PMSM model with phase-to-phase short-circuit and diagnosis by ESA and EPVA

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- c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 522 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER 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) c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 523 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER 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. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 524 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER 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 c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 525 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER   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. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 526 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER 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 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 527 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 |NUMBER: 5 |2016 |DECEMBER 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- c 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. 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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. c 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 530