Physical Modeling of Switched Reluctance Motorsusing Modelica

Y. Ji J. Bals

Abstract—This paper presents a novel Modelica library forphysical modeling of switched reluctance machines. In orderto deal with the nonlinear characteristics of switched reluc-tance drives, an analytical approximation function is appliedwhen building a motor model. Furthermore, the look-up tablebased approach derived by the finite element method forcomputing the nonlinear model is also considered. Comparedwith other modeling approaches, physical modeling using theobject-oriented modeling language-Modelica often exhibits asignificant progress regarding model reusability, flexibility andrange of modeling. One application example with a 16 stator 12rotor poles 4 phase witched reluctance machine is presented toillustrate the use of the developed Modelica switched reluctancemachine library.

Index Terms—switched reluctance machine, modeling andsimulation, motion control.

I. INTRODUCTION

ASwitched reluctance machine is a doubly salient polemachine fed by an unipolar power converter. Concern-

ing its simplicity, robustness, low cost and high efficiency, theswitched reluctance machine become a good competitor toconventional ac machines in aircraft and automobile industry[1]. Some new research works have presented the possibilityto use the switched reluctance machine as generator in moreelectric aircraft [2] and as major actuator in the upcomingelectric vehicle. Computer modeling and simulation canease the whole product development process and controllerdesign. Model based design is getting more and more at-tention in the last years. However, current modeling toolssupporting switched reluctance machines e.g. Simpower byMathworks does not provide users full flexibility to buildmodels. In this work, a switched reluctance drive libraryhas been made using Modelica- an object oriented modelinglanguage to achieve the maximum flexibility, motor typeconverge and model reusability. In this library, all neededfundamental components for modeling switched reluctancemachine are addressed. Modelica is a non-proprietary, object-oriented, equation based language to conveniently modelcomplex physical systems containing, e.g., mechanical, elec-trical, electronic, hydraulic, thermal, control, electric power.Modelica Simulation Environments are available commer-cially and free of charge, such as CATIA Systems, Dymola,LMS AMESim, JModelica.org, MapleSim, MathModelica,OpenModelica, SCICOS, SimulationX. Modelica models canbe imported conveniently into Simulink using export featuresof Dymola, MapleSim and SimulationX. or process-orientedsubcomponents. Considering the good support of the newestModelica standard, the Dymola system is selected to imple-ment the switched reluctance machine library.

Y. Ji and J. Bals are with the Department of System Dynamics andControl, Institute of Robotics and Mechatronics, German Aerospace Center,Muenchnerstr. 20, Wessling, Germany yang.ji@dlr.de

6 2 Fundamental of Switched Reluctance Drives

q

L

Lmax

Lmin

unaligned unalignedaligned

beginningof overlap

beginning offull overlap

beginningof overlap

tactive

tactive

tflat

q

T

0 180 360(°elec.)

Figure 2.4: Phase inductance and torque as a function of rotor position

On the electrical side, switched reluctance machines are described by the generalized

machine equation,

v(t) = Ri(t) +dΨ(t)

dt(2.2)

Equation 2.2 is generally valid for both linear and nonlinear operations of switched reluc-

tance machines. For the linear operation, (2.2) is developed further by the assumption

that the flux-linkage Ψ is a product of inductance L and current i and the inductance

characteristic L(θ) remains unchanged for all current levels (no magnetic saturation). The

voltage equation with a link to the mechanical side via rotor speed is expressed by (2.3).

Fig. 1. Ideal inductance function of rotor position

II. BASIC CHARACTERISTICS OF SRM

A. Operation principle

In contrast to conventional DC-machine, synchronous andinduction machine whose output torque can be presentedby the vector product between current and magnetic field,switched reluctance machines work on the principle of re-luctance force. The torque is developed from the physicalnature of magnetic paths which always attempt to minizethe magnetic resistance in the magnetic loop [3].

