Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l. 5,
N
o
.
1
,
Ju
ly 20
14
, pp
. 93
~100
I
S
SN
: 208
8-8
6
9
4
93
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
/
IJPEDS
Concurrent Detection and Classifi
cation of Faults in Matrix
Converter using Trans-Conductance
Sa
ra
h
Azimi*
, Mehdi VejdaniAmiri**
* Departement o
f
Electr
i
cal
and
Computer Engin
eering
,
Isfah
a
n
University
of
Technolog
y
,
Is
fa
h
a
n
, Iran
** Departement
of Electr
i
cal
Eng
i
n
eer
ing, Univer
sity
of C
a
lgar
y
,
Al
be
rt
a, C
a
na
d
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Apr 6, 2014
Rev
i
sed
May 22
, 20
14
Accepte
d
J
u
n 2, 2014
This pap
e
r pres
ents a fault diag
nostic
algorithm for detecting
and locating
open-cir
c
uit an
d short-circiu
t faults
in switch
i
ng components of matrix
converters (MCs) which can
be effectively
used to
drive
a perman
ent magnet
s
y
nchronous motor for resear
ch in criti
cal
applications. The propo
sed method
is based on monitoring th
e voltages a
nd
currents of the switches. Thes
e
measurements are used
to
ev
aluate the forwar
d trans-condu
ctance of
each
transistor for different v
a
lu
es of
switch voltages. These trans-conductan
ce
values
are
then
com
p
ared to
the
nom
inal v
a
lues
. Under h
e
a
lth
y
conditions
,
the valu
es obtai
ned for the fau
lt
signal is less tha
n
the tol
e
rabl
e v
a
lue
.
Under
the open/short-
circuit
condition
s, the
fault sig
n
al exceeds th
e threshold,
hence enables the matrix converter driv
e to
detect
and exactly
identif
y
th
e
location of th
e f
a
ulty
IGBT. Th
e main
advantages of this diagnos
tic method
includ
e fast detection and lo
cating
of the faulty
IGBT, easiness of
implementation
and independ
ency
of
the
modulation strateg
y
of the
converter.
Keyword:
Fau
lt d
e
tection
Matrix
conv
ert
e
r
Op
en-circu
it fau
lt
Sho
r
t-ci
rcu
it fau
lt
Trans-c
o
nductance
Copyright ©
201
4 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
:
Sarah
Azimi,
Depa
rtem
ent of Electrical a
nd Co
m
p
u
t
er
Engin
eer
ing
,
Isfa
ha
n
Uni
v
er
si
t
y
of t
ech
n
o
l
ogy
,
Isfa
ha
n, Ira
n.
Em
a
il: Sarah
.
Azimi8
8
@
g
m
ail.co
m
1.
INTRODUCTION
Matrix conve
rters ha
ve rece
ived c
onsi
d
era
b
le a
tten
tio
n
d
u
e
t
o
th
e recen
t u
s
es in
au
to
m
o
tiv
e,
aeros
pace
a
n
d m
i
litary
applications [1]-[2]. The
c
o
m
m
e
rcialization, m
odulation tec
hni
que a
nd c
o
m
m
u
t
ation
issu
e
o
f
th
e m
a
trix
co
nv
erter
h
a
v
e
b
e
en
t
h
oro
ugh
ly in
v
e
stig
ated
and
h
a
ve reach
e
d th
eir
matu
rity.
Matrix conve
r
ter placed th
e traditional voltage source inve
nters an
d curre
nt source inverters by their
effective a
d
va
ntages s
u
c
h
as
unity power
fa
ctor, t
h
e lack
of
bu
lk
y cap
acito
r
s
, h
i
g
h
nu
m
b
er
of
v
o
ltag
e
vecto
r
s
avai
l
a
bl
e f
o
r
m
odul
at
i
on a
n
d si
nus
oi
dal
i
n
put
c
u
rre
nt
[
3
]
,
[
5
]
.
It
h
a
s m
i
nim
a
l
energy
st
ora
g
e
req
u
i
r
e
m
ent
,
wh
ich
allows t
o
g
e
t ri
d
o
f
bu
lk
y and
lifetim
e
,
li
m
i
t
e
d ener
g
y
,
st
ori
n
g
capa
c
i
t
o
rs
fre
que
nc
y
con
v
e
r
t
e
rs.
