pmsm model with phase-to-phase short-circuit and diagnosis

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 14 | NUMBER: 5 | 2016 | DECEMBER

PMSM Model with Phase-to-Phase Short-Circuitand Diagnosis by ESA and EPVA

Chourouk BOUCHAREB, Mohamed Said NAIT SAID

Electrical Engineering Department, Laboratory LSPIE Batna 2000, Batna University,Route de Biskra, 05078, Algeria

[email protected], [email protected]

DOI: 10.15598/aeee.v14i5.1928

Abstract. One of the most frequent faults in PMSMstator is the insulation failure due to the degradationof the main isolation in the motor winding. This paperis aimed at suggesting a dynamic model of PMSM withphase-to-phase fault based on an equivalent electric cir-cuit model including the real form of back EMF. Thefaulty model is used for studying the machine behaviorand extracting the fault signatures for diagnosis. Twodiagnostic techniques the Spectral Analysis (ESA) andExtend Park’s Vectors Approach (EPVA) based on fre-quency analysis are applied to detect this kind of fault.

Keywords

EPVA, ESA, Inter-turn fault, phase-to-phasefault, PMSM model.

1. Introduction

In recent years, Permanent Magnet Synchronous Mo-tor (PMSM) has become one of most important elec-tric machines because of the inherent advantages ofhigh power density, high efficiency, small weight, highreliability and easy control of external torque of sta-tor’s current control. Consequently, it is widely usedin industry, e.g. in traction, automobiles, robotics andaerospace technology, as well as electric vehicles andship propulsion systems [1], [2] and [3].

The fault diagnosis of electrical machines had beenthe target of an intense amount of interesting re-searches during the last 30 years. Reducing mainte-nance costs and preventing unscheduled down-times,which result in losses of production and financial in-comes and benefitting from their utility in safety-sensitive applications, are the priorities of electricaldrives for manufacturers and operators [4], [5] and [6].

In fact, correct diagnosis and early detection of incipi-ent faults require the development of an accurate modelfor electrical machine, able to simulate electrical faultsand to apply an effective diagnostic technique.

However, model accuracy and computation time rep-resents two opposite criteria. Conventional model(equivalent electric circuit or equivalent magnetic cir-cuit) obtained with Park transformation for instanceis based on restrictive assumptions and does not re-quire long computation time [7] and [8]. On the otherhand, model obtained with the finite elements methodis based on minimal assumption and requires long com-putation time [9] and [10]. There is a real need to estab-lish an alternative model, which offers a good balancebetween accuracy and computation time.

One of the most common faults, called insulationfailure, is the inter-turn short circuit in one of the sta-tor coils. Since the coil insulation material is under thehigh voltage and temperature stress, it degrades grad-ually and finally loses the insulating characteristic [6].The inter-turn fault is mostly caused by mechanicalstress, moisture and partial discharge, which is accel-erated for inverter supplied electrical machines [11].

In this paper, a dynamic model of a stator surfacemounted PMSM with inter-turn fault is presented. Wefocus on phase-to-phase fault of the stator winding.This model based on equivalent electric circuit exhibitsa trade-off between simplicity and precision, and it isused for studying a machine behavior under fault con-ditions for different levels of fault severity using MAT-LAB Simulink software.

Exploiting this faulty model to extract fault signa-tures in order to diagnose and to predict the insula-tion failure breakdown when the fault is not very se-vere in order to avoid the machine winding damages.To detect this fault, we chose two simple and usefultechniques based on frequency analysis. These tech-niques are Electric Spectral Analysis (ESA) and Ex-

c© 2016 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 522


tend Park’s Vectors Approach (EPVA). The contribu-tion of this work is the addition of the real waveformof back Electro Motive Force (EMF) of healthy ma-chine which contains a harmonic at 3 · fs of supplyfrequencies, because if the model does not take the un-certainties, like real back-EMF, the indicator will givea wrong diagnostic.

