Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
V
o
l.
6, N
o
. 1
,
Febr
u
a
r
y
201
6,
pp
. 1
~
1
1
I
S
SN
: 208
8-8
7
0
8
,
D
O
I
:
10.115
91
/ij
ece.v6
i
1.8
305
1
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
A A New Validation Approach
of a New T
h
ree-Ph
as
e Hi
gh
Voltage Power Supply for Microw
aves Generators with one
Magnetron by Phase
M.
B
a
ss
oui
*
, M. Ferfr
a
*
,
M. Chr
a
yg
an
e**
* Res
ear
ch
te
am
in power
and
co
ntrol
EM
I, M
oha
m
e
d –V Univers
i
t
y
,
Raba
t,
M
o
rocco
** M
S
TI Labo
ra
tor
y
,
ES
T Ibn
Z
ohr Univers
i
t
y
,
Agadir-M
orocco
Univers
i
t
y
,
M
o
r
o
cco
Article Info
A
B
STRAC
T
Article histo
r
y:
Received J
u
n
9, 2015
Rev
i
sed
O
c
t 25
, 20
15
Accepted Nov 16, 2015
In order
to validating
the n
e
w
three-
ph
ase Hig
h
voltag
e
power
supply
for
microwave generators with one
magnetr
on b
y
p
h
ase, th
is paper
presents
a
new validation
approach to evaluate
the pro
posed model with sever
a
l
evalu
a
tions.
This approach is based
on the cal
cu
lation
and m
eas
urem
ent of
the performance and th
e power
f
actor
of
th
is new three-ph
ase p
o
wer supply
,
also the stud
y o
f
the oper
a
tion
of this new s
y
st
em
in case of f
a
ilur
e
. Th
e
design of th
is po
wer supply
is co
mposed of new three-phase tr
ansformer with
magnetic shunt, supply
i
ng b
y
p
h
ase a
voltag
e
doubler cell co
mposed of a
capacitor
and a
diode.
Each cell in turn
, supplies a single magn
etron. In
this
paper we have
presented
the new three-
ph
ase tr
ansformer b
y
its
equiv
a
len
t
m
odel; it
’s a
π
quadruple model composed of s
t
orable indu
ctan
ces ab
le
to
transla
ting the nonline
a
r
satur
a
tion
phenomen
a for stab
ilization of th
e
magnetron current. The voltage
and curre
nt cur
v
es obtained b
y
simulation
with MATLAB
SIMULINK are in good conformity
with those
obtain
e
d b
y
experimental of
conventi
onal po
wer supply
usin
g a single phase transformer
for one magnetr
on.
The
sam
e
cu
rves will a
llow
us to plot th
e in
stantan
e
ous
power abs
o
rbed b
y
ea
ch m
a
gnetron. Th
is
lead
s
to determ
ine
the aver
ag
e
power em
itted
b
y
each
m
a
gnetr
on, and
establ
ish the b
a
lan
ce o
f
the powe
r
m
i
crowave gen
e
rator b
y
com
puting its
p
e
rform
ance whi
c
h is
co
m
p
ared t
o
that ob
ta
ined fro
m
experim
e
nta
l
.
After th
at we
wi
ll com
put
e th
e p
o
wer fac
t
or
of this power su
pply
and we will stud
y
its operation in case of f
a
ilure of on
e
or two magnetro
n
s.
Keyword:
Inst
a
n
t
a
ne
ou
s po
we
r
Perform
a
nce
Po
wer facto
r
Pow
e
r
supp
ly
Three
-
phase
transform
e
r
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
:
M
oham
e
d B
a
s
s
oui
,
Depa
rtem
ent of Elect
ri
cal
E
n
gi
nee
r
i
n
g,
MO
HA
MED-V
U
n
i
v
er
sity,
M
oham
m
adi
a
sch
ool
of
en
gi
neri
nrs
R
a
bat
.
M
o
r
o
cco
Em
a
il: b
a
sso
u
i
m
o
h
a
m
e
d
@
gmail.co
m
1.
INTRODUCTION
C
u
r
r
ent
l
y
, t
o
sup
p
l
y
one m
a
gnet
r
on
, t
h
e cur
r
ent
si
n
g
l
e
-p
ha
se po
wer s
u
p
p
l
y
of t
h
e t
ube m
i
crowa
v
e
gene
rat
o
r use
s
a si
ngl
e-
phas
e
t
r
ansf
orm
e
r wi
t
h
m
a
gnet
i
c
shu
n
t
s
by
m
a
gnet
r
o
n
[
2
-
1
2]
. To co
nt
ri
but
e t
o
t
h
e
d
e
v
e
l
o
p
m
en
t o
f
t
h
e techn
o
lo
g
i
cal inn
o
v
a
tio
n
in
t
h
e man
u
f
actur
ing
i
n
du
str
y
o
f
t
h
e p
o
w
e
r
supply f
o
r
m
a
gnet
r
ons
, t
h
i
s
wor
k
i
s
part
of t
h
e
deve
l
o
p
m
ent
and val
i
d
at
i
on o
f
a new t
y
pe
of
H
V
po
w
e
r
s
u
p
p
l
y
w
i
t
h
a thre
e-pha
se
cha
r
acter
for
one m
a
gnetron
by phas
e.
