar
e
eq
u
al
to
th
e
v
o
ltag
es
o
n
th
e
p
r
im
ar
y
s
i
d
e,
m
in
u
s
th
e
ze
r
o
-
s
eq
u
en
ce
v
o
ltag
e.
T
h
e
e
x
am
p
les
ar
e
Yy
t
r
an
s
f
o
r
m
er
with
o
n
e
o
r
b
o
th
p
o
in
ts
n
o
t
g
r
o
u
n
d
e
d
an
d
a
d
elta
-
d
elta
(
Dd
)
co
n
n
e
cted
tr
an
s
f
o
r
m
er
.
T
h
e
f
o
llo
win
g
is
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
o
f
a
ty
p
e
2
tr
an
s
f
o
r
m
er
.
2
=
1
3
[
2
−
1
−
1
−
1
2
−
1
−
1
−
1
2
]
(
2
)
−
T
y
p
e
3
:
T
r
a
n
s
f
o
r
m
er
s
th
at
s
wap
lin
e
an
d
p
h
ase
v
o
ltag
es.
Fo
r
th
ese
tr
an
s
f
o
r
m
e
r
s
,
ea
ch
s
ec
o
n
d
ar
y
v
o
ltag
e
eq
u
als
th
e
d
if
f
er
en
ce
b
etwe
en
two
p
r
im
ar
y
s
id
e
v
o
ltag
es.
T
h
e
ex
am
p
les
ar
e
d
elta
-
s
tar
(
Dy
)
an
d
th
e
s
tar
-
Delta
(
Yd
)
tr
an
s
f
o
r
m
er
s
.
T
h
e
f
o
llo
win
g
is
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
atio
n
m
atr
ix
o
f
a
t
y
p
e
3
tr
an
s
f
o
r
m
er
(
3
)
.
3
=
√
3
[
0
1
−
1
−
1
0
1
1
−
1
0
]
(
3
)
T
h
e
p
r
ev
io
u
s
d
is
cu
s
s
io
n
s
o
n
th
e
tr
an
s
f
o
r
m
er
v
o
ltag
e
tr
an
s
f
o
r
m
atio
n
s
ar
e
v
er
y
im
p
o
r
tan
t
to
co
n
s
id
er
,
as
it
is
d
ir
ec
tly
lin
k
ed
with
th
e
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
e
r
s
.
T
h
e
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
s
will
h
av
e
th
e
two
s
ec
o
n
d
ar
y
win
d
in
g
s
wh
er
e
o
n
e
is
d
elta
-
co
n
n
ec
ted
,
a
n
d
th
e
o
th
er
o
n
e
is
s
tar
-
co
n
n
ec
ted
.
T
h
e
p
r
im
ar
y
win
d
in
g
ca
n
b
e
eith
er
a
s
tar
o
r
a
d
elta
c
o
n
n
ec
tio
n
.
So
,
th
e
v
o
ltag
e
tr
an
s
f
o
r
m
atio
n
in
th
e
s
ec
o
n
d
ar
y
w
in
d
in
g
s
ca
n
b
e
an
y
o
n
e
o
f
th
e
th
r
ee
tr
an
s
f
o
r
m
atio
n
m
o
d
els as sh
o
wn
in
(
1
)
,
(
2
)
,
an
d
(
3
)
b
ased
o
n
th
e
t
r
an
s
f
o
r
m
er
ar
r
an
g
em
en
t.
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
:
123
-
1
40
126
4.
T
YP
E
O
F
VO
L
T
AG
E
SAG
S
T
h
e
v
o
ltag
e
s
ag
s
ar
e
class
if
ied
as
ty
p
e
A
t
o
ty
p
e
D
s
ag
s
,
as
s
h
o
wn
in
th
e
T
a
b
le.
1
.
T
y
p
e
A
s
ag
is
th
e
b
alan
ce
d
s
ag
,
a
n
d
o
th
er
s
ag
s
a
r
e
u
n
b
alan
ce
d
s
ag
s
.
