Dynamic Simulation of Maximizing the Starting Torque for Super-High-Speed Drive of a 4-2 Switched Reluctance Motor

8/4/2019 Dynamic Simulation of Maximizing the Starting Torque for Super-High-Speed Drive of a 4-2 Switched Reluctance Mo

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Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1110

978-1-4244-1736-0/08/$25.00 2008 IEEE 1

Dynamic Simulation of Maximizing the StartingTorque for Super-High-Speed Drive of

a 4/2 Switched Reluctance MotorIsmet Rahmad Kartono, Kouta Kajiwara, and Hideo Dohmeki*, Member, IEEE

Dept. of Electrical and Electronic Engineering, Musashi Institute of Technology1-28-1, Tamazutsumi, Setagaya, Tokyo 158-8557, Japan

Tel : (+81)-3-3703-3111, Fax : (+81)-3-5707-2215e-mail* : [email protected]

Abstract-modification of the structure and the operationprinciple of Switched Reluctance Motor (SRM) would make itpossible to obtain super-high-speed drive. Therefore, we adopt 4/2structure of SRM. In this paper, we examine the optimum designand the dynamic characteristics of 4/2 SRM for super-high-speeddrive by maximizing the starting torque. In this design, theparameters, such as the outside diameter of stator and the length

of gap, are fixed. We analyze the structure of 4/2 SRM formaximizing the starting torque using the two-dimensional finiteelement method (2D FEM), and simulate the dynamics model of4/2 SRM at the maximum starting torque usingMATLAB/SIMULINK.

I. INTRODUCTIONRecently, there is a demand for a super-high-speed motor

drive system. There are two reasons. First, the load machine of

electric motor or the drive machines of a generator essentially

need to be driven at super-high speed. Secondly, production

cost reduction is required. Therefore, the electric machines

such as the small gas turbine, the direct connection turbocompressor, motor driver for hybrid cars must be smaller and

lighter. The motors used in these machines are usually the

permanent-magnet synchronous motor (PMSM) and the

induction motor (IM). However, these kinds of motor are not

entirely suitable for super-high-speed drive according to their

characteristics.

In the PMSM, the scattering of the permanent magnet occurs

because of installation of a permanent magnet on the surface of

the rotor. A maintenance ring becomes necessary to prevent the

scattering. Therefore, the permanent magnet makes the

structure of the rotor complex and this leads to an increase in

the production cost. Moreover, the existence of the permanent

magnet on the rotor also causes an increase in heat. However,

although the structure of the IM is stronger then that of the

PMSM, the existence of wiring in the rotor makes the rotor

even hotter. Moreover, these two motors have a large induced

electromotive force that increases the rotating losses.

Therefore, attention is paid to the switched reluctance motor

(SRM). So far, SRM was only used in limited-purpose

applications, such as starters and the fuel pumps in aircraft.

However, lately, it is hoped that the SRM can be used in many

applications such as drive motor of the electric vehicles and

vacuum cleaners, following the improvement of power

electronic technology in recent years and the progress of

element technology, such as silicon steel sheets.

One of the characteristics of SRM is that, the rotor and stator

are assembled by laminated silicon steel sheet in a salient-pole

shape. Therefore, compared to the PMSM and the IM, the

SRM do not utilize a permanent magnet or a winding on therotor that makes the structure more simple and solid. Moreover,

in addition to the fact that the SRM can become smaller and

lighter, the cost is low and the rotation inertia is small. And

also, since SRM does not have a permanent-magnet, it can be

used in severe environmental conditions such as high-

temperature engine rooms. Furthermore, it also has a small

induced electromotive force and low rotary losses. For these

reasons, the SRM is considered to be suitable for the super-

high-speed motor drive systems.

This research studies the motor drive system for a super-

high-speed drive that adopted a 4/2 structure of SRM (4/2

SRM) consist of 4 poles in the stator and 2 poles in the rotor.This papers report a result study about maximum starting

torque of rotor shape with a fixed gap length, by using the two

dimension finite element method (2D FEM). Moreover, it also

reports a result study about the dynamic simulation of SRM

using MATLAB/SIMULINK at maximum starting torque.

II. OVERVIEW OF 4/2SRMThe structure and the parameters of 4/2 SRM are shown in

Fig. 1 and Fig. 2, respectively. The winding on the stator

consist of two phases winding that serial connection with

concentrated-type of winding at each pole. The winding at each

pole made of 16-turn coils with winding resistance is 0.19,Inductance value is 0.34 mH (1 kHz) and the thickness of the

both rotor and stator is 0.2 mm. The shape of the rotor is

asymmetrical because this 4/2 SRM is designed to rotate in a

counter clockwise direction (CCW).

