Reluctance Flux

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FLUX-LINKAGE CHARACTERISTICS OF SWITC ED RELUC''I'ANCEMOTOR

V. Ramanarayanan L.V&tah Debiprasad Pandaw m fEl-Ea-W

Indm Institute of scienoe Indmn Inshtute of Saence

Bangalore 560012 INDIA Eangdore 560012 INDIA Bangalore 560012 INDTA

Dep"ent of ElectricalEngheri@ DepartpentofElectrical EngineeringIndian Instituteof Science

Abstract: An important requirement in modelling ofSwitched reluctance motor (SRM) i s the knowledge of its

flux-linkage characteristics. Idealisation of the flux-linkagecharacteristics will result in a model which cannot predictthe performance of the machine with s afficient accuracy. Itis necessary therefore to determine fludinkagecharacteristicsas closely as &sible.In this paper, the method of finding the flux-linkagecharacteristics is explahed. The same i s demonstrated on acommercially available 4Kw, 8/6 pole OULTONSUM Thevalidity of the test result is cheeked by compnth g the Statictorque characteristics based on the measured flux-linkagech~nteteristiosand compmhg it WMhe experimentally

measured Static torque characteristics. The sources ofmeasurement error are discussed.

JNTRODUCTIONSRMs are drawing considerable attention for variable

speed drive application, owing to its high energy

conversion efficiency. It has sewed advantages over the

COW~X I ~ ~Q I U ~C andDC drives, namely,

.simpleand robust c o me t io n

.brushlessoperation

.low inertia and high torque o weight ratio

.simple power c o m e r tructure

.noshoot through faul tsbetweenDC uses.

The performanceof SRM is innuencedby its flux-linkage

characteristics, and the control strategy. It is to be stressed

that SRM has to be necessarily run from an electronic

power converter. A satisfactory control strategy can be

developed if accurate knowledge of flux-linkagecharacteristicsof the machine is available.

The flux-lhkage in SRM is a function of both rotor

position and the current. The m y f flux-linkage

c b a r i s t i c s (for different rotor positions) will have to be

determined as accurately aspossible. This paper gives, the

method of measurement, sources of experimental error,

andprecaution required in order to reduce the error.

BASIC PRINCIPLEOF OPERATION

Figure 1, shows the construction of an 8/ 6 poles SR motor.

It is doubly salient and has no rotor windings. The torque

in t h i s motor is due to the tendescyof rotor poles to align

wththe poles of the excited stator phase. The direction of

the torque is independent of the direction of the phasecurrent. The phases are cyclically fed by unipolar currents

to get unidirectional torque. A shaft position sensor is

used to facilitate the turn on and turn off of the phasewindings (position sensors can be eliminated with an

indirect position sensing scheme).

Fig1 Cmstrudicmof 816pole SRM

Differentmodes of control are explained in [1-21.

E"LUX-LINKAGE CHARACTERISTICSAN D ITSM E A S ~ M E N T

The flux-linkage characteristics of SRM depends on the

rotor position. Due to its doubly salient construction, he

machine is prone for saturation._Thedegree of saturation

ais0 depends on the rotor position. The flux-linkage

characteristics at different rotur position is explained here

in brief. When a pair of rotor poles align with the poles of

a stator phase (aligned position), the reluctance for theflux path is at its minimum and the magnetic circuit

saturates considerably. The flux-linkage characteristics in

aligned position is representedby m e in Fig. 2. When

the inter polar axis of the stator coincides with the rotor

pole, (unaligned psition), the magnetic circuit reluctance

will be higher and it is not susceptible for saturation as in

aiigned position. The flux-linkage 'characteristics in the

unaligned position is as shown in Fig. 2 by c w e 3. As,the rotor position is changed from unaligned to aligned

position, till the overlap of pole is approached the

flux-linkage characteristics do not change appreciably.As

the overlap begins, the flux path experiences local

saturation in the pole tips and it spreads to the entire

magnetic circuit with increase ip current The

flux-linkage characteristics n the intermediate position isas shown in Fig. 2 by curve 2. The flux-linkage can be

obtained by Finite element methods [3]. The accuracy ofthe result depends on the skill of the user in choosing the

elements. These methods are suitable at design stage and,

it is computationally complex

0-7803-2795-0 281



currenrt

Fig. 2 Flux-linkage&arac te i iAcs ofSRM st cfifferpnl

rotorpitions.

rimntal method ,which makes use of voltage

discussed n detail.When a voltageof thephasesO f S R I q with all other

e quation isgivenby,

(1 )=Ri+d*l&

; R

is the ~~n~~~ voltage acfoss the phase

is its resistance and i the current. The

ted for di€fkrelltvalues of

mtent. One of the s of the motor is

current reach nearly 20 to 30% more than

ament encountered during the

J 11 I

I iJ---Jl I I 1-7 T I

J

0 0005 0 01 0015 002 0025 003 00% 004

io5 t/ov0 00% 001 0015 00 2 0025 003 0035 004

@)

Fig 4 V o b ndCumntwaveform

a) v vasusTime ~ ~ ~ e

operation. The voltage

recorded (shown in Figcurrent feveIs are dbtai

rotated to a set ofequally rotor positionsb e e nunaligned toalignedpositionandprocedure is repeatedateach rotor position.The flux-linkagecharacteristics willbe symmetric after thealignedposition.

Following the above method,of a 4 KW, 816 pole SRM

used as a switching device.