T
y
p
e
B
sa
g
is
m
ag
n
itu
d
e
u
n
b
alan
ce
d
s
ag
,
wh
er
e
ty
p
e
C
an
d
ty
p
e
D
ch
an
g
es b
o
th
m
ag
n
itu
d
e
an
d
p
h
ase
an
g
le.
[
%
]
=
[
−
∅
]
(
4
)
=
+
+
3
(
5
)
W
h
er
e
V
avg
is
th
e
a
v
er
ag
e
v
alu
e
o
f
th
e
th
r
ee
-
p
h
ase
v
o
ltag
es
.
V
Ø
is
th
e
in
d
iv
id
u
al
p
h
ase
v
o
lt
ag
e.
Fig
u
r
e
2
s
h
o
ws
th
e
p
h
aso
r
d
iag
r
am
o
f
th
r
ee
-
p
h
ase
v
o
ltag
es
u
n
d
e
r
s
u
ch
s
ag
s
ce
n
ar
io
s
.
T
h
ese
s
ag
s
r
e
f
lect
b
alan
ce
d
an
d
u
n
b
alan
ce
d
co
n
d
itio
n
s
ac
co
r
d
i
n
g
to
th
eir
ch
ar
ac
ter
is
tics
.
T
h
e
am
o
u
n
t
o
f
u
n
b
alan
ce
is
ex
p
r
ess
ed
ac
co
r
d
in
g
to
I
E
E
E
is
g
iv
e
n
in
(
4
)
,
wh
er
e
V
avg
is
s
h
o
wn
in
(
5
)
.
T
ab
le
1
p
r
esen
ts
th
e
p
h
ase
v
o
ltag
e
eq
u
atio
n
s
f
o
r
d
if
f
er
en
t
ty
p
es
o
f
s
ag
s
,
wh
er
e
h
is
th
e
s
ag
d
ep
th
in
p
.
u
.
V
=V
L
/√
3
p
h
as
e
to
g
r
o
u
n
d
v
o
ltag
e.
T
h
ese
s
ag
s
will
b
e
m
ain
ly
g
e
n
er
ated
d
u
e
to
s
in
g
le
-
p
h
ase
f
au
lts
an
d
lin
e
-
to
-
lin
e
f
au
lts
,
as
th
r
ee
-
p
h
ase
f
au
lts
ar
e
n
o
t
co
m
m
o
n
in
m
an
y
o
f
th
e
s
ce
n
ar
i
o
s
.
T
h
e
ch
ar
ac
ter
is
tic
eq
u
atio
n
s
o
f
th
ese
s
ag
s
ar
e
g
iv
en
in
eq
u
atio
n
s
in
T
ab
le
1
.
T
h
e
v
o
ltag
e
p
h
aso
r
s
cr
ea
te
an
u
n
b
alan
ce
d
s
itu
atio
n
in
m
o
s
t o
f
th
e
s
a
g
co
n
d
itio
n
s
,
ex
ce
p
t
f
o
r
ty
p
e
A
s
ag
.
T
h
e
t
y
p
e
C
an
d
ty
p
e
D
s
ag
s
p
r
o
d
u
ce
p
h
ase
u
n
b
alan
ce
s
,
alo
n
g
with
m
ag
n
itu
d
e
u
n
b
alan
ce
s
.
Fig
u
r
e
2
.
Fo
u
r
ty
p
es
o
f
s
ag
s
in
p
h
aso
r
d
ia
g
r
am
s
o
b
tai
n
ed
[
3
]
T
ab
le
1
.
