Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 3
,
Ju
n
e
201
6, p
p
. 1
248
~ 12
59
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
3.9
222
1
248
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
Breakdowns' Di
agnosis of A Ne
w Character Three-Phase High
Voltage Power Supply for Indus
trial Microwave
Generators
with N=2 Magnetrons per Phase
R. B
a
ti
t
1
, M
.
C
h
ra
yga
ne
1
, M
.
Ferf
ra
2
, M
.
F
a
del
3
, A. Ds
oul
1
, B. Baha
ni
1
1
Agadir High
School of
Technolog
y
,
MSTI R
e
search
Team, Ibno
u Z
ohr Univ
ersity
, Agadir
-Morocco
2
Mohammadia’s School of
Eng
i
n
eers, Resear
ch
Team in
Electr
i
cal Energ
y
& Contr
o
l,
Moha
me
d V Unive
r
si
ty
, Ra
ba
t
-
Moroc
c
o
3
Laborator
y
of
Electronic, Sign
al
Processing and
Ph
y
s
ic
al Modeling, Ibn
Zohr
University
, Agadir-
M
orocco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 12, 2015
Rev
i
sed
Jan
5, 2
016
Accepte
d
Ja
n 20, 2016
This paper tr
ea
ts the m
odelisa
tion of
a new
three ph
as
e cha
r
act
er high
voltag
e
supply
(HV) for in
dustrial micro
w
ave gener
a
tor
s
with N=2
magnetrons per phase.
T
h
i
s
a
lime
nt
a
t
i
on i
s
ba
se
d on t
h
e
pre
s
ent
a
t
i
on of a
n
equivalent
circuit model of
a n
e
wly
dimens
ion
e
d high voltag
e
transformer.
Each
phase of
the three phase s
y
st
em supplies two pa
rallel cell
voltag
e
doublers and
current stabilizer
. Each of
th
ese cells in
turn s
upplies one
magnetron 800Watts / 2.45GHz.
This power supply
is
a star connection of
three
iden
tic
al
m
odels of the si
ngle-
phase power for N=2 mag
n
etrons.
Th
e
simulation under EMTP (Electr
o
Magneti
c Tr
ansients Program) in nominal
conditions
a
llo
ws
concluding
that th
eore
tic
al
res
u
lts
are ad
j
acen
t to the
experim
e
nt
al m
e
as
urem
ents
.
Furthermore,
a failur
e
stud
y
of six
magnetron
of
the m
i
crowave g
e
nera
tor is
als
o
proces
s
e
d. Th
e r
e
sults perm
it to
observe tha
t
the in
ter
action b
e
tween
magnetr
ons dosn’
t influence th
e nominal
operation of
the s
y
s
t
em
.
Keyword:
Breakdowns'
diagnosis
M
a
gnet
r
o
n
EMTP
M
odel
l
i
n
g
R
e
gul
at
i
o
n
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
R
e
do
ua
ne B
A
TIT,
R
e
search
Tea
m
of M
odel
i
s
at
i
on,
Sy
st
em
s a
n
d In
for
m
at
io
n of
Tech
no
log
y
,
I
bno
u Zohr
U
n
iv
er
sity,
H
i
gh
Scho
o
l
of
Techno
log
y
, BP:
33
/S 8
0000
, Ag
ad
i
r
-
M
o
r
o
cco.
Em
a
il: red
o
u
a
ne.b
atit@edu
.
u
i
z.ac.m
a
1.
INTRODUCTION
Th
e Fi
g
u
r
e
1A in
d
i
cates a m
i
cr
ow
av
e pow
er
su
pp
ly fo
r
i
n
d
u
s
t
r
ial app
licatio
n
requ
ir
ing 48
00
W
a
tts
of power for
N=6 m
a
gnetrons
(each m
a
gnetron
needs a
powe
r
of 800
Watts to
ge
nerate a hi
gh frequenc
y
wave
of
2.
4G
Hz)
.
These m
a
gnet
r
o
n
s are
p
o
we
re
d by
6 o
r
di
nary
t
r
ans
f
o
r
m
e
rs wi
t
h
m
a
gnet
i
c
sh
u
n
t
,
t
h
r
o
ug
h
six
cell vo
ltage d
oub
lers. In
Fig
u
re
1
B
, th
e co
nfigurati
on
of t
h
i
s
m
i
crowave s
u
p
p
l
y
sy
st
em
i
s
im
prov
ed b
y
red
u
ci
n
g
t
h
e
n
u
m
b
er of t
r
a
n
sfo
r
m
e
rs t
o
3 t
r
ans
f
o
r
m
e
rs, newl
y
di
m
e
nsi
one
d, eac
h o
f
whi
c
h i
s
capa
b
l
e
of
sup
p
l
y
i
n
g t
h
e
po
we
r o
f
t
w
o
m
a
gnet
r
ons
si
m
u
lt
aneou
s
l
y
. Last
but
not
l
east
a new t
h
r
ee pha
se m
i
cr
owa
v
e
po
we
r su
ppl
y
i
s
devel
ope
d i
n
or
der t
o
be abl
e
t
o
pr
ovi
de t
h
e usef
ul
p
o
we
r
req
u
i
r
e
d
fo
r t
h
e 6 m
a
gnet
r
o
n
s
.
Thi
s
n
e
w
po
wer supp
ly is
m
o
re o
p
t
i
m
al
in
term
s o
f
its
m
a
ss an
d
its v
o
l
u
m
e; also
it red
u
c
ed
th
e
wiring
cong
est
i
o
n
,
whic
h
reduces
the costs of m
a
nu
fact
u
r
i
n
g a
n
d m
a
i
n
t
e
nance.
Fi
gu
re 2 sh
o
w
s t
h
e schem
a
tic di
agram
of the ne
w
three
-
phase cha
r
acter high
vo
ltag
e
po
w
e
r
supp
ly
for N=
2 m
a
gnetrons. It is a star connection of three
hi
gh voltage leakage field tr
a
n
s
f
orm
e
rs that e
ach one
su
pp
lies two
do
ub
lers cells vo
ltag
e
an
d cu
rren
t
stab
ilizers.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Break
dow
ns
' D
i
agnosis of
A N
e
w Character
Three
Phase
H
i
gh
Voltage
Power Supply for.
... (
R
.
B
a
tit)
1
249
Fi
gu
re
1.
(A
) C
l
assi
cal
si
ngl
e
pha
se m
i
crowa
v
e
po
we
r s
u
p
p
l
y
fo
r
N=6
m
a
gnet
r
ons
(B
) T
h
e
ne
w
si
ngl
e
p
h
ase m
i
cro
w
ave
p
o
w
e
r
s
u
p
p
l
y
f
o
r
N
=
6 m
a
gnet
r
ons
(C
) T
h
e
new three
phase m
i
crowa
v
e p
o
w
e
r su
pp
ly
for
N
=
6
m
a
g
n
e
tr
on
s
Th
is article con
s
ists of two
main
p
a
rts: In
th
e firs
t
part
,
we p
r
ese
n
t
an
equi
val
e
nt
ci
rc
ui
t
di
ag
ram
of
th
e n
e
w ch
aracter th
ree-ph
ase h
i
gh
vo
ltag
e
po
wer su
pp
ly
co
n
s
titu
ted
of three id
en
ti
cal mo
d
e
ls
star-co
nnected
o
f
sin
g
l
e-ph
ase h
i
gh
vo
ltag
e
p
o
w
e
r
sup
p
l
y
f
o
r
N
=
2
m
a
g
n
e
tro
n
s
[
1
]-[3
].
Th
e sim
u
lati
o
n
o
f
th
e n
e
w th
r
ee-
pha
se hi
gh
v
o
l
t
age p
o
w
er s
u
p
p
l
y
el
ect
ri
cal
ope
rat
i
o
n al
l
o
wed t
o
obse
r
ve
i
t
s
di
ffe
rent
t
i
m
e
depe
nde
nt
cur
v
es
of di
ffe
rent
c
u
r
r
ent
s
a
nd
v
o
l
t
a
ges.
A
nd t
h
at
t
o
co
m
p
are with
th
o
s
e
ob
tain
ed
ex
peri
men
t
ally [4
]-[6
] in
con
v
e
n
t
i
onal
s
i
ngl
e-
p
h
ase
hi
gh
v
o
l
t
a
ge
p
o
w
er
su
p
p
l
y
fo
r
si
ngl
e
m
a
gnet
r
o
n
(Fi
g
u
r
e
6.
B
)
. Fi
nal
l
y
, t
h
e an
ode
cur
r
ent
re
gul
at
i
o
n
p
r
ocess i
n
e
ach m
a
gnet
r
on
has
bee
n
c
o
m
p
l
e
t
e
l
y
veri
fi
e
d
.
Fi
gu
re
2.
C
h
a
r
act
er t
h
r
ee
pha
se hi
gh
v
o
l
t
a
ge
p
o
we
r s
u
ppl
y
fo
r t
w
o m
a
gnet
r
o
n
s
pe
r
phase
C
once
r
ni
ng
t
h
i
s
ne
w cha
r
act
e
r
t
h
re
e-
pha
se h
i
gh
vol
t
a
ge p
o
w
er s
u
ppl
y
f
o
r
t
w
o m
a
gnet
r
on
s per
p
h
ase,
t
h
e sec
o
n
d
pa
r
t
of
t
h
i
s
a
r
t
i
c
l
e
was
de
v
o
t
e
d t
o
st
udy
i
n
g t
h
e
i
n
fl
uence
o
f
o
n
e
or
m
o
re m
a
gnet
r
o
n
s
fai
l
u
r
e
s o
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
4
8
– 12
59
1
250
th
e electric op
eration
o
f
the rest o
f
t
h
e
o
t
h
e
r fu
n
c
tional
m
a
g
n
e
tron
s. In
t
h
is failure’s st
u
d
y
; we will
successi
vely analyze the
foll
owi
n
g cases:
-
One
fa
ul
t
y
m
a
gnet
r
o
n
a
n
d fi
v
e
m
a
gnet
r
o
n
s i
n
se
rvi
ce.
