POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER
PMSM Model wi h Phase- o-Phase Sho -Ci cui
and Diagnosis by ESA and EPVA
Chou ouk BOUCHAREB, Mohamed Said NAIT SAID
Elec ical Enginee ing Depa men , Labo a o y LSPIE Ba na 2000, Ba na Uni e si y,
Rou e de Bisk a, 05078, Alge ia
c.boucha eb@li e. , medsnai said@yahoo.
DOI: 10.15598/aeee. 14i5.1928
Abs ac . One o he mos equen aul s in PMSM
s a o is he insula ion ailu e due o he deg ada ion
o he main isola ion in he mo o winding. This pape
is aimed a sugges ing a dynamic model o PMSM wi h
phase- o-phase aul based on an equi alen elec ic ci -
cui model including he eal o m o back EMF. The
aul y model is used o s udying he machine beha io
and ex ac ing he aul signa u es o diagnosis. Two
diagnos ic echniques he Spec al Analysis (ESA) and
Ex end Pa k’s Vec o s App oach (EPVA) based on e-
quency analysis a e applied o de ec his kind o aul .
Keywo ds
EPVA, ESA, In e - u n aul , phase- o-phase
aul , PMSM model.
1. In oduc ion
In ecen yea s, Pe manen Magne Synch onous Mo-
o (PMSM) has become one o mos impo an elec-
ic machines because o he inhe en ad an ages o
high powe densi y, high e iciency, small weigh , high
eliabili y and easy con ol o ex e nal o que o s a-
o ’s cu en con ol. Consequen ly, i is widely used
in indus y, e.g. in ac ion, au omobiles, obo ics and
ae ospace echnology, as well as elec ic ehicles and
ship p opulsion sys ems [1], [2] and [3].
The aul diagnosis o elec ical machines had been
he a ge o an in ense amoun o in e es ing e-
sea ches du ing he las 30 yea s. Reducing main e-
nance cos s and p e en ing unscheduled down- imes,
which esul in losses o p oduc ion and inancial in-
comes and bene i ing om hei u ili y in sa e y-
sensi i e applica ions, a e he p io i ies o elec ical
d i es o manu ac u e s and ope a o s [4], [5] and [6].
In ac , co ec diagnosis and ea ly de ec ion o incipi-
en aul s equi e he de elopmen o an accu a e model
o elec ical machine, able o simula e elec ical aul s
and o apply an e ec i e diagnos ic echnique.
Howe e , model accu acy and compu a ion ime ep-
esen s wo opposi e c i e ia. Con en ional model
(equi alen elec ic ci cui o equi alen magne ic ci -
cui ) ob ained wi h Pa k ans o ma ion o ins ance
is based on es ic i e assump ions and does no e-
qui e long compu a ion ime [7] and [8]. On he o he
hand, model ob ained wi h he ini e elemen s me hod
is based on minimal assump ion and equi es long com-
pu a ion ime [9] and [10]. The e is a eal need o es ab-
lish an al e na i e model, which o e s a good balance
be ween accu acy and compu a ion ime.
One o he mos common aul s, called insula ion
ailu e, is he in e - u n sho ci cui in one o he s a-
o coils. Since he coil insula ion ma e ial is unde he
high ol age and empe a u e s ess, i deg ades g ad-
ually and inally loses he insula ing cha ac e is ic [6].
The in e - u n aul is mos ly caused by mechanical
s ess, mois u e and pa ial discha ge, which is accel-
e a ed o in e e supplied elec ical machines [11].
In his pape , a dynamic model o a s a o su ace
moun ed PMSM wi h in e - u n aul is p esen ed. We
ocus on phase- o-phase aul o he s a o winding.
This model based on equi alen elec ic ci cui exhibi s
a ade-o be ween simplici y and p ecision, and i is
used o s udying a machine beha io unde aul con-
di ions o di e en le els o aul se e i y using MAT-
LAB Simulink so wa e.
Exploi ing his aul y model o ex ac aul signa-
u es in o de o diagnose and o p edic he insula-
ion ailu e b eakdown when he aul is no e y se-
e e in o de o a oid he machine winding damages.
To de ec his aul , we chose wo simple and use ul
echniques based on equency analysis. These ech-
niques a e Elec ic Spec al Analysis (ESA) and Ex-
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end Pa k’s Vec o s App oach (EPVA). The con ibu-
ion o his wo k is he addi ion o he eal wa e o m
o back Elec o Mo i e Fo ce (EMF) o heal hy ma-
chine which con ains a ha monic a 3· so supply
equencies, because i he model does no ake he un-
ce ain ies, like eal back-EMF, he indica o will gi e
a w ong diagnos ic.
2. PMSM Faul Dynamic
Model
2.1. Phase- o-Phase Faul Dynamic
Model
The phase- o-phase aul deno es insula ion ailu es be-
ween wo windings o wo phases a he s a o . The
insula ion ailu e is modeled by a esis ance, whe e i s
alue depends on he aul se e i y. The s a o wind-
ing o a PMSM machine wi h phase- o-phase aul is
ep esen ed by Fig. 1. In his igu e, he aul occu s
be ween ’a’ and ’b’ phases, deno es he aul insula-
ion esis ance. The sub-windings (as1) and (as2) ep-
esen espec i ely, he heal hy and aul y pa o he
phase winding a, and sub-windings (bs1) and (bs2) ep-
esen , he heal hy and aul y pa o he phase winding
b espec i ely. When he aul esis ance dec eases
owa ds ze o, he insula ion aul e alua es owa ds an
in e - u n ull sho -ci cui .
l
lbs1 lbs2
Rbs1, Lbs1
Rcs, Lcs
Ras1, Las1 Ras2, Las2
las1 las2
las
lbs
lcs
Rbs2, Lbs2
Fig. 1: Th ee-phases winding wi h phase- o-phase aul .
2.2. PMSM Heal hy Model in
abc-Coo dina es
The ol ages equa ions om he ci cui in Fig. 1 wi h-
ou aul (heal hy machine), gi en by in ini e alue,
as in [2], [12] and [13] a e:
[Vs]=[Rs]·[Is]+[Ls]·
d
d ·[Is]+[Es],(1)


