Intorduction to Switched Reluctance Motor

8/17/2019 Intorduction to Switched Reluctance Motor

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INTRODUCTION

1.1Introduction

The concept of the switched reluctance motor (SRM) was established by Davidson of

Scotland in 1838 The SRM could not reali!e its potential until the modern era of power

electronics and computer"aided electroma#netic desi#n Since the mid" 1$%&s' SRM performance

has risen to levels competitive with D' and brushless D drives *owadays' the SRM

control is better achieved due to the improvements of the di#ital si#nal processor (DS+)

technolo#y' and the desi#n and modelin# of SRMs throu#h the finite element analysis (,-)

simple motor construction and fault"tolerant power converter topolo#y ma.es the SRM

an attractive alternative to the induction machine /i.e machines' SRMs do not re0uire

commutators and brushes n addition' the SRM does not have rotor windin#s or ma#nets This

implies smaller rotor losses than are typical in other machines' and there is usually no need to

cool the rotor2 most of the losses occur in the stator' which is easily cooled dditionally' the

SRM has low cost' hi#h tor0ue density' hi#h reliability and can operate in a wide speed ran#e

Due to the simple rotor structure' the low inertia allows a fast dynamic response' which is ideal

for hi#h speed applications SRM stator windin#s are concentrated and electrically separated and

the tor0ue produced by the machine is independent of the polarity of the feedin# current2 hence'

the choice of converter topolo#y and control has more fleibility than any other drive system

lso' the converter structure is fault tolerant' since it is not possible to short circuit the D bus

volta#e The SRM phases are independently controlled by the converter and controller 415

The SRM also has lower efficiency and power density' and hi#her tor0ue ripple and

acoustic noise compared to its competitor the permanent ma#net (+M) machine 6owever' by

increasin# the number of machine phases and poles' tor0ue ripple and acoustic noise can be

reduced The research trend in SRM controller technolo#y is to develop novel position sensorless

techni0ues' methods for phase advancin# and overlappin# conduction to minimi!e tor0ue ripple

and to increase power output These types of improvements will place this machine at a

competitive advanta#e for a lar#e number of applications The SRM is used in applications such

as pumps' vacuum blowers' starter7#enerators' electric and hybrid vehicles' electric power


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steerin# systems and electromechanical bra.es SRMs have a #reat potential in harsh

environments' such as in hi#h temperatures and dusty environments The modern power

electronic drives enable si#nificant improvements in the machine performance' ma.in# the SRM

a respectable competitor to the +M machine 45

The rotor is ali#ned whenever diametrically opposite stator poles are ecited n a

ma#netic circuit' the rotatin# member prefers to come to the minimum reluctance position at the

instance of ecitation 9hile two rotor poles are ali#ned to the two stator poles' another set of

rotor poles is out of ali#nment with respect to a different set of stator poles Then' this set of

stator poles is ecited to brin# the rotor poles into ali#nment /i.ewise' by se0uentially switchin#

the currents into the stator windin#s' the rotor is rotated The movement of the rotor' hence the

production of tor0ue and power' involves switchin# of currents into stator windin#s when there is

a variation of reluctance2 therefore' this variable speed motor drive is referred to as a switched

reluctance motor drive45

1.2Advantages And Disadvantages of SRM

The advantages 435 of the SRM can be summari!ed as follows:

• Simple machine construction and low cost due to the absence of permanent ma#nets or

rotor windin#s and the use of concentric stator windin#s

• ,ault"tolerant drive due to the structure of the power converter The D bus cannot be

short"circuited due to the presence of the stator windin# in series with the switchin#

elements

• ndependent stator phases that do not prevent drive operation in the case of the loss of

one or more phases

• ;nidirectional currents which facilitates the drive structure and reduces the number of

power switches in certain applications

• /osses present mainly in the stator which is easier to cool

•

6i#h permissible rotor temperature since there are no permanent ma#nets•


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• 6i#h tor0ue ripples inducin# current ripples in the D bus' which ma.es it necessary to

add a lar#e capacitor filter on the D bus

• coustic noise

• *eed to .now the rotor position at each instant of time usin# a sensor or throu#h other

means

1.3 A!ications of SRM

SRM provides an attractive solution for a number of applications 435' such as

• ero space' Traction

• 9ind power #eneration

• ,luid +umps' vacuum blowers +rocess control industries

• 6ybrid7-lectric vehicles

•-lectromechanical bra.e system

• -lectric power steerin#

• Starter"#enerator system

• ,uel pump operation

• reduction of about 1=>= d? noise level is achieved with the low"noise desi#n

methodolo#y

• +osition and speed sensorless SRM drive is reali!ed usin# slidin#"mode observer