-
Tw
o fa
ul
t
y
m
a
gnet
r
o
n
s a
n
d
f
o
u
r
m
a
gnet
r
on
s i
n
se
r
v
i
ce.
-
Three
fa
ul
t
y
m
a
gnet
r
o
n
s a
n
d t
h
ree
m
a
gnet
r
o
n
s i
n
se
rvi
ce.
-
Fo
ur
fa
ul
t
y
m
a
gnet
r
o
n
s a
n
d t
w
o
m
a
gnet
r
o
n
s
i
n
se
rvi
ce.
-
Fi
ve
faul
t
y
m
a
gnet
r
o
n
s a
n
d
o
n
e m
a
gnet
r
on
i
n
se
rvi
ce.
-
Si
x faul
t
y
m
a
gnet
r
ons
.
2.
PROPOSE
D
METHOD FOR T
H
E MODELING
OF
THE NEW THREE PHASE HIGH
VOLTA
GE P
O
WER
SU
PP
LY FO
R T
W
O M
A
G
N
ET
RO
NS PE
R
P
H
ASE
The eq
ui
v
a
l
e
n
t
ci
rcui
t
di
agr
a
m
shoul
d re
f
l
ect
t
h
e beha
v
i
or o
f
t
h
e e
n
t
i
r
e po
we
r su
p
p
l
y
ci
rcui
t
i
n
cl
udi
ng
t
h
e
m
a
gnet
r
on a
n
d
t
h
e t
r
an
sf
orm
e
r wi
t
h
m
a
gnet
i
c sh
unt
.
O
n
t
h
e
one
ha
n
d
t
h
e s
o
l
v
i
n
g
of t
h
e el
ect
ri
c
and
m
a
gnet
i
c
equat
i
o
ns
o
f
t
h
e
w
hol
e sy
st
em
i
s
t
oo c
o
m
p
l
i
c
at
ed, a
nd t
h
e s
o
l
u
t
i
o
n
co
ul
d
be
onl
y
num
eri
c
u
s
i
n
g
th
e EMTP simu
latio
n
so
ft
ware, with
t
h
e po
ssib
ility o
f
stu
dyin
g
th
e select
io
n
o
f
m
a
terial
s and
d
i
m
e
n
s
ion
s
of
th
e tran
sfo
r
m
e
r fo
r fu
rt
h
e
r opti
m
izatio
n
.
On
th
e o
t
h
e
r h
a
nd
th
e EMTP soft
ware [7
]-[9
] tak
e
s i
n
to
accoun
t th
e
nonlinea
rities of the system
, by accepti
ng the
data relating to
the satura
ble
inductors.
The ad
vant
a
g
e
of t
h
e seco
nd
m
odel
of q
u
a
d
r
u
pol
e i
n
π
[10]
-
[
12]
i
s
i
n
i
t
s
si
ngl
e phas
e
equi
val
e
nt
ci
rcui
t
w
h
i
c
h
wo
ul
d
be
m
o
re co
nve
ni
ent
f
o
r st
u
d
y
i
n
g
t
h
e
t
r
ans
f
o
r
m
e
r’s f
unct
i
o
ni
n
g
wi
t
h
EM
T
P
. T
h
i
s
m
odel
is natural, beca
use each iron c
o
re induct
o
r is a function
of its reluctance, so it’s a
function of the
perm
e
a
bility
of a specific part in the
m
a
gnetic
circu
it, th
at is assu
m
e
d
fictiv
ely clo
s
e
d
on
wh
ich
are wou
n
d
n
2
s
e
co
nd
ar
y
tu
rn
s. Th
e immed
i
ate b
e
n
e
fit o
f
th
is m
o
d
e
l
,
is b
e
ing
ab
le
to
assign
to
each
indu
cto
r
a
n
o
n
lin
ear relat
i
o
n
s
h
i
p
“current
-flow”
in the form of n2
Φ
(i), f
r
om
the geo
m
etrical param
e
te
rs of a specific portion of the
tran
sform
e
r’s
mag
n
e
tic circuit, wh
ich
allows to
i
n
terpret its reel
o
p
e
ration
in non
lin
ear reg
i
m
e
.
There i
s
a
not
h
e
r eq
ui
val
e
nt
el
ect
ri
cal
m
odel
of t
h
e t
r
a
n
s
f
o
r
m
e
r wi
t
h
m
a
gnet
i
c
sh
u
n
t
,
nam
e
d t
h
e
m
o
d
e
l
in
T [13],[14
], b
u
t
it do
esn
’
t reflect
t
h
e n
o
n
lin
ear
ity of th
e ind
u
c
t
o
rs, asso
ciated to
each
p
o
rtion
o
f
th
e
tran
sform
e
r.
2.
1.
Single-ph
a
se high voltage
p
o
wer
sup
p
ly fo
r
two m
a
gne
t
rons: E
quival
e
nt circuit m
o
del
Th
e tran
sfo
r
m
e
r in
Figu
re
3
is con
s
id
ered
wit
hou
t iron
lo
sses
du
e to
h
y
steresis an
d
Fou
c
au
lt
cur
r
ent
s
;
o
n
l
y
t
h
e sat
u
rat
i
o
n
phe
n
o
m
e
non i
s
t
a
ke
n i
n
t
o
acc
ou
nt
.
Th
e fu
nct
i
o
ni
n
g
of t
h
e t
r
a
n
s
f
o
r
m
e
r i
s
characte
r
ized
by the following syste
m
of m
a
gnet
i
c
an
d el
ect
r
i
c equat
i
ons:
(1
)
(2
)
(3
)
(4
)
(5
)
After th
e tran
sfo
r
m
a
tio
n
o
f
the fiv
e
abo
v
e
equ
a
tio
ns (1) to
(5
), we ob
tain
th
e six
fo
llo
wi
ng
equ
a
tio
ns
(6
) t
o
(
1
0),
w
h
i
c
h
refl
ect
t
h
e
e
qui
val
e
nt
el
ect
ri
c m
odel
i
n
π
o
f
th
e tran
sformer with
m
a
g
n
etic sh
un
t.
(6
)
(7
)
(8
)
=
(9
)
=
(1
0)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Break
dow
ns
' D
i
agnosis of
A N
e
w Character
Three
Phase
H
i
gh
Voltage
Power Supply for.
... (
R
.
B
a
tit)
1
251
a
a
a
a
a
a
3a
2a
5a
6a
b
a=
2
5
m
m
b=
6
0
m
m
U
1
U
2
Φ
3
/2
Φ
1
Φ
2
Φ
3
/2
Figure
3. Ge
ometrical char
acteristics o
f
m
a
g
n
e
tic an
d electric ci
rcu
it
o
f
t
h
e tran
sform
e
r with
m
a
g
n
e
tic
shunt
Th
e
f
i
gu
r
e
4 sh
ow
s t
h
e sch
e
me
π
of t
h
is
powe
r s
u
pply.
We
note
t
h
at
each
of the t
h
ree satura
ble
in
du
ctors is a
fun
c
tion
o
f
its o
w
n
relu
ctan
ce [1
5
]
,[16
], so it’s also
a fu
nctio
n
o
f
its o
w
n
p
e
rm
eab
ility
in
a
p
r
écised
p
a
rt of th
e correspon
d
e
n
t
e m
a
g
n
e
tic circu
it, wh
ich
is sup
p
o
s
ed
fictitio
u
s
ly clo
s
ed
, an
d
i
n
which
n
2
seconda
ries turs are rolled. T
h
is m
odel was
success
f
u
lly verified
[17]-[19] and
showed that each m
a
gnetron
d
e
liv
ers its fu
ll d
e
sired
po
wer.
Fi
gu
re
4.
El
ect
ri
cal
eq
ui
val
e
n
t
m
odel
o
f
t
h
e
si
ngl
e
p
h
ase
hi
gh
v
o
l
t
a
ge
p
o
w
er
su
p
p
l
y
f
o
r
t
w
o m
a
gnet
r
o
n
s
2.
2.
N
e
w t
h
re
e
-
pha
s
e
h
i
g
h
vo
ltag
e
po
we
r
su
pp
ly
f
o
r t
w
o ma
gn
e
t
ro
n
s
p
e
r p
h
a
s
e
To ac
hieve
the
ne
w three-pha
s
e system
in
th
e two Figu
res
2
an
d 5,
we
h
a
v
e
j
u
st to
star
co
up
le three
m
o
d
e
ls (id
e
n
t
i
cal to
th
at
d
e
scrib
e
d
in Figure
3
th
at
will b
e
sup
p
lied resp
ectiv
ely b
y
sin
g
l
e-ph
ase
vo
ltag
e
s
with
a
phase diffe
rence of 120
degrees
.
It should
be recalled that each m
odel of the sec
ondary side c
o
m
p
rises
a hi
gh
v
o
l
t
a
ge t
r
ans
f
o
r
m
e
r wi
t
h
app
r
op
riate sized shunts
which drives t
w
o id
en
tical lo
ad
s in
p
a
rallel t
h
at are
com
posed
by
a
v
o
l
t
a
ge
do
u
b
l
e
r (ca
p
aci
t
o
r a
n
d
di
ode
) a
n
d
m
a
gnet
r
on
.
3.