Fi
gu
re
1 s
h
ows
t
h
e set
up
o
f
t
h
e
ne
w t
h
ree-
p
h
a
s
e hi
g
h
vol
t
a
ge
p
o
w
er
sup
p
l
y
o
f
m
i
crowa
v
es
ge
nera
t
o
rs
wi
t
h
o
n
e
m
a
gnet
r
on
by
pha
se. T
h
i
s
sc
hem
e
i
s
co
m
p
o
s
ed
of
a
n
e
w th
ree-p
h
a
se tran
sform
e
r, su
pp
lying
b
y
ph
ase a cell
d
oublers c
o
m
pose
d
of ca
pacitor
and a di
ode, ea
ch cell
su
pp
lies at its ou
tpu
t
a sing
le m
a
g
n
e
tron. Th
e n
e
w
t
h
ree-phase m
a
gnetic leakag
e
tr
an
sf
or
m
e
r
,
no
t yet
manufact
ure
d
, is the ba
sic ele
m
ent of
th
is n
e
w power su
pp
ly. Th
is special th
ree-p
h
a
se tran
sfo
r
m
e
r wit
h
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
. 1, Feb
r
uar
y
20
1
6
:
1 – 1
1
2
mag
n
e
tic shu
n
t
s en
su
res th
e stab
ilizatio
n
of
th
e anod
ic curren
t in
each
m
a
g
n
e
t
r
on
th
ank
s
to
th
e sat
u
rati
o
n
of
its
mag
n
e
tic circu
it. Co
m
p
ared
to
th
e co
nv
en
tio
n
a
l tran
sf
orm
e
r, th
e leak
ag
e flux
in
th
e sh
un
t is o
f
th
e sa
me
or
der as
bot
h t
h
e p
r
i
m
ary
an
d seco
n
d
ary
fl
uxe
s. Th
us
, t
h
e t
h
eory
o
f
cl
assi
cal
t
r
ansf
or
m
e
rs does
not
appl
y
i
n
th
e case
o
f
th
e
tran
sform
e
r with
sh
un
ts.
[1
]
Th
e aim
o
f
th
is article is to
v
a
lid
ate u
n
d
e
r
M
A
TLAB
S
I
M
U
LI
NK t
h
e pr
o
pose
d
m
o
d
e
l
wi
t
h
several
eval
uat
i
o
ns.
T
h
e
pa
per
i
s
o
r
ga
ni
zed a
s
f
o
l
l
o
ws:
on
t
h
e
fi
rs
t
st
ep
we
prese
n
t
e
d t
h
e e
q
ui
v
a
l
e
nt
m
odel
of
a n
e
w
th
ree-ph
ase tran
sfo
r
m
e
r. Th
is
m
o
d
e
l will b
e
in
teg
r
ated
in
o
v
e
rall sch
e
m
e
o
f
th
e po
wer su
pp
ly to
b
e
su
itab
l
e
fo
r t
h
e m
odel
i
ng
of t
h
e w
h
ol
e devi
ce,
usi
n
g
num
eri
cal
sim
u
l
a
t
i
on s
o
ft
war
e
M
A
TLAB
SI
M
U
LI
NK c
o
d
e
. Th
e
vol
t
a
ge a
n
d cur
r
ent
cu
r
v
es
obt
ai
ne
d
by
si
m
u
latio
n
co
mp
ared
with
tho
s
e ob
tain
ed
ex
p
e
rim
e
n
t
all
y
b
y
a
con
v
e
n
t
i
onal
p
o
we
r su
p
p
l
y
usi
ng a si
ngl
e
-
p
h
a
se t
r
ansf
orm
e
r fo
r o
n
e m
a
gnet
r
o
n
[2
-1
2]
. I
n
t
h
e seco
nd st
ep we
st
udy
t
h
e
p
o
we
r
bal
a
nce
o
f
t
h
i
s
ne
w t
h
ree
-
ph
ase p
o
w
er
su
p
p
l
y
by
det
e
rm
ini
n
g t
h
e
val
u
e
of
t
h
e
i
n
st
ant
a
neo
u
s
powe
r curve, t
h
is lead to establis
h the ave
r
a
g
e powe
r em
i
t
t
e
d by each m
a
gnet
r
on, the
n
we will establish the
energetic bala
nce of the
power m
i
crowave
gene
rator by
c
o
m
put
i
ng t
h
ei
r
per
f
o
r
m
a
nce
that m
u
st be identical
to
th
at o
b
t
ain
e
d
exp
e
rim
e
n
t
al y. Nex
t
we will co
m
p
u
t
e th
e p
o
wer fact
o
r
o
f
th
is n
e
w th
ree-p
h
a
se po
wer
su
pp
ly. Fi
n
a
lly we
will stu
d
y
th
e po
ssi
b
ility
o
f
th
e
fun
c
tion
i
ng
o
f
t
h
is n
e
w system
in
case of break
down of
one
o
r
t
w
o
m
a
gnet
r
o
n
s.