as
bs
cs

=

Rs0 0
0Rs0
0 0 Rs



Ias
Ibs
Ics

+
+

L M M
M L M
M M L

·
d
d ·

Ias
Ibs
Ics

+

eas
ebs
ecs

,
(2)
whe e he heal hy machine a iable and pa ame e s
a e:
• as,bs,cs - h ee phase s a o ol ages,
•Ias,bs,cs - h ee phase s a o cu en s,
•eas,bs,cs - h ee phase back EMF,
•Rs- s a o esis ance,
•L- sel induc ance o he s a o ,
•M- mu ual induc ance o he s a o .
2.3. PMSM Faul y Model in
abc-Coo dina e
Vol age equa ions, which desc ibe he aul y ci cui
p esen ed in Fig. 1, can be exp essed as:
[Vs] =  as1 as2 bs1 bs2 cs T,(3)
whe e:
• as1- he ol age o he heal hy pa phase a,
• as2- he ol age o aul y pa o phase a,
• bs1- he ol age o he heal hy pa phase b,
• bs2- he ol age o aul y pa o phase b.
The new esis ances o heal hy and aul y pa s o
phase ’a’ and ’b’ a e calcula ed as ollows:
Ras1= (1 −σ)·Ras,(4)
Ras2=σ·Ras,(5)
Rbs1= (1 −σ)·Rbs,(6)
Rbs2=σ·Rbs,(7)
σ=N
Ns
.(8)
The s udy o he elemen a y ci cui s o he phases
has gi en he ollowing ela ions:
as = as2+ as1,(9)
bs = bs2+ bs1,(10)
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Ias1=Ias,(11)
Ibs1=Ibs,(12)
whe e Ras1is he s a o phase esis ance o heal hy
pa s o ’a’ phase while Ras2is he aul y s a o phase
esis ance. Rbs1i is he s a o phase esis ance o
heal hy pa s o ’b’ phase while Rbs2is i s aul y s a o
phase esis ance, σis he a ioo numbe o he u ns
(N ) o e he phase winding numbe o he u ns (Ns).
The sel -induc ances o he aul y and heal hy pa s
o winding (aas1,aas2), and winding (bbs1,bbs2) a e
p opo ional o he squa e o he ac ion o sho ed
u ns σ, and also he mu ual induc ance is p opo ional
o his numbe o bo h pa s. The e o e, we assume:
Las1= (1 −σ)2Las,(13)
Las2=σ2Las,(14)
Mas2b=σM, (15)
Mas1as2=σ(1 −σ)L, (16)
whe e Las1is he s a o phase induc ance o heal hy
pa s o a phase while Las2is he s a o phase induc-
ance o aul y pa s o a phase, I is he addi ional
cu en engende ed by he sho ci cui , is he in-
sula ion aul y esis ance and is he co esponded
aul y ol age.
The s a o cu en s become:
[Is]=[Ias (Ias −I )Ibs (Ibs +I )Ics]T.(17)
The equa ion which desc ibes he sho ci cui loop
is in Eq. (18).
F om p e ious analysis, we ob ain he global equa-
ions go e ning he beha io o he machine wi h he
p esence o his sho -ci cui aul as he Eq. (19).
In he Eq. (19):
R0=Ras +Rbs +Rcs,(20)
L =−(−La2+Ma2b2−Lb2+Mb2a2),(21)
Mb =−Ma1a2+Ma1b2−La2+Ma2b2,(22)
Mc =−Mca2+Mcb2.(23)
The exp ession o he elec omagne ic o que can be
w i en as ollows:
Te=eas ·Ias +ebs ·Ibs +ecs ·Ics −e ·I
Ω,(24)
whe e Ωis he mechanical angula speed.
2.4. PMSM Faul y Model in
α, β-Coo dina es
The machine equa ions wi h in e - u n aul in s a ion-
a y αand βaxis e e ence ame a e in Eq. (25), whe e:
R = 2
3−Ra2−
Rb2
2,(26)
=Ra2+Rb2+R ,(27)
b2=1
2√2Rb2,(28)
M α = 2
3Ma −
Mb
2−
Mc
2,(29)
M β =1
2√2 (Mb −Mc ),(30)
Ls=L−M, (31)
wi h,
•Iα,β -αand βaxis componen s o s a o cu en s,
•eα,β -αand βcomponen s o s a o back EMF.
Then he elec omagne ic o que exp ession o he
phase- o-phase aul model becomes:
Te=eα·Iα+eβ·Iβ−e ·I
Ω.(32)
We conside o all he s udies ha he elec omo i e
o ce o he heal hy mo o has a sinusoidal o m as
shown in Fig. 2(a) and con ains a 3 d ha monic a 3· s
o supply equencies as seen in Fig. 2(b).
00.01 0.02 0.03 0.04 0.05 0.06 0.07 0.0
8
−40
−20
0
20
40
Time (s)
EMF (V)
(a) Elec omo i e o ce.
050 100 150 200 250 300
0
10
20
30
40
F equency (Hz)
|EMF(V)|
3 d ha monic
(b) Spec um analysis.
Fig. 2: Elec omo i e o ce and i s spec um analysis.
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0 = −Ra2·Ias +Rb2·Ibs −(La2+Ma1a2−Mb2a1−Mb2a2)·dIas
d −(Ma2b1+Ma2b2−Lb2−Mb2b1)·dIbs
d +
−(Ma2c−Mb2c)·dIcs
d −e +Ra2+Rb2+ ·I −(−La2+Ma2b2−Lb2+Mb2a2)·dI
d
.(18)




