Static and Dynamic Fault Analysis of Switched Reluctance Motor

Vladimir Kacenka*, Pavol Rafajdus*, Pavol Makys* Vladimir Vavrus*, Loránd Szabó† * University of Zilina, Faculty of Electrical Engineering, Department of Power Electrical Systems,

Zilina, Slovakia, e-mail: pavol.rafajdus@kves.uniza.sk † Technical University of Cluj-Napoca, Department of Electrical Machines and Drives

Cluj-Napoca, Romania, e-mail: Lorand.Szabo@mae.utcluj.ro

Abstract—This paper deals with static and dynamic analysis of the Switched Reluctance Motor (SRM) under fault operating conditions. The static analysis is carried out by means of Finite Element Method (FEM) to investigate static parameters of the SRM for health and some defined faults of the phases. These static parameters are used in the dynamic model of the SRM and some transients are simulated for normal condition and also for fault operation. The comparison with experimental results is presented.

Keywords—switched reluctance motor, fault operation, parameter analysis

I. INTRODUCTION The Switched Reluctance Motor (SRM) is one of the

simplest and robust electrical machines. The manufacturing costs of this machine are lower in comparison with others electrical machines. These features of SRM are very important in competition with other electrical machines [1].

The SRM construction is very simple. The both stator and rotor have salient poles and only stator carries winding coils, which are suitable connected to create phase. The magnetic flux is provided by phase current to develop a reluctance torque [2], [3], [4]. The cross-section area of the three phase 6/4 SRM is shown in the Fig. 1a. In the Fig. 1b, there is photo of the investigated SRM.

During industrial processes, the drive reliability is very important task from point of view fault operation. Several fault conditions of electrical drive can occurred during its operation. It could be mechanical, magnetic or electric fault of the motor. This paper is focused into electrical faults of the SRM and their impact on motor behavior.

The electrical faults could be: short circuit in one coil of a phase (all turns or some turns), a whole coil is bridged by a short circuit, the whole phase is short circuited, open circuit in one coil of a phase, a short circuit between two different phases, a short circuit from one winding to ground [5].

In [6], there is studied the most frequent faults of the SRMs and their detection. By means of numeric field analysis the effects of winding faults are investigated. By using advanced co-simulation techniques the dynamic behavior of the SRM in healthy and several faulty conditions are described. In [7], there is described the winding faults of the SRMs and their detection. The effects of winding faults are investigated in details by means of advanced

numeric field analysis based on the finite element method (FEM).

In this paper, a real three phase 6/4 SRM is investigated from point of view static and dynamic fault analysis. The static analysis is carried out by means of FEM and the phase inductance, flux linkage and air gap torque are analyzed, when the SRM is health and for some faults. These static parameters are used in the dynamic mathematical model of the SRM and transients are calculated also for health and fault operated motor. The simulated results are compared with experimental ones.

The nameplate of the investigated SRM is shown in the Table I.

a) b)

Fig. 1. The investigated SRM, a) cross-section area, photo of open motor.

TABLE I. THE NAMEPLATE OF THE INVESTIGATED 6/4 SRM

MEZ EM Brno TYPE SR 40N 3x 10V 28.5A 5000 rpm

II. FEM ANALYSIS OF SRM STATIC PARAMETERS Exists several methods, how to analyze the static

parameters of the SRM [8]. Very useful and accurate is Finite Element Analysis (FEA), which is used in this paper. For the FE magnetostatic analysis the following input data are needed: geometrical dimensions of the machine, current density of one phase, material constants (winding conductivity and relative permeability, B-H curve of SRM ferromagnetic circuit material) and boundary conditions. The parametric model of SRM has been created in LUA script in the FEMM 4.2 software for more convenient calculation with lower time consumption. The LUA script also enables the SRM

B'+ B'-

B+ B-

C'-

A'-

C+

A+C'+

A'+

C-

A-

978-1-4673-1179-3/12/$31.00 ©2012 IEEE 206

model configurations (changes of the mor other parameters) during the executio

The static characteristics of SRM haby means of FEM under four differconditions. Namely 0%, 20%, 50%, 70%has been in the short circuit that corresp6 winding turns respectively.

The accuracy of the result depends omesh and accuracy of the input paramet10.083 nodes have been used. The calcuout for each individual rotor position static condition. The rotor position ϑ aligned ϑa to unaligned position ϑu witeach position the current was changed wrange from 1 to 28 A. In the Fig. 2 tmagnetic flux lines of health SRM unaligned position can be seen. In coFig.3, there is the distribution of magnfault SRM for aligned and unaligned pcoil "B" turns are in short circuit.

a)

Fig. 2. FEM analysis of the SRM, flux lines ofaligned rotor position, b) unaligned rot

a)

Fig. 3. FEM analysis of the SRM, flux lines of thcoil "B" turns are in short circuit, a) aligned rotor

rotor position.