Fi
gu
re
1.
Th
re
e-p
h
ase
p
o
we
r
sup
p
l
y
f
o
r m
a
gnet
r
on
by
p
h
as
e
2.
MODELING OF
THE NE
W
THREE-PHASE POWE
R
SUPPL
Y
WITH ONE
MAGNETRON
2.1 Descripti
o
n
of the New Three-
Phase Transformer
with
Shunts
In
o
u
r
desi
gn
o
f
t
h
i
s
new
t
h
re
e-p
h
ase t
r
a
n
s
f
o
r
m
e
r wi
t
h
m
a
gnet
i
c
sh
unt
,
we
use a
n
a
r
m
o
red st
r
u
ct
u
r
e
tetrah
edron
ty
p
e
(Figu
r
e
2) to
rep
r
esen
t
th
e equ
i
v
a
len
t
m
a
g
n
e
tic circu
it o
f
th
e tran
sfo
r
m
e
r,
wh
i
c
h
will
u
ndo
ub
ted
l
y allo
w to redu
ce th
e co
ng
esti
o
n
and
t
h
e
vo
lu
m
e
o
f
t
h
is n
e
w
d
e
v
i
ce
an
d m
a
k
e
s it m
o
r
e
eco
no
m
i
cal. T
h
is stru
ct
u
r
e
o
f
th
e n
e
w three-p
h
a
se tran
sf
o
r
mer with
shu
n
t
s, no
t yet
m
a
n
u
fact
u
r
ed
, th
at
will b
e
use
d
i
n
t
h
e H
V
p
o
we
r su
p
p
l
i
e
s for N m
a
gnet
r
ons
per p
h
a
se (t
reat
ed ca
se:
N = 1
m
a
gnet
r
on
per p
h
a
s
e). Th
e
mag
n
e
tic shunt ser
v
es to d
i
ver
t
an im
p
o
r
tan
t
p
a
r
t
o
f
f
l
ux cir
c
u
l
ating
b
e
tw
een
t
h
e
p
r
i
m
ar
y an
d secon
d
a
r
y
wi
n
d
i
n
gs of
ea
ch pha
se.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE
ISS
N
:
2088-8708
A A N
e
w
Val
i
dat
i
o
n
Ap
pr
oa
ch
of
a
N
e
w
T
h
ree-P
hase
Hi
g
h
V
o
l
t
a
ge P
o
w
e
r S
u
ppl
y f
o
r
…
(M. Bass
oui)
3
Fi
gu
re
2.
Di
a
g
r
a
m
of t
h
e e
qui
val
e
nt
m
a
gnet
i
c
ci
rcui
t
of
t
h
e
new
t
h
ree-
pha
s
e
t
r
ans
f
orm
e
r wi
t
h
m
a
gnet
i
c
shu
n
t
2.
2 E
l
ectri
c
a
l
and
M
a
gne
t
i
c
E
qua
ti
ons
In t
h
e
pr
o
pose
d
st
u
d
y
,
we co
nsi
d
e
r
t
h
e ne
w
t
h
r
ee-p
h
ase tran
sform
e
r wit
h
ou
t iron
lo
sses (h
ysteresi
s
loss and eddy curre
nt). And to sim
p
lif
y t
h
e stud
y, w
e
co
nsid
er
th
e
St
ar Star (Yy)
coupling bet
w
een the
pri
m
ary
and secon
d
a
r
y
wi
nd
i
ngs
. B
y
t
h
e appl
i
cat
i
o
n of
Ohm
’
s gene
ral
i
zed l
a
w t
o
t
h
e pri
m
ary wi
ndi
n
g
s
(receive
r c
o
nvention) a
n
d se
conda
r
y on
es
(ge
n
erat
or convention) a
n
d the
Hopkins
o
n’s law, we
obta
in the
fo
llowing
co
mp
lete electric an
d m
a
g
n
e
tic eq
u
a
tion
s
go
v
e
r
n
i
n
g t
h
e
o
p
era
t
i
ng
of t
h
e
thre
e-phase trans
f
orm
e
r.
To sim
p
lify the study we
take the
pha
se
A a
s
exam
ple:
Fi
gu
re
3.
Di
a
g
r
a
m
of t
h
e e
qui
val
e
nt
m
a
gnet
i
c
ci
rcui
t
of
t
h
e
new
t
r
a
n
sf
orm
e
r
(Phase
A as
exa
m
ple)
Electric equations
(
1
)
(
2
)
1
..