as
bs
cs
0




=




Rs0 0 Ra2
0Rs0Rb2
0 0 Rs0
−Ra2Rb20R0








Ias
Ibs
Ics
I




+




L M M Ma
M L M Mb
M M L Mc
Ma Mb Mc L




d
d




Ias
Ibs
Ics
I




+




eas
ebs
ecs
−e




.(19)
3. Dynamic Faul Model
Simula ion Resul s
The s udy o he beha io o PMSM unde aul con-
di ions using he p oposed aul dynamic model e-
qui es an accu a e knowledge o ci cui pa ame e s.
The PMSM pa ame e s a e gi en as shown in AppA
[2].
00.2 0.4 0.6 0.8 11.2
−40
−20
0
20
40
Time (s)
Ia−Ib−Ic (A)
= 100 Ω
= 7 Ω
= 0.5 Ω
(a) Phase cu en s.
00.2 0.4 0.6 0.8 11.2
−60
−40
−20
0
20
40
Time (s)
I (A)
= 100 Ω = 7 Ω
= 0.5 Ω
(b) Faul y cu en .
−15
−10
−5
0
5
10
00.2 0.4 0.6 0.8 1 1.2
Time (s)
= 100 Ω = 7 Ω
= 0.5 Ω
Te(N m)
(c) Elec omagne ic o que.
−2000
−1000
0
1000
2000
Pa (Wa )
00.2 0.4 0.6 0.8 1 1.2
Time (s)
= 100 Ω
= 7 Ω
= 0.5 Ω
(d) Abso bed powe .
Fig. 3: Phase cu en s, aul y cu en , elec omagne ic o que
and abso bed powe e sus ime o h ee alues o aul
esis ances: = 100 Ω, = 7 Ω and = 0.5 Ω.
The machine is supposed o be supplied by 3-phases
sinusoidal balanced ol age sou ce wi h s a connec ion
and wi hou neu al connec ion and ope a es a syn-
ch onous speed (speed and supply equency a e 1000
pm and 66.67 Hz espec i ely). Simula ion o he p o-
posed model is ealized using MATLAB en i onmen .
00.2 0.4 0.6 0.8 11.2
−60
−40
−20
0
20
40
Time (s)
Ia−Ib−Ic (A)
0.5
0.1 0.7
(a) Phase cu en s.
00.2 0.4 0.6 0.8 1 1.2
−100
−50
0
50
Time (s)
I (A)
0.1
0.7
0.5
(b) Faul y cu en .
−30
−20
−10
0
10
00.2 0.4 0.6 0.8 1 1.2
Time (s)
0.1
0.7
0.5
Te (N m)
(c) Elec omagne ic o que.
0.8 1.2
−3
−2
−1
0
1
2
Pa (kWa )
0 0.2 0.4 0.6 1
Time (s)
0.1
0.7
0.5
(d) Abso bed powe .
Fig. 4: Phase cu en s, aul y cu en , elec omagne ic o que
and abso bed powe e sus ime a h ee alues o he
ac ion o sho ed u ns: (σ= 0.1,σ= 0.5and σ= 0.7)
and = 0.5 Ω.
Fo his model, Fig. 3 shows he cha ac e is ics phase
cu en s (a, b, c), aul y cu en (I ), elec omagne ic
o que and abso bed powe o di e en alues o aul
insula ion esis ance such as = 100 Ω,0.5 Ω and
7 Ω. The ac ion o sho ed u ns is ixed a 50 %.
Figu e 4 shows he cha ac e is ics (phase cu en s (a,
b, c), aul y cu en (I ), elec omagne ic o que and
abso bed powe o di e en alues o he ac ion o
sho ed u ns (σ= 10 %, σ= 50 % and σ= 70 %),
whe e he aul insula ion esis ance is ixed o =
0.5 Ω.
As i can be seen om Fig. 3, o h ee di e en al-
ues o aul esis ances (heal hy case: = 100 Ω and
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