The m
a
t
r
i
x
conve
rt
er
bel
o
ng
s t
o
t
h
e di
rect
con
v
e
r
si
o
n
fa
m
i
ly
si
nce i
t
di
rect
l
y
connect
s t
h
e i
n
p
u
t
a
c
l
i
n
es t
o
t
h
e o
u
t
put
ac l
i
n
es t
h
r
o
u
g
h
bi
di
rect
i
o
nal
swi
t
c
hes
w
i
t
hout
t
h
e
nee
d
for e
n
e
r
gy
st
o
r
age
devi
ces s
u
ch as
capaci
t
o
rs
o
r
i
n
d
u
ct
o
r
s.
As
a co
nse
que
n
ce, t
h
ei
r st
ren
g
t
h
s a
r
e i
m
port
a
nt
wei
ght
/
v
ol
um
e reduct
i
on
an
d
i
nhe
rent
f
o
u
r
-
q
uad
r
a
n
t
o
p
e
r
at
i
o
n
,
whi
c
h
a
r
e desi
ra
bl
e
feat
u
r
es fo
r
t
r
a
n
s
p
o
r
t
a
t
i
on sy
st
em
s.
T
h
e
l
ack
of e
n
er
gy
sto
r
ag
e d
e
v
i
ces d
o
e
s
favo
r the p
o
ssi
b
ility to
arrang
e sem
i
c
o
ndu
ctors in
su
ch
a way th
at
h
i
g
h
e
r vo
ltag
e
s an
d
m
o
re vol
t
a
ge
l
e
vel
s
ca
n
be r
e
ached
[
4
]
.
Howe
ver, syste
m
reliability re
m
a
ins an
ope
n
issue
a
n
d ha
s not recei
ved
m
u
ch attention. As a t
h
ree
pha
se
m
a
trix conve
r
ter is an array of
nine
bidirectio
nal powe
r switches
,
if each switch is
made of an anti-
series conn
ectio
n
of two
stand
a
rd
IGBT's, th
ere
will b
e
ei
g
h
t
een
IGBTs
p
e
r
con
v
e
rter. Th
e h
i
gh
nu
mb
er of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 1
,
Ju
ly 20
14
:
93
–
10
0
94
com
pone
nts increases the probability of
occ
u
rrence
of fa
ul
ts, giving additi
onal im
porta
nce to the diagnosis of
fau
lts in th
ese
syste
m
s.
There
have
be
en seve
ral
m
e
tho
d
s i
n
vest
i
g
at
i
ng t
h
e
d
e
tectio
n
an
d
lo
cating
o
f
switch
faults in
matrix
con
v
e
r
t
e
rs.
Th
e fi
rst
m
e
t
hod
of
det
ect
i
n
g
ope
n
-
ci
rcui
t
fa
ul
t
i
n
s
w
i
t
c
he
s o
f
M
C
was
pr
o
pose
d
i
n
[
6
]
an
d
devel
ope
d i
n
[
7
]
-
[
9
]
.
Thi
s
m
e
t
h
o
d
com
p
are
s
t
h
e m
easured
val
u
e o
f
t
h
e
M
C
out
p
u
t
v
o
l
t
a
ge an
d t
h
e re
fere
nce
val
u
e ac
qui
red
fr
om
t
h
e
m
odul
at
i
o
n al
g
o
ri
t
h
m
.
The pr
op
ose
d
m
e
t
hod i
n
[
12]
,
uses t
h
e m
easured
out
put
currents
, the
re
fere
nce a
ngles
of t
h
e input and
out
put
vo
ltag
e
v
ectors an
d th
e
v
a
lu
es
of
the duty-cycle of
t
h
e
swi
t
c
hi
n
g
st
at
e fo
r det
ect
i
n
g
ope
n
-
ci
rcui
t
fa
ul
t
s
whe
n
t
h
e
opt
i
m
u
m
Al
esina-
Ve
nt
uri
n
i
m
odul
at
i
on m
e
t
h
o
d
i
s
u
s
ed
. It is i
m
p
o
r
tan
t
to
fo
cu
s o
n
th
e
p
o
ssib
i
lity o
f
o
ccu
rring
fau
lts in
o
n
e
o
r
bo
th
tran
si
sto
r
s
o
f
b
i
d
i
rectio
n
a
l
swi
t
c
hes. T
h
e
m
e
t
hod p
r
op
o
s
ed i
n
[
11]
i
s
based o
n
di
s
c
ret
e
wavel
e
t
t
r
ans
f
o
r
m
analy
s
i
s
of t
h
e
m
e
asur
e
d
out
put
c
u
r
r
ent
wave
f
o
rm
. Thi
s
wo
rk
has
foc
u
se
d o
n
t
h
e det
ect
i
ng o
f
fa
ul
t
s
i
n
onl
y
o
n
e o
r
bot
h t
r
ansi
st
or
s of
a
bi
di
rect
i
o
nal
swi
t
c
he. H
o
wev
e
r, t
h
e exi
s
t
i
n
g
st
udi
es ha
ve b
een m
a
i
n
l
y
concer
ne
d wi
t
h
t
h
e det
ect
i
on
of
ope
n-
circuit fa
ult,
but the topic
of
s
h
ort-
circ
uit det
ection is
relatively ne
w a
n
d
has receive
d m
o
re isolated attention.