Magnetic flux linkage calculation The first parameter which has been a

linkage versus phase current for differen=f(I,x). The area bounded by maximal by both ψ-I curves for aligned and unaequal to mechanical energy, which electromagnetic force [1]. In the Fig. 4curves obtained by means of FEM fpositions, if the phase current has beenAmps (45o is equal to unaligned rotor pequal to aligned rotor position). The invB. As it can be seen from this Fig., tdecreased with increasing of phase turns

machine geometry n of the script. ave been analyzed rent winding fault % of winding turns onds to 25, 20, 13,

on the size of FEM ters. In this model, ulation was carried and current under was moved from

th step of 1oand in within its working the distribution of

for aligned and omparison, in the netic flux lines of position if 50% of

b)

f the health SRM, a) tor position.

b)

he SRM, where 50% of r position, b) unaligned

analyzed is the flux nt rotor position ψ phase current and

aligned position is is converted to

4 can be seen the for different rotor n kept constant 13 position and 90o is vestigated phase is the flux linkage is s in short circuit.

Fig. 4. FEM analysis of the SRM, fluxconstant phase c

A. Phase inductance calculatioThe phase inductance L=f(I,x

full current range is a static parSRM mathematical model for analysis was made for the wphase inductance profiles are results are obtained by meanaccordance with the following e

2I

JAL � ⋅

=

where A is magnetic vectdensity, V is volume and I is ph

Fig. 5. FEM analysis of the SRM, pposition for constant ph

B. Electromagnetic torque calThe electromagnetic torque

means of FEM. The static toobtained for the whole workintensor prescribes the torque permagnetic field in the air gap of torque produced is:

( ) (( HBnBHdT +⋅=21

where n denotes the directiothe point of interest, B is flux dmagnetic field.

In the Fig. 6, there is showntorque of phase B in the air positions and constant phase cu

45 50 55 60 650

0.002

0.004

0.006

0.008

0.01

0.012

0.014

Θ [°

ΨB [W

b]

ΨB = f(Θ) I

0 % of short circuited turns20 % of short circuited turns50 % of short circuited turns70 % of short circuited turns

45 50 55 60 650

0.2

0.4

0.6

0.8

1

1.2x 10-3

Θ

L B [H

]

LB = f (Θ)

0 % of short circuited turns20 % of short circuited turns50 % of short circuited turns70 % of short circuited turns

x linkage versus rotor position for urrent 13 A

on x) versus rotor position for rameter which is needed in dynamic simulations. The

whole working range. The shown in the Fig. 5. The ns of FEM for SRM in equation:

2

dVJ. (1)

tor potential, J is current hase current.

phase inductance versus rotor hase current 13 A

lculation e was also calculated by orque characteristics were ng range. Maxwell’s stress r unit area produced by the

f the motor. The differential

) ( ) )nBHnH ⋅−⋅ . (2)

on normal to the surface at density and H is intensity of

n the static electromagnetic gap Tδ for various rotor

urrent.

70 75 80 85 90°]

IB = 13A

70 75 80 85 90[°]

IB = 13A

207

Fig. 6. FEM analysis of the SRM, the static electromagnetic torque of phase B in the air gap Tδ for various rotor position and constant phase

current 13 A

In the Fig. 7, there is shown the static electromagnetic torque of phase B in the air gap Tδ for various rotor positions and various phase currents.

Fig. 7. FEM analysis of the SRM, the static electromagnetic torque of phase B in the air gap Tδ for various rotor position and various phase

currents

III. MATHEMATICAL MODEL OF SRM As it is known, the flux linkage, phase inductance,

developed electromagnetic torque of SRM are static parameters and depend on both: rotor position and phase current. To calculate dynamic torque of the SRM, these parameters are needed to input into mathematical model of motor.

As it is known, the electromagnetic torque of SRM can be calculated from:

θ∂

Ψ∂

=�i

e

di

T 0 (3)

where i is phase current, Ψ is phase flux linkage and θ is rotor position. To obtain dynamic total torque of SRM, the simulation its mathematical model is needed.

The mathematical model of SRM consists of following equations, if:

- leakage inductances between phases are neglected, - iron losses are neglected, - phase inductance depends on phase current and rotor

position. The voltage equation of one SRM phase is given as:

dt

dRiv ψ+= . (4)

where R is phase resistance, is phase current and ψ is flux linkage. The flux linkage depends on both parameters: phase current and rotor position (ψ = f (i, θ ). Then

dt�d

��

dtdi

i�

dt�d

∂∂+

∂∂=

. (5)

The phase current is calculated from combination of (4) and (5) as:

( )

( )θ

ωθ

θ

,

,

iL

id

idLRv

dtdi ��

�

����

�+−

= . (6)

The real angular speed is calculated from equation:

���

����

�−=

=

m

jloadj TiT

Jdtd

1),(1 ϑω . (7)

where J is the moment of inertia and Tload is load torque.