For the basic understanding, switched reluctance machinesare often analyzed assuming linear operation without mag-netic saturation in the iron lamination. This greatly simplifiesthe mathematical machine model since without the magneticsaturation the machine characteristic, i.e. phase inductance,can be considered as a function of rotor position only. In thelinear consideration, the phase torque product of the switchedreluctance machine is described as

T =1

2i2dL(θ)

dθ(1)

Fig.1 shows the phase inductance curve as a function ofrotor position for one electrical period. It starts at the rotorposition with the minimum inductance defined as ”unalignedposition”.

According to Eq. 1, torque can be produced in the positionwhere the inductance gradient dL(θ)/dθ is nonzero. Torquecan be produced for both negative and positive directions.This also implies that switched reluctance machines arebasically capable of breaking or generating operation. Notethat the input current influences only the amplitude of theoutput torque due to the quadratic term i2. Hence, theonly possibility to command the direction of the outputtorque is controlling the phase excitation period according tothe rotor position. The electrical characteristic of switchedreluctance machines can be described by the generalizedmachine equation

2.1 Operation Principle and Characteristics 9

By applying differentiation, the instantaneous torque T is expressed as

T (i, θ) =dW

dθ=

∫ i

0

∂Ψ(i, θ)

∂θdi (2.5)

As a conclusion, a mathematical model of a switched reluctance machine with nonlinear

operation can be derived from the nonlinear flux-linkage characteristic Ψ(i, θ). By applying

(2.5) to the flux-linkage characteristic, the torque characteristic as a function of rotor

position for different currents can be determined, as depicted on the right of Fig. 2.6.

Note that the representation using the flux-linkage-current diagram is widely employed in

literature to illustrate the nonlinear torque production of switched reluctance machines

[Sta95][Kri01][Mil01].

By considering a switched reluctance machine as a system with state variables, there are

totally four variables representing the behavior of the machine, i.e. current, flux-linkage,

rotor position and torque as summarized in Fig. 2.7. Since the direction of output torque

depends only on the rotor position, an unambiguous relationship between the electrical

and mechanical side can be drawn only by using rotor position as an input variable.

In addition, both current and rotor position can be accurately measured using physical

sensors, e.g. hall sensors for current measurement and resolvers for rotor position. As

a result, two fundamental characteristics for describing switched reluctance machines are

preferably formulated as a function of current and rotor position, Ψ(i, θ) and T (i, θ) as

shown in Fig. 2.7(right).

These characteristics can be determined by analytical calculations, finite element sim-

ulations (FEM) [Moa90][Ome97] or experimental measurements [Kri89a] [Ras98][Che01]

[Fue06]. During the design stage and optimization, analytical calculations or finite element

simulations are generally used to study the performance and characteristics of the designed

machines. For the design verification and control purposes, experimental measurements

are preferred since the measured data incorporate imperfections in manufacturing and

physical effects often neglected in finite element calculations.

rotor position

Sta

teva

ria

ble

so

fS

RM

s

me

ch

.

flux-linkage

current i

Y

q

ele

c.

torque T0

180

360

0

100

200

300-300

-200

-100

0

100

200

300

0

180

360

0

100

200

3000

0.05

0.1

0.15

0.2

0.25

torq

ue

T

flux-lin

kageY

current i rotor position q current i rotor position q

T i( , )qY ( , )i q

Figure 2.7: State variables and characteristics of a switched reluctance machineFig. 2. Magnetic flux and torque functions of current and rotor position

v(t) = Ri(t) +dΨ(t)

dt(2)

Substituting the Ψ(t) by L(θ)i(t) Eq. 2 can be developed to

v(t) = Ri(t) + L(θ)di(t)

dt+ i

dL(θ)

dθ

dθ

dt(3)

where dθ/dt = ω The last term can be considered asinduced back-emf. However, it should be noted that theproduct of the phase current and the induced back-emfin switched reluctance machines does not represent themechanical power conversion in the same way like in theconventional machines, since only the half of the power flow-ing into the equivalent back-emf voltage source is convertedinto mechanical energy while the other half is stored in aform of magnetic energy. When the machine runs with highvelocity, back-emf will be dominant in the Eq. 3. As result,the maximum speed of a switched reluctance machine canbe approximately considered as proportional to the phasevoltage. The description in Eq. 2 is generally valid forboth linear and nonlinear operations of switched reluctancemachines.