III. ANALYSIS OF 4/2SRM STARTING TORQUEThe static magnetic field is analyzed by 2D FEM at

maximum starting torque. The analysis model is shown in Fig.

2. it is assumed that the unaligned position of the rotor in Fig. 2


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Proceedings of the 2008 International Conference on Electrical Machines

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is at 0o and the aligned position is at 90o. The static magnetic

field is analyzed by supplying DC current to the A-phase and

changing it to a CCW direction every 3.6o, from 0o to 90o.

The analysis result of static characteristic is shown in Fig. 3.

From this figure, the torque is small in the interval 0o to 30o. It

means starting is difficult unless the torque is added from

outside. Therefore, the starting torque is defined from 0o to 30o,the stator is analyzed by a 2-D FEM when starting torque is at

the maximum condition with some fixed parameters, such as

the outside diameter of the stator and the gap length. The

parameters which varing are the width of the stator yoke Wsy,

the width of the stator pole Wsp, the width of the rotor pole Wrp,

the height of the rotor pole Hrp, the opening of the rotor pole

Orp, and the width of the rotor Wr. the static magnetic field is

analyzed by only paying attention to one parameter at one time.

First, attention is paid to the parameter of the stator. The

width of the stator yoke is varied every 1 mm from 16 mm to

19 mm, and the width of the stator pole every 1.3 mm from 6.2

mm to 10.1 mm.Fig. 4 and Fig. 5 show when the width of the stator yoke and

the stator pole are varied, respectively. From Fig. 4, a

remarkable increase of the starting torque is not observed.

However, in Fig. 5, an increasing is seen. It means that the

generate place of torque waveform and maximum torque is

shifted because the generated magnetic flux that excited from

the stator pole increases. However, the starting torque increase,

the characteristic of the torque waveform it self changed. Here,

the static magnetic field is analyzed when the generated

magnetif flux assumes to be constant. Moreover, the generated

place of maximum torque shifted because the maximum torque

is generated when the stator and the rotor poles are nearly the

aligned position.After that, attention is paid to the parameters of the rotor.

The width of rotor is varied every 1.3 mm from 6.2 mm to 10.1

mm, the height is varied at 1 mm intervals from 0 mm to 6 mm,

the opening of the rotor pole is varied every 6o from 66o to 90o,

and the width of the rotor is varies every 1.1 mm from 11.8

mm to 18.4 mm.

.

Fig. 2. Analysis model of 4/2 SRM

Fig. 1. The structure of 4/2 SRM

TABLE I

The parameters of 4/2 SRM

Fig. 3. Analysis result of static characteristic

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90

Rotor position [deg]

TorqueT

[Nm]

AnalysisMeasured

Items Dimensions

Stator outside diameterD s [mm] 60

Stator yoke width Wsy [mm] 16

Stator salient pole width Wsp [mm] 7.5

Stator yoke thickness Tsy [mm] 40

Air gap width Wair[mm] 0.2

Rotor outside diameterD r[mm] 21.5

Rotor salient pole width Wrp [mm] 7.5

Rotor salient pole heightHrp [mm] 2

Rotor yoke thickness Try [mm] 40Rotor salient pole opening O rp [deg] 66

Rotor width Wr[mm] 14

Shaft diameterD sh [mm] 6

Coil

Rotor

0deg

90deg


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Fig. 6, Fig. 7, Fig.8 and Fig. 9 show when the width of the

rotor pole, the height of the rotor pole, the opening of the rotor

pole and the width of the rotor are varied, respectively. From

Fig. 6, a remarkable increase of the starting torque was not

observed, although the generated part of maximum torque is

shifting. The maximum torque is generated when the rotor pole

and the stator pole are nearly the aligned. This result is similarto the variation in the width of the stator pole. From Fig. 7, the

starting torque increased exceedingly at 1 mm intervals.

According to this, the starting torque is considered to increase

because of the asymmetry of the rotor shape. The generated

place of maximum torque is shifted because of the change of

the rotor pole width at 0 mm. From Fig. 8, starting torque

increase within all ranges from 0o to 30o in 78o. Therefore, 78o

seems suitable. From Fig. 9, the starting torque increase from

0o to 30o within all ranges in 15.1 mm. therefore, 15.1 mm

seems suitable.

According to these, varying the height of the rotor pole is

useful to increase the starting torque because it is consideredthat the shape of the rotor becomes more asymmetrical.

The static magnetic field is analyzed with all combinations

of the parameters. The combination of three parameters, the the

height of the rotor pole, the opening of the rotor pole and the

wide of the rotor, produces a remarkable increase of the

starting torque Those three combination parameters and height

of the rotor pole is fixed at 1 mm, and after that the opening of

the rotor pole is varied. And, parameter of the obtained result is

fixed, after that the width of the rotor is varied. The variation of

the value applies with the above-mentioned value.