The SRM is controlled on the base of rotor position, therefore it is as following

�= dtωθ. (8)

IV. DYNAMIC SIMULATION OF SRM Simulation model has been created under Matlab. The

model of single phase is shown in the Fig. 8.

Fig. 8. Dynamic model of the SRM, one phase is shown only

Two methods to control rotor speed have been used: PI controller and hysteresis controller. The PI controller has been implemented in the discrete version therefore the control signal u(k) is given as:

])()([)(1

0

−

=

+=k

iiP ie

TTkeKku . (9)

where k is discrete time instant and T is sampling time. The hysteresis controller have been used to control

phase current. The phase voltage in (4) is given by DC voltage source, which supplied the converter of SRM. By this control the voltage can have three values, if the voltage drops on the transistors and diodes are neglected:

a) v = + Vs, if the phase current i is lower than low limit of the hysteresis region,

b) v = 0, if the phase current is higher than high limit of the hysteresis region,

c) v = - Vs, if the phase current is switched off

45 50 55 60 65 70 75 80 85 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Θ [°]

T δ [Nm

]

Tδ = f(Θ) IB = 13A

0 % of short circuited turns20 % of short circuited turns50 % of short circuited turns70 % of short circuited turns

208

Consequently two control structures have been used in order to simulate SRM's transient. The first one is shown in Fig.9. The coefficients of PI controller have been tuned by trial and error method.

Fig. 9. The block diagram of SRM speed control with PI controller

The second structure is shown in Fig.10. The bandwidth of speed hysteresis controller and current hysteresis controller has been set up at 11 rpm and 0.2 A respectively.

Fig. 10. The block diagram of SRM speed control with PI controller

The SRM investigation has been made for different

speeds. In dynamic simulation, the start up of the SRM has

been simulated for two demand speeds. In the first case the start up of healthy motor has been simulated up to time 0.071 (see Fig. 11) and then, the phase fallout is occurred. The load torque has been kept constant 0.1 Nm. In the Fig. 11 can be seen also comparison of both rotor speed control method PI and hysteresis. After the phase fallout, the speed decreases under demand speed value.

Fig. 11. Dynamic simulation of SRM, the start up of health motor and

the phase fallout occurred.

In the Fig. 12, there can be seen simulation result of the start up of the SRM if two phases have been used instead of three phases. It is obvious that SRM is capable to operate with two phases but the speed ripple is about 91%. In the Fig. 13, there is the start up of the motor up to 1000 rpm with three phases and in time t = 0.13 s one phase fault is occurred.

Fig. 12. Dynamic simulation of SRM, the fault start up of motor if the

phase fallout is occurred in the phase B

Fig. 13. Start up with three phases and fallout is occurred in the phase B

In the Fig. 14, there is simulation of start up with two phases with demand speed 1000 rpm.

Fig. 14. The simulation of start up with two phases with demand speed

1000 rpm

V. EXPERIMENTAL RESULTS To verify simulated dynamic result a experimental

stand with SRM coupled with BLDC load has been used. This stand is shown in the Fig.15. The control board equipped with Digital Signal Controller by Freescale has been used [9], [10].This control board is connected with low power and low voltage converter which supply the SRM. Control loop consist upper speed loop with PI controller and slave current loop made by hysteresis current controllers.

0 0.05 0.1 0.150

50

100

150

200

250

300

350

t [s]

n [rp

m]

n = f(t) mL = 0.1 Nm

nPI+HRnHRndem

The phase fallout

0 0.05 0.1 0.150

50

100

150

200

250

300

350

400

t [s]

n [rp

m]

n = f(t) mL = 0.1 Nm

nHRnPI+HRndem

0 0.05 0.1 0.15 0.2 0.250

200

400

600

800

1000

t [s]

n [rp

m]

n = f(t) mL = 0.1 Nm

nPI+HR

nHR

ndem

The phase fallout

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40

200

400

600

800

1000

t [s]

n [rp

m]

n = f(t) mL = 0.1 Nm

nHRnPI+HRndem

209

Fig. 15. Experimental stand equipped with SRM and BLDC load

In the Fig. 16, there is shown measured speed start up of the health SRM. The load torque has been kept constant 0.1 Nm.

Fig. 16. The measured speed start up of the health SRM.

In the Fig. 17, there are shown the measured phase currents for start up and steady state of the health SRM.

Fig. 17. The measured phase current for start up of the health SRM.

In the Fig. 18, there is shown the measured start up of the health SRM, where demand speed is 1000 rpm.

In the Fig. 19, there are shown the measured phase currents for start up and steady state of the health SRM for demand speed 1000 rpm.