α
β
0

=

Rs0R
0Rs b2
R b2

·

Iα
Iβ
I

+

Ls0M α
0LsM β
M α M β L

·d
d ·




Ias
Ibs
Ics
I




+

eα
eβ
−e

.(25)
aul y case: = 7 Ω and = 0.5 Ω) when he aul
esis ance dec eases, he h ee phases cu en s inc ease
o compensa e he nega i e e ec s o he sho -ci cui
aul . I can cause a cu en unbalance in he powe
supply, and he inc ease o he abso bed powe . We can
obse e a o que ipple when he aul y case is applied.
Changing he ac ion o sho - u ns means changing
he se e i y o applying aul . F om Fig. 4, i is clea
ha he magni ude o he o que ipple is mainly de-
e mined by he se e i y o he aul . The magni ude
o he phase cu en s and abso bed powe change p o-
po ionally wi h he se e i y o he aul and become
unbalanced.
I would be e y help ul o p edic he insula ion ail-
u e, b eakdown when he aul is no high de eloped
ino de o a oid he machine winding damages [14].
4. Diagnos ic o S a o Faul
by ESA and EPVA
Techniques
Two echniques based on equency analysis a e ap-
plied o de ec aul s in s a o , consecu i ely de ined
in [15], [16] and [17]. Fi s is ESA, based on he Fas
Fou ie decomposi ion o he phase cu en s winding,
he elec omagne ic o que and he abso bed powe .
The second is EPVA, which is based on he equency
analysis o he module o he Pa k’s Vec o ’s o cu en s
as shown below.
4.1. Elec ic Spec al Analysis
(ESA)
We applied his echnique on he phase s a o cu en s,
he ins an aneously abso bed powe and he elec o-
magne ic o que. The ins an aneous abso bed powe
is illus a ed by he ollowing equa ion [18]:
p( ) = as( )ias( ) + bs( )ibs( ) + cs( )ics( ).(33)
The phase s a o cu en s, he ins an aneous ab-
so bed powe and elec omagne ic o que spec um
analysis esul s o bo h heal hy and aul y condi ions
wi h di e en alues o aul y esis ance ( = 100 Ω,
= 7 Ω and = 0.5 Ω) o simula ion machine a e
p esen ed in Fig. 5, Fig. 6, and Fig. 7 espec i ely.
1) Cu en s Spec al Analysis
The ESA signa u es e eal he exis ence o a spec al
componen in phase ’a’ and ’b’, wi h a small ampli ude
a he equency wi h alue h ee imes highe han he
supply due he exis ence o an in e - u n sho ci cui
in he s a o winding and i s ampli ude inc ease wi h
he inc ease o se e i y o aul as seen in Fig. 5(b),
Fig. 5(c) and Fig. 5(d), whe e = 0.5 Ω and in
Fig. 5(e), whe e = 7 Ω, he exis ence o his ha -
monic is due o he p esence o he hi d ha monic o
he elec omo i e o ce p esen ed in Fig. 2(b). We can
obse e no exis ence o his ha monic in phase ’c’ be-
cause he sho ci cui occu s be ween phase ’a’ and
’b’. No e ha a heal hy condi ions he cu en does
no ha e his componen ( hi d ha monic), as seen in
Fig. 5(a).
2) Elec omagne ic To que Spec al
Analysis
I is no iceable om Fig. 7, ha in case o aul , we no-
ice he appea ance o high ha monic a double alue o
supply equency, especially i = 0.5 Ω. The inc ease
o he ha monic ampli ude is in e sely p opo ional o
he alues o aul esis ance.
3) Abso bed Powe Spec al Analysis
Figu e 6 shows he abso bed powe spec um wi h and
wi hou aul . We can obse e only a ze o equency
componen a heal hy condi ions. In aul y condi ions
he same analysis as ha o he elec omagne ic o que
is no ed. F om he compa a i e analysis o esul s un-
de heal hy and aul y condi ions, i is clea ha he