Fo
u
r
ty
p
es o
f
s
ag
s
in
eq
u
atio
n
s
o
b
tain
e
d
[
3
]
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
Ty
p
e
A
S
a
g
=
ℎ
=
−
1
2
ℎ
−
1
2
ℎ
√
3
=
−
1
2
ℎ
+
1
2
ℎ
√
3
Ty
p
e
B
S
a
g
=
ℎ
=
−
1
2
−
1
2
√
3
=
−
1
2
+
1
2
√
3
Ty
p
e
C
S
a
g
=
=
−
1
2
−
1
2
ℎ
√
3
=
−
1
2
+
1
2
ℎ
√
3
Ty
p
e
D
S
a
g
=
ℎ
=
−
1
2
ℎ
−
1
2
√
3
=
−
1
2
ℎ
+
1
2
√
3
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
I
mp
a
ct
a
n
d
r
elia
b
ilit
y
a
n
a
lysi
s
o
f v
o
lta
g
e
s
a
g
s
in
a
mu
lti
-
p
u
l
s
e
tr
a
n
s
fo
r
mer
…
(
R
.
Go
va
r
th
a
n
a
n
)
127
5.
SAG
P
RO
P
AG
AT
I
O
N
I
N
T
WE
L
VE
-
P
U
L
S
E
T
RA
NSF
O
RM
E
R
5
.
1
.
T
welv
e
-
pu
ls
e
t
ra
ns
f
o
rmer
co
nfig
ura
t
io
ns
T
welv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
co
n
s
is
ts
o
f
two
s
ec
o
n
d
a
r
y
win
d
in
g
s
an
d
o
n
e
p
r
im
ar
y
win
d
in
g
.
T
h
e
s
ec
o
n
d
ar
y
win
d
in
g
s
u
s
ed
to
h
av
e
s
tar
an
d
d
elta
co
n
n
ec
tio
n
s
.
Du
r
in
g
th
e
b
alan
ce
d
v
o
ltag
e
at
th
e
p
r
im
a
r
y
,
t
h
e
p
h
ase
s
h
if
t b
etwe
en
th
ese
two
s
ec
o
n
d
ar
y
win
d
in
g
s
will b
e
3
0
°
b
ased
o
n
th
e
co
n
f
ig
u
r
atio
n
t
o
elim
in
ate
5
th
an
d
7
th
h
ar
m
o
n
ics
in
th
e
r
ec
tifie
r
.
So
,
in
a
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
’
s
p
r
im
ar
y
cu
r
r
e
n
t,
1
1
th
an
d
1
3
t
h
o
r
d
er
h
ar
m
o
n
ics
will
b
e
th
e
m
ajo
r
.
T
h
e
cu
r
r
en
ts
s
h
ar
ed
b
y
two
s
ec
o
n
d
ar
y
win
d
in
g
s
will
b
e
eq
u
al
d
u
r
in
g
b
ala
n
ce
d
v
o
ltag
e
an
d
b
ala
n
ce
d
l
o
ad
c
o
n
d
itio
n
s
.
I
n
th
e
ca
s
e
o
f
twelv
e
-
p
u
ls
e
th
r
ee
-
p
h
ase
r
ec
tifie
r
s
,
as
s
h
o
wn
in
Fig
u
r
e
1
,
an
d
th
e
s
ec
o
n
d
a
r
y
lo
ad
s
ar
e
b
a
lan
ce
d
,
th
e
cu
r
r
en
ts
o
r
cu
r
r
en
t
h
ar
m
o
n
ics ca
r
r
ied
b
y
th
e
in
d
iv
id
u
al
r
ec
tifie
r
will
b
e
b
alan
ce
d
u
n
til
th
e
b
alan
ce
d
v
o
ltag
e
is
p
r
esen
t
in
th
e
p
r
im
ar
y
tr
an
s
f
o
r
m
er
.
Few
ea
r
lier
r
esear
ch
er
s
h
av
e
ad
d
r
ess
ed
th
e
an
aly
s
is
o
f
twel
v
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
f
u
n
ctio
n
ality
[
4
]
,
[
5
]
an
d
b
r
ie
f
ly
ex
p
lain
ed
th
is
.
A
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
with
a
d
elta
p
r
im
ar
y
win
d
in
g
is
co
n
s
id
e
r
ed
f
o
r
th
is
an
aly
s
is
.