A
AA
Ur
i
n
t
2
..
a
aa
a
Ur
i
n
t
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
. 1, Feb
r
uar
y
20
1
6
:
1 – 1
1
4
M
a
gnet
i
c
e
qua
t
i
ons
(
3
)
(
4
)
(
5
)
(
7
)
B
y
t
r
ansf
o
r
m
i
ng
t
h
e
eq
uat
i
o
ns
(1
) t
o
(7
),
we
obt
ai
n t
h
e
fol
l
o
wi
n
g
e
q
ua
t
i
ons
(8
) t
o
(1
3)
g
o
uve
rni
n
g
th
e op
eration
of th
e
π
q
u
a
d
r
u
pl
e m
odel
[13]
-[
14]
re
pre
s
ent
a
t
i
v
e of t
h
e t
r
a
n
sf
orm
e
r refe
r
e
d t
o
sec
o
n
d
a
r
y
(Fo
r
m
o
r
e
d
e
tails see [1
5
]-[
16
])
.
(
8
)
(
9
)
(
1
0
)
(
1
1
)
(
1
2
)
(
1
3
)
The p
r
evi
o
u
s
equat
i
o
ns re
sp
o
nd t
o
t
h
e e
qui
v
a
l
e
nt
di
gram
of t
h
e fi
rst
p
h
as
e A of t
h
e
new
t
h
ree-
pha
se
t
r
ans
f
o
r
m
e
r.
Thus we obt
ai
n a
π
m
odel
of t
h
i
s
t
r
ans
f
orm
e
r com
posed
of
t
h
ree nonlinea
r inductances referre
d
to
seco
nd
ar
y,
L’
p-A
o
n
th
e primary sid
e
, L
s-A
on
t
h
e
seco
n
d
a
r
y
si
de a
n
d L
’
Sh
-
A
on t
h
e s
h
u
n
t
s
si
de
(Fi
g
u
r
e
3)
.
Fi
gu
re
4.
Ne
w
qua
d
r
u
p
l
e
m
o
d
e
l
of
t
h
ree
-
pha
se t
r
an
sf
orm
e
r wi
t
h
s
h
unt
s
By p
e
rfectly similar calcu
lati
o
n
s
, t
h
e eq
u
a
ti
o
n
syst
em
whi
c
h
resp
o
n
d
s
t
o
t
h
e e
q
ui
val
e
nt
di
ag
ram
o
f
t
h
e p
h
ase
B
a
n
d C
pe
rm
it
s t
o
fi
n
d
t
h
e
m
odel
s
i
n
di
cat
ed
o
n
t
h
e Fi
g
u
r
e
5.
T
h
e e
qui
val
e
nt
c
i
rcui
t
s
h
o
u
l
d
re
fl
ect
th
e b
e
h
a
v
i
or
o
f
th
e to
tal
po
wer su
pp
ly in
cludin
g
t
h
e m
a
g
n
e
t
r
on
and
th
e tran
sfo
r
m
e
r with
sh
un
ts.
1
..
A
As
h
A
s
h
A
A
RR
n
i
2
..
.
s
hA
s
h
A
a
a
a
RR
n
i
12
..
.
-
.
AA
a
a
A
a
R
Rn
i
n
i
Aa
s
h
A
'
'
.'
(
'
.'
)
A
A
pA
pA
Ur
i
L
i
t
.(
.
)
aa
a
s
a
s
a
Ur
i
L
i
t
2
.(
.
)
'
.
'
A
s
as
a
s
h
A
s
h
A
nL
i
L
i
tt
t
''
'
A
pA
s
h
A
ii
i
'
s
as
h
A
a
ii
i
2
.
(
')
*
(
')
(
'
)
*
(
'
)
)
f
fe
e
sh
A
s
h
A
sh
A
s
h
A
sh
A
nL
i
L
i
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A A N
e
w
Val
i
dat
i
o
n
Ap
pr
oa
ch
of
a
N
e
w
T
h
ree-P
hase
Hi
g
h
V
o
l
t
a
ge P
o
w
e
r S
u
ppl
y f
o
r
…
(M.
Ba
ssou
i)
5
Fi
gu
re
5.
M
o
d
e
l
i
ng
of
t
h
e
ne
w t
h
ree-
p
h
ase t
r
ans
f
orm
e
r wi
t
h
m
a
gnet
i
c
sh
u
n
t
s
usi
n
g M
A
T
L
AB
S
I
M
U
L
I
NK
code
2.