RESULTS
A
N
D
DI
SC
US
S
I
ON
The sim
u
lation
under EMT
P
of the
electrical oper
ation of the t
h
ree
-
pha
se cha
r
acte
r
HV
powe
r
supply for
N=
2 m
a
gnetrons
per
pha
se was
perform
e
d fo
r each case of
brea
kdown.
T
h
e obse
rvation of the
o
b
t
ain
e
d
w
a
v
e
f
o
r
m
s f
r
o
m th
e cu
r
r
e
n
t
s and v
o
ltag
e
s allow
e
d
m
a
k
i
n
g
th
e co
rr
esp
ondin
g
an
alysis of
th
e
d
i
fferen
t
ch
aracteristics o
f
its
h
i
gh
v
o
ltage ci
rcu
it an
d p
a
rticu
l
arly th
at
o
f
th
e m
a
g
n
e
tro
n
cu
rren
t.
3.
1.
The simulati
on in EMTP
of the e
quivale
nt circu
it
m
o
del
of the ne
w
charac
ter three-phase high
vol
tage power
suppl
y
The el
ect
ri
cal
ope
rat
i
o
n of t
h
e new t
h
ree
-
p
h
ase p
o
we
r su
ppl
y
desc
ri
be
d
i
n
Fi
gure
5 of
m
i
crowav
e
g
e
n
e
rator with six
m
a
g
n
e
trons in
to
tal (two
mag
n
e
tro
n
s
p
e
r ph
ase)
was si
m
u
la
ted
in
EMTP, wh
ich
al
lo
wed
u
s
to
ob
tain
the ti
m
e
cu
r
v
es (Fig
ur
e 6.a)
of
v
o
ltag
e
s (
C
onden
s
er, d
i
od
e and
m
a
g
n
e
tr
on
)
an
d
cu
rr
en
ts
(
d
io
d
e
,
m
a
gnet
r
on a
n
d
secon
d
a
r
y
)
. T
h
e t
h
ree
pri
m
ari
e
s nom
i
n
al
s vol
t
a
ges o
f
t
h
e s
t
udi
ed
p
o
we
r s
u
p
p
l
y
ha
ve t
h
e
sam
e
r
m
s 2
2
0
V
-
50H
z an
d ar
e ph
ase sh
i
f
ted
12
0
d
e
gr
ees.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
4
8
– 12
59
1
252
L’
Sh
1
f
L'
P1
L
S1
65
Ω
i
12
0.9
µF
35
0
Ω
38
00V
i’
11
100
Ω
U’
11
U
12
D
1
Ma
g
n
é
t
r
o
n
1
35
0
Ω
38
00V
Ma
g
n
é
t
r
o
n
2
3,
562
H
D
2
L’
Sh
2
f
L'
P2
L
S2
65
Ω
i
22
0.9
µF
350
Ω
380
0V
i’
21
100
Ω
U’
21
U
22
D
3
Ma
g
n
é
t
r
o
n
3
350
Ω
380
0V
Ma
g
n
é
t
r
o
n
4
3
,
56
2 H
D
4
L’
Sh
3
f
L'
P3
L
S3
65
Ω
i
32
0.
9
µF
350
Ω
380
0V
i’
31
10
0
Ω
U’
31
U
32
D
5
M
agné
t
ron
5
350
Ω
380
0V
Ma
g
n
é
t
r
o
n
6
3,5
62 H
D
6
Fi
gu
re
5.
C
h
a
r
act
er t
h
r
ee
pha
se hi
gh
v
o
l
t
a
ge
p
o
we
r s
u
ppl
y
fo
r t
w
o m
a
gnet
r
o
n
s
pe
r
phase
(Eq
u
i
v
al
e
n
t
ci
r
c
ui
t
m
odel
)
0
,
6
0
0,
61
0,
62
0
,
63
0
,
64
-
8
000
-
6
000
-
4
000
-
2
000
0
2
000
4
000
6
000
8
000
SE
COND
AR
I
E
S V
O
L
T
AG
ES (
V
)
TI
M
E
(
s
)
u
s2
u
s1
u
s3
0,
60
0,
6
1
0
,
62
0
,
63
0,
6
4
-3
-2
-1
0
1
2
3
is
2
SE
COND
A
R
I
E
S C
U
RREN
T
S
(
A
)
TI
M
E
(
s
)
is
1
is
3
0,
60
0,
61
0,
62
0,
6
3
0,
6
4
-
800
0
-
600
0
-
400
0
-
200
0
0
200
0
400
0
600
0
800
0
(u
c3
;
u
c4
)
CO
N
D
EN
SERS
V
O
LT
AGES
TI
M
E
(
s
)
(u
c1
;
u
c2
)
(u
c5
; u
c6
)
0,
60
0,
61
0,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
D
I
O
D
ES
C
U
RR
EN
TS
(
A
)
TI
M
E
(
s
)
(i
d
3
;
id
4
)
(i
d
1
; id
2
)
(i
d
5
; i
d
6
)
0
,
6
0
0,
61
0,
6
2
0,
63
0
,
6
4
-
800
0
-
600
0
-
400
0
-
200
0
0
200
0
400
0
600
0
800
0
M
A
GN
ETRO
N
S
VO
L
T
A
G
ES (V)
TI
M
E
(
s
)
(u
m3
; u
m4
)
(u
m1
; u
m2
)
(u
m5
; u
m6
)
0,
60
0,
61
0,
62
0,
63
0,
64
-1
,5
-1
,0
-0
,5
0,
0
0,
5
1,
0
1,
5
M
A
GN
ET
RO
N
S
C
U
RREN
T
S
(
V
)
TI
M
E
(
s
)
(im
3
; i
m
4
)
(i
m
1
;
i
m
2
)
(i
m
5
;
i
m
6
)
a.
b.
Fi
gu
re
6.
Si
m
u
l
a
t
i
on an
d
ex
pe
ri
m
e
nt
al
resul
t
s
, a)
.
T
h
e
sim
u
lation’s res
u
lts with
EMT
P
of a
cha
r
acter
t
h
ree
p
h
ase
hi
g
h
vol
t
a
ge
p
o
w
e
r
s
u
p
p
l
y
f
o
r
t
w
o m
a
gnet
r
ons
per
p
h
ase,
b
)
.
The e
x
peri
m
e
nt
al
wave
fo
rm
s
of
cu
rre
nt
s a
n
d
v
o
l
t
a
ges
of
a s
i
ngl
e
pha
se
hi
g
h
vol
t
a
ge
p
o
w
e
r
s
u
p
p
l
y
f
o
r
o
n
e
m
a
gnet
r
o
n
(
n
om
i
n
al
m
ode)
For
each
of t
h
e two m
a
gnetrons
of sam
e
phase in
nom
i
n
a
l ope
ration
(220V a
nd
50Hz
in prim
ary
si
de), t
h
e el
ect
ri
c cur
r
e
n
t
’
s si
gnal
s
(di
ode
,
m
a
gnet
r
on a
n
d
seco
nda
ry
si
d
e
) an
d
vol
t
a
ge
s
(capaci
t
o
r, m
a
gnet
r
o
n
an
d seco
nd
ary
sid
e
) m
a
y co
n
s
titu
te an asse
m
b
ly wh
ich
h
a
v
e
th
e sam
e
form
as th
at o
f
sing
le m
a
g
n
e
tro
n
’s
co
nv
en
tio
n
a
l feed
ing
.
Th
ese sig
n
a
ls
are p
e
ri
o
d
i
c v
a
riab
le qu
an
tities
(b
u
t
t
h
ey
are no
t
sinu
so
i
d
al),
g
l
o
b
a
lly
fo
r
all th
ree p
h
a
ses si
m
u
ltan
e
o
u
s
ly feed
in
g
two
m
a
g
n
e
tron
s,
t
h
ere
f
ore there are three s
u
cce
ssive sets of si
gnals
whi
c
h are p
h
a
s
e shi
f
t
e
d
by
1
20
deg
r
ees.
It
can be c
oncl
u
ded t
h
at
t
h
e c
u
rves
obt
ai
n
e
d t
h
r
o
ug
h si
m
u
l
a
ti
on i
n
EM
TP o
f
ne
w
sim
u
l
t
a
neous
po
we
r su
p
p
l
y
’
s
t
h
ree
-
p
h
ase
devi
ce
of t
w
o
m
a
gnet
r
ons
pe
r p
h
ase
(i
n
no
n-l
i
n
ea
r
regim
e
), are in accorda
n
ce
with the
experim
e
ntal waveform
s recorde
d
in the case of single m
a
gnetron’s
si
ngl
e-
p
h
ase p
o
we
r
s
u
ppl
y
(F
i
g
u
r
e 6.
b).
We obse
rve t
h
at the
m
a
xim
u
m valu
e of c
u
rrent m
a
gnitude
in each of
bot
h
ide
n
tical
m
a
gnet
r
ons in
each
of three
phases
rem
a
ins less
tha
n
t
h
e lim
it
(<1,2A),
whic
h
res
p
ects the
c
ons
traints im
posed a
nd
recom
m
ended
by
t
h
e m
a
nufa
c
t
u
rer
of m
a
gn
et
ro
ns t
h
us en
s
u
ri
ng t
h
e co
rre
ct
oper
a
t
i
on
of
t
h
e m
i
crowa
v
e t
ube.
Taking int
o
account the fore
goi
ng, th
e inform
ations m
e
ntione
d
before
,
the electrical curr
ent stabilization
p
r
o
cess in
each m
a
g
n
e
tron
is co
m
p
letely v
e
rified
, as shown in
Fi
g
u
re
7
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Break
dow
ns
' D
i
agnosis of
A N
e
w Character
Three
Phase
H
i
gh
Voltage
Power Supply for.
... (
R
.