aul appea s in he ESA signa u edue o he p esence
o ha monic o e en ows on he spec um analysis o
elec omagne ic o que and abso bed powe and by he
appea ance o he ha monic o odd ows on he spec-
um analysis o phase cu en s. The appea ances o
hese ha monics a e di ec ly ela ed o he exis ence
o asymme ies caused by he sho -ci cui in he s a-
o winding. Wi h he consump ion ha we ha e a
balanced ol age sou ce, he appea ance o ha monics
in phase ’a’ and ’b’ indica es he sho -ci cui be ween
hese wo phases.
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0 50 100 150 200 250 300
0
5
10
15
F equency (Hz)
|Ia (A)|
(a) Heal hy case o = 100 Ω.
0
10
20
30
|Ia (A)|
150 200 250
0
1
2
3 d ha monic
0 50 100 150 200 250 300
F equency (Hz)
(b) Faul y case o = 0.5 Ω (Phase a).
0
5
10
15
20
25
|Ib (A)|
3 d ha monic
150 200 250
0
1
2
0 50 100 150 200 250 300
F equency (Hz)
(c) Faul y case o = 0.5 Ω (Phase b).
0 50 100 150 200 250 300
0
5
10
15
F equency (Hz)
|Ic (A)|
(d) Faul y case o = 0.5 Ω (Phase c).
0 50 100 150 200 250 300
0
5
10
15
F equency (Hz)
|Ia (A)|
3 d ha monic
(e) Faul y case o = 7 Ω
Fig. 5: Spec um o phase cu en s.
4.2. Ex end Pa k’s Vec o App oach
(EPVA)
This echnique is based on he wo equi alen cu en s
in e e ence ame ob ained by Pa k’s ans o ma ion
[18]:
Id= 2
3·Ias −1
√6·Ibs −1
√6·Ics,(34)
Iq=1
√2·Ibs −1
√2·Ics,(35)
whe e Idand Iqa e he ins an aneous alues o elec ic
cu en s in di ec and quad a u e axis. Idis always a
sine wa e and Iqhas a cosine wa e in heal hy condi-
ions. These wo componen s ha e he same alues and
hei locus is a ci cle as seen in Fig. 8(a). In case o
he in e - u n sho ci cui , he cu en becomes unbal-
050 100 150 200 250 300
0
200
400
600
800
1000
F equency (Hz)
|Pa (Wa )|
(a) Heal hy case o = 100 Ω.
0 20 40 60 80 100 120 140 160 180 20
0
0
200
400
600
800
1000
F equency (Hz)
|Pa (Wa )|
2nd ha monic
(b) Faul y case o = 0.5 Ω.
0
500
1000
1500
|Pa (Wa )|
2nd ha monic
0 20 40 60 80 100 120 140 160 180 200
F equency (Hz)
(c) Faul y case o = 7 Ω.
Fig. 6: Spec um o abso bed powe .
0
1
2
3
4
5
|Te (N m)|
050 100 150 200 250 300
F equency (Hz)
(a) Heal hy case o = 100 Ω.
0
2
4
6
2nd ha monic
|Te (N m)|
0 20 40 60 80 100 120 140 160 180 200
F equency (Hz)
(b) Faul y case o = 0.5 Ω.
0
1
2
3
4
5
2nd ha monic
0 20 40 60 80 100 120 140 160 180 200
F equency (Hz)
|Te (N m)|
(c) Faul y case o = 7 Ω.
Fig. 7: Spec um o elec omagne ic o que.
anced and i can be exp essed as he sum o a posi i e
sequence and a nega i e sequence componen . As a e-
sul o his aul , he Conco dia’s ec o locus shape
de ia es and becomes ellip ic as shown in Fig. 8(b).
I he mo o ope a es unde heal hy condi ions (i.e.
unde symme ical condi ions), he h ee cu en s o m
a balanced sys em and cons i u e a posi i e sequence
c
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sys em. Hence, idand iqcan be w i en as below [18]:
ip=qi2
d+i2
q,(36)
id=√6
2·imax ·sin(ω ),(37)
iq=√6
2·imax ·sin ω −
π
2,(38)
whe e imax is a maximum alue o he cu en posi i e
sequence, ωis he angula supply equency, and ip
is he Pa k’s equi alen cu en module. When he
sys em is balanced, he cu en Pa k’s ec o modulus
is cons an as illus a ed in Fig. 9(a). Unde aul y
condi ion he cu en s will con ain o he componen s