B. Modeling approaches

To model switched reluctance machines in practical work-ing conditions, the magnetic saturation has to be treated.Some main factors, which affect the performance of aswitched reluctance machine, are machine structure, rotorand stator poles, magnetization characteristic of the lamina-tions and control strategy. The highly complex characteristicis presented by two nonlinear relations. As first one, themachine flux linkage is dependent on the stator current androtor angular position such as

ψ = ψ(i, θ) (4)

The second nonlinear functions reveals that the electro-magnetic torque produced by each phase of the switchedreluctance machine is determined by

τ = τ(i, θ) (5)

The motor performance is fixed once these two nonlinearrelationships are known. Such kind of state variable de-pendencies can be presented by Fig.2. These characteristicscan be typically determined by analytical calculations, finiteelement methods [4], [5] or experimental measurements [6],[7], [8]. The Modelica switched reluctance machine library

physical dimensions and characteristics of the SRM. The

details usually required for this calculation are: laminations

dimensions and magnetic characteristics, air gap length, stator

and rotor poles arcs, size and number of turns of the stator

windings. These construction details are available only if you

are designing your own SRM. Otherwise, they are not avail-

able from the manufacturer.

Finite-element computation of the SRM magnetization

curves is also a time-consuming process.

3) Analytical expression of the magnetization curves: For

converter and control system design purpose, it would be con-

venient and desirable to calculate the magnetization curves

from main parameters normally available or easily measurable.

The details on the machine geometry will be supposed to be

those of a “standard construction” SRM. In this way, the

generic model can represent a category of SRM of standard

construction having common main parameters.

In the proposed generic model, the extreme magnetization

curves, corresponding to aligned and unaligned rotor positions,

are approximated by analytical functions as shown in Fig. 5.

The magnetization curve at unaligned rotor position (q axis)

is represented as a straight line with slope equal to the mini-

mum inductance Lq:

(3)

The magnetization curve at aligned rotor position (d axis) is

a nonlinear function of the stator current i:

(4)

where Ldsat is the d-axis saturated inductance, and A and B are

constants determined by conditions at i = 0 and i = Im (Im is the

maximum current in stator windings).

In supposing that the machine is really saturated at i = Im,

one have and the constants A and B can be deduced

as:

(5)

(6)

where Ld is the d-axis non-saturated inductance and �m is the

flux linkage at i = Im.

The intermediate magnetizations curves corresponding to

rotor positions between the aligned position (d-axis) and the

unaligned position (q-axis) can be deduced from the two

extreme curves �d and �q by using a nonlinear function f(�)

that approximately represents the variation of magnetic flux

linkage in function of the rotor position in a standard structure

SRM. This nonlinear function can be written for a general case

as:

(7)

where Nr is the number of rotor poles.

The magnetization characteristic of the SRM can be thus

expressed as a function of stator current and rotor position:

(8)

D. Torque characteristicThe SRM electromagnetic torque is equal to the sum of the

individual torques developed in each phase. Due to the nonlin-

earity of the magnetization curves, the developed torque is a

nonlinear function of the stator current and the rotor position.

The electromagnetic torque developed by one phase of the

SRM can be calculated as the derivative of the machine co-

energy:

(9)

where W’ is calculated as

(10)

In case where the magnetization curves are calculated from

experimental data or from finite-element results, the torque

characteristic Te(i,�) can be numerically calculated using Eq. 9.

Figure 6 shows the SRM torque characteristic calculated

from the magnetization curves shown in Fig. 4.