Ad
d
itio
n
ally
,
f
o
r
s
im
p
licity
,
in
s
tead
o
f
co
n
s
id
er
in
g
o
n
e
s
in
g
le
th
r
ee
-
win
d
in
g
tr
an
s
f
o
r
m
er
,
two
two
-
win
d
in
g
t
r
an
s
f
o
r
m
er
s
ar
e
co
n
s
id
er
ed
.
T
h
e
v
ec
to
r
g
r
o
u
p
o
f
th
ese
two
tr
an
s
f
o
r
m
er
s
is
Dy
1
(
d
elta
-
s
tar
)
an
d
Dd
0
(
d
elta
-
d
elta
).
5
.
2
.
Sa
g
pro
pa
g
a
t
io
n in
a
t
w
elv
e
-
pu
ls
e
t
ra
ns
f
o
rm
er
Du
r
in
g
th
e
n
o
r
m
al
b
alan
ce
d
o
p
er
atin
g
co
n
d
itio
n
s
o
f
a
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
,
th
e
tr
an
s
f
o
r
m
atio
n
o
f
v
o
ltag
es
f
r
o
m
p
r
im
ar
y
to
s
ec
o
n
d
ar
y
win
d
in
g
s
is
d
escr
ib
ed
i
n
ea
r
lier
s
ec
tio
n
s
.
B
u
t
d
u
r
in
g
t
h
e
s
ag
s
ce
n
ar
io
,
th
e
p
h
ase
an
d
am
p
litu
d
e
will v
ar
y
b
etwe
en
th
e
s
ec
o
n
d
a
r
y
win
d
i
n
g
s
b
ec
au
s
e
o
f
t
h
e
tr
an
s
f
o
r
m
er
co
n
f
ig
u
r
atio
n
s
an
d
d
if
f
er
en
t
s
ag
tr
a
n
s
f
o
r
m
atio
n
p
h
en
o
m
en
a
.
C
o
n
s
id
er
in
g
th
e
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
co
n
f
ig
u
r
atio
n
as
p
er
Fig
u
r
e
1
,
th
e
tr
an
s
f
o
r
m
atio
n
o
f
s
ag
ty
p
e
in
th
e
s
ec
o
n
d
a
r
y
s
id
e
,
as
s
h
o
wn
in
T
ab
le
2
,
r
e
f
er
r
i
n
g
to
[
1
]
.
So
,
th
e
ex
p
ec
te
d
v
o
ltag
e
an
d
c
u
r
r
en
t
v
ar
iatio
n
s
in
th
e
s
ec
o
n
d
ar
y
win
d
in
g
s
will
b
e
d
if
f
er
e
n
t
in
th
e
ca
s
e
o
f
th
e
twelv
e
-
p
u
ls
e
r
ec
tifie
r
s
d
u
r
in
g
s
ag
an
d
u
n
b
alan
ce
d
co
n
d
itio
n
s
.
Fo
r
e
x
am
p
le,
in
th
e
ca
s
e
o
f
a
ty
p
e
B
s
ag
s
ce
n
ar
io
,
th
e
r
ef
lecte
d
ef
f
ec
t
a
t
th
e
s
ec
o
n
d
ar
y
win
d
in
g
’
s
d
elta
an
d
s
tar
o
f
th
e
tr
an
s
f
o
r
m
e
r
will
b
e
ty
p
e
D
an
d
ty
p
e
C
,
r
esp
ec
tiv
ely
.
T
h
is
cr
ea
tes
d
if
f
er
en
t
p
h
ase
an
d
m
ag
n
itu
d
e
d
ef
lectio
n
b
etwe
en
th
e
two
s
ec
o
n
d
ar
y
win
d
in
g
s
co
m
p
a
r
ed
to
th
e
b
ala
n
ce
d
o
p
er
atin
g
c
o
n
d
itio
n
.
T
h
is
cr
ea
tes
a
d
if
f
er
en
t
s
ce
n
a
r
io
in
r
ec
tifie
r
co
n
d
u
ctio
n
as
well.