besides he posi i e sequence componen and in his
case he Pa k’s Vec o modulus will con ain a dominan
DC and AC le el o he mo o cu en supply [15] and
hei exis ence is di ec ly ela ed o he asymme ies,
as we can see in Fig. 9(b).
(a) Heal hy case.
(b) Faul y case.
Fig. 8: Conco dia’s cu en s ec o locus.
The aim o EPVA echnique is o apply he equency
analysis o he Pa k’s ec o modulus in o de o ob ain
he EPVA signa u e when he sys em is unbalanced.
A e simula ion and analysis, we ob ain he esul s o
heal hy condi ion ( = 100 Ω) and aul y condi ions
( = 7 Ω and = 0.5 Ω) as shown in Fig. 10.
F om hese esul s, he EPVA signa u e e eals he
exis ence o a aspec al componen a a equency o
00.2 0.4 0.6 0.8 11.2
0
5
10
15
Time (s)
Ip (A)
(a) Heal hy case.
0 0.2 0.4 0.6 0.8 11.2
0
5
10
15
20
25
Time (s)
Ip (A)
(b) Faul y case.
Fig. 9: Pa k’s ec o modulus.
66.67 Hz- wice he undamen al supply equency and
i is so clea om esul s when he aul esis ance de-
c eases ( he se e i y o aul inc eases) he ampli ude
o he spec al componen makes i a good indica o o
he occu ed aul .
050 100 150 200 250 300
0
10
20
30
F equency (Hz)
|Ip (A)|
(a) Heal hy case o = 100 Ω.
0 20 40 60 80 100 120 140 160 180 200
0
20
40
60
F equency (Hz)
|Ip (A)|
2nd ha monic
(b) Faul y case o = 0.5 Ω.
020 40 60 80 100 120 140 160 180 200
0
10
20
30
40
F equency (Hz)
|Ip (A)|
2nd ha monic
(c) Faul y case o = 7 Ω.
Fig. 10: Spec um o Pa k’s ec o modulus.
5. Conclusion
This pape p oposed a dynamic model o su ace
moun ed PMSM machine unde phase- o-phase sho -
ci cui in he s a o winding. The eal o m o back
EMF is p esen ed and included in he model. This
aul y model is used o s udy he beha io o he ma-
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2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 528
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER
chine unde a ious aul condi ions and se e i y. F om
he analysis o he simula ion esul s, phase- o-phase
sho -ci cui aul causes high o que ipples and cu -
en unbalance in he sys em. Highe ci cula ing cu -
en s could be gene a ed by he mo o winding sho -
ci cui . Mo e impo an ly, he de ec ion o hese kinds
o aul sis c ucial in he design and de elopmen p o-
cedu e o he mo o d i e and i s diagnosis. Two sim-
ple and e ec i e diagnosis me hod as ESA and EPVA
based on equency analysis a e used o analyze and o
indica e he p esence o he sho -ci cui aul be ween
wo phases in he s a o . The appea ance o he 2nd
and 3 d ha monic indica es he p esence o his aul
and he ampli ude o he ha monics is p opo ional o
he se e i y o his aul . The shape o Conco dia’s
cu en s ec o locus is a good indica o o he p es-
ence o he aul when i s o m changes om he ci cle
ajec o y o an ellip ical one.
Re e ences
[1] HADEF, M., M. R. MEKIDECHE and A. O.
N’DIAYE. Diagnosis o s a o winding sho
ci cui aul s in a di ec o que con olled
in e io pe manen magne synch onous mo-
o . In: IEEE Vehicle Powe and P opulsion.
Chicago: IEEE, 2011, pp. 1–8. ISBN 978-61284-
247-9. DOI: 10.1109/VPPC.2011.6043166.
[2] VASEGHI, B., B. NAHID-MOBAREKEH, N.
TAKORABET and F. MEIBODY-TABAR. Mod-
eling o non-salien PM synch onous machines
unde s a o winding in e - u n aul condi-
ion: dynamic model-em mode. In: IEEE Ve-
