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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
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[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.
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