2. PMSM Fault DynamicModel

2.1. Phase-to-Phase Fault DynamicModel

The phase-to-phase fault denotes insulation failures be-tween two windings of two phases at the stator. Theinsulation failure is modeled by a resistance, where itsvalue depends on the fault severity. The stator wind-ing of a PMSM machine with phase-to-phase fault isrepresented by Fig. 1. In this figure, the fault occursbetween ’a’ and ’b’ phases, rf denotes the fault insula-tion resistance. The sub-windings (as1) and (as2) rep-resent respectively, the healthy and faulty part of thephase winding a, and sub-windings (bs1) and (bs2) rep-resent, the healthy and faulty part of the phase windingb respectively. When the fault resistance rf decreasestowards zero, the insulation fault evaluates towards aninter-turn full short-circuit.

lfrf

lbs1 lbs2

Rbs1, Lbs1

Rcs, Lcs

Ras1, Las1 Ras2, Las2las1 las2las

lbs

lcs

Rbs2, Lbs2

Fig. 1: Three-phases winding with phase-to-phase fault.

2.2. PMSM Healthy Model inabc-Coordinates

The voltages equations from the circuit in Fig. 1 with-out fault(healthy machine), given by rf infinite value,as in [2], [12] and [13] are:

[Vs] = [Rs] · [Is] + [Ls] ·d

dt· [Is] + [Es] , (1)

vasvbsvcs

=

Rs 0 00 Rs 00 0 Rs

IasIbsIcs

+

+

L M MM L MM M L

· ddt·

IasIbsIcs

+

easebsecs

,(2)

where the healthy machine variable and parametersare:

• vas,bs,cs - three phase stator voltages,

• Ias,bs,cs - three phase stator currents,

• eas,bs,cs - three phase back EMF,

• Rs - stator resistance,

• L - self inductance of the stator,

• M - mutual inductance of the stator.

2.3. PMSM Faulty Model inabc-Coordinate

Voltage equations, which describe the faulty circuitpresented in Fig. 1, can be expressed as:

[Vs] =[vas1 vas2 vbs1 vbs2 vcs

]T, (3)

where:

• vas1 - the voltage of the healthy part phase a,

• vas2 - the voltage of faulty part of phase a,

• vbs1 - the voltage of the healthy part phase b,

• vbs2 - the voltage of faulty part of phase b.

The new resistances of healthy and faulty parts ofphase ’a’ and ’b’ are calculated as follows:

Ras1 = (1− σ) ·Ras, (4)

Ras2 = σ ·Ras, (5)

Rbs1 = (1− σ) ·Rbs, (6)

Rbs2 = σ ·Rbs, (7)

σ =NfNs

. (8)

The study of the elementary circuits of the phaseshas given the following relations:

vas = vas2 + vas1, (9)

vbs = vbs2 + vbs1, (10)



Ias1 = Ias, (11)

Ibs1 = Ibs, (12)

where Ras1 is the stator phase resistance of healthyparts of ’a’ phase while Ras2 is the faulty stator phaseresistance. Rbs1 it is the stator phase resistance ofhealthy parts of ’b’ phase while Rbs2 is its faulty statorphase resistance, σ is the ratioof number of the turns(Nf ) over the phase winding number of the turns (Ns).

The self-inductances of the faulty and healthy partsof winding (aas1, aas2), and winding (bbs1, bbs2) areproportional to the square of the fraction of shortedturns σ, and also the mutual inductance is proportionalto this number of both parts. Therefore, we assume:

Las1 = (1− σ)2Las, (13)

Las2 = σ2Las, (14)

Mas2b = σM, (15)

Mas1as2 = σ (1− σ)L, (16)

where Las1 is the stator phase inductance of healthyparts of a phase while Las2 is the stator phase induc-tance of faulty parts of a phase, If is the additionalcurrent engendered by the short circuit, rf is the in-sulation faulty resistance and vf is the correspondedfaulty voltage.

The stator currents become:

[Is] = [Ias (Ias − If ) Ibs (Ibs + If ) Ics]T. (17)

The equation which describes the short circuit loopis in Eq. (18).

From previous analysis, we obtain the global equa-tions governing the behavior of the machine with thepresence of this short-circuit fault as the Eq. (19).

In the Eq. (19):

R′ = Ras +Rbs +Rcs, (20)

Lf = − (−La2 +Ma2b2 − Lb2 +Mb2a2) , (21)

Mbf = −Ma1a2 +Ma1b2 − La2 +Ma2b2, (22)

Mcf = −Mca2 +Mcb2. (23)

The expression of the electromagnetic torque can bewritten as follows:

Te =eas · Ias + ebs · Ibs + ecs · Ics − ef · If

Ω, (24)

where Ω is the mechanical angular speed.