B
a
tit)
1
253
0,
6
0
0,
61
0,
6
2
0,
6
3
0,
6
4
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
U
1
=U
2
=U
3
=
200V
MAG
N
ET
RONS C
U
RREN
T
S (A
)
TI
M
E
(
s
)
(i
m
3
;
im
4
)
(i
m
1
;
im
2
)(
i
m
5
;
im
6
)
0,
6
0
0,
61
0,
62
0,
63
0
,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
U
1
=U
2
=U
3
=
2
40V
M
A
GNETRONS
CU
RR
ENT
S
(
A
)
TI
M
E
(
s
)
(i
m
3
;
im
4
)
(i
m
1
;
im
2
)
(i
m
5
;
im
6
)
Fig
u
re
7
.
Stab
i
lizatio
n
of th
e
an
od
e curren
t
o
f
th
e m
a
g
n
e
tro
n
in
relatio
n
with
v
a
riation
s
in
th
e m
a
in
s vo
ltag
e
+10
%
of
t
h
e n
o
m
i
nal
vol
t
a
ge
3.
2.
C
a
s
e
of
o
n
e fau
l
t
y
m
a
g
n
et
ron
a
nd
five
magne
t
rons in s
e
rvice
The si
m
u
l
a
t
i
on res
u
l
t
s
u
nde
r
EM
TP co
de
of
t
h
e assem
b
l
y
of
Fi
g
u
re
8.a
a
r
e i
n
di
cat
ed i
n
Fi
g
u
re
8B
.
We o
b
ser
v
e t
h
at
t
h
e
m
a
gnet
r
on
brea
kd
o
w
n
of p
h
ase 1 re
duce
s
t
h
e ope
r
a
t
i
on of t
h
e c
o
rres
p
on
di
n
g
v
o
l
t
a
ge
d
oub
ler
s
wh
ich supp
lies it, com
p
o
s
ed
o
f
on
e d
i
od
e D
1
an
d
one
c
o
n
d
e
n
ser
C
1
havi
n
g
0.
9
µ
F.
Th
e latter
h
a
s t
o
be c
h
ar
ge
d t
h
r
o
u
g
h
t
h
e
di
ode
D
1
at
t
h
e sec
o
nda
ry
peak
v
o
l
t
age del
i
vere
d
by
t
h
e
hi
g
h
v
o
l
t
a
ge t
r
a
n
sf
orm
e
r.
The o
p
erat
i
n
g
poi
nt
of eac
h r
u
n
n
i
n
g m
a
gnet
r
o
n
i
s
not
di
st
u
r
be
d. T
h
e bre
a
k
d
o
w
n
of o
n
e
bet
w
ee
n si
x
po
we
red
m
a
gnet
r
o
n
s
doe
s
no
t
chan
ge t
h
e
o
p
erat
i
o
n
of
t
h
e fi
ve
rem
a
i
n
i
n
g
m
a
gnet
r
o
n
s
i
n
se
rvi
ce.
F
o
r t
h
e
pha
se co
nt
ai
ni
ng t
w
o m
a
gnet
r
o
n
s, a m
a
gnet
r
o
n
i
n
brea
k
d
o
w
n
an
d a r
u
n
n
i
n
g m
a
gnet
r
o
n
, we
obse
r
ve at
t
h
e
co
mm
u
t
at
io
n
ti
m
e
o
f
th
e d
i
od
e th
e
p
r
esen
ce o
f
tran
sien
t o
s
cillatio
n
s
, at
th
e lev
e
l of th
e vo
ltag
e
s acro
ss t
h
e
fu
nct
i
o
nal
m
a
g
n
et
r
on a
nd t
h
e seco
nda
ry
of t
h
e t
r
an
sf
orm
e
r (Fi
g
ure
8.
b)
. Thi
s
i
s
sim
p
l
y
due t
o
t
h
e cha
nge
o
f
t
h
e n
o
m
i
nal
op
erat
i
n
g
p
o
i
n
t
o
f
t
h
e m
a
gnet
r
o
n
r
u
nni
n
g
o
f
t
h
i
s
pha
se. E
ach
of t
h
e t
w
o
ot
he
r p
h
ases
co
nt
ai
ni
n
g
two
run
n
i
n
g
m
a
g
n
e
t
r
on
s, t
h
e
ab
sen
ce of tran
sien
t oscilla
ti
o
n
s
at th
e lev
e
l o
f
vo
ltag
e
s i
n
d
i
cates th
e co
rrect
electrical ope
ra
tion
of these t
w
o m
a
gnetrons
.
For t
h
e
phase
cont
ai
ni
ng t
w
o
m
a
gnet
r
o
n
s, a
m
a
gnet
r
o
n
i
n
brea
k
d
o
w
n an
d a ru
nni
ng m
a
gnet
r
o
n
, w
e
o
b
s
erv
e
at t
h
e co
mm
u
t
atio
n
ti
m
e
o
f
t
h
e
d
i
od
e the
p
r
esen
ce
o
f
tran
sien
t oscillatio
n
s
, at th
e lev
e
l
of the
vol
t
a
ge
s acros
s t
h
e funct
i
ona
l
m
a
gnet
r
o
n
and t
h
e sec
o
n
d
a
r
y
of t
h
e t
r
ans
f
o
r
m
e
r (Fi
gure
8.b
)
. Thi
s
i
s
sim
p
l
y
due
t
o
t
h
e ch
a
nge
o
f
t
h
e
n
o
m
i
n
al
ope
rat
i
n
g
poi
nt
o
f
t
h
e
m
a
gnet
r
on
r
u
n
n
i
n
g
of t
h
i
s
p
h
a
se. Eac
h
of t
h
e t
w
o
o
t
h
e
r
p
h
a
ses co
n
t
ain
i
n
g
two
runn
ing
m
a
g
n
e
tron
s, t
h
e ab
se
n
ce
o
f
transient o
s
cillatio
n
s
at
th
e lev
e
l
of
v
o
ltag
e
s
indicates the
c
o
rrect electrical ope
rat
i
o
n
of
t
h
ese t
w
o
m
a
gnet
r
o
n
s.
L’
Sh
1
f
L'
P1
L
S1
65
Ω
i
12
0.
9
µF
35
0
Ω
38
00
V
i’
11
10
0
Ω
U’
11
U
12
D
1
M
agn
é
t
r
o
n
1
en
p
a
n
n
e
35
0
Ω
3
800
V
M
agn
é
t
r
o
n
2
3
,
56
2 H
D
2
L’
Sh
2
f
L'
P2
L
S2
65
Ω
i
22
0.9
µF
35
0
Ω
3
800
V
i’
21
100
Ω
U’
21
U
22
D
3
M
agn
é
t
r
o
n
3
35
0
Ω
3
800
V
M
agn
é
t
r
o
n
4
3
,
562
H
D
4
L’
Sh
3
f
L'
P3
L
S3
65
Ω
i
32
0.9
µF
35
0
Ω
3
800V
i’
31
10
0
Ω
U’
31
U
32
D
5
Ma
g
n
étr
o
n
5
35
0
Ω
3
800V
M
agné
t
r
o
n
6
3
,
562
H
D
6
0,
60
0,
61
0,
62
0,
63
0,
64
-
8
000
-
6
000
-
4
000
-
2
000
0
2
000
4
000
6
000
8
000
SE
CO
ND
A
R
I
E
S V
O
L
T
A
G
E
S
(V
)
TI
M
E
(
s
)
u
s3
u
s2
u
s1
0,
60
0,
61
0,
62
0,
63
0
,
6
4
-3
-2
-1
0
1
2
3
SE
C
O
NDA
R
I
E
S C
U
R
R
E
N
TS
(A
)
TI
M
E
(
s
)
is
3
is
2
is
1
0,
60
0,
61
0,
62
0,
63
0,
64
-
800
0
-
600
0
-
400
0
-
200
0
0
200
0
400
0
600
0
800
0
CO
N
D
E
N
S
E
R
S
V
O
L
T
AG
E
S
(
V
)
TI
M
E
(
s
)
u
c1
(u
c3
;
u
c4
)
u
c2
(u
c5
; u
c6
)
0
,
6
0
0,
61
0,
62
0,
6
3
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
DI
O
D
E
S
C
U
R
R
EN
T
S
(A
)
TI
M
E
(
s
)
id
1
=0
A
(i
d
3
;
id
4
)
id
2
(i
d
5
;
id
6
)
0,
60
0,
61
0,
6
2
0,
6
3
0,
6
4
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
u
m1
MA
G
N
E
T
R
O
N
S
V
O
L
T
A
G
ES
(
V
)
TI
M
E
(
s
)
(u
m3
;
u
m4
)
u
m2
(u
m5
; u
m6
)
0,
60
0,
61
0,
62
0,
63
0,
6
4
-1
,5
-1
,0
-0
,5
0,
0
0,
5
1,
0
1,
5
MA
GN
E
T
RO
N
S
C
U
RR
E
N
T
S
(A
)
TI
M
E
(
s
)
im
1
=0
A
(i
m
3
; im
4
)
im
2
(i
m
5
; im
6
)
a. b.
Fi
gu
re
8.
C
i
rcu
i
t
M
odel
s
:
case
o
f
one
fa
ul
t
y
m
a
gnet
r
on
an
d
fi
ve
m
a
gnet
r
o
n
s i
n
se
rvi
ce a
)
. C
i
rcui
t
m
odel
o
f
a
ch
ar
acter
thr
e
e ph
ase
H
V
p
o
w
e
r supp
ly fo
r
N
=
2 m
a
g
n
e
tr
on
s
p
e
r ph
ase,
b)
.
W
a
v
e
fo
r
m
s o
f
cur
r
e
n
t
s an
d vo
ltag
e
s
o
f
th
e circu
it in
Fi
g
u
re
8
.
a.
3.
3.