Thi
s
pa
pe
r p
r
e
s
ent
s
a ne
w m
e
t
h
o
d
t
o
det
ect
and l
o
cate op
en
-circu
it and
sh
ort-circu
it faults in
o
n
e
o
r
m
o
re t
r
ansi
st
or
s of m
a
t
r
i
x
conve
rt
ers (M
C
s
). I
n
sect
i
on
II
t
h
e possi
bl
e f
a
ul
t
s
t
h
at
m
a
y
occu
r i
n
t
h
e M
C
s are
prese
n
t
e
d
.
The
pr
op
ose
d
di
a
g
nosi
s
m
e
t
hod
f
o
r t
h
e
s
e fa
ul
t
s
i
s
t
h
en desc
ri
b
e
d i
n
sect
i
o
n II
I. Si
m
u
l
a
t
i
on resul
t
s
and
t
h
e
val
i
d
at
i
on
o
f
t
h
e
p
r
o
p
o
se
d m
e
t
hod a
r
e p
r
esent
e
d i
n
sect
i
on
IV
.
2.
FAULTS
I
N
MAT
R
I
X
CO
NVE
RTERS
A three phase
matrix conver
t
e
r con
s
ists of a
n
array
o
f
thre
e by
th
ree b
i
d
i
rectio
n
a
l switch
e
s. Usu
a
lly
con
s
t
r
uct
e
d
by
t
w
o
po
wer
t
r
ansi
st
o
r
s
(I
GB
T) a
n
d t
w
o a
n
t
i
-
paral
l
e
l
di
od
es, eac
h
bi
-
d
i
r
ect
i
onal
s
w
i
t
c
h m
a
y
have t
h
e c
o
m
m
on em
i
t
t
e
r or
t
h
e com
m
on col
l
ect
or t
o
p
o
l
ogy
.
Wh
e
n
t
h
e
gat
e
i
s
fi
re
d t
h
en
de
pe
ndi
ng
on
t
h
e
switch
vo
ltag
e
p
o
l
arity, it will co
n
d
u
c
t in
one o
f
th
e two
d
i
rectio
n
s
. Two
maj
o
r typ
e
s
o
f
fau
lts can
appear in
th
ese
IGBTs. Th
ese fau
lts
co
n
s
ist o
f
op
en-circu
it fau
lts
an
d short-circu
it fau
lts
o
f
on
e
o
r
m
o
re tran
sistors.
Po
ssi
b
l
e cau
ses o
f
op
en-circu
it fau
lts in
cl
ud
e driv
er fau
l
t
,
a po
we
r t
r
an
si
st
or
ru
pt
u
r
e ca
use
d
by
s
h
o
r
t
-
ci
rcui
t
or a sol
d
eri
ng
faul
t
cause
d b
y
hi
gh cu
rre
nt
s. The sh
o
r
t
-
ci
rcui
t
faul
t
o
f
a po
wer t
r
a
n
si
st
or m
a
y caused
by
an
ove
r-
v
o
l
t
a
ge, a
t
e
m
p
erat
ure o
v
ers
h
oot
o
r
a wr
on
g
vol
t
a
ge
at
t
h
e gat
e
due
t
o
a dri
v
e
r
fau
l
t
,
a DC
suppl
y
faul
t
or
/
di
st
ur
ba
nce
.
An op
en
-ci
r
cu
i
t
fau
lt
resu
lts in
a power fail
u
r
e at
th
e m
o
to
r driv
e. Sho
r
t
-
circu
it
fau
lt on
t
h
e
o
t
h
e
r
han
d
m
a
y
cause u
n
c
ont
r
o
l
l
a
bl
e dam
a
ge t
o
t
h
e sy
st
em
due t
o
t
h
e
res
u
l
t
i
ng hi
gh
cu
rr
ent
s
. T
h
e
r
ef
or
e, i
t
i
s
im
port
a
nt
t
o
be
abl
e
t
o
t
i
m
el
y
det
ect
t
h
e
occ
u
rre
nce
of
fa
ul
t
s
.
3.
MC
F
AULT DIAGNOSI
S BASED
O
N
T
R
A
N
S
-
C
O
N
D
UCT
AN
CE E
S
TIM
A
TIO
N
As e
xpl
ai
ne
d
bef
o
re
, o
p
e
n
a
nd
sh
ort
-
ci
rcui
t
faul
t
s
m
a
y
cause c
onsi
d
era
b
l
e
dam
a
ges t
o
t
h
e sy
st
em
.