Fig. 10 and Fig. 11 show the analysis result of static

characteristic and inductance characteristic when three of the

parameters are varied, respectively. Type 1 of the 4/2 SRM isthe original of experimental machine. Type 2 is the

modification type when three parameter of type 1 is varied. The

parameters of the type 2 are the height of the rotor pole is 1

mm, the opening of the rotor pole is 84 o and the width of the

rotor is 12.9 mm.. From Fig. 10, Torque (peak to peak value)

of type 2 increases 0.06 Nm compare to type 1. According to

this, there is also strong evidence from Fig. 11 that the slope of

inductance value increases.

From the above-mentioned, high expectation of high starting

torque can be obtained from enlargement of the rotor pole

opening and shortened the width of the rotor and the height of

the rotor pole.The obtained results above is a static characteristic.

Therefore, the dynamic characteristic also should be evaluated.

Then, The obtained shape result of maximum starting torque is

applied to the simulation model and dynamic simulation is

carried out in section IV.

Fig. 4. The variation of the stator yoke width

Fig. 5. The variation of the stator pole width

Fig. 6. The variation of the rotor pole width

Fig. 7. The variation of the rotor pole height

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


TorqueT

[Nm

]

6.2mm

7.5mm

8.8mm

10.1mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


TorqueT

[Nm]

0mm

1mm

2mm

6mm

3mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


Torq

ueT

[Nm]

16mm19mm

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


TorqueT

[Nm] 6.2mm

7.5mm8.8mm

10.1mm


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Fig. 8. The variation of the pole opening

Fig. 9. The variation of the rotor width

IV. DYNAMIC SIMULATION OF 4/2SRM STARTING TORQUEIn dynamic simulation, the simulation model of 4/2 SRM

should be constructed considering the non-linearity because thenon-linearity of 4/2 SRM is strong. Then, the nonlinearity isdetermined by applying the result of 2D FEM to the simulationmodel.

The static magnetic field was analyzed using a 2D FEM. Theanalytical result of a magnetic characteristic and the staticcharacteristic of type 1 are shown in Fig. 12 and Fig. 13,respectively. Meanwhile, analysis results of magnetic and staticcharacteristic of type 2 are shown in Fig. 14 and 15,respectively. The analysis model of 4/2 SRM is the same as themodel that is mentioned in Fig. 2 and phase-A is supplied with

dc current source from 0 ~ 50 A at 5 A intervals. From Fig. 12and Fig. 14, the linearly and smallest slope of magnetic fieldcharacteristic could be observed when the rotor position at 0oor unaligned position. The reason is, the stator pole is arranged between rotor poles, even an equal current was supplied, thegenerated electromagnetic was small. Therefore, the slope ofthe generated electromagnetic is small moreover, since theelectromagnetic density is not increase, the slope is linear.Meanwhile, the magnetic characteristic of the rotor is thelargest slope and nonlinear when position completely at 90osince or aligned position the current is saturating at 25 A.

Fig. 10. The analysis result of static characteristic (the variation of threeparameters)

Fig. 11. Inductance characteristic (the changed of three parameters)

Fig. 12. The analysis result of magnetic field characteristic (type 1)

Fig. 13. The analysis result of Static characteristic (type 1)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


Torq

ueT

[Nm]

66deg

72deg78deg

84deg

90deg

0.0

6.5

13.0

19.5

26.0

0 15 30 45 60 75 90


InductanceL

[mH]

Type1

Type2

0

0.5

1

1.5

2

0 10 20 30 40 50

Current i [A]

Fluxlinkage

[T]

90deg

0deg

0.00

0.25

0.50

0.75

1.00

0 15 30 45 60 75 90


TorqueT

[Nm]

50A

5A

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90

Rotor position ? [deg]

TorqueT[Nm]

Type1

Type2

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 15 30 45 60 75 90


TorqueT

[Nm] 12.9mm

11.8mm

14mm

15.1mm

18.4mm


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Fig. 14. The analysis result of magnetic field characteristic (type 2)

Fig. 15. The analysis result of Static characteristic (type 2)

Fig. 16 shows the nonlinear simulation model. It consist of

the speed loop and the current loop. Angular velocity iscalculated by differentiating the rotor position which isdetected with a position sensor. The angular speed deviation is derived from the angular speed and the reference angularspeed ref.

The angular speed deviation decides the reference currentiref through the speed controller. The switching is done fromdeflection current i derived from actual current of thereference current and the winding to rotor position, then 4/2SRM is driven.

The loop from the defection current to the drive system of4/2 SRM that is the part enclosed with the dotted line in Fig. 16,is a non-linear simulation model of the motor part. Althoughthere are various types of speed and current controller, in thisresearch, the speed controller employs a PI controller and thecurrent controller employs a hysteresis controller. Thehysteresis controller determines a positive link voltage or anegative link voltage of the current deviation.