(YOKOGAWA 3556) is used to acquireand store current

MOSFET i s 1

1, I

09

E oea

$ ;;f ::-

3 0 3

0 2

01

0

-

5 10 15 25

Current inA

computer and then

are given in Fig.

andvenfpng the m echeckedby evaluating



30

i?.H 20

.G 25

fi15

10

5

0255 10 15 20

Rotor position in degrees

Fig. 6 Com putd static torque characteristics

ENERGY CONVERSIONPRINCIPLEAND STATICiORQUECHARACTERISTICS

The most general expression for torque producedby one

phase at any rotor positions given by, 4]

(3 )

where w' is the coenergy. For any given phase current

and rotor position, the co-energy is the area under the

corresponding magnetisation curve from origin to the

point consideredThis canbe expressed as,

1 i lI W = i q d i

ij(4)

From the Eqs (3). and (4) it is possible to get a set of the

torque vs. rotor position characteristics for Merentcurrent levels. This set of characteristics is known as

Static torque characteristics. The Static torque

characteristics for the test motor is obtained. first by

finding coenergy using spline fit to the flux-linkage

characteristics, and then Werentiating numerically the

coenergy function with respect to rotor position at

constant current. A commercially available package is

used for this purpose.The results are shown in Fig. 6.

EXPERIMENTAL MEA!SUREMENT OF STATICTORQUE

The experimental set up is shown in Fig. 7. Theset up is

almost same as that of Fig. 3 except that a torque

transduceris placed in between SRM and the Indexinghead. A calibrated Torque transducer (Vibrometer),

which has an accuracy of OS% , is used to record the

torque producedby the motor. One ofthe phases of the

motor is excited till the desired steady state current flows

tlirough the motor, with all other phases open. The torque

produced is recorded. The magnitudeof the steady state

Fig. 7 ExpwimenEelsetup for the static torque ch&erktks

350 t."

k m5

10

5

00 5 10 15 20 25 30

Rotor positionindegrees

F ig 8Ekpaimentallyobtained static torque ehcCtaiStics(for 0 to 18A in stepsof 1A)

curre& is varied with the help of rheostat, and the

corresponding torque arenoted This procedure s repeated

for different rotor positions, in the same way as in theflux-linkage characteristics. Static torque characteristics

obtainedexperimentally is shown in Fig. 8.

SOURCES OFERROR AND ITS INFLUENCE

1. Error due to the movernenl of the rotor

During the experiment the SRM produces torque h i ethan the rated nominal torque in certain torque producing

regions and it is essential to hold the rotor in position toget reliable results. Change in position dwilrig

measurement will lead to wrong flux-linkage

characteristics corresponding o that angle. If thedeviation

is considerabie it ma y even lead to intersecting curves for

angles closer to aligned position. The influence of rotormotion during the measurement on the instantaaews

torque Caacdationcanbe eqlained using the Fig. 9. In

figure, m e , and curve 2 are the act4 flux-linkage

characteristics corresponding to 81and 82 respe&vely.Let

c u r v e 3 bethemeasuredfludinkage at 82 with

deviation in position during the experiment.The

.283





increases in the winding. (the maximum error is found tobe around 5% ,inthis case).

Although the results obaimxi by th is method are better , tis t d o u s and ime consuming ,as he number of ests tobe

COlKRLctedare higher to get a completeset of flux-linkagecharacteristics.Presscot bridge"dan also be used o

eliminate the eddy current effect [ 5 ] .

1

4. Error due to improper resistance and otherfactors

The resistance o f t he phasewinding has to be measuredaccurately by suitable bridge method. Improper value of

resistance can lead to driA in flux-linkage characteristics.

The variation of resistance due emperature can introduce

error in EN DL This can be minimised by

conducting the test, after allowing the machine to cool to

the ambient *temperature if it is loaded earlier.

Measwwnents are made with sui6cient time gap betweenmeasurements, $0 that the temperature ef fec ts are

minimisedTheeffective resistancechangesduring the experiment

due to the eddy ame nt loss in the coupled conducting

parts. l% s can be aken into account by adapting the

resistance arbiuarily in numerical integration, such that

when i = O , 9 =0 [4].

Error can also occur due o the non linearity in the current

transducer. The current probes has to be calibrated andadjusted or any offsets.

COMPAREON AND CONCLUSION

The Static torque characteristics as measured and as

predicted are both shown in Fig. 11. The qualitative

match is good Error in actual numbers is around loo/,

which is within accqtable range for the design purpose.

Accuracy can be improved further by taking appropriate

measures o reducethe error influencingfactors.

Ln this paper, a practical way of finding and cross

checking of the flux-linkslge characteristics of SRM. s

descri bed,This s very much useful in simulation of the

SR Drive and its control strategy.

REFERENCES

[11 P.J.Lawrenson, J.M.Stephenson, P.T.Blenkiwp,

J.Cor& and N.M.Fulton "Variable-speed Switched

reluctance motors" LEE PROC.,vol. 127. R. . No. ,

July 1980.

[2] M.R.Harris et al, "Discussions on yariable-speed

Switched reluctance motor" IEE PROC., ol.128, Pt.B.No. . Sept.1981.

131 Mehdi Moallem and Chee-Mun Ong " Predicting the

steady-state performance of a Switched reluctance

machine " EEE Transactions on LA. , Vo1.27, N0.6,Nov/Dec 199 1.

141 T.J.E.Miller "Switched keluctance Motors an d theircontrol " Magna Physics Publishing and Clarendon

Word 1993.

[ 5 ] JonesC.V. "The unified theory of electrical machines",

Butterworth&Co., London, 1967.

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Reluctance Flux