3. Simula
tio
n
w
i
th M
a
tla
b
-
Sim
u
link of
the No
mi
nal
F
uncti
oni
n
g of the
Three
-Phase Power
Supply
To
v
a
lid
ate th
is m
o
d
e
l we hav
e
in
tegrated th
e m
o
d
e
l o
f
th
e n
e
w tran
sfo
r
m
e
r in
th
e hig
h
v
o
ltage
po
we
r su
p
p
l
y
ci
rcui
t
fr
om
t
h
e so
urce t
o
t
h
e
m
a
gnet
r
ons
Each m
a
gnet
r
on i
s
rep
r
ese
n
t
e
d by
an e
q
ui
val
e
nt
diagram
deduc
ed from
its
ele
c
trical ch
aracteristics wh
ich
is fo
rm
ally s
i
mil
a
r to
th
at o
f
a
d
i
od
e with
d
yna
m
i
c
r
e
sistan
ce R=35
0 Oh
m
s
an
d
th
r
e
sh
o
l
d
v
o
ltag
e
E=38
00
Volts. The
nonli
n
ear inductors s
t
udied in
Figure
5
depe
nd on the reluctance of the
m
a
gnetic circuit por
ti
on
with a section S and average length l
.
The
i
m
p
l
e
m
en
tatio
n
of each
nonlin
ear ind
u
c
tan
ce with its
anal
y
t
i
c
expre
s
si
ons
u
nde
r
M
A
TLAB
-
S
I
M
U
LI
NK
soft
ware
was
r
eal
i
zed by
usi
n
g t
h
e
bl
ock
s
s
h
ow
n i
n
Fi
gu
re
6
[1
4]
.
Figure 6.
Im
ple
m
entation of each nonlin
ear inductance
under
MATLAB
-
SIMULINK
We v
a
lid
ate this
m
o
d
e
l b
y
co
m
p
arin
g
sim
u
latio
n
resu
lts (Fig
ure 7) with th
o
s
e ob
tain
ed
fro
m
test
s
already carried out [2
]-
[3
]-
[1
3
]
of
conv
entio
n
a
l po
w
e
r
su
pp
ly u
s
ing
a sin
g
l
e ph
ase
tr
an
sf
or
m
e
r
f
o
r
on
e
m
a
gnet
r
on (Fi
g
u
r
e 8).
T
h
e si
m
u
l
a
t
i
on o
f
t
h
e pr
o
pose
d
sy
s
t
em
i
s
carri
ed out
on t
h
e M
A
TLAB
versi
o
n
7.
10
.
0
(2010a
)
using t
h
e sim
power
s
y
stem
(SPS) toolbox and
disc
re
te step
sol
v
er of
1e-5.
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
. 1, Feb
r
uar
y
20
1
6
:
1 – 1
1
6
Fig
u
re
7
.
Sim
u
latio
n
with M
A
TLAB SIMULINK:
F
o
r
m
s
o
f
cu
rr
en
ts
an
d vo
lta
g
e
s
w
a
v
e
s
Fi
gu
re
8.
Ex
pe
ri
m
e
nt
al
s form
s o
f
c
u
r
r
ent
s
an
d
vol
t
a
ge
s
waves
o
f
c
o
n
v
e
n
t
i
o
n
a
l
po
we
r s
u
p
p
l
y
usi
n
g a
si
ngl
e
p
h
ase t
r
ansf
o
r
m
e
r for
one
m
a
gnet
r
o
n
[
2
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A A N
e
w
Val
i
dat
i
o
n
Ap
pr
oa
ch
of
a
N
e
w
T
h
ree-P
hase
Hi
g
h
V
o
l
t
a
ge P
o
w
e
r S
u
ppl
y f
o
r
…
(M.
Ba
ssou
i)
7
The electrical signal obtaine
d
(voltages and cu
rre
nts)
fr
o
m
sim
u
lation with M
A
TL
A
B
SIM
U
L
I
N
K
ar
e cu
rv
es of
var
i
ou
s sizes, per
i
od
ic, no
n-
si
n
u
s
o
i
d
a
l an
d
dep
h
a
sing
b
y
(
2
π
/3
) b
e
tween th
e
m
. Th
ese sig
n
a
ls
have t
h
e sam
e
fo
rm
as t
hose of e
xpe
ri
m
e
ntal
and
si
m
u
l
a
ted o
f
co
n
v
e
n
t
i
onal
po
we
r su
ppl
y
usi
n
g a s
i
ngl
e
pha
se t
r
ans
f
o
r
m
e
r for o
n
e m
a
gnet
r
on
,
i
n
part
i
c
ul
a
r
, t
h
e
m
a
xim
u
m
val
u
e of t
h
e m
a
gnet
r
on cu
rre
nt
whi
c
h
respect
t
h
e c
o
n
s
t
r
ai
nt
i
m
posed
by
t
h
e
m
a
nufa
c
t
u
rer
o
f
t
h
e m
a
gnt
e
g
t
r
on
(
I
ma
x
<1
.2
A
)
.
3.
V
A
L
IDA
T
ION
OF THE
NEW MOD
E
L OF THE
N
E
W POWER
SU
PPLY
UNDER
MA
TLAB
SIMULINK
3.1 Ener
gy Balance
of the
New Three-Ph
ase
Power Supply and
its Pe
rform
a
nce
3.
1.