2.4. PMSM Faulty Model inα, β-Coordinates

The machine equations with inter-turn fault in station-ary α and β axis reference frame are in Eq. (25), where:

Rr =

√2

3

(−Ra2 −

Rb22

), (26)

rf = Ra2 +Rb2 +Rf , (27)

rb2 =1

2

√2Rb2, (28)

Mfα =

√2

3

(Maf −

Mbf

2− Mcf

2

), (29)

Mfβ =1

2

√2 (Mbf −Mcf ) , (30)

Ls = L−M, (31)

with,

• Iα,β - α and β axis components of stator currents,

• eα,β - α and β components of stator back EMF.

Then the electromagnetic torque expression for thephase-to-phase fault model becomes:

Te =eα · Iα + eβ · Iβ − ef · If

Ω. (32)

We consider for all the studies that the electromotiveforce of the healthy motor has a sinusoidal form asshown in Fig. 2(a) and contains a 3rd harmonic at 3 ·fsof supply frequencies as seen in Fig. 2(b).

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08−40

−20

0

20

40

Time (s)

EM

F (

V)

(a) Electromotive force.

0 50 100 150 200 250 3000

10

20

30

40

Frequency (Hz)

|EM

F(V

)|

3rd harmonic

(b) Spectrum analysis.

Fig. 2: Electromotive force and its spectrum analysis.



0 = −Ra2 · Ias +Rb2 · Ibs − (La2 +Ma1a2 −Mb2a1−Mb2a2) · dIasdt− (Ma2b1 +Ma2b2 − Lb2 −Mb2b1) · dIbs

dt+

− (Ma2c −Mb2c) · dIcsdt − ef +(Ra2 +Rb2 + rf

)· If − (−La2 +Ma2b2 − Lb2 +Mb2a2) · dIf

dt

. (18)

vasvbsvcs0

=

Rs 0 0 Ra20 Rs 0 Rb20 0 Rs 0−Ra2 Rb2 0 R′

IasIbsIcsIf

+

L M M Maf

M L M Mbf

M M L Mcf

Maf Mbf Mcf Lf

ddt

IasIbsIcsIf

+

easebsecs−ef

. (19)

3. Dynamic Fault ModelSimulation Results

The study of the behavior of PMSM under fault con-ditions using the proposed fault dynamic model re-quires an accurate knowledge of circuit parameters.The PMSM parameters are given as shown in AppA[2].

0 0.2 0.4 0.6 0.8 1 1.2−40

−20

0

20

40

Time (s)

I a−

I b−

I c (

A)

f r = 100 Ω f r = 7 Ω

f r = 0.5 Ω

(a) Phase currents.

0 0.2 0.4 0.6 0.8 1 1.2−60

−40

−20

0

20

40

Time (s)

I f (A

)

rf = 100 Ω rf = 7 Ω

rf = 0.5 Ω

(b) Faulty current.

−15

−10

−5

0

5

10

0 0.2 0.4 0.6 0.8 1 1.2Time (s)

rf = 100 Ω rf = 7 Ω

rf = 0.5 Ω

Te

(Nm

)

(c) Electromagnetic torque.

−2000

−1000

0

1000

2000

Pa

(W

att)

0 0.2 0.4 0.6 0.8 1 1.2Time (s)

rf = 100 Ω

rf = 7 Ω

rf = 0.5 Ω

(d) Absorbed power.

Fig. 3: Phase currents, faulty current, electromagnetic torqueand absorbed power versus time for three values of faultresistances: rf = 100 Ω, rf = 7 Ω and rf = 0.5 Ω.

The machine is supposed to be supplied by 3-phasessinusoidal balanced voltage source with star connectionand without neutral connection and operates at syn-chronous speed (speed and supply frequency are 1000rpm and 66.67 Hz respectively). Simulation of the pro-posed model is realized using MATLAB environment.

0 0.2 0.4 0.6 0.8 1 1.2−60

−40

−20

0

20

40

Time (s)

I a−

I b−

I c (

A)

0.50.10.7

(a) Phase currents.

0 0.2 0.4 0.6 0.8 1 1.2−100

−50

0

50

Time (s)

I f (A

)

0.1

0.70.5

(b) Faulty current.

−30

−20

−10

0

10

0 0.2 0.4 0.6 0.8 1 1.2Time (s)

0.1

0.70.5T

e (

Nm

)

(c) Electromagnetic torque.