0 Im

�m

i

�

Aligned

Unaligned

�q

�dSlope = Ld

Slope = Lq

Slope = Ldsat

Fig. 5 Aligned and unaligned magnetization curves used to build the SRM ana-

lytical model

�q Lqi=

�d Ldsati A 1 eBi–

–� �+=

eBIm–

0�

A �m LdsatIm–=

B Ld Ldsat–� � �m LdsatIm–� ��=

f �� � 2Nr

3 �3�� ��33Nr

2 �2�� ��2– 1+=

� i �� � Lqi Ldsati A 1 eBi–

–� � Lqi–+ �f �� �+=

Te i �� ����

W i �� �=

W i �� � � i �� � id0

i

�=

0 5 10 15 20 25 30 35 40 450

50

100

150

200

250

300Machine SRM 6/4 (60 kW)

Couple

(N

.m)

Position du rotor (degre)

Fig. 6 Torque characteristic calculated from the magnetization

curves shown in Fig. 4.

i = 50 A

i = 100 A

i = 150 A

i = 200 A

i = 250 A

i = 300 A

i = 350 A

i = 400 A

i = 450 A

1558

Fig. 3. Aligned and unaligned magnetization curves for building SRManalytical model

presented in this paper can deal with all three modeling meth-ods. For fast prototyping the converter and control strategy,analytical approximation of the magnetization curves andtorque characteristic is very convenient and desirable. Bythe analytical approximation approach [9], the magnetizationflux performance can be presented by

ψq = Lqi

ψd = Ldsati+A(1 − e−Bi)

f(θ) = (2N3r /ψ

3)θ3 − (3N2r /ψ

2)θ2 + 1

ψ = Lqi+ [Ldsati+A(1 − e−Bi) − Lqi]f(θ) (6)

where

A = ψm − LdsatIm

B = (Ld − Ldsat)/(ψm − LdsatIm) (7)

Furthermore, the electromagnetic torque results from thesum of the individual torques developed in each phase. Theanalytical expression for the torque of each phase can bewritten as

τe(i, θ) = [0.5(Ldsat − Lq)i2 +Ai+A(1 − e−Bi]f ′(θ)

f ′(θ) = (6N3r /φ

3)θ2 − (6N2r /φ

2)θ (8)

The parameters used in Eq. 6-Eq. 8 are explained in Tab. Iand graphically interpreted in Fig. 3.

TABLE ISYMBOLS USED FOR ANALYTICAL EXPRESSION OF THE

MAGNETIZATION CURVES

Parameter DescriptionLq Non-saturated inductance at unaligned positionLd Non-saturated inductance at aligned positionLdsat Saturated inductance at aligned positionIm Maximum current in stator windingsψq Magnetization curve at aligned positionψd Magnetization curve at unaligned positionψm Flux linkage with imNr Rotor pole number

III. IMPLEMENTATION OF MODELICA SWITCHEDRELUCTANCE DRIVE LIBRARY

The components needed for modeling a switched reluc-tance drive mainly contain power converter, air gap, mechan-ical parts, control unit, communication bus system, human

Fig. 4. Graphical interface to model an air gap

machine interface and power supply. Using the Modelicastandard library, which covers a wide range of infrastructuralmodel in numerous physical domains, the major parts ofswitched reluctance machine library can be easily modularlyestablished.

A. Model of rotor

The rotor of switched reluctance machine primarily com-prises a number of air gaps. To model the air gap of aswitched reluctance machine, the analytical representationdescribed in the last section is applied. Typically, the alignedand unaligned magnetization curves in Fig. 3 are derivedby finite element method or measurement. The result tablescan be imported directly into the Modelica library. After-wards all the parameters needed in the analytical model areautomatically computed and put into the machine model.The rotor of a switched reluctance machine is modeled byobject oriented approach, which allows to easily build adesired rotor model by putting air gap models together. Thesetup window to model an air gap is depicted in Fig. 4.A rotor model with 12 rotor poles is depicted in Fig. 5.The rotor model in Fig. 5 primarily consists of 4 air gapsbesides some current sensor, data bus system and machineinertial. Additionally, some test blocks for verifying theanalytical representation of magnetization curves are offeredin the library. For example, the magnetization performanceby analytical modeling approach is depicted in Fig. 6, wherethe phase current i = 200A and the rotor position variesfrom 0 to 30 degree.