The non-linear simulation model of the motor is shown inFig. 17. The Model consist of a converter, a magnetic fluxcalculation, a current look-up table, a torque look-up table, aspeed calculation and rotor position calculation parts.

In the converter part, the applied phase voltage v from theconverter is decided from excitation start angularb, excitationwidth w, to the rotator position.

In flux calculation part, flux linkages

are calculatedfrom voltage and current phase. Because it only has to integrate

the induce voltage of the winding to calculate flux linkage, it isexpressed by (4.1).

( ) dtriv (4.1)Here, r represents one-phase winding resistance.In the current look-up table, Fig. 12 and Fig. 14 are stored

as the 2D look-up table, and are assumed to be an index,and i is the output.

In the torque look-up table, Fig. 13 and Fig. 15 are storedas 2D look-up table, i and are assumed to be index and phasetorque tis the output. All reluctance torque Tall is resultant ofthe torque of each phase.

In the speed calculation, the angular speed is calculatedby (4.2)

( )dtDTTJ

Lall

1 (4.2)Here, J is Inertia moment, TL is a load torque, and D is

viscous resistance. In the rotor position calculation part, therotor position is calculated by using (4.3).

dt (4.3)The calculated is output to the converter and each look-up

table part. The above-mentioned simulation model isconstructed by MATLAB/SIMULINK.

The dynamics of 4/2 SRM is simulated at maximum starting

torque. First of all, the starting characteristic is simulated. refis sets to 6000 rpm, and TL is assumed 0 Nm.

Fig. 18 shows the simulation result of starting characteristic.From Fig. 18, type 2 is compared to type 1, the torquedecreases 0.0032 Nm in p-p and the time is 0.5 msec faster toattain maximum torque. From that, compared to type 1, torqueresponse of type 2 is faster, and considered to be easy to start.

After that, the acceleration characteristic is simulated. Thereference step that accelerates ref from 0 to 6000 rpm is set,and TL is assumed 0 Nm at 0.2 msec. Furthermore, the amountof overshoot to the reference value of type 1 and type 2 iscompared.

The simulation result of acceleration characteristic is shown

in Fig. 19. From this figure, Type 2 has accelerated faster thantype 1 regarding its reference value. According to this, type 2that acceleration characteristic is faster than type 1, isconsidered start easily.

V. CONCLUSIONThis paper clarified from the minimum until the maximum

starting torque of the 4/2 SRM with using analysis staticmagnetic field. However, the dynamic characteristic need to beobserved, the non-linear dynamic model of the motor issimulated by using a MATLAB/SIMULINK. Furthermore,according to the dynamic simulation result, the highest torque

response and the easiest starting condition are achieved at theshape of the motor that the starting torques becomes maximum.

0

0.5

1

1.5

2

0 10 20 30 40 50

Current i [A]

Fluxlinkage[

T]

0deg

90deg

0.00

0.25

0.50

0.75

1.00

0 15 30 45 60 75 90


TorqueT

[Nm

] 50A

5A


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REFERENCES

[1] T.J.E.Miller, Switched Reluctance Motors and their Control, MagnaPhysics Publishing Oxford Science Publications, pp.1-51(1992)

[2] F.Soares, P.J.Costa Branco, Simulation of a 6/4 Switched ReluctanceMotor Based on Matlab/Simulink Environment, IEEE Transactions On

Aerospace And Electronic Systems, vol.37, pp.989-1003(2001)[3] Yu-Long Cui, Xin-Chang YuThe Simulation Study For Switched

Reluctance Motor Drives Based On Matlab 6.5, Proceeding of the 4thInternational Conference on Machine Learning and Cybernetics, pp.1076-1081(2005)

Fig. 16. Non-linear simulation model

Fig. 17. Non-linear simulation model (motor part)

Fig. 18. Starting characteristics (simulation)

Fig. 19. Acceleration characteristics (simulation)

-0.002

0.000

0.002

0.003

0.005

0.006

0.008

61 63 65 67 69 71

Time t [msec]

Torque

T[Nm]

Type1

Type2

( )dtriv

dt ( )dtDTTJ Lall 1

v i

D

TL

tTall

Current

lookup

Torque

lookupConverter

i

Equation (4.1)

Equation (4.2)Equation (4.3)

0

2000

4000

6000

8000

0 0.1 0.2 0.3 0.4 0.5 0.6

Time t [sec]

RotationalspeedN[

rpm

]

Reference valueType1

Type2

Speedcontroller

Currentcontroller

Currentsensor

Positionsensor

Converter4/2SRM

d/dt

ref

iiref

i

Documents

Dynamic Simulation of Maximizing the Starting Torque for Super-High-Speed Drive of a 4-2 Switched Reluctance Motor