In the Fig. 20, there is shown the start up of the health SRM and fallout of one phase in time 1.9 s, the demand speed is 180 rpm.

In the Fig. 21, there are shown the measured phase currents for start up of the health SRM for demand speed 180 rpm and in time 1.9 s and fallout of one phase.

The speed and currents are measured via exponential filter to remove the noice.

Fig. 18. The measured speed start up of the health SRM.

Fig. 19. The measured phase current for start up of the health SRM.

Fig. 20. The start up of the health SRM and fallout of one phase

Fig. 21. The measured phase current for start up of the health SRM and

fallout of one phase

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

50

100

150

200

250

300

350

t [s]

n, n

dem

[rpm

]

n, ndem = f(t) ndem=300[rpm]

nrealndem

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

5

10

15

20

25

30

35

t [s]

i phA, i

phB, i

phC

[A]

iphA, iphB, iphC = f(t) ndem = 300 rpm

iphA iphB iphC

0 0.2 0.4 0.6 0.8 1 1.20

200

400

600

800

1000

1200

t [s]

n, n

dem

[rpm

]

n, ndem=f(t) ndem=1000 [rpm]

nreal

ndem

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15

20

25

30

35

40

t [s]

i phA, i

phB, i

phC

[A]

iphA, iphB, iphC=f(t) ndem=1000 [rpm]

iphA iphB iphC

0 0.5 1 1.5 2 2.5 30

50

100

150

200

250

t [s]

n, n

dem

[rpm

]

n, ndem=f(t) ndem=180 [rpm]

nrealndem

The phase fallout

0 0.5 1 1.5 2 2.5 30

5

10

15

20

25

t [s]

i phA, i

phB, i

phC

[A]

iphA, iphB, iphC=f(t) ndem=180 [rpm]

iphA iphB iphC

The phase fallout

210

VI. CONCLUSION In this paper, the static and dynamic analysis of the

SRM fault operations have been presented. The SRM static parameters have been calculated by means of FEM for health and short circuit phase. The mathematical model of the SRM has been derived and used for dynamic simulation. The dynamic health and the phase fallout start up of the motor is analyzed by simulations and the results have been compared with measured ones.

On the base of this analysis verification, the simulation model can be used for other fault operation investigation and some recommendations can be done.

ACKNOWLEDGMENT This work was supported by the Slovak Research and

Development Agency under the Contract No. SK-RO-0016-10 and R&D operational program Centre of excellence of power electronics systems and materials for their components II. No. OPVaV-2009/2.1/02-SORO, ITMS 26220120046 funded by European regional development fund (ERDF). Authors also like to thank to Freescale Semiconductors in Czech Republic for their support.

REFERENCES [1] T.J.E. Miller, Electronic Control of Switched Reluctance

Machines. Oxford (U.K.): Newnes, 2001. [2] Miller, T. J. E. Switched Reluctance Motors and their Control,

Magna Physics, 1992 [3] Pyrhonen, J.; Jokinen, T.; Hrabovcova, V.: Design of rotating

electrical machines, John Wiley & Sons, 2008 [4] Krishnan, R.: Switched Reluctance Motor Drives – Modeling,

Simulation, Analysis, Design, and Applications, CRC Press LLC, FLA, USA, 2000.

[5] B. Schinnerl and D. Gerling, "Analysis of winding failure of switched reluctance motors," in Proceedings of the IEEE International Electric Machines and Drives Conference (IEMDC '09), Miami (USA), pp. 738-743.

[6] Rare� Terec, Ioana Ben�ia, Mircea Ruba, Loránd Szabó, Pavol Rafajdus “Effects of Winding Faults on the Switched Reluctance Machine's Working Performances,” LINDI 2011 • 3rd IEEE International Symposium on Logistics and Industrial Informatics • August 25–27, 2011, Budapest, Hungary.

[7] Rare� Terec, Ioana Ben�ia, Mircea Ruba, Loránd Szabó, Pavol Rafajdus: On the Usefulness of Numeric Field Computations in the Study of the Switched Reluctance Motor's Winding Faults, ISCIII 2011• 5th International Symposium on Computational Intelligence and Intelligent Informatics • September 15-17, 2011, Floriana, Malta

[8] Pavol Rafajdus, Valeria Hrabovcova, Peter Hudak: Investigation of Losses and Efficiency in Switched Reluctance Motor, EPE-PEMC 2006, Portoroz, Slovenia

[9] DiRenzo, M. T.: „Switched Reluctance Motor Control – Basic Operation and Example Using the TMS320F240“, Application Report, Texas Instruments, 2000

[10] Visinka, R., Balazovic, P.: „3-Phase Switched Reluctance Motor Control with Encoder Using DSP56F80x“, MOTOROLA Inc., 2002

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