Hence
fault di
agnosis of MCs seem
s
to be a necessary
part
of t
h
e sy
st
em
. In t
h
i
s
sect
i
o
n
a no
vel
t
echni
que t
o
detect and l
o
ca
te a fa
ult in the
s
e converters
is explaine
d.
The m
a
in idea of t
h
e propose
d tech
nique is to estim
a
t
e the trans
-
c
o
nductance of t
h
e IGBT
s at prope
r
ti
m
e
i.e. w
h
en
th
e I
G
BT is in
its O
N
state. Usin
g
th
e esti
m
a
ted
v
a
lu
es of
th
e tr
ans-
co
nductan
ce du
r
i
n
g
a g
a
te
p
u
l
se
on
e can
co
m
p
are it to
t
h
e
n
o
m
in
al v
a
lu
e to bu
ild
a fau
lt sign
al.
A
n
e
w fau
lt signal is p
r
op
o
s
ed
in
th
is
p
a
p
e
r t
o
ind
i
cate h
ealth
y
o
r
fau
lty co
nd
ition
s
.
To
esti
m
a
te
th
e tran
s-con
d
u
c
tan
ce, it is n
e
c
e
ssary
to
m
easure the curre
nt
s and the voltages of the
switches
and t
h
en
deduce t
h
e IGBT
volta
ges. In each s
w
itc
hing
pe
riod i.e. during
a
gate pulse,
only three
switches (si
x
IGBTs) are sele
cted by
th
e con
t
ro
l u
n
it. Th
erefo
r
e, it is n
e
cessary to
m
e
a
s
u
r
e th
e cu
rrents an
d
the volta
ges of these six IGB
T
s. The
c
u
rrents of theIGBTs
are the sam
e
as the phase
output currents
whic
h
are m
easu
r
ed
du
ri
n
g
th
e
v
e
l
o
city co
n
t
ro
l
p
r
ocess of t
h
e syst
e
m
. Hen
ce,
no
ad
d
ition
a
l m
e
a
s
u
r
em
en
ts are
mad
e
b
y
con
s
id
ering th
ese
v
a
riab
les. To
ob
tain
th
e co
llect
or-e
mitter voltage
s of the
IGBT
s, one ca
n
rea
d
the
measu
r
ed values of
the inpu
t and ou
tpu
t
ph
ase
vo
ltages. T
h
e
difference
betwee
n these
value
s
can be
considere
d
as the collector e
m
itter
v
o
ltag
e
s o
f
th
e activ
e IGBTs. As a matter o
f
fact, th
e v
o
ltag
e
an
d
the
cur
r
ent
of a
n
IGB
T
a
r
e n
o
t
con
s
t
a
nt
d
u
ri
n
g
a gat
e
pul
se
.
As are s
h
ow
n i
n
Fi
gu
res
1
and
2 t
h
e m
easure
d
vol
t
a
ge a
n
d cu
rre
nt
acr
oss an
IGB
T
s
h
ows
f
l
uct
u
at
i
o
ns.
Ac
cordingly, the
trans
-
con
ducta
nce of the
IGB
T
can
be estim
ated as the
deri
vative
of cu
rren
t
with resp
ect to
t
h
e
v
o
ltag
e
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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PED
S
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8-8
6
9
4
Co
n
c
u
rren
t
Detectio
n
and
Cl
a
ssifica
tio
n o
f
Fau
lts in
Ma
trix Con
verter
u
s
in
g
…
(Sa
r
ah
Azimi)
95
Figure 1
.
The
beha
vi
o
r
of
t
h
e
fa
ul
t
si
gnal
ve
rsus
t
r
a
n
s-c
o
nd
uct
a
nce
(1
)
In
wh
ich
th
e fi
rst o
r
d
e
r d
e
rivativ
e is i
m
p
l
e
m
en
ted
b
y
fin
ite d
i
fferen
ces.
Dep
e
nd
ing
on
th
e sa
m
p
ling
rate, th
e n
u
m
b
e
r o
f
sam
p
les
alo
n
g
a g
a
te p
u
l
se is li
mited
.
To
bu
ild
a sen
s
itiv
e fau
lt fu
n
c
tion
,
it
m
a
y b
e
n
ecessary to
in
terpo
l
ate th
e v
o
ltag
e
-t
rans
-c
onductance
pairs to increase the
num
ber of sa
m
p
l
e
s. In t
h
i
s
pape
r,
u
s
ing
t
h
e lin
ear
in
terpo
l
atio
n, th
e
nu
m
b
er
of po
in
ts
w
a
s in
cr
eased to 50
.