Case
o
f
tw
o f
a
ulty
ma
gne
t
r
o
ns
and
four m
a
gnetr
o
ns
in s
ervice
3.
3.
1.
Case
o
f
tw
o
f
a
ulty
ma
gne
t
r
o
ns in
the s
a
me
ph
ase
Th
e sim
u
latio
n’s
resu
lts
with
EMTP co
d
e
of th
e assem
b
ly i
n
Fi
g
u
r
e
9
.
a are show
n in Figu
r
e
9.b.
I
t
is
not
e
d
t
h
at
eac
h o
f
t
h
e
t
w
o f
a
ul
t
y
m
a
gnet
r
ons
o
f
sam
e
phase
1 re
d
u
ces
t
h
e o
p
er
at
i
o
n
of i
t
s
c
o
r
r
es
p
o
n
d
i
n
g
vol
t
a
ge
d
o
ubl
e
r
, c
onsi
s
t
i
n
g
o
f
o
n
e
di
o
d
e an
d o
n
e c
o
nde
ns
er ha
vi
n
g
0.
9
µF. T
h
i
s
co
nd
enser
has t
o
c
h
ar
ge
th
ro
ugh
th
e d
i
od
e
D1 at th
e
seco
nd
ary p
e
ak
vo
ltag
e
sup
p
lied b
y
th
e h
i
g
h
voltag
e
tran
sfo
r
m
e
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
4
8
– 12
59
1
254
For eac
h o
f
t
h
e
ot
her t
w
o
pha
ses, t
h
e o
p
erat
i
ng
poi
nt
of eac
h o
f
t
h
e t
w
o m
a
gnet
r
o
n
s i
n
se
rvi
ce i
s
n
o
t
di
sr
upt
e
d
.
The
fai
l
u
re
of
b
o
t
h
m
a
gnet
r
on
s
of
t
h
e
sam
e
phase
d
o
esn
’
t
a
ffect
t
h
e
ope
ra
t
i
on
of
t
h
e
re
m
a
i
n
i
n
g
fo
ur
m
a
gnet
r
o
n
s i
n
se
rvi
ce
o
f
t
h
e
ot
her
t
w
o
p
h
ases.
T
h
e t
w
o
fa
ul
t
y
m
a
g
n
et
r
ons
o
f
s
a
m
e
p
h
ase
(
phase
1
)
hav
e
n
o
in
teractio
n
effect on
th
e op
eration
of th
e fou
r
o
t
her
fu
n
c
t
i
onal
m
a
gnet
r
o
n
s (
p
hase 2
and
pha
se 3)
.
Gi
ve
n
t
h
at
t
h
ei
r o
p
era
t
i
ng poi
nt
s
ar
e not
di
st
u
r
be
d.
0,
60
0,
61
0,
62
0,
63
0,
64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
200
0
400
0
600
0
800
0
SE
CO
ND
A
R
IES
TENSI
O
NS
(
V
)
TI
M
E
(
s
)
u
s3
u
s2
u
s1
=0
V
0,
60
0,
61
0,
62
0
,
6
3
0,
64
-2
-1
0
1
2
SEC
O
N
D
AR
IES CU
R
R
EN
TS
(A)
TIM
E
(
s
)
is
3
is
2
is
1
=0
A
0,
60
0,
61
0,
62
0
,
6
3
0,
64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
CON
D
ENS
E
R
S
V
O
L
T
AG
ES
(
V
)
TI
M
E
(
s
)
(u
c1
; u
c2
)
(u
c4
; u
c3
)
(u
c5
; u
c6
)
0,
60
0,
61
0,
62
0
,
6
3
0
,
6
4
-1
,5
-1
,0
-0
,5
0,
0
0,
5
1,
0
1,
5
D
I
OD
ES
CU
R
R
E
NTS
(
A
)
TI
M
E
(
s
)
(i
d
3
;
id
4
)
id
1
=i
d
2
=0
A
(id
5
; i
d
6
)
0,
60
0
,
61
0,
6
2
0
,
63
0,
6
4
-80
0
0
-60
0
0
-40
0
0
-20
0
0
0
20
00
40
00
60
00
80
00
M
A
G
N
ETR
O
NS V
O
L
T
A
G
ES (
V
)
TI
M
E
(
s
)
(u
m1
; u
m2
)
(u
m4
;
u
m3
)
(u
m5
;
u
m6
)
0,
60
0,
61
0,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
MA
GNE
T
R
O
N
S
C
U
RRE
NTS
(
A
)
TI
M
E
(
s
)
(i
m
3
;
i
m
4
)
(i
m
1
; im
2
)
(im
5
; i
m
6
)
a. b.
Fi
gu
re
9.
C
i
rcu
i
t
m
odel
:
C
a
se
of
t
w
o fa
ul
t
y
m
a
gnet
r
ons
i
n
t
h
e sam
e
phase
, a)
. C
i
rc
ui
t
m
o
del
o
f
a
cha
r
act
er t
h
ree
pha
se
HV
p
o
w
e
r s
u
p
p
l
y
f
o
r
N
=
2 m
a
gnet
r
ons
pe
r
phase
,
b)
.
Wave
f
o
rm
s of
cur
r
ent
s
an
d
v
o
l
t
a
ges
of
t
h
e
c
i
rcui
t
i
n
Fi
gu
re 9.a
.
3.
3.
2.
C
a
s
e
of
t
w
o
fau
l
t
y
m
a
g
n
et
ron
s
th
at
ea
ch
one is pl
aced in differe
nt phase
Th
e sim
u
latio
n’s resu
lts
with
EMTP
o
f
t
h
e assem
b
l
y
i
n
Fi
gure
1
0
.a
are
sh
ow
n i
n
Fi
gu
re
10
.b
.
0,
60
0,
61
0,
6
2
0
,
6
3
0
,
6
4
-8
00
0
-6
00
0
-4
00
0
-2
00
0
0
20
00
40
00
60
00
80
00
SE
C
O
N
D
A
R
I
E
S V
O
L
T
A
G
E
S
(
V
)
TIM
E
(
s
)
u
s3
u
s2
u
s1
0,60
0,61
0,62
0,63
0,64
-2
-1
0
1
2
SECOND
A
R
I
E
S VOLT
A
G
ES (
A
)
TI
M
E
(s
)
is
1
is
3
is
2
0,60
0,61
0,62
0,63
0,64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
C
O
ND
ENSER
S
VOLT
A
G
ES (V)
TIM
E
(
s
)
(u
c4
; u
c2
)
u
c3
u
c1
(u
c5
; u
c6
)
0,60
0,61
0,62
0,63
0,64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
D
I
OD
ES C
U
R
R
ENT
S
(A
)
TI
ME
(s)
id
4
=id
2
=0A
id
3
id
1
(i
d
5
;
id
6
)
0,60
0,61
0,62
0,63
0
,
6
4
-80
0
0
-60
0
0
-40
0
0
-20
0
0
0
20
00
40
00
60
00
80
00
u
m3
(u
m2
; u
m4
)
MA
G
N
ETRONS VO
L
T
A
G
ES (
V
)
TI
M
E
(
s
)
u
m1
(u
m5
; u
m6
)
0,60
0,61
0,62
0,63
0,64
-1
,
5
-1
,
0
-0
,
5
0,0
0,5
1,0
1,5
im
4
=i
m
2
=0
A
MA
GNET
RONS CURR
ENT
S
(
A
)
TIM
E
(
s
)
im
3
im
1
(i
m
5
;
i
m
6
)
a. b.
Figure
10. Circ
uit m
odels : Case of two
fa
ulty
m
a
gnetr
ons
that each one
is placed
in diffe
r
ent phase,
a
)
.
C
i
rcui
t
m
odel
of
a c
h
aract
er
t
h
ree
p
h
ase
H
V
p
o
we
r s
u
ppl
y
fo
r
N=2
m
a
gnet
r
o
n
s
per
p
h
ase
,
b
)
.
W
a
vef
o
rm
s o
f
cu
rren
ts and
vo
ltag
e
s
o
f
th
e circu
it in
Figu
re 10
.a.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Break
dow
ns
' D
i
agnosis of
A N
e
w Character
Three
Phase
H
i
gh
Voltage
Power Supply for.
... (
R
.
B
a
tit)
1
255
I
t
is no
ted th
at
on
e f
a
u
lty m
a
g
n
e
t
r
on
o
f
ph
ase 1
r
e
d
u
ces the op
eration
o
f
its co
rrespon
d
i
n
g
vo
ltag
e
do
ub
ler,
con
s
i
s
t
i
ng
of
d
i
ode
D
1
an
d c
o
n
d
e
n
ser
C
1
h
a
vi
n
g
0.
9 µF.
Thi
s
ca
paci
t
o
r
has t
o
cha
r
g
e
t
h
r
o
ug
h t
h
e
di
o
d
e
D
1
wi
t
h
t
h
e
seco
nda
ry
pea
k
v
o
l
t
a
ge s
u
p
p
l
i
e
d by
t
h
e hi
g
h
vol
t
a
ge t
r
a
n
s
f
o
r
m
e
r. The
o
p
erat
i
n
g
poi
nt
of t
h
e
fu
nct
i
o
nal
m
a
gnet
r
on
o
f
sam
e
p
h
ase i
s
n
o
t
d
i
st
urbe
d.
In th
e sam
e
way, the fau
lty m
a
g
n
e
tron
o
f
th
e
ph
ase 2
red
u
ces t
h
e
o
p
e
rat
i
on
of i
t
s
c
o
r
r
es
po
n
d
i
n
g v
o
l
t
a
ge d
o
ubl
e
r
,
con
s
i
s
t
i
ng
of
one
di
o
d
e
D
3
an
d
on
e cond
enser
C
3
h
a
v
i
n
g
0
.