B. Model of control unit

Output torque of switched reluctance machines is com-manded by two variables, i.e. excitation level represented bycurrent or flux-linkage and rotor position. Therefore, a high-grade torque controller must possess two feedback signals,for either current or flux-linkage and for rotor position, toobtain a full access on output torque. There are two majorcontrol strategies e.g current based torque control and directtorque control [10], [12]. The major difference between twocontrol strategies is that output torque is directly managedas a control variable and there is no inner current control

L=L(theta,i)

onePhaseStator1

L=L(theta,i)

onePhaseStator2

L=L(theta,i)

onePhaseStator3

torq

ue

tau

iner

tia

J=1e

-6

Mod

Mod

pow erDeMultiplex3Ppow erDeMultiplex3P

pow erDeMultiplex…pow erDeMultiplex…

angl

eSen

sor ph

i

A

currentSensor

A

currentSensor1

A

currentSensor2

torq

ueS

enso

r

tau

Mod

ModA

currentSensor3

L=L(theta,i)

onePhaseStator4

Taumeasure

Anglephase1

Anglephase2

Phimeasure

Anglephase3

Anglephase4

Imeasure1

Imeasure2

Imeasure3

Imeasure4

flange_b1

positiveP…

negative…

cont

rolB

us Mechanical

Electrical

Fig. 5. Rotor model from a 12 rotor poles switched reluctance machine

0 5 10 15 20 25 300.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46Inductance function verification

[Wb]

RotorPosition

Fig. 6. Testing of magnetization curve

2.4 Control of Switched Reluctance Drives 13

states. Note that the sign of the current slope in freewheeling states is decisive for selecting

the proper excitation scheme. Applying a wrong excitation scheme may lead to damages

due to overcurrent. Hence, the controller must be designed to be able to assign proper

excitations corresponding to the current operating mode. Examples of control solutions

capable of both motoring and generating modes are presented in [Fue05b] and [Car04].

2.4 Control of Switched Reluctance Drives

Output torque of switched reluctance machines is commanded by two variables, i.e. excita-

tion level represented by current or flux-linkage and rotor position. Therefore, a high-grade

torque controller must possess two feedback signals, for either current or flux-linkage and

for rotor position, to obtain a full access on output torque. Fig. 2.10 shows two generalized

forms of torque controllers for switched reluctance machines [Vas98]. The main difference

between both controllers is the secondary control variable, current or flux-linkage.

- Current-based torque controller

q

SRMConverter

Tref

iph

irefph sph

vdc (optional)

Current referenceand

Commutationcontrol

(look-up table)

q

SRMConverterFlux-linkage

controller

(PWM)

Tref

iph

sph

vdc (optional)

Flux-linkagereference

andCommutation

control

(look-up table)Flux-linkage

estimator

Yph

Currentcontroller

(hysteresis,delta mod.or PWM)

refphY

a) Current-based torque control

b) Flux-linkage-based torque control

Figure 2.10: Fundamental torque controllers for switched reluctance machines [Vas98]

Fig. 7. Schematic current based torque control

loop any more. In this paper, only the current based torquecontrol unit is considered. The schematic diagram of currentbased torque control is depicted in Fig. 7. Besides analyticalmodeling approach, the result of the finite element methodfor modeling the magnetic and mechanic characteristics inEq. 4 and 5 can also be imported into the library by lookuptables. Based on those lookup tables, the model of a switchedreluctance machine can also be done. However, those kindsof models are not quite suitable for control design due to highcomputation cost. The major components in a current basedtorque control unit are power converter, current controllerand some signal sensors for current and rotor angle.