hicle Powe and P opulsion Con e ence. A ling-
on: IEEE, 2007, pp. 635–640. ISBN 0-7803-9761-
4. DOI: 10.1109/VPPC.2007.4544200.
[3] CAPOLINO, G. A., C. BRUZZESE, R. PUSCA
and J. ESTIMA. T ends in aul diagnosis o
elec ical machines: a e iew o diagnos ic ech-
niques. IEEE Indus ial Elec onics Magazine.
2014, ol. 8, iss. 2, pp. 31–42. ISSN 1932-4529.
DOI: 10.1109/MIE.2013.2287651.
[4] PROGOVAC, D., L. Y. WANG and G. YIN.
Sys em iden i ica ion o pe manen magne ma-
chines and i s applica ions o in e - u n aul
de ec ion. In: IEEE T anspo a ion Elec i i-
ca ion Con e ence and Expo (ITEC). De i
MI: IEEE, 2013, pp. 1–5. ISBN 978-1-4799-0148-7.
DOI: 10.1109/ITEC.2013.6573486.
[5] VASEGHI, B., B. NAHID-MOBAREKEH, N.
TAKORABET and F. MEIBODY-TABAR. Mod-
eling o IM wi h s a o winding in e - u n
aul alida ed by em. In: Elec ical Machines
Con e ence. Hammama : IEEE, 2008, pp. 1–
5. ISBN 978-1-4244-1736-0. DOI: 10.1109/ICEL-
MACH.2008.4800130.
[6] GWAN GU, B., J. HYUK CHOI and I. SOUNG
JUNG. In e u n sho aul model o PMSMs
wi h se ies and pa allel winding connec ion.
In: Ene gy Con e sion Cong ess Con e ence. A h-
lan a: IEEE, 2013, pp. 4388–4395. ISBN 978-1-
4799-0336-8. DOI: 10.1109/ECCE.2013.6647287.
[7] TALLAM, R. M., T. G. HABTLER and
R. G. HARLEY. T ansien model o induc-
ion machines wi h s a o winding u n aul s.
IEEE T ansac ions on Indus y Applica in. 2002,
ol. 38, iss. 3, pp. 632–637. ISSN 0093-9994.
DOI: 10.1109/TIA.2002.1003411.
[8] ARKAN, M., D. KASTIC-PEROVIC and P. J.
NSWORTH. Modeling and simula ion o induc-
ion mo o s wi h in e u n aul o diagnos ics.
ELSEVIER Jou nal o Elec ic Powe Sys em Re-
sea ch (EPSR). 2005, ol. 75, iss. 1, pp. 57–66.
ISSN 0378-7796. DOI: 10.1016/j.eps .2004.08.015.
[9] DAI, M. and A. SEBASTIAN. Faul analysis o
a PM b ishless DC mo o using ini e elemen
me hod. IEEE T ansac ion On Ene gy Con e -
sion. 2005, ol. 20, iss. 1, pp. 1–4. ISSN 0885-8969.
DOI: 10.1109/TEC.2004.841516.
[10] MOHAMMED, O. A., Z. LIU, S. LIU and
N. Y. ABED. In e u n sho ci cui aul
diagnosis o PM machines using FE based
o phase a iable model and wa ele anal-
ysis. IEEE T ansac ion On Magne ic. 2007,
ol. 43, iss. 4, pp. 1729–1732. ISSN 0018-9464.
DOI: 10.1109/TMAG.2006.892301.
[11] JOENG, I. I. S. U., B. J. HYON and K.
NAM. Dynamic modeling and con ol o
SPMSMs wi h in e nal u n sho aul s.
IEEE T ansac ionon Powe Elec onic. 2013,
ol. 28, iss. 7, pp. 3495–3508. ISSN 0885-8993.
DOI: 10.1106/TPEL.2012.2222049.
[12] KIM, K.-T., J. HUR, B.-W. KIM and G.-H.
KANG. Ci cula ing cu en calcula ion us-
ing aul modeling o IPM ype BLCD mo o
o in e - u n aul . In: IEEE Elec ic ma-
chines and Sys emscon e enc. Tokyo: IEEE,
2011, pp. 1–5. ISBN 9781-4577-1043-8.
DOI: 10.1109/ICEMS.2011.6073686.
[13] VASEGHI, B., B. NAHID-MOBAREKEH, N.
TAKORABET and F. MEIBODY-TABAR. Ex-
pe imen ally alida ion dynamic aul model o
PMSM wi h s a o winding in e - u n aul .
In: Indus y Applica ion Socie y Annual Mee ing.
Edmon on: IEEE, 2008, pp. 1–5. ISBN 978-1-
4244-2279-1. DOI: 10.1109/08IAS.2008.24.
c
2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 529
POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER
[14] LAI, C., A. BALAMURALI, V. BOUSABA, K. L.
V. IYER and N. KAR. Analysis o s a o winding