A
s
su
m
i
n
g
th
at
th
e tan
s
-
c
o
nductan
c
e
in
h
ealth
y
cond
itio
n
s
is d
e
no
ted
b
y
t
h
en t
h
e
faul
t
si
g
n
al
wa
s de
fi
ne
d as
be
l
o
w:
(2
)
In
w
h
ich
.
de
n
o
t
e
s t
h
e
e
xpec
t
at
i
on
ope
rat
o
r
an
d
represents th
e sam
p
le
n
u
m
b
e
r. Th
is
fau
lt
sig
n
a
l h
a
s
th
e p
r
op
erty
th
at
for the
open-circuit case i.e
.
0
will b
e
1
and i
n
the case
of s
h
ort-circ
ui
t
i.e.
∞
Fi
gu
re 2.
The
m
easured
curre
nt across
an IGBT
W
ill tak
e
th
e
1
v
a
lu
e and
in the h
ealth
y con
d
i
tio
n
i.e
will
b
e
zero
.
Th
e
n
e
x
t
step is to
find
a th
resho
l
d
to
com
p
are th
e fault sig
n
a
l with
resp
ect to
it.
To
o
b
t
ain
a
th
resh
o
l
d
,
th
e
so
urces
o
f
error in
th
e syste
m
sh
ou
ld
b
e
rec
o
gnized first. There
a
r
e
two
main
typ
e
s o
f
erro
r i
n
th
e system
. Th
e first
on
e is t
h
e sen
s
or
u
n
c
ertain
ty o
r
no
ise l
e
v
e
l wh
ich is
rep
r
esen
ted b
y
. The
ot
her
so
u
r
ce
of e
r
r
o
r m
a
y
com
e
from
the tolerance
o
f
the tran
s-cond
u
c
tan
ce wh
ich
is called
. To
set
th
e thresho
l
d
it is
n
ecessary to
esti
m
a
te th
e fau
lt sign
al in th
e
p
r
esen
ce
of th
ese
no
n-id
ealities. Assu
m
i
n
g
th
at t
h
e m
e
asured
t
r
ans
-
co
n
duct
a
nce
ca
n be wri
t
t
e
n
as:
1.
46
1.
48
1.
5
1.
52
x 1
0
-3
0.
5
1
1.
5
2
T
i
m
e
(
s
econds
)
Cur
r
e
n
t
T
i
me
Se
r
i
e
s
Pl
o
t
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
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-86
94
I
J
PED
S
Vo
l. 5
,
No
. 1
,
Ju
ly 20
14
:
93
–
10
0
96
(3
)
Th
en
, t
h
e fau
lt
sig
n
a
l
will tak
e
th
e
fo
llowing
form
:
(4
)
Th
is in turn can
b
e
written
as
fo
llows:
(5
)
Fi
gu
re 2 de
pi
ct
s t
h
e beha
vi
o
r
of fa
ul
t
si
gnal
vers
us di
ffe
ren
t
val
u
es of t
r
a
n
s-co
n
duct
a
nce
.
As can be
seen
fro
m
th
is
eq
u
a
tion
,
if th
e n
u
m
b
e
r
o
f
sam
p
les d
u
r
ing
a g
a
te pu
lse is
h
i
gh
enou
gh
, th
en
t
h
e m
easu
r
em
en
t
erro
r effect wi
ll b
e
n
e
g
lig
i
b
le i.e.
0
. B
u
t
i
n
pract
i
ce t
h
i
s
d
e
pen
d
s
on t
h
e
sam
p
l
i
ng f
r
eq
uency
.
F
o
r
h
i
gh
er
sam
p
lin
g
rates th
is erro
r
will h
a
v
e
less effect
on
th
e
esti
m
a
t
i
o
n
.
Howev
e
r,
du
e to th
e limited
n
u
m
b
e
r
of
sam
p
les in
th
e sim
u
lat
i
o
n
s
perfo
r
m
e
d
in
t
h
is p
a
p
e
r, it is
necessary to inc
l
ude t
h
e e
ffect
of this a
v
e
r
age. It i
s
well-kno
wn
[12
]
th
at th
e v
a
ri
ance of the sa
m
p
le
mean, for
as th
e
n
u
m
b
e
r of sam
p
les u
s
ed
to
estim
ate
the
sam
p
le
m
ean
of a
wh
ite no
ise with stand
a
rd
d
e
v
i
ation
o
f
, will
b
e
. Th
eref
or
e, t
h
e standar
d
d
e
v
i
atio
n
of
sam
p
le
m
ean
will b
e
√
. Accord
ing
l
y, th
e
fau
lt sig
n
a
l at
m
u
l
tip
le o
f
th
e
stan
d
a
rd
d
e
v
i
ation
will b
e
:
(6
)
Wh
ich
in turn
can
b
e
u
s
ed
as th
e thresh
o
l
d
to
m
a
in
tain
co
nst
a
nt
fal
s
e al
a
r
m
.