Fig. 8. Determination of phase related angle

Asymmetric bridge type power converter is addressed inthe Modelica switched reluctance machine library. UsingModelica standard library, a power converter depicted in Fig.9 can be easily modeled. Even more detail model convergingthermal effects and power loss could also be treated. Sincethe turn on/off angles of each phase in rotor play a crucialrole for torque control. The current angle in relation to eachphase/rotor pair has to be conducted by the measured rotorrotation angle. Taking the example of a 16 stators 12 rotorpoles switched reluctance machine, the angle between rotorand phase i , θmi with the assumption that the rotor at thestarting point shown in Fig. 8 can be described as

θmi = Θ mod 30 − (i− 1) × 7.5 (9)

where Θ is the measured rotor rotation angle.Besides major components to build a switched reluctance

machine, the infrastructure models of current controller pro-vide user a convenient way to implement own control unit.The hysteresis current regulator offers a very fast dynamicresponse by keeping the output current in a given hysteresisband. Its switching frequency varies considerably with torquespeed operation points and rotor position [11]. The hysteresisbased approach for current control is incorporated in theModelica library. The hysteresis band of current control ismade by the Hysteresis block from Modelica standard library.Furthermore, some algorithms of direct torque control willalso be included in the library.

In order present the physical model in reality, all data ofcontrol commands and sensor measurements are collectedin a special bus system, which is implemented by theexpandable connector in Modelica. A structural overview ofthe Modelica switched reluctance machine library is shownin Fig. 12. Additionally, the Modeling templates for threemostly used motor types (6/4, 8/6 16/12) are already includedin the Modelica switched reluctance machine library.

IV. APPLICATION EXAMPLE: MODELING OF A 16/12 4PHASES SWITCHED RELUCTANCE MACHINE

As demonstration, the Modelica switched reluctance ma-chine library has been applied to build a test rig of 16stators/12 rotors 4 phases switched reluctance machine. Thetest rig in Fig. 13 comprises a human machine interfacefor defining desired current and turn on/off angle, a powersupply, a motor control unit including current controller

idealClosingS

witch

idea

lDio

de

idea

lDio

de1

idealClosingS

wit…

u

dc

NVdc

PAmat…

NAm

Fig. 9. Asymmetric bridge power converter

hysteresis

uL… uH…

hysteresis1

uL… uH…

hysteresis2

uL… uH…

-

feedback

-

feedback1

-

feedback2

-

feedback3

hysteresis3

uL… uH…

Imeasure1

Imeasure2

Imeasure3

Id

Id

Id

Imeasure4

Id

y

cont

rolB

usImeasure

Idesired

Fig. 10. Implementation of current controller

currentController

uLow uHigh

powerMultiplex3PpowerMultiplex3P

powerMultiplex3NpowerMultiplex3N

Ph…

Ph…

Ph…

Ph…

CurrentIs

Angleon

Angleoff

Angleon

Angleoff

Angleon

Angleoff

Angleon

Angleoff

Anglephase1

Anglephase2

Anglephase3

Anglephase4

pin_p pin_n

positiveP

negative

CurrentIs

Ang

les

Fig. 11. Control unit for a 4 phase switched reluctance machine

Fig. 12. Overview of the switched reluctance machine library

and the 16/12 switched reluctance machine as well as amechanical load. The test rig is depicted in the Fig. 13.The parameters used for the test rig are listed in Tab. II.Two test cases have been performed. With the first test case,the switched reluctance machine is simulated without anyload to indicate the idealized operation boundary. Simulationresults of phase current, output torque and motor velocityare depicted in Fig. 14. With the second test case, a negativetorque has been placed as load at 0.1s. The performance ofthe motor is shown by the phase current, output torque andvelocity simulation results in Fig.15.