1 Rese
arc
h
Me
th
od
Power is on
e
of th
e m
o
st i
m
p
o
rtan
t q
u
a
n
tities o
f
electricity. It d
e
scri
b
e
s the en
erg
y
requ
ire
m
en
ts o
f
a
syste
m
. Du
ring
th
is work, we will v
a
lid
ate th
e no
m
i
n
a
l fu
n
c
tio
n
i
n
g
of this n
e
w th
ree-ph
ase power sup
p
l
y by
com
puting t
h
e
instanta
neous
powe
r c
u
rves
of each m
a
gne
tron, t
h
is lead to estab
lish the
ave
r
a
g
e power of
each m
a
gnetron (Figure 9). T
h
is indicat
es that the transformer delivers a
n
ave
r
age
power equal to 3821 watts.
Th
at is to
say th
ere
will b
e
127
3
watts fo
r each
m
a
g
n
e
tron
.
W
itch
confirms fu
ll pow
er op
eration
o
f
t
h
e
n
e
w
t
h
ree-
p
h
ase p
o
w
er s
u
p
p
l
y
wi
t
h
o
n
e m
a
gnet
r
on
by
pha
se. T
h
e cu
rves
obt
a
i
ned by
si
m
u
l
a
t
i
on wi
t
h
M
A
TLA
B
SIM
U
L
I
NK
co
de a
r
e t
h
e sam
e
f
o
rm
s of
t
h
at
o
b
t
a
i
n
e
d
by
e
xpe
ri
m
e
nt
al
of
a c
o
n
v
e
n
t
i
ona
l
p
o
we
r s
u
ppl
y
usi
n
g
a sing
le ph
ase t
r
an
sfo
r
m
e
r with
m
a
g
n
e
tic shun
t (Figu
r
e
10
) [1
7
]-[1
8
]
.
3.
1.
2 Resul
t
s
a
nd Com
p
ari
s
o
n
s
Fi
gu
re 9.
A
v
er
age po
we
r
a
n
d
i
n
st
ant
a
ne
o
u
s po
we
r
obt
ai
ne
d
by
M
a
t
l
a
b-Si
m
u
l
i
nk f
o
r a
t
h
ree-
pha
se
po
we
r s
u
p
p
l
y
Fig
u
r
e
10
.
Av
er
ag
e pow
er
and
instan
tan
e
ous po
w
e
r
obt
ai
ne
d
by
e
x
peri
m
e
nt
al
of a
si
n
g
l
e
-p
hase
p
o
we
r
supply [17]
From
the c
u
rves of
power obtained,
we ca
n the
r
afat
e
r
de
duce
t
h
e
pe
rf
o
r
m
a
nce of t
h
i
s
ne
w t
h
ree-
pha
se p
o
we
r s
u
p
p
l
y
whi
c
h i
s
92%
, nam
e
l
y
and
93
% ex
pe
ri
m
e
nt
al
, ei
t
h
er.
W
e
not
e t
h
a
t
t
h
e nam
p
l
a
t
e
of t
h
e
si
ngl
e
phas
e
t
r
ansf
o
r
m
e
r i
ndi
cat
e an ap
pa
re
nt
e p
o
we
r
on
t
h
e ord
e
r
16
50
V
w
ith
a f
act
or
of
pr
im
ar
y p
o
w
er
0.
82
5.
ƞ
P
P
3821
4142
0
.
9
2
ƞ
1275
1650
∗
0
.825
0
.
9
3
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
. 1, Feb
r
uar
y
20
1
6
:
1 – 1
1
8
W
e
see th
at the p
e
r
f
or
m
a
n
ce
o
b
t
ain
e
d
b
y
MA
TLA
B
SI
M
U
I
N
K
cor
e
sp
ondin
g
to
th
e
n
e
w
th
r
ee-ph
ase
po
we
r su
p
p
l
y
i
s
i
d
ent
i
cal
t
o
t
h
at
obt
ai
ne
d
f
r
om
experi
m
e
nt
al
of a c
o
n
v
e
nt
i
onal
po
we
r
supl
y
usi
n
g a si
ngl
e
pha
se tra
n
sf
o
r
m
e
r fo
r
o
n
e m
a
gnet
r
o
n
.
3.2 P
o
wer F
a
c
t
or
of
the
New
Three-P
h
ase
Transformer
3.
2.
1 Rese
arc
h
Me
th
od
During rece
nt years the incre
a
se
i
n
react
i
v
e po
we
r co
nsum
pt
i
on i
n
el
ect
ri
cal
di
st
ri
but
i
o
n
sy
st
em
s has
e
m
erged a
new term
that is the powe
r
factor (PF). T
h
is
term
is u
s
ed
to ex
press how
e
f
fectively the electrical
en
erg
y
is converted
in
t
o
u
s
efu
l
fo
rm
an
d
i
n
d
i
catin
g
t
h
e
q
u
ality o
f
th
e serv
ice to
th
e electricity au
th
o
r
ized
and
end-users
.
Power
factor is t
h
e rati
o
between
th
e activ
e
(P) an
d th
e apparen
t
(S)
p
o
w
e
r
s.