in e - u n sho ci cui aul in in e io and su ace
moun ed pe manen magne ac ion machines.
In: T anspo a ion Elec i ica ion Con e ence and
Expo. Dea bo n: IEEE, 2014, pp. 1–6. ISBN 978-
1-4799-2262-8. DOI: 10.1109/ITEC.2014.6861775.
[15] CRUZ, S. M. A. and A. J. M. CAR-
DOSO. S a o winding aul diagnosis in h ee
phasessync h onous and asynch onous mo o , by
he ex ended Pa k’s ec o app oach. IEEE
T ansac ion On Indus y Applica ions. 2001,
ol. 37, iss. 5, pp. 1227–1233. ISSN 1939-9367.
DOI: 10.1109/28.952496.
[16] CRUZ, S. M. A. and A. J. M. CARDOSO. Mul-
iple e e ence ames heo y: a new me hode o
he diagnosis o s a o aul in h ee phases induc-
ion mo o s, by he ex ended Pa k’s ec o ap-
p oach. IEEE T ansac ion On Ene gy Con e sion.
2005, ol. 20, iss. 3, pp. 611–619. ISSN 1558-0059.
DOI: 10.1109/TEC.2005.847975.
[17] DYONOSIOS, V. S. and D. M. EPAMINONDAS.
Induc ion Mo o S a o Faul Diagnosis Tech-
nique Using Pa k Vec o App oach and Com-
plex Wa ele s. In: IEEE In e na ional Con e ence
on Elec ic Machine y (ICEM). Ma seille: IEEE,
2012, pp. 1730–1734. ISBN 978-1-4673-0142-8.
DOI: 10.1109/ICEIMach.2012.6350114.
[18] PARRA, A. P., M. C. A. ENCICO, J.
O. OCHOA and J. A. P. PENAR. S a o
aul diagnosis on squi el cage induc ion mo-
o by ESA and EPVA. In: Powe Elec-
onics and Powe Quali y Applica ions. Bo-
go a: IEEE, 2014, pp. 1–6. ISBN 978-1-4799-1007-
6. DOI: 10.1109/PEPQA.2013.6614937.
Abou Au ho s
Chou ouk BOUCHAREB was bo n in 1975,
in Algie s, Alge ia. She ecei ed an Enginee
Diploma in Elec ical Enginee ing in 1999 and an
M.Sc. deg ee in Con ol enginee ingin 2005, bo h
om Elec ical Enginee ing Depa men o Ba na
Uni e si y. He esea ch in e es s include he elec ic
machines and hei con ol d i es and diagnosis. She
is a membe a he Labo a o y Uni e si y, named
Elec omagne ic Induc ion and P opulsion Sys ems
(LSPIE) o Ba na Uni e si y.
Mohamed-Said NAIT-SAID was bo nin 1958, in
Ba na, Alge ia, He ecei ed an Enginee Diploma in
Elec ical Enginee ing om he Na ional Poly echnic
High School o Algie s, Alge ia (Feb ua y 1983),
and he M.Sc. deg ee in Elec onics and Con ol
Enginee ing om Elec onics Depa men a Con-
s an ine Uni e si y in 1992. He ecei ed he Ph.D.
deg ee in Elec ical Enginee ing om Uni e si y o
Ba na a e he accomplished his ee scien i ic esea ch
accomplished in Au oma ic Labo a o y o Amiens
Uni e si y in F ench om 1996 o 1999. Cu en ly
he is a ull p o esso a he Elec ical Enginee ing
Depa men o Ba na Uni e si y II and is esponsible
o he Mas e cou se o Con ol and Diagnosis o he
Elec ical Sys ems. F om 2000–2005, D . Nai -Said
was he head o he i s c ea ed esea ch labo a o y in
Ba na Uni e si y, named Elec omagne ic Induc ion
and P opulsion Sys ems (LSPIE) o Ba na and also in
2006 he has been appoin ed he head o he scien i ic
commi ee o he same depa men . LSPIE has been
e alua ed by he Alge ian minis y o he uni e si ies
as he bes labo a o y in Ba na Uni e si y (100 pe cen
sa is ied. D . Nai -Said has supe ised wen y i e
Mas e s and en Ph.D. heses. His esea ch in e es s
include he elec ic machines and hei con ol d i es
and diagnosis.
Appendix A - AC D i e
Pa ame e s
•PN= 5 kW,
•P= 4,
•EMF a 1000 pm = 34 V,
•IN= 19 A.
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