TABLE IIPARAMETERS IN THE DEMONSTRATION

Parameter ValueLq 0.9e-3 HenryLd 40e-3 HenryLdsat 0.2e-3 HenryIm 450 Ampereψm 0.5 WeberNr 12Rs 0.02 Ohm

Current Command 200 ATurnon angle 18 DegTurnoff angle 25 Deg

Load -1000 Nm

V. CONCLUSION

In this paper, a novel Modelica library for modelingswitched reluctance machines are presented. The basic com-ponents to build a arbitrary type of switched reluctance ma-chine have been implemented using object oriented physicalmodeling approach. Additionally, control units for switchedreluctance machines are also partly incorporated e.g. hystere-sis current based torque controller. The work addressed hereis a part from an ongoing project of a Modelica Power Drivelibrary, which will contain mostly up-to-date machine types

Virtual Switched Reluctance Motor (16/12) Test Rig

inertia

J=0.5

HMI

Motion ControlPow er Sup… SRM 16…

torqueStep

time

cont

rolB

us

Fig. 13. Testrig of a 16/12 switched reluctance machine

0.00 0.05 0.10 0.15 0.20

0

100

200

Phase current

[A]

0.00 0.05 0.10 0.15 0.20-1000

0

1000

2000

3000

4000

Output Torque

[N.m

]

0.00 0.05 0.10 0.15 0.20

0

100

200

Machine speed

[rad

/s]

Fig. 14. Simulation result without load

and their corresponding intelligent controllers. In the nearfuture, the direct torque control unit will also be implementedin the Modelica switched reluctance machine library.

ACKNOWLEDGMENT

The research leading to these results has received fundingfrom the European Union’s Seventh Framework Programme(FP7/2007-2013) for the Clean Sky Joint Technology Initia-tive under grant agreement Nr. CSJU-GAM-SGO-2008-001.

REFERENCES

[1] R. Krishnan, Switched Reluctance Motor Drives. CRC Press, 2001.[2] L. Han, J. Wang, and D. Howe, “Small-signal stability studies of

270v dc power system for more electric aircraft employing switchedreluctance generator technology,” 25th Internatinal Congress of theAeronautical Sciences, 2006.

[3] T. J. E. Miller, Switched reluctance motos and their control. MagnaPhsics Publishing, 1993.

[4] M. Moallem and C. Ong, “Predicting the torque of a switchedreluctance machine from its finite element field solution,” IEEETransactions on Energy Conversion, vol. 5, 1990.

[5] A. Omekanda, C. Broche, and M. Renglet, “Calculation of the electro-magnetic parameters of a switched reluctance motor using an improvedfembiem application to different models for the torque calculation,”IEEE Transactions on Industry Applications, vol. 33, pp. 914–918,1997.

0.00 0.05 0.10 0.15 0.20

0

100

200

Phase current[A

]

0.00 0.05 0.10 0.15 0.20-1000

0

1000

2000

3000

4000

Output Torque

[N.m

]

0.00 0.05 0.10 0.15 0.20-50

0

50

100

150

200

Machine speed

[rad

/s]

Fig. 15. Simulation result with predefined load profile

[6] R. Krishnan and P. Materu, “Measurement and instrumentation of aswitched reluctance motor,” IEEE Industry Application Society AnnualMeeting, 1989.

[7] P. O. Rasmussen, G. Andersen, L. Helle, F. Blaabjerg, and J. K. Peder-sen, “Fully automatic characterization system for switched reluctancemotors,” ICEM, 1998.

[8] N. H. Fuengwarodsakul, S. E. Bauer, and R. W. D. Doncker, “Charac-teristic measurement system for automotive class switched reluctancemachines,” European Power Electronics and Drives Journal, vol. 16,2006.

[9] H. Le-Huy and B. P., “Versatile nonlinear switched reluctance motormodel in simulink using realisic and analytical magnetization charac-teristics,” 31st Annual Industrial Electronics Society Conference, 2005.

[10] A. D. Cheok and Y. Fukuda, “A new torque and flux control methodfor switched reluctance motor drives,” IEEE TRANSACTIONS ONPOWER ELECTRONICS, vol. 17, 2002.

[11] F. Blaabjerg, P. C. Kjaer, P. O. Rasmussen, and C. Cossar, “Improveddigital current control methods in switched reluctance motor drives,”IEEE Transactions on Power Electronics, 1999.

[12] R. Inderka and R. Doncker, “Ditc-direct instantaneous torque controlof switched reluctance drives,” IEEE Transactions on Industrial Ap-plications, vol. 39, 2003.