T
h
is
s
ce
n
ar
io
will
cr
e
ate
an
u
n
b
alan
ce
d
cu
r
r
en
t
c
o
n
d
u
ctio
n
i
n
b
etwe
en
th
e
r
ec
tifie
r
s
an
d
th
e
DC
lin
k
in
d
u
cto
r
s
.
T
h
is
will
lead
to
th
e
cr
ea
tio
n
o
f
h
i
g
h
r
ip
p
le
cu
r
r
e
n
ts
in
th
e
DC
lin
k
ca
p
ac
ito
r
s
d
u
e
to
th
e
p
r
esen
ce
o
f
lo
w
-
f
r
eq
u
e
n
cy
co
m
p
o
n
en
ts
o
t
h
er
th
a
n
3
0
0
Hz.
T
h
e
n
e
x
t
s
ec
t
io
n
will
an
aly
ze
th
is
p
h
en
o
m
e
n
o
n
in
d
etail
th
r
o
u
g
h
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
r
esu
lts
.
T
h
e
p
ap
er
will
f
o
c
u
s
o
n
th
e
im
p
ac
t
o
f
ty
p
e
A
an
d
ty
p
e
B
s
ag
s
in
th
e
p
r
im
ar
y
s
id
e
o
f
a
twelv
e
-
p
u
ls
e
r
ec
tifie
r
s
y
s
te
m
an
d
th
e
r
eli
ab
ilit
y
o
f
d
if
f
er
en
t
d
ev
ices.
T
h
e
r
esu
ltan
t
ef
f
ec
ts
ex
p
ec
ted
ar
e
lik
e
th
e
s
ce
n
ar
io
s
o
f
ty
p
e
C
an
d
ty
p
e
D,
as m
en
t
io
n
ed
in
T
a
b
le
2
.
I
n
th
e
f
u
r
th
e
r
s
ec
tio
n
s
,
o
n
ly
th
e
ef
f
ec
t o
f
s
ag
s
an
d
u
n
b
alan
ce
s
p
r
o
d
u
ce
d
b
y
ty
p
e
A
an
d
t
y
p
e
B
s
ag
s
will b
e
d
is
cu
s
s
ed
b
ec
au
s
e
o
f
th
is
.
T
ab
le
2
.
T
r
a
n
s
f
o
r
m
atio
n
o
f
s
ag
ty
p
e
to
s
ec
o
n
d
ar
y
win
d
in
g
s
v
s
v
ar
io
u
s
p
r
im
a
r
y
s
ag
s
P
r
i
m si
d
e
sa
g
(
d
e
l
t
a
)
Ty
p
e
A
Ty
p
e
B
Ty
p
e
C
Ty
p
e
D
R
e
f
l
e
c
t
e
d
se
c
.
S
i
d
e
s
a
g
(
d
e
l
t
a
)
Ty
p
e
A
Ty
p
e
D
Ty
p
e
C
Ty
p
e
D
R
e
f
l
e
c
t
e
d
se
c
.
S
i
d
e
s
a
g
(
st
a
r
)
Ty
p
e
A
Ty
p
e
C
Ty
p
e
D
Ty
p
e
C
6.
E
F
F
E
C
T
S O
F
SAG
S I
N
RE
CT
I
F
I
E
R
CO
M
P
O
NE
NT
S
A
7
.
5
k
W
,
5
0
0
V,
twelv
e
-
p
u
ls
e
VFD
s
etu
p
is
u
s
ed
to
ev
alu
a
te
th
e
d
r
iv
e
c
h
ar
ac
ter
is
tics
wit
h
DC
lin
k
in
d
u
cto
r
ch
a
r
ac
ter
is
tics
.
Fig
u
r
e
3
(
a
)
.
s
h
o
ws
th
e
ex
p
er
im
e
n
tal
an
d
m
ea
s
u
r
em
en
t
s
etu
p
with
an
in
d
u
ctio
n
m
o
to
r
lo
ad
s
etu
p
,
an
d
t
h
e
m
ea
s
u
r
ed
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
3
(
b
)
.