9
µF. Th
is cond
en
ser
h
a
s t
o
ch
ar
g
e
th
r
ough
th
e d
i
o
d
e
D
3
with
t
h
e secon
d
a
ry p
e
ak
vo
ltag
e
supp
lied
by
t
r
ans
f
o
r
m
e
r. The
ope
rat
i
n
g p
o
i
n
t
o
f
t
h
e
fu
nct
i
o
nal
m
a
g
n
et
r
on
of t
h
i
s
pha
se i
s
not
di
st
ur
bed
.
F
o
r ea
ch o
n
e
of
t
h
e t
h
ree
p
h
a
ses w
h
i
c
h
c
o
nt
ai
ns t
w
o
m
a
gnet
r
o
n
s:
o
n
e f
a
ul
t
y
m
a
gnet
r
o
n
a
n
d
one
m
a
gnet
r
on
i
n
ser
v
i
ce, we
o
b
s
erv
e
in th
e
d
i
od
e switch
i
ng
tim
e, th
e p
r
esen
ce
o
f
tran
si
en
t oscillatio
n
s
at th
e lev
e
l of th
e
v
o
ltag
e
s acro
ss
th
e fun
c
tion
a
l mag
n
e
tro
n
an
d th
e tran
sformer’s seco
nd
ary (F
igu
r
e
1
0
.b). Th
is is si
m
p
ly
d
u
e
to
th
e ch
an
g
e
of
th
e no
m
i
n
a
l o
p
eratin
g po
in
t
of th
e fu
n
c
tion
a
l
m
a
g
n
e
tron
in th
is
p
h
a
se.
For
one
o
f
t
h
e t
h
ree
p
h
ases
w
h
i
c
h c
o
nt
ai
ns t
w
o
f
unct
i
o
nal
m
a
gnet
r
o
n
s
, t
h
e
abse
nce
o
f
t
r
a
n
si
e
n
t
o
s
cillatio
n
s
at
th
e vo
ltag
e
s ind
i
cates th
at the electrical o
p
eratio
n
o
f
two
mag
n
e
t
r
on
s is p
e
rfectly no
m
i
n
a
l. At
th
e lev
e
l o
f
th
is p
h
a
se, th
e wav
e
fo
rm
’s te
mp
oral ch
ar
acte
r
istic obtained from
the secondary curre
nt presents,
in eve
r
y insta
n
t, double am
plitude t
h
an
that
of t
h
e sam
e
current i
n
the ca
se
of two fa
ulty magnetrons
tha
t
each
one is
placed
in differe
n
t phase. This
is
due to the
fact
that these two
m
a
gnetrons
debit their full powe
r
sim
u
l
t
a
neousl
y
i
n
a pr
ope
r m
a
nne
r. F
r
om
t
h
e st
udy
o
f
t
h
e
t
w
o cases
, we
concl
ude t
h
at
t
h
e fai
l
u
re o
f
t
w
o
of
t
h
e si
x
p
o
w
ere
d
m
a
gnet
r
ons
doe
sn
’t
cha
n
ge
t
h
e
ope
rat
i
o
n
of
t
h
e
ot
he
r
fo
ur
m
a
gnet
r
o
n
s
i
n
ser
v
i
ce.
3.
4.
Case
of three
faul
ty
m
a
gnetrons
and thre
e
magne
t
rons in
service
3.
4.
1.
C
a
s
e
of
Thr
e
e
fa
u
l
ty
mag
n
et
r
o
n
s
wh
ic
h
ev
e
r
y
o
n
e is
in
ea
c
h
p
h
a
s
e
On
t
h
e on
e
h
a
nd
, th
e sim
u
lati
o
n
’s resu
lts thro
ugh
EMTP
o
f
th
e assem
b
ly i
n
Figu
re
11
.a are shown
i
n
Fi
gu
re
10
.b
. It
i
s
not
e
d
t
h
at
ea
ch fa
ul
t
y
m
a
gnet
r
o
n
s (i
n o
n
e
of t
h
e t
h
ree
ph
ases) re
d
u
ces t
h
e f
u
nct
i
oni
ng
of i
t
s
cor
r
es
po
n
d
i
n
g
vol
t
a
ge
d
o
ubl
e
r
, c
onsi
s
t
i
n
g
of
one
di
o
d
e a
n
d
one c
o
nd
ense
r
havi
ng
0.
9 µF
. Thi
s
c
o
n
d
e
n
s
e
r has
to
ch
arg
e
thr
oug
h th
e
d
i
od
e
D
1
at th
e seco
ndary p
e
ak
vo
ltag
e
sup
p
lied b
y
th
e h
i
g
h
vo
ltage tran
sfo
r
m
e
r.
On
t
h
e
o
t
h
e
r han
d
, we ob
serv
e in
t
h
e
d
i
ode switch
i
ng
ti
me th
e p
r
esence o
f
transien
t
o
s
cillatio
n
s
at
th
e lev
e
l o
f
th
e v
o
ltag
e
s acro
s
s th
e fun
c
tio
n
a
l
m
a
g
n
e
tron
and the trans
f
ormer’s seconda
ry (
F
ig
ur
e 11
.b
). Th
is
is si
m
p
ly d
u
e
t
o
th
e ch
an
g
e
of th
e
n
o
m
in
al o
p
e
rating
po
int o
f
the fu
nctio
n
a
l m
a
g
n
e
tron
. Th
e
failu
re
o
f
t
h
is
m
a
gnet
r
on
d
o
e
s
n’t
di
st
u
r
b
t
h
e f
unct
i
o
ni
n
g
of
t
h
e
ot
he
r m
a
gnet
r
o
n
s i
n
s
e
rvi
ce.
T
h
e t
h
r
ee fa
ul
t
y
m
a
gnet
r
on
s
have
n
o
i
n
t
e
ra
ct
i
on e
ffect
o
n
t
h
e
f
unct
i
on
i
ng
of
t
h
e t
h
r
ee ot
he
r
fu
nct
i
onal
m
a
gnet
r
ons
.
Gi
ve
n t
h
at
t
h
ei
r
ope
rat
i
n
g poi
nt
s
are n
o
t
di
st
ur
bed
.
3.
4.
2.
Case
of Three
faulty m
a
gne
t
rons
w
h
i
c
h t
w
o
are
i
n
the same ph
ase
Th
e sim
u
latio
n
’
s resu
lts
with
EMTP of t
h
e assem
b
ly
i
n
Fi
gure
1
2
.a a
r
e s
h
ow
n i
n
Fi
gu
re
12
.b
. It
i
s
n
o
t
ed
th
at each
of
th
e two
f
a
u
lty
m
a
g
n
e
tro
n
s
o
f
sam
e
p
h
ase r
e
du
ces th
e op
er
ation
of
its co
r
r
e
spond
ing
vol
t
a
ge
d
o
ubl
e
r
, c
o
nsi
s
t
i
n
g
o
f
o
n
e
di
o
d
e a
n
d
one
co
n
d
en
ser
havi
ng
0
.
9
µF.
0,
60
0,
61
0,
62
0,
63
0,
64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
u
S3
u
S2
SECOND
AR
IES V
O
L
T
AG
ES (
V
)
TI
M
E
(
s
)
u
S1
0
,
6
0
0,
61
0,
6
2
0,
6
3
0,
64
-2
-1
0
1
2
is
3
is
2
SECON
D
AR
I
E
S CU
R
R
E
NTS (A)
TI
M
E
(
s
)
is
1
0,
60
0,
61
0
,
6
2
0,
63
0
,
6
4
-
8000
-
6000
-
4000
-
2000
0
2000
4000
6000
8000
u
c2
=u
c4
=u
c6
C
O
ND
EN
SE
R
S
V
O
L
T
AG
E
S
(
V
)
TI
M
E
(
s
)
u
c3
u
c1
u
c5
0,
6
0
0,
61
0,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
D
I
OD
ES
CU
R
R
E
N
T
S (
A
)
TI
M
E
(
s
)
(id
2
=i
d
4
=i
d
6
=0
A
)
id
3
id
1
id
5
0,
60
0,
61
0,
62
0,
63
0
,
6
4
-
800
0
-
600
0
-
400
0
-
200
0
0
200
0
400
0
600
0
800
0
M
A
G
N
E
T
R
O
NS
V
O
L
T
AG
ES
(
V
)
TI
M
E
(
s
)
u
c2
=u
c4
=u
c6
u
c3
u
c1
u
c5
0,
6
0
0,
61
0
,
6
2
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
(im
2
=i
m
4
=i
m
6
=0
A
)
M
A
G
N
ET
R
O
NS
CUR
R
E
NTS
(
A
)
TI
M
E
(
s
)
im
3
im
1
im
5
a. b.
Figure
12. Circ
uit m
odel: Case of T
h
ree
fa
ul
ty
m
a
gnetr
ons
in each phase
,
a). Circ
uit m
odel of a c
h
aracte
r
t
h
ree
p
h
ase
H
V
po
wer
s
u
p
p
l
y
fo
r
N=2
m
a
gnet
r
ons
pe
r
p
h
a
se,
b).
W
a
ve
f
o
rm
s of
cu
rre
n
t
s an
d
vol
t
a
ges
o
f
t
h
e
circu
it in
Figu
re 11
.a.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E
V
o
l
.
6,
No
. 3,
J
u
ne 2
0
1
6
:
12
4
8
– 12
59
1
256
Thi
s
co
nde
nse
r
has t
o
char
ge t
h
r
o
ug
h t
h
e di
o
d
e D
1
at
t
h
e secon
d
a
r
y
peak
v
o
l
t
a
ge su
p
p
l
i
e
d
by
t
h
e hi
gh
vo
l
t
a
ge
t
r
ans
f
o
r
m
e
r. The fai
l
u
re
of
t
h
ese m
a
gnet
r
o
n
s
does
n
’t
di
s
t
ur
b t
h
e
fu
nct
i
oni
ng
o
f
t
h
e
ot
he
r m
a
gnet
r
ons
i
n
service.