Thi
s
t
h
re
s
hol
d i
s
obt
ai
ne
d at
standa
rd
de
viation of the noi
s
e. One can trade off th
is
va
lue to re
duce t
h
e false alarms. Acc
o
rdingly, the
p
r
ob
ab
ility
o
f
d
e
tectio
n
will d
e
grad
e.
4.
PROB
ABILITY OF INCORRE
CT
DETECTION
Sin
ce the
v
o
ltag
e
an
d cu
rren
t
un
certain
ty
o
r
no
ise
influe
nc
e on t
h
e estimated tra
n
s-c
onducta
nce,t
h
e
effect
of
no
ise on th
e pro
p
o
s
ed
d
e
tection
m
e
th
od
is inv
e
st
ig
ated
.
is th
e
sa
m
p
le m
ean
, fo
r wh
ich
is the
num
ber
of
sam
p
l
e
s
used
t
o
e
s
t
i
m
a
t
e
. The va
ri
ance
of
is
√
.
(7
)
Accord
ing
to Eq
u
a
tion
s
(3
) and
(4), t
h
e
fau
lt
sig
n
a
l
will b
e
:
(8
)
To
ob
tain
th
e
p
r
ob
ab
ility o
f
in
correct alarm wh
en
th
e
IGBT is h
ealthy, th
e d
i
stribu
tio
n
fun
c
tio
n
of
the
fault
signal s
h
ould
be
considere
d
.Si
n
ce
has
Ga
ussi
a
n
di
st
ri
b
u
t
i
o
n
a
n
d
fa
ul
t
si
g
n
al
i
s
depe
n
d
ent
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
n
c
u
rren
t
Detectio
n
and
Cl
a
ssifica
tio
n o
f
Fau
lts in
Ma
trix Con
verter
u
s
in
g
…
(Sa
r
ah
Azimi)
97
th
en
, as it is well-k
nown
[1
0
]
for th
e prob
abilit
y d
e
n
s
ity
fun
c
tio
n (PDF)
o
f
a fu
n
c
ti
o
n
of a rand
o
m
v
a
riab
le
with
k
nown PDF, th
e
PDF
of th
e fau
lt signal can
b
e
o
b
t
ai
n
e
d
:
(9
)
In
w
h
ich
is th
e prob
ab
ility d
i
strib
u
tion
fu
n
c
t
i
o
n
of
. Th
e d
e
riv
a
tiv
e can
b
e
written
as:
(
1
0
)
Knowing
th
at:
(
1
1
)
The
n
,
t
h
e di
st
ri
but
i
o
n o
f
can
be ob
tain
ed as
fo
llo
ws:
(
1
2
)
C
o
n
s
id
e
r
in
g
as:
(13)
Whe
r
e
is th
e
sig
n
a
l to no
ise
ratio
fo
r t
h
e tran
sco
ndu
ctan
ce
sig
n
a
l. Th
e th
e v
a
rian
ce
o
f
noise will th
en b
e
:
(14)
Co
n
s
equ
e
n
tly,
th
e pro
b
a
b
ility d
i
stribu
tio
n fun
c
tio
n (PDF) can
o
b
t
ain
e
d
as:
(15)
Hav
i
n
g
PDF, Prab
ab
ility o
f
t
h
e in
correct
alarm
can
b
e
d
e
termin
ed
.
Accord
ing
to th
e Equ
a
tio
n (6) th
e th
resho
l
d
is d
e
fi
n
e
d as:
(16)
Th
en
th
e prob
ab
ility o
f
in
correct alarm
fo
r this th
resho
l
d
wi
ll b
e
:
(17)
If t
h
e
fo
llowing
d
e
ffin
ition
s
are ap
p
lied to
t
h
e in
tegral:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 1
,
Ju
ly 20
14
:
93
–
10
0
98
(18)
Th
en
th
e p
a
robab
ilityo
f
in
co
rrect alarm
can
be ob
tain
ed b
y
:
(19)
In
wh
ich
,
erf(.) d
e
no
tes th
e erro
r fun
c
tion
.