Fig
u
r
e
3
(
c
)
co
n
f
ir
m
s
v
e
r
y
g
o
o
d
a
g
r
ee
m
en
t
with
th
e
s
im
u
lated
r
esu
lts
wi
th
th
e
b
alan
ce
d
i
n
p
u
t
v
o
ltag
e
.
T
h
e
twelv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
h
as
p
r
im
ar
y
s
tar
co
n
f
ig
u
r
atio
n
h
as
b
ee
n
co
n
s
i
d
er
ed
f
o
r
th
e
an
al
y
s
is
.
T
h
e
s
im
u
latio
n
an
d
p
r
ac
tical
ex
p
e
r
im
en
ts
h
av
e
b
ee
n
ex
ten
d
ed
with
d
if
f
er
en
t
s
ag
s
ce
n
ar
io
s
ac
co
r
d
in
g
to
T
ab
le
2
t
o
an
aly
ze
th
e
ef
f
ec
t
o
f
th
e
s
ag
s
o
n
th
e
twelv
e
-
p
u
ls
e
VFD
s
ec
tio
n
s
in
th
e
n
ex
t sectio
n
s
.
6
.
1
.
T
y
pe
A
s
a
g
a
nd
t
he
ef
f
e
ct
T
y
p
e
A
s
ag
is
a
v
o
ltag
e
-
b
ala
n
ce
d
s
ag
.
T
h
e
in
cr
ea
s
ed
s
ag
d
e
p
th
p
r
o
d
u
ce
s
th
e
b
alan
ce
d
s
ag
r
ef
lectio
n
in
b
o
th
th
e
s
ec
o
n
d
ar
y
s
id
es
o
f
th
e
tr
an
s
f
o
r
m
e
r
s
.
B
ec
au
s
e
o
f
th
is
f
ac
t,
d
u
r
in
g
an
y
s
ag
,
th
e
r
ec
tifie
r
s
will
b
e
s
tr
ess
ed
eq
u
ally
.
Fig
u
r
e
4
s
h
o
ws th
e
s
im
u
latio
n
r
esu
lts
at
ty
p
e
A
s
ag
s
ce
n
ar
io
.
6
.
2
.
T
y
pe
B
s
a
g
a
nd
t
he
ef
f
e
ct
T
y
p
e
B
s
ag
is
an
u
n
b
alan
ce
d
s
ag
with
r
esp
ec
t
to
th
e
m
ag
n
itu
d
e.
B
u
t
wh
en
th
e
ty
p
e
B
s
ag
is
ap
p
lied
at
th
e
p
r
im
ar
y
win
d
in
g
o
f
th
e
tw
elv
e
-
p
u
ls
e
tr
an
s
f
o
r
m
er
,
it
r
ef
l
ec
ts
in
to
ty
p
e
C
an
d
ty
p
e
D
s
ag
in
s
tar
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
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4
I
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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
I
mp
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129
Fig
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9
)
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
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&
Dr
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s
t
,
Vo
l.
1
7
,
No
.
1
,
Ma
r
c
h
20
2
6
:
123
-
1
40
130
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b
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u
r
e
6
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ar
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d
r
iv
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c
o
m
p
o
n
en
ts
.
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
I
mp
a
ct
a
n
d
r
elia
b
ilit
y
a
n
a
lysi
s
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f v
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lta
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mu
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-
p
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s
e
tr
a
n
s
fo
r
mer
…
(
R
.
Go
va
r
th
a
n
a
n
)
131
Fig
u
r
e
7
.
T
h
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m
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r
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v
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r
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d
ep
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m
0
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7
7.
DC
L
I
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it
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h
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t
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atin
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u
r
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DC
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I
n
d
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cto
r
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g
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f
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ctu
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ac
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o
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it,
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h
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w
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u
r
e
8
.
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h
e
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e
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z
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ig
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o
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twelv
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u
r
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ty
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Fig
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.
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r
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ar
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elta
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[
8
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ar
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6
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c
is
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r
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,
E
h
is
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e
am
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litu
d
e
Evaluation Warning : The document was created with Spire.PDF for Python.