0.8 1.2−3

−2

−1

0

1

2

Pa

(kW

att)

0 0.2 0.4 0.6 1Time (s)

0.1

0.7

0.5

(d) Absorbed power.

Fig. 4: Phase currents, faulty current, electromagnetic torqueand absorbed power versus time at three values of thefraction of shorted turns: (σ = 0.1, σ = 0.5 and σ = 0.7)and rf = 0.5 Ω.

For this model, Fig. 3 shows the characteristics phasecurrents (a, b, c), faulty current (If ), electromagnetictorque and absorbed power for different values of faultinsulation resistance such as rf = 100 Ω, 0.5 Ω and7 Ω. The fraction of shorted turns is fixed at 50 %.

Figure 4 shows the characteristics (phase currents (a,b, c), faulty current (If ), electromagnetic torque andabsorbed power for different values of the fraction ofshorted turns (σ = 10 %, σ = 50 % and σ = 70 %),where the fault insulation resistance is fixed to rf =0.5 Ω.

As it can be seen from Fig. 3, for three different val-ues of fault resistances (healthy case: rf = 100 Ω and



vαvβ0

=

Rs 0 Rr0 Rs rb2Rr rb2 rf

· IαIβIf

+

Ls 0 Mfα

0 Ls Mfβ

Mfα Mfβ Lf

· ddt·

IasIbsIcsIf

+

eαeβ−ef

. (25)

faulty case: rf = 7 Ω and rf = 0.5 Ω) when the faultresistance decreases, the three phases currents increaseto compensate the negative effects of the short-circuitfault. It can cause a current unbalance in the powersupply, and the increase of the absorbed power. We canobserve a torque ripple when the faulty case is applied.

Changing the fraction of short-turns means changingthe severity of applying fault. From Fig. 4, it is clearthat the magnitude of the torque ripple is mainly de-termined by the severity of the fault. The magnitudeof the phase currents and absorbed powerchange pro-portionally with the severity of the fault and becomeunbalanced.

It would be very helpful to predict the insulationfail-ure, breakdown when the fault is not high developedinorder to avoid the machine winding damages [14].

4. Diagnostic of Stator Faultby ESA and EPVATechniques

Two techniques based on frequency analysis are ap-plied to detect faults in stator, consecutively definedin [15], [16] and [17]. First is ESA, based on the FastFourier decomposition of the phase currents winding,the electromagnetic torque and the absorbed power.The second is EPVA, which is based on the frequencyanalysis of the module of the Park’s Vector’s of currentsas shown below.

4.1. Electric Spectral Analysis(ESA)

We applied this technique on the phase stator currents,the instantaneously absorbed power and the electro-magnetic torque. The instantaneous absorbed poweris illustrated by the following equation [18]:

p(t) = vas(t)ias(t) + vbs(t)ibs(t) + vcs(t)ics(t). (33)

The phase stator currents, the instantaneous ab-sorbed power and electromagnetic torque spectrumanalysis results of both healthy and faulty conditionswith different values of faulty resistance (rf = 100 Ω,rf = 7 Ω and rf = 0.5 Ω) of simulation machine arepresented in Fig. 5, Fig. 6, and Fig. 7 respectively.

1) Currents Spectral Analysis

The ESA signatures reveal the existence of a spectralcomponent in phase ’a’ and ’b’, with a small amplitudeat the frequency with value three times higher than thesupply due the existence of an inter-turn short circuitin the stator winding and its amplitude increase withthe increase of severity of faultas seen in Fig. 5(b),Fig. 5(c) and Fig. 5(d), where rf = 0.5 Ω and inFig. 5(e), where rf = 7 Ω, the existence of this har-monic is due to the presence of the third harmonic ofthe electromotive force presented in Fig. 2(b). We canobserve no existence of this harmonic in phase ’c’ be-cause the short circuit occurs between phase ’a’ and’b’. Note that at healthy conditions the current doesnot have this component (third harmonic), as seen inFig. 5(a).

2) Electromagnetic Torque SpectralAnalysis

It is noticeable from Fig. 7, that in case of fault, we no-tice the appearance of high harmonic at double value ofsupply frequency, especially if rf = 0.5 Ω. The increaseof the harmonic amplitude is inversely proportional tothe values of fault resistance.