Th
is equ
a
tio
n, g
e
n
e
rally, sh
ows th
at by u
s
in
g
t
h
e
th
resh
o
l
d
in
(16
)
, th
e
p
r
ob
ab
i
lity o
f
in
correct alar
m
will b
e
in
d
e
p
e
n
d
e
n
t
of th
e
n
o
i
se
statistics, sa
m
p
le size,
SNR an
d will
b
e
co
nstan
t
.
5.
RESULT AND DIS
C
USSI
ON
5.
1.
Simulati
on Model
Sim
u
l
a
t
i
ons o
f
t
h
e pr
o
pose
d
di
ag
n
o
st
i
c
app
r
oach
hav
e
been car
ri
ed o
u
t
usi
n
g a devel
o
p
e
d
M
a
t
l
a
b/
Sim
u
l
i
nk
m
odel
of
an
M
C
. The
m
o
tor
pa
ram
e
t
e
rs are s
h
o
w
n i
n
t
a
bl
e I
.
A
di
rect
t
o
r
que
co
nt
r
o
l
(DTC
)
i
s
used
t
o
dri
v
e perm
anent
m
a
gnet
sy
nch
r
on
ous
m
o
t
o
r.
DT
C
di
rect
l
y
cont
rol
s
bot
h t
h
e t
o
r
q
ue an
d
fl
u
x
of a
n
electrical
m
a
c
h
ine.
The m
a
in adva
ntag
es
of th
is con
t
ro
l strateg
y
are its
structure sim
p
licity and robus
t
ness,
sin
ce it d
o
e
s no
t d
e
p
e
nd
on
th
e m
o
to
r p
a
rameters. Th
e switch
i
ng
frequen
c
y o
f
th
e DTC d
r
iv
e is a v
a
riab
le
q
u
a
n
tity th
at d
e
p
e
nd
s
n
o
t
only o
n
th
e con
t
ro
ller
h
y
steresis b
a
nd
s
b
u
t
also
on
th
e slope o
f
th
e
d
e
v
e
l
o
ped
t
o
r
que
.
Tabl
e 1. PM
S
M
param
e
t
e
rs
2A
Rated cur
r
e
nt
200w
Output power
8.
3 m
H
s
d
l
per
phase
100v
Voltage
6m
H
s
q
l
per
phase
4
Pole pairs
3000r
pm
Rated speed
0.
64Nm
T
o
r
que
4500r
pm
M
a
x
i
mu
m s
p
e
e
d
2.
5
Ω
Stator resistance
5.
2.
Simula
ti
o
n
Results
Using
th
e simu
latio
n
m
o
d
e
l d
e
scri
b
e
d
b
e
fore, th
e m
a
trix
co
nv
erter th
e fau
lt sig
n
a
l o
f
t
h
e sp
ecific
IGBT in
h
ealthy co
nd
itio
n is sh
own
in Figure 4
.
Fig
u
re
4
.
Th
e fau
lt sign
alun
d
e
r
h
ealth
y cond
istio
n
At t=1
.
3
m
s
, an
o
p
e
n
-
ci
rcu
it
fau
lt is in
t
r
oduced
in IGBT
nu
m
b
er th
ree,
wh
ich
co
nn
ect
s th
e inpu
t
p
h
a
se C to th
e
o
u
t
p
u
t
ph
ase
A. Th
is fau
lt is si
m
u
latedas an i
n
crease
in t
h
e
resistance of t
h
e IGBT.
0
1
2
3
4
5
6
7
8
x 1
0
-3
-0.
0
8
-0.
0
6
-0.
0
4
-0.
0
2
0
0.02
0.04
0.06
0.08
t
i
m
e(
s
e
c
ond)
T
h
e F
a
u
l
t
S
i
g
n
al
R
S
i
gn
al
th
1
th
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
Co
n
c
u
rren
t
Detectio
n
and
Cl
a
ssifica
tio
n o
f
Fau
lts in
Ma
trix Con
verter
u
s
in
g
…
(Sa
r
ah
Azimi)
99
Fi
gu
re
5 de
pi
c
t
s t
h
e res
u
l
t
s
obt
ai
ne
d
wh
en
ope
n
-
ci
rc
ui
t
faul
t
occ
u
rs
. I
f
t
h
e o
u
t
p
ut
s p
h
ase
vol
t
a
g
e
ch
ang
e
s, th
e co
llecto
r
-em
i
tte
r vo
ltag
e
will
increase. T
h
e
r
efore
,
the tr
a
n
s-c
o
nd
uct
a
nc
e decrease
s
fr
om
it
s
n
o
m
in
al v
a
lu
e
an
d causes th
e
fau
lt sign
al ex
ceed
th
e threshold
.
Fig
u
re
5
.