C
once
r
ni
ng t
h
e phase w
h
i
c
h
cont
ai
n
s
t
w
o
m
a
gnet
r
ons:
o
n
e faul
t
y
m
a
gn
et
ro
n and
one
m
a
gnet
r
on i
n
serv
ice,
we observ
e
i
n
th
e d
i
o
d
e
switch
i
ng ti
m
e
,
th
e p
r
esen
ce of tran
sien
t o
s
cillatio
ns at th
e lev
e
l o
f
the
vol
t
a
ge
s acr
oss
t
h
e fu
nct
i
o
nal
m
a
gnet
r
on a
n
d
t
h
e t
r
ans
f
orm
e
r’s sec
o
nda
ry
(
F
i
g
u
r
e
12
.b
). T
h
i
s
i
s
sim
p
l
y
due t
o
t
h
e cha
nge
of t
h
e n
o
m
i
nal
op
erat
i
ng
p
o
i
n
t
o
f
t
h
e f
u
nc
tio
n
a
l
m
a
g
n
e
tron
. Th
e failure of this
m
a
g
n
e
tron
do
esn
’
t
di
st
ur
b t
h
e f
u
n
c
t
i
oni
n
g
o
f
t
h
e
ot
her m
a
gnet
r
ons i
n
ser
v
i
ce.
The t
h
ree fa
ul
t
y
m
a
gnet
r
ons
have
no i
n
t
e
ra
ct
i
o
n
effect
on
t
h
e f
unct
i
o
ni
n
g
o
f
t
h
e
t
h
ree ot
he
r fu
nct
i
o
nal
m
a
gnet
r
ons
. Gi
ve
n
t
h
at
t
h
ei
r o
p
er
at
i
ng poi
nt
s
ar
e
n
o
t
di
st
ur
be
d.
0,
60
0,
61
0
,
6
2
0
,
6
3
0,
64
-
800
0
-
600
0
-
400
0
-
200
0
0
20
00
40
00
60
00
80
00
u
s3
u
s2
SE
COND
A
R
I
E
S
VOLT
A
G
E
S
(V
)
TI
M
E
(
s
)
u
s1
=0V
0,
60
0,
61
0
,
6
2
0,
63
0
,
6
4
-2
-1
0
1
2
SE
COND
A
R
I
E
S C
U
RREN
T
S
(
A
)
TI
M
E
(
s
)
is
3
is
2
is
1
=0
A
0,
6
0
0,
61
0,
62
0,
63
0
,
6
4
-
8000
-
6000
-
4000
-
2000
0
2000
4000
6000
8000
(u
c1
; u
c2
)
u
c4
C
O
N
D
EN
S
E
R
S
VO
L
T
A
G
ES
(
V
)
TI
M
E
(
s
)
u
c3
(u
c5
; u
c6
)
0,
6
0
0,
61
0
,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
D
I
O
D
ES CU
RREN
T
S
(
A
)
TI
M
E
(
s
)
id
3
(id
1
=i
d
2
=d
4
=0
A
)
(id
5
; id
6
)
0
,
6
0
0,
61
0,
62
0,
6
3
0,
64
-
8000
-
6000
-
4000
-
2000
0
2000
4000
6000
8000
MA
G
N
E
T
R
O
N
S
VO
L
T
A
G
ES
(
V
)
TI
M
E
(
s
)
(u
m1
; u
m2
; u
m4
)
u
m3
(u
m5
; u
m6
)
0,
60
0,
6
1
0,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
M
A
GN
ETRO
N
S
CU
RRE
N
T
S (A)
TI
M
E
(
s
)
im
3
(i
m
1
=i
m
2
=m
4
=0
A
)
(im
5
;
im
6
)
a. b.
Fi
gu
re
1
2
. C
i
rc
ui
t
m
odel
:
C
a
se o
f
T
h
ree
fa
ul
t
y
m
a
gnet
r
o
n
s
wh
ich
two
are
in
th
e
sam
e
p
h
ase, a). Circu
it
m
o
d
e
l
of a c
h
aracter three
phase
HV powe
r s
u
pply
for
N=2 m
a
gnet
r
o
n
s
per
p
h
ase
,
b
)
.
W
a
vef
o
rm
s o
f
c
u
r
r
ent
s
an
d
v
o
ltag
e
s o
f
t
h
e circu
it
in
Figu
re
12
.a
3.
5.
C
a
s
e
of
f
o
u
r
fa
u
l
ty
mag
n
et
ro
n
s
a
n
d
t
w
o
m
a
g
n
e
t
ro
ns
in
s
e
r
v
ic
e
3.
5.
1.
Case
of Two faulty m
a
gne
t
r
o
ns in the tw
o of the
three
phases
(phase1
and phase
2
)
Th
e sim
u
latio
n’s resu
lts t
h
ro
ug
h EMTP of the assem
b
ly in
Fig
u
re
13
.a are sho
w
n
i
n
Fi
gure
1
3
.b.
0,60
0,61
0
,
6
2
0
,
6
3
0,
6
4
-
8
000
-
6
000
-
4
000
-
2
000
0
2
000
4
000
6
000
8
000
SE
C
O
N
D
A
R
I
E
S V
O
L
T
A
G
E
S
(V
)
TI
M
E
(
s
)
u
s3
u
s1
=u
s2
=0
V
0,
60
0,
61
0
,
62
0
,
63
0
,
64
-2
-1
0
1
2
SE
CONDAR
I
E
S CUR
R
E
N
T
S
(A)
TI
M
E
(
s
)
is
3
is
1
=i
s
2
=0
A
0,
60
0
,
6
1
0,
62
0,
6
3
0
,
64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
C
O
ND
E
N
S
E
R
S
V
O
L
T
AG
ES (
V
)
TI
M
E
(
s
)
(u
c5
; u
c6
)
(u
c1
; u
c2
; u
c3
; u
c4
)
0
,
6
0
0,
61
0
,
62
0,
63
0,
6
4
-1
,5
-1
,0
-0
,5
0,
0
0,
5
1,
0
1,
5
DIO
D
E
S
C
U
RRE
N
T
S
(
A
)
TI
M
E
(
s
)
(id
6
; i
d
5
)
id
1
=i
d
2
=i
d
3
=i
d
4
=0
A
0,
60
0,
61
0
,
62
0,
63
0
,
64
-8
0
0
0
-6
0
0
0
-4
0
0
0
-2
0
0
0
0
20
00
40
00
60
00
80
00
MA
G
N
ET
R
O
NS
V
O
L
T
AG
ES (
V
)
TI
M
E
(
s
)
(u
m6
;
u
m5
)
(u
m1
; u
m2
;
u
m3
;
u
m4
)
0,
60
0,
61
0,
62
0,
63
0,
64
-1
,5
-1
,0
-0
,5
0,
0
0,
5
1,
0
1,
5
M
A
GN
E
T
RO
N
S
C
U
RRE
N
T
S
(
A
)
TI
M
E
(
s
)
(im
6
; i
m
5
)
im
1
=i
m
2
=i
m
3
=i
m
4
=0
A
a.
b.
Fi
gu
re
1
3
. C
i
rc
ui
t
m
odel
:
C
a
se o
f
T
w
o
fa
ul
t
y
m
a
gnet
r
ons
i
n
one
p
h
ase
(
p
hase
1
or
p
h
ase
2
)
, a
)
. C
i
rc
ui
t
m
odel
of a c
h
aracter three
phase
HV powe
r s
u
pply
for
N=2 m
a
gnet
r
o
n
s
per
p
h
ase
,
b
)
.
W
a
vef
o
rm
s o
f
c
u
r
r
ent
s
an
d
v
o
ltag
e
s o
f
t
h
e circu
it
in
Figu
re
13
.a.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
Break
dow
ns
' D
i
agnosis of
A N
e
w Character
Three
Phase
H
i
gh
Voltage
Power Supply for.
... (
R
.
B
a
tit)
1
257
It is noted tha
t
each
of the
two
fa
ulty
m
a
gnet
r
ons
(in one am
ong the
two phases
1 and
2) re
duc
es t
h
e
f
u
n
c
tion
i
ng
o
f
its co
rr
espon
d
i
n
g
vo
ltag
e
doub
ler
,
con
s
isting
o
f
on
e
d
i
od
e and
on
e co
nden
s
er h
a
v
i
n
g
0.9
µF.
Thi
s
co
n
d
ens
e
r has t
o
cha
r
ge
t
h
ro
u
gh t
h
e di
ode at
t
h
e sec
o
n
d
a
r
y
pea
k
v
o
l
t
a
ge s
u
p
p
l
i
e
d by
t
h
e
hi
g
h
vol
t
a
g
e
t
r
ans
f
o
r
m
e
r. Each
faul
t
y
m
a
gnet
r
on
d
o
es
n’t
di
st
ur
b t
h
e
fu
n
c
t
i
oni
n
g
of
t
h
e
ot
he
r m
a
gnet
r
o
n
s i
n
se
rvi
ce.
The t
w
o faul
t
y
m
a
gnet
r
o
n
s o
f
sam
e
phase (
pha
se 1 an
d p
h
ase 2
)
ha
ve n
o
i
n
t
e
ract
i
o
n effect
o
n
t
h
e
fu
nct
i
o
ni
n
g
o
f
t
h
e t
w
o ot
her
fu
nct
i
onal
m
a
gnet
r
o
n
s (
o
f
p
h
ase 3
)
. Gi
ve
n
t
h
at
t
h
ei
r ope
rat
i
ng
poi
nt
s are n
o
t
di
st
ur
be
d.