3) Absorbed Power Spectral Analysis

Figure 6 shows the absorbed power spectrum with andwithout fault. We can observe only a zero frequencycomponent at healthy conditions. In faulty conditionsthe same analysis as that of the electromagnetic torqueis noted. From the comparative analysis of results un-der healthy and faulty conditions, it is clear that thefault appears in the ESA signaturedue to the presenceof harmonic of even rows on the spectrum analysis ofelectromagnetic torque and absorbed power and by theappearance of the harmonic of odd rows on the spec-trum analysis of phase currents. The appearances ofthese harmonics are directly related to the existenceof asymmetries caused by the short-circuit in the sta-tor winding. With the consumption that we have abalanced voltage source, the appearance of harmonicsin phase ’a’ and ’b’ indicates the short-circuit betweenthese two phases.



0 50 100 150 200 250 3000

5

10

15

Frequency (Hz)

|I a (

A)|

(a) Healthy case for rf = 100 Ω.

0

10

20

30

|I a (

A)|

150 200 2500

1

2

3rd harmonic

0 50 100 150 200 250 300Frequency (Hz)

(b) Faulty case for rf = 0.5 Ω (Phase a).

0

5

10

15

20

25

|I b (

A)| 3rd harmonic

150 200 2500

1

2

0 50 100 150 200 250 300Frequency (Hz)

(c) Faulty case for rf = 0.5 Ω (Phase b).

0 50 100 150 200 250 3000

5

10

15

Frequency (Hz)

|Ic (

A)|

(d) Faulty case for rf = 0.5 Ω (Phase c).

0 50 100 150 200 250 3000

5

10

15

Frequency (Hz)

|I a (

A)|

3rd harmonic

(e) Faulty case for rf = 7 Ω

Fig. 5: Spectrum of phase currents.

4.2. Extend Park’s Vector Approach(EPVA)

This technique is based on the two equivalent currentsin reference frame obtained by Park’s transformation[18]:

Id =

√2

3· Ias −

1√6· Ibs −

1√6· Ics, (34)

Iq =1√2· Ibs −

1√2· Ics, (35)

where Id and Iq are the instantaneous values of electriccurrents in direct and quadrature axis. Idis always asine wave and Iq has a cosine wave in healthy condi-tions. These two components have the same values andtheir locus is a circle as seen in Fig. 8(a). In case ofthe inter-turn short circuit, the current becomes unbal-

0 50 100 150 200 250 3000

200

400

600

800

1000

Frequency (Hz)

|Pa

(W

att)

|


0 20 40 60 80 100 120 140 160 180 2000

200

400

600

800

1000

Frequency (Hz)

|Pa

(W

att)

| 2nd harmonic

(b) Faulty case for rf = 0.5 Ω.

0

500

1000

1500

|Pa

(W

att)

|

2nd harmonic

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

(c) Faulty case for rf = 7 Ω.

Fig. 6: Spectrum of absorbed power.

0

1

2

3

4

5

|Te

(N

m)|

0 50 100 150 200 250 300Frequency (Hz)


0

2

4

62nd harmonic

|Te

(N

m)|

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)


0

1

2

3

4

5

2nd harmonic

0 20 40 60 80 100 120 140 160 180 200Frequency (Hz)

|Te

(N

m)|


Fig. 7: Spectrum of electromagnetic torque.

anced and it can be expressed as the sum of a positivesequence and a negative sequence component. As a re-sult of this fault, the Concordia’s vector locus shapedeviates and becomes elliptic as shown in Fig. 8(b).

If the motor operates under healthy conditions (i.e.under symmetrical conditions), the three currents forma balanced system and constitute a positive sequence



system. Hence, id and iq can be written as below [18]:

ip =√i2d + i2q, (36)

id =

√6

2· imax · sin(ωt), (37)

iq =

√6

2· imax · sin

(ωt− π

2

), (38)

where imax is a maximum value of the current positivesequence, ω is the angular supply frequency, and ipis the Park’s equivalent current module. When thesystem is balanced, the current Park’s vector modulusis constant as illustrated in Fig. 9(a). Under faultycondition the currents will contain other componentsbesides the positive sequence component and in thiscase the Park’s Vector modulus will contain a dominantDC and AC level of the motor current supply [15] andtheir existence is directly related to the asymmetries,as we can see in Fig. 9(b).

(a) Healthy case.

(b) Faulty case.

Fig. 8: Concordia’s currents vector locus.