Th
e fau
lt sign
al under
o
p
e
n
-
ci
rcu
it
co
nd
itio
n
Fig
u
re
6
illu
strates th
e fau
lt sig
n
a
l in
t
h
e
case o
f
a sho
r
t-circu
it fau
lt o
ccurri
n
g
i
n
t
o
th
e
IGB
T
num
ber three.
The c
o
llector
curren
t inc
r
eas
e dram
atically and acc
ordi
ng
ly, th
e tran
s-co
nductance i
n
crease
from
its nom
inal val
u
e a
nd allows
detect
ing t
h
e
fa
ulty IGBsT
by e
x
ceeding t
h
e fa
ulty signal
from
the
t
h
res
hol
d.
Using
th
is d
i
ag
no
stic m
e
th
od
, it is p
o
ssi
b
l
e to
d
e
tect faults in
an
y transisto
r
ind
e
p
e
nd
en
tly o
f
t
h
e
ex
isten
ce of
fau
lts
in
o
t
h
e
r IGBTs.
Hen
ce, allo
wing
a
fast
and
con
c
urrent d
e
tectio
n and id
en
tification
o
f
th
e
faulty com
ponents. T
h
ese re
sults dem
onstrate the effec
t
i
v
ene
ss o
f
t
h
e
pr
o
pose
d
t
ech
ni
q
u
e f
o
r
det
e
ct
i
on o
f
o
p
e
n-circu
it and
sh
ort-circu
it
fau
lts in MC.
Fig
u
re
6
.
Th
e fau
lt sign
al under sh
ort-circu
it con
d
ition
6.
CO
NCL
USI
O
N
Thi
s
pape
r pr
esent
a new m
e
t
hod fo
r de
t
ect
i
ng
an
d
l
o
cat
i
ng
t
h
e fa
u
l
t
y
IGB
T
i
n
bi
di
rect
i
o
nal
swi
t
c
hes
of
m
a
t
r
i
x
c
o
n
v
ert
e
r
.
The
p
r
op
ose
d
m
e
t
hod i
s
b
a
sed
on
m
oni
t
o
ri
ng t
h
e
vol
t
a
ges a
n
d
cu
rre
nt
s o
f
IGBTs
for a
ppraising tra
n
s-c
o
nductance
of each
tra
n
sistor. When
any
of t
h
e IGBTs c
a
us
es open/s
hort-c
ircuit
faul
t
,
t
h
e
dedi
cat
ed val
u
e
of
t
r
ans-c
o
nd
uct
a
nce m
a
kes t
h
e faul
t
si
gnal
of t
h
e
faul
t
y
I
G
B
T
excee
d f
r
om
t
h
e
t
h
res
hol
d,
whi
c
h hel
p
t
h
e sy
s
t
em
i
d
ent
i
f
y
a faul
t
y
IGB
T
an
d al
so t
h
e t
y
pe
of
faul
t
t
h
at
ha
ppe
ne
d.
It
’s
w
o
rt
h t
o
say
t
h
at
t
h
e al
go
ri
t
h
m
i
s
based o
n
di
vi
si
o
n
s, s
u
m
s
and deri
vat
i
v
es. T
h
ere
f
o
r
e, i
t
i
s
not
com
put
at
i
onal
l
y
in
ten
s
iv
e. Using
th
is alg
o
rithm
,
it
is p
o
ssib
l
e to
d
e
tect
th
e
ex
isten
ce of mo
re th
an
on
e fau
lty tran
sisto
r
at th
e
sam
e
tim
e. Therefore
,
allows
a fast
an
d con
c
u
r
ren
t
d
e
tection
an
d id
en
tificatio
n
o
f
th
e
faulty co
m
p
o
n
en
ts.
0
0.
0
1
0.
0
2
0.
0
3
0.
0
4
0.
0
5
-1.5
-1
-0.5
0
0.
5
1
1.
5
T
i
me
(
s
econds
)
S
i
g
n
a
l
Va
lu
e
T
i
m
e
Se
r
i
e
s
Pl
o
t
:
R S
i
g
n
a
l
fa
u
l
t
t
i
m
e
th
1
th
2
0
0.
00
2
0.
004
0.0
0
6
0.
008
0.
0
1
-0.
4
-0.
2
0
0.
2
0.
4
0.
6
0.
8
1
1.
2
T
i
me (
s
econ
d
s
)
S
i
g
n
a
l V
a
lu
e
T
i
m
e
Se
r
i
e
s
Pl
o
t
:
R sig
n
a
l
f
a
u
l
t tim
e
th
1
th
2
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 5
,
No
. 1
,
Ju
ly 20
14
:
93
–
10
0
10
0
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