It is also
de
fine
d as
the cosine
value of the Pha
s
e Diffe
re
nce
(PD)
betwee
n the voltage (V) a
nd current (I) of a
n
AC electrical
powe
r syste
m
. Power
factor is
a very
im
portant param
e
ter in power electr
onics
because it gives a m
eas
ure
of
h
o
w effecti
v
e
th
e real
po
wer u
tilizatio
n
in
th
e system
is. In ord
e
r t
o
m
easu
r
e th
e power facto
r
,
we
use th
e
fo
rm
ul
a:
[19]
-
[
20]
PF
cos
P
S
whe
r
e
i
s
t
h
e a
ngl
e
val
u
e
o
f
t
h
e
pha
se
di
ffe
r
e
nce
bet
w
ee
n t
h
e
vol
t
a
ge
a
n
d
t
h
e cu
rre
nt
si
g
n
al
s.
The Meas
urement of the Power Factor
of this th
ree-ph
ase
tran
sform
e
r u
n
d
e
r Matlab
Si
m
u
l
i
n
k
is p
e
rfo
r
m
e
d
usi
n
g Si
m
P
ow
erSy
st
em
s l
i
b
rary
.
We
calculate active power, appa
rent
powe
r
and power factor usi
n
g
the
fol
l
o
wi
n
g
bl
oc
ks (Fi
g
ur
e 11
).
Mea
n
: Th
is
b
l
o
c
k
calcu
lates th
e av
erag
e
va
lue of the inst
antane
ous pow
er i
n
c
onse
q
ue
nce de
d
u
ct
t
h
e
active powe
r.
Rms
: Th
is
b
l
ock
calcu
lates t
h
e
rm
s o
f
cu
rren
t and
vo
ltag
e
.
In th
is case, the th
ree-ph
ase syste
m
is co
n
s
i
d
ered
with
l
o
ad
b
a
lan
c
ing
.
Th
erefore we
calcu
l
ated
:
The Active power
as
the
ave
r
age value of
i
v
i
v
i
The A
ppa
rent
po
we
r
V
I
V
I
V
I
The Power
fact
or
3.2.2 Results
and Discussion
Fi
gu
re 1
1
. Di
a
g
ram
bl
oc
k of po
we
r
fact
or
m
easurem
ent
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I
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208
8-8
7
0
8
A A N
e
w
Val
i
dat
i
o
n
Ap
pr
oa
ch
of
a
N
e
w
T
h
ree-P
hase
Hi
g
h
V
o
l
t
a
ge P
o
w
e
r S
u
ppl
y f
o
r
…
(M.
Ba
ssou
i)
9
Th
e sim
u
latio
n
resu
lts of PF calcu
lated
by p
r
o
p
o
s
ed
me
thod are i
ndi
cate that the powe
r fact
or
of t
h
is
tr
an
sf
or
m
e
r
is o
n
th
e
or
d
e
r
o
f
0
.
89
, m
ean
in
g 89
%
o
f
th
e
pow
er is b
e
i
n
g used
f
o
r
u
s
efu
l
wo
rk
.
3.3 Verfic
ation
of the Oper
ati
o
n of
the New
Three-Phase
Power Supply
in Case of Failure
3.
3.
1 Rese
arc
h
Me
th
od
Th
e st
u
d
y
o
f
t
h
e op
er
atio
n of
th
e thr
ee m
a
g
n
e
t
r
on
s i
n
nor
m
a
l o
p
e
r
a
tio
n is p
e
rf
or
m
e
d
.
N
o
w
w
e
are
goi
ng t
o
study the case whe
r
e any of
th
e
th
ree m
a
g
n
e
tro
n
s
fails to
env
i
sag
e
t
h
e in
fl
u
e
n
ce
of th
e failu
re
mag
n
e
tro
n
on
th
e
o
p
e
ratio
n
o
f
th
e rem
a
in
in
g m
a
g
n
e
tron
s.
To
d
o
th
is we will rep
eat t
h
e sim
u
latio
n
an
d we
obs
er
ve t
h
e
wa
vef
o
rm
s of c
u
r
r
ent
s
a
nd
v
o
l
t
a
ges
by
usi
n
g
M
A
TLAB
SI
M
U
LI
NK
co
d
e
. Fi
g
u
re
1
2
s
h
ows t
h
e
wav
e
fo
rm
s
o
f
cu
rren
ts
and
vo
ltag
e
s ob
tain
ed
fro
m
th
is
si
mu
latio
n
.