The aim of EPVA technique is to apply the frequencyanalysis to the Park’s vector modulus in order to obtainthe EPVA signature when the system is unbalanced.After simulation and analysis, we obtain the results forhealthy condition (rf = 100 Ω) and faulty conditions(rf = 7 Ω and rf = 0.5 Ω) as shown in Fig. 10.

From these results, the EPVA signature reveals theexistence of a aspectral component at a frequency of

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

Time (s)

I p (

A)

(a) Healthy case.

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

20

25

Time (s)

I p (

A)

(b) Faulty case.

Fig. 9: Park’s vector modulus.

66.67 Hz-twice the fundamental supply frequency andit is so clear from results when the fault resistance de-creases (the severity of fault increases) the amplitudeof the spectral component makes it a good indicator ofthe occurred fault.

0 50 100 150 200 250 3000

10

20

30

Frequency (Hz)

|I p (

A)|


0 20 40 60 80 100 120 140 160 180 2000

20

40

60

Frequency (Hz)

|I p (

A)|

2nd harmonic


0 20 40 60 80 100 120 140 160 180 2000

10

20

30

40

Frequency (Hz)

|I p (

A)|

2nd harmonic


Fig. 10: Spectrum of Park’s vector modulus.

5. Conclusion

This paperproposed a dynamic model for surfacemounted PMSM machine under phase-to-phase short-circuit in the stator winding. The real form of backEMF is presented and included in the model. Thisfaulty model is used to study the behavior of the ma-



chine under various fault conditions and severity. Fromthe analysis of the simulation results, phase-to-phaseshort-circuit fault causes high torque ripples and cur-rentunbalance in the system. Higher circulating cur-rents could be generated by the motor winding short-circuit. More importantly, the detection of these kindsof faultsis crucial in the design and development pro-cedure of the motor drive and its diagnosis. Two sim-ple and effective diagnosis method as ESA and EPVAbased on frequency analysis are used to analyze and toindicate the presence of the short-circuit fault betweentwo phases in the stator. The appearance of the 2ndand 3rd harmonic indicates the presence of this faultandthe amplitude of the harmonics is proportional tothe severity of this fault. The shape of Concordia’scurrents vector locus is a good indicator of the pres-ence of the fault when its form changes from the circletrajectory to an elliptical one.

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About Authors

Chourouk BOUCHAREB was born in 1975,in Algiers, Algeria. She received an EngineerDiploma in Electrical Engineering in 1999 and anM.Sc. degree in Control engineeringin 2005, both

from Electrical Engineering Department of BatnaUniversity. Her research interests include the electricmachines and their control drives and diagnosis. Sheis a member at the Laboratory University, namedElectromagnetic Induction and Propulsion Systems(LSPIE) of Batna University.

Mohamed-Said NAIT-SAID was bornin 1958, inBatna, Algeria, He received an Engineer Diploma inElectrical Engineering from the National PolytechnicHigh School of Algiers, Algeria (February 1983),and the M.Sc. degree in Electronics and ControlEngineering from Electronics Department at Con-stantine University in 1992. He received the Ph.D.degree in Electrical Engineering from University ofBatna after he accomplished his free scientific researchaccomplished in Automatic Laboratory of AmiensUniversity in French from 1996 to 1999. Currentlyhe is a full professor at the Electrical EngineeringDepartment of Batna University II and is responsiblefor the Master course of Control and Diagnosis of theElectrical Systems. From 2000–2005, Dr. Nait-Saidwas the head of the first created research laboratory inBatna University, named Electromagnetic Inductionand Propulsion Systems (LSPIE) of Batna and also in2006 he has been appointed the head of the scientificcommittee of the same department. LSPIE has beenevaluated by the Algerian ministry of the universitiesas the best laboratory in Batna University (100 percentsatisfied. Dr. Nait-Said has supervised twenty fiveMasters and ten Ph.D. theses. His research interestsinclude the electric machines and their control drivesand diagnosis.

Appendix A - AC DriverParameters

• PN = 5 kW,

• P = 4,

• EMF at 1000 rpm = 34 V,

• IN = 19 A.


http://dx.doi.org/10.1109/ITEC.2014.6861775

http://dx.doi.org/10.1109/28.952496

http://dx.doi.org/10.1109/TEC.2005.847975

http://dx.doi.org/10.1109/ICEIMach.2012.6350114

http://dx.doi.org/10.1109/PEPQA.2013.6614937

pmsm model with phase-to-phase short-circuit and diagnosis

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