3.
5.
2.
C
a
s
e
of
Two fa
u
l
ty
mag
n
et
ro
n
s
in on
e
pha
s
e
a
n
d
one
faulty magne
t
r
o
n in e
a
ch
of the other
two
phase
s
Th
e sim
u
latio
n
’
s resu
lts th
ro
ug
h
EMTP of th
e assem
b
ly in
Fig
u
re 14
.a are sh
own
in
Figu
re
1
4
.b. It
is noted t
h
at each of the t
w
o
faulty m
a
gnet
r
ons
of
sa
me phase (phase 1)
reduces
the functioning
of its
cor
r
es
po
n
d
i
n
g
vol
t
a
ge
d
o
ubl
e
r
, c
onsi
s
t
i
n
g
of
one
di
o
d
e a
n
d
one c
o
nd
ense
r
havi
ng
0.
9 µF
. Thi
s
c
o
n
d
e
n
s
e
r has
t
o
cha
r
g
e
t
h
ro
ug
h t
h
e
di
o
d
e
at
t
h
e seco
n
d
a
r
y
pea
k
vol
t
a
g
e
su
ppl
i
e
d
by
t
h
e hi
gh
v
o
l
t
a
ge t
r
a
n
sf
o
r
m
e
r. Th
e
fai
l
u
re
o
f
t
h
es
e
t
w
o
m
a
gnet
r
o
n
s
do
esn
’
t
di
st
ur
b t
h
e f
u
nct
i
o
ni
n
g
of
t
h
e
ot
h
e
r m
a
gnet
r
o
n
s
i
n
ser
v
i
ce.
For eac
h o
n
e o
f
t
w
o ot
her p
h
a
ses ( phase
2 and
phase
3) w
h
i
c
h co
nt
ai
ns t
w
o m
a
gnet
r
o
n
s
:
one fa
ul
t
y
m
a
gnet
r
on a
n
d
one m
a
gnet
r
o
n
i
n
servi
ce,
w
e
obse
r
ve i
n
t
h
e di
ode s
w
i
t
c
h
i
ng t
i
m
e
, t
h
e presence
of t
r
a
n
si
ent
o
s
cillatio
n
s
at
th
e lev
e
l of the v
o
ltag
e
s acro
ss th
e
fu
n
c
ti
o
n
a
l m
a
g
n
e
tron
and
t
h
e transform
e
r’s secon
d
a
ry
(Fi
g
ure
14
.b
).
Thi
s
i
s
sim
p
l
y
due t
o
t
h
e cha
nge
of t
h
e
nom
i
n
al
ope
rat
i
ng
poi
nt
of t
h
e
fu
nct
i
onal
m
a
gn
et
ro
n i
n
t
h
i
s
p
h
ase.
T
h
e fai
l
u
re
o
f
o
n
e m
a
gnet
r
on
i
n
eac
h
pha
s
e
d
o
es
n
o
t
di
st
ur
b t
h
e
f
u
nc
t
i
oni
n
g
of
t
h
e
ot
he
r
m
a
gnet
r
ons i
n
servi
ce. T
h
e f
o
ur
faul
t
y
m
a
gn
et
ro
ns ha
ve n
o
i
n
t
e
ract
i
on e
f
f
ect
on t
h
e f
u
nc
t
i
oni
n
g
o
f
t
h
e
ot
he
r
t
w
o f
unct
i
o
nal
m
a
gnet
r
ons
, gi
ven
t
h
at
t
h
ei
r o
p
erat
i
n
g p
o
i
n
t
s
are n
o
t
di
st
u
r
b
e
d.
0,
60
0
,
61
0,
62
0
,
63
0,
64
-
800
0
-
600
0
-
400
0
-
200
0
0
200
0
400
0
600
0
800
0
SECO
ND
A
R
I
E
S VO
LT
A
G
ES (
V
)
TI
M
E
(
s
)
u
S3
u
S2
u
S1
=0
V
0,
60
0,
61
0,
6
2
0,
6
3
0,
64
-2
-1
0
1
2
SE
CON
D
A
R
I
E
S CU
RR
EN
TS
(
A
)
TI
M
E
(
s
)
is
3
is
2
is
1
=0A
0,
60
0,
6
1
0,
6
2
0,
63
0,
64
-
8000
-
6000
-
4000
-
2000
0
2000
4000
6000
8000
(u
c3
;
u
c5
)
C
O
N
D
EN
SER
S
V
O
LTA
G
ES
(V)
TI
M
E
(
s
)
(u
c1
;
u
c2
)
u
c4
u
c6
0,
60
0
,
61
0
,
62
0,
63
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
id
6
D
I
OD
E
S
CU
RRE
NT
S
(
A
)
TI
M
E
(
s
)
id
4
id
1
=i
d
2
=i
d
3
=i
d
5
=0
A
0
,
60
0
,
61
0
,
62
0,
63
0,
64
-
8
000
-
6
000
-
4
000
-
2
000
0
2
000
4
000
6
000
8
000
MA
GN
ET
RO
NS
V
O
L
T
A
G
E
S
(V
)
TI
M
E
(
s
)
u
m4
(u
m1
;
u
m2
;
u
m3
;
u
m5
)
u
m6
0,
60
0,
61
0
,
62
0
,
6
3
0,
64
-1
,
5
-1
,
0
-0
,
5
0,
0
0,
5
1,
0
1,
5
M
A
GNE
T
RON
S
CU
RRE
NT
S
(
A
)
TI
M
E
(
s
)
id
6
id
4
im
1
=i
m
2
=i
m
3
=i
m
5
=0
A
a. b.
Fi
gu
re
1
4
. C
i
rc
ui
t
M
o
del
:
C
a
se o
f
T
w
o
fa
ul
t
y
m
a
gnet
r
ons
i
n
one
p
h
ase
an
d
one
fa
ul
t
y
m
a
gnet
r
o
n
i
n
eac
h
of
t
h
e ot
her
t
w
o
p
h
ases,
a)
. T
h
re
e p
h
ase
H
V
po
wer
su
p
p
l
y
f
o
r
N=2
m
a
gnet
r
o
n
s
per
p
h
ase
,
b
)
.
Wa
vef
o
rm
s of
cu
rren
ts and
vo
ltag
e
s
o
f
th
e circu
it in
Figu
re 14
.a
3.
6.
C
a
s
e
of
f
i
v
e
fau
l
t
y
m
a
g
n
et
ron
s
an
d
o
n
e mag
n
et
r
o
n
in
s
e
rv
ic
e
Th
e sim
u
latio
n
’
s resu
lts th
ro
ug
h
EMTP of th
e assem
b
ly in
Fig
u
re 15
.a are sh
own
in
Figu
re
1
5
.b. It
is note
d
that
each
of the two
fa
ulty
m
a
gnet
r
ons
(in
one am
ong t
h
e
two
phases
1 and
2) re
duces the
f
u
n
c
tion
i
ng
o
f
its co
rr
espon
d
i
n
g
vo
ltag
e
doub
ler
,
con
s
isting
o
f
on
e
d
i
od
e and
on
e co
nden
s
er h
a
v
i
n
g
0.9
µF.
Thi
s
co
n
d
ens
e
r has t
o
cha
r
ge
t
h
ro
u
gh t
h
e di
ode at
t
h
e sec
o
n
d
a
r
y
pea
k
v
o
l
t
a
ge s
u
p
p
l
i
e
d by
t
h
e
hi
g
h
vol
t
a
g
e
t
r
ans
f
o
r
m
e
r. The fai
l
u
re o
f
t
h
ese t
w
o m
a
gnet
r
o
n
s d
o
es
n’t
d
i
st
urb t
h
e fu
nc
t
i
oni
n
g
o
f
t
h
e
ot
he
r m
a
gnet
r
ons i
n
service.
C
once
r
ni
ng
t
h
e ot
he
r rem
a
i
n
i
n
g
phase
(
p
hase
3)
w
h
i
c
h c
ont
ai
ns
t
w
o m
a
gnet
r
o
n
s:
o
n
e fa
ul
t
y
m
a
gnet
r
on a
n
d
one m
a
gnet
r
o
n
i
n
servi
ce,
w
e
obse
r
ve i
n
t
h
e di
ode s
w
i
t
c
h
i
ng t
i
m
e
, t
h
e presence
of t
r
a
n
si
ent
o
s
cillatio
n
s
at
th
e lev
e
l of the v
o
ltag
e
s acro
ss th
e
fu
n
c
ti
o
n
a
l m
a
g
n
e
tron
and
t
h
e transform
e
r’s secon
d
a
ry
(Fi
g
ure
15
.b
).
Thi
s
i
s
sim
p
l
y
due t
o
t
h
e cha
nge
of t
h
e
nom
i
n
al
ope
rat
i
ng
poi
nt
of t
h
e
fu
nct
i
onal
m
a
gn
et
ro
n i
n
t
h
i
s
phase
. Th
e fai
l
u
re of
o
n
e m
a
gnet
r
o
n
i
n
t
h
i
s
phase
does n
o
t
di
st
ur
b t
h
e fu
nct
i
oni
ng
of t
h
e
ot
he
r
m
a
gnet
r
ons i
n
servi
ce. T
h
e fi
ve fa
ul
t
y
m
a
gnet
r
o
n
s ha
ve n
o
i
n
t
e
ract
i
on ef
f
ect
on t
h
e f
unc
t
i
oni
n
g
o
f
t
h
e ot
he
r
m
a
gnet
r
on
,
gi
v
e
n t
h
at
i
t
s
o
p
er
at
i
ng
poi
nt
s a
r
e n
o
t
di
st
ur
bed
.
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