3.3.2 Results
and Discussion
Fig
u
re 12
. Simu
latio
n
resu
lts o
f
th
e n
e
w p
o
wer
system
in
t
h
e n
o
n
lin
ear m
o
d
e
with
the MATLAB
SIM
U
L
I
NK
co
de (M
2 &
M
3
of
f)
From
t
h
e Fi
gu
re 12
we see t
h
at
t
h
e fu
nct
i
o
ni
n
g
o
f
t
h
i
s
ne
w sy
st
em
i
n
case of b
r
ea
kd
o
w
n
of t
w
o
m
a
gnet
r
ons i
s
per
f
o
r
m
e
d. Th
e si
gnal
s
obt
ai
ned
fr
om
t
h
i
s
sim
u
l
a
t
i
on are i
d
ent
i
cal
t
o
t
h
os
e i
n
n
o
rm
al
op
erat
i
o
n
(withou
t fail).
Th
is con
f
irm
s
th
at th
e
failu
re of
o
n
e
o
r
two m
a
g
n
e
tr
on
does no
t af
f
ect t
h
e
o
p
er
ation
of
th
e
rem
a
i
n
i
ng m
a
gnet
r
on
i
t
su
ffi
c
e
s t
o
repl
ace
t
h
e m
a
gnet
r
o
n
of
f
by
o
ne
w
o
n
e
.
4.
CO
NCL
USI
O
N
In
t
h
i
s
pa
per, we
p
r
o
p
o
se
d
a val
i
d
at
i
o
n
ap
pr
oach of
a ne
w t
h
ree-
p
h
ase po
wer
s
u
ppl
y
f
o
r
m
i
crowa
v
e
gene
rat
o
r
by
com
put
i
ng t
h
e
i
r pe
rf
orm
a
nce w
h
i
c
h i
s
i
d
ent
i
cal
t
o
t
h
at
o
b
t
a
i
n
ed
f
r
o
m
experi
m
e
ntal
fo
r a
con
v
e
n
t
i
onal
p
o
we
r s
u
p
p
l
y
us
i
ng a si
ngl
e
p
h
a
se t
r
ans
f
o
r
m
e
r for
one m
a
gnetron. In
our
re
search, we
ha
ve also
com
puting t
h
e
powe
r fact
or of this
ne
w thre
e-phase t
r
an
s
f
o
r
m
e
r.
On
t
h
e o
t
her ha
nd
t
h
e f
a
i
l
u
re of o
n
e o
r
t
w
o
m
a
gnet
r
on
d
o
e
s
n
o
t
af
fect
t
h
e
o
p
erat
i
o
n
of
t
h
e rem
a
i
n
i
ng m
a
gnet
r
o
n
.
Fo
r i
n
d
u
s
t
r
ial ap
p
lication
s
, Th
e en
cou
r
ag
ing
and
th
e satisfyin
g
resu
lts ob
tain
ed d
u
ring
thi
s
v
a
lid
ation
appro
a
ch
; will certain
ly en
cou
r
ag
e
u
s
to
r
ealize th
e n
e
w t
h
ree-ph
ase tran
sfo
r
m
e
r with
mag
n
e
ti
c
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I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
6, No
. 1, Feb
r
uar
y
20
1
6
:
1 – 1
1
10
sh
un
ts fo
r a new g
e
n
e
ration
o
f
ind
u
s
t
r
ial
microwav
es
ge
nerato
rs.
Th
is
will con
t
ribu
te to
t
h
e techno
lo
g
i
cal
in
no
v
a
tion
.
As pe
rspe
ct
i
v
e
s
, t
h
i
s
wo
rk ca
n be ext
e
nde
d
fo
r t
h
e st
u
d
y
o
f
t
h
e ener
get
i
c
bal
a
nce o
f
ne
w
t
h
ree-
pha
se
o
r
six-
ph
ase
pow
er supp
ly fo
r
sev
e
r
a
l m
a
g
n
e
t
r
on
s
b
y
p
h
a
se.
APPE
NDI
X
Figure 13. Geometr
y
of
tr
ansformer with
magnetic shunt (Phase A
as example)
Du
ri
n
g
t
h
i
s
w
o
r
k
,
we ha
ve t
a
ken as
refe
re
nce t
h
e f
o
l
l
o
w
i
ng
geom
et
ri
cal
dim
e
nsi
ons
o
f
t
h
e t
h
ree-
p
h
a
se tran
sformer HV wit
h
mag
n
e
tic shun
ts:
The wi
dt
h of
t
h
e no
n
-
w
o
un
d core:
a
= 25
m
m
Th
e
wid
t
h
o
f
t
h
e m
a
g
n
e
tic circu
it: b =
1
2
0
mm
N
u
m
b
er
o
f
stack
e
d sh
eets of
th
e sh
un
t: n3
= 18
N
u
m
b
er
o
f
turn
s i
n
th
e pr
im
a
r
y: n1
=
22
4
N
u
m
b
er
o
f
seco
nd
ar
y tu
rn
s:
n2
=
24
00
Hei
g
ht
o
f
t
h
e s
h
eet
st
ack
o
f
s
h
u
n
t
s
:
h =
0.
5
n3
.
Surface of
the
core
:
S1 = S2
= a.b
Surface
of s
h
unt: S3 =h.b
Thickness
of t
h
e air ga
p: e =
0.75 mm
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