• @nline adaptation with sensorless operation

ndirect estimation shows the promise of sophisticated control (tor0ue"ripple minimi!ation)

reali!ation with sensorless operation

1."Motivation #or Research

n the hi#h"technolo#y industry' a motion control system with hi#h"speed and hi#h"

position trac.in# combined with a simple' ru##ed' and reliable electrical motor is in hi#h

demand switched reluctance motor (SRM) could be an attractive candidate because it

concentrates all these advanta#es 6owever' it has never been a popular choice in hi#h"precision

position actuators' due to the drawbac. of hi#her tor0ue ripple compared with conventionalmachines that cause vibrations and acoustic noise n addition' the characteristics of an SRM are

hi#hly dependent on its comple ma#netic circuit' and therefore' it is difficult to model' simulate'

and control them 415


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n recent years' SRMs have attracted renewed interest due to the tendency to shift from

the comple desi#n and precise manufacturin# to the hi#hly effective and more sophisticated

control The improvement in control al#orithms and techni0ues can etract #ood performance

from a simple SRM drive and result in increasin# the penetration of the SRM drives in hi#hly

demandin# applications 45

The SRM phase inductance varies periodically with respect to the rotor position2 an

indirect method of position estimation can be developed usin# this position dependent

inductance The doubly"salient pole construction in SRMs' which is responsible for the

inductance variation' facilitates this position sensorless operation at low and !ero speeds This

will increase the reliability of the system' althou#h it will add some compleity in the controller

The primary obAective of this research is to develop a 6i#h" precision position controller

and a speed controller for four"phase SRM drives n order to derive a low"compleity model of

the SRM that is suitable for speed and position controls' the machine dynamics are classified into

#roups with respect to their time constants Therefore' a cascade control approach with two

closed"loop controllers is used ,or speed control' a + controller has been adopted to provide

0uic. transient response and to ensure !ero steady"state error ,or position control' a +D

controller has been used to compensate the delay effect of the inte#ration applied in the speed

control loop and to suppress the overshoot in the position response

S$ITC%&D R&'UCTANC& MAC%IN&S AND T%&IR

O(&RATION

n this chapter' we first introduce the mechanical structures of typical SR machines Then'

the electromechanical couplin# in an SR machine' ie' the principle of tor0ue production' is

described ,inally' the basic characteristics of electrical hardware used for SR machines are

introduced

2.1Mechanica! Structure


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n SR machine is a brushless drive' that is' it operates without any mechanical

commutation components t has a doubly salient #eometry cross"section of a typical 87% SR

machine (havin# 8 stator poles and % rotor poles) is shown in ,i#ure 1 stator is a stationary

component that has ecitation windin#s around its poles The windin#s are connected in

diametrically opposite pairs in either series or parallel' inducin# additive rna#netic flu in order

to form phases The windin#s for each phase are independently connected to a remote switchin#

circuit for its commutation

The other salient component' called a rotor' rotates about the ais of the motor t can be

eternal but is usually situated inside the stator The stator and rotor are assembled from steel

laminations of the same #rade and thic.ness and do not contain any permanent ma#nets

#igure 2.1 87% SR machine cross"section (9indin#s for only one phase are shown)

;nli.e induction machines' there are no concentrated windin#s on the rotor of an SR machine

because its tor0ue production is based on a variable reluctance principle' which is illustrated in

the net section

There is a variety of motor confi#urations with different shapes of stator and rotor' as

well as different numbers of poles and phases Two main classifications of SR machines are

re#ular and irre#ular machines The cross"sections of re#ular and irre#ular SR machines are

shown in ,i#ure n a re#ular machine' the stator and rotor poles are symmetrical about the


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center lines'ls ' and

lr , respectively shown in the fi#ure They are also e0ually spaced

around the stator and rotor' respectively

n irre#ular machine is one that is not re#ular Typically' an irre#ular machine is

desi#ned to accommodate special needs' such as the capability of startin# rotation from any

initial rotor position Different pole"arc an#les of the stator and rotor poles are chosen to meet

desired machine performance ,or applications that re0uire hi#h tor0ue in low speed operation'

such as robotic arms' a specific type of SR machine called variable reluctance (


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m= N s

2 ∈=

2π

mN r

where N s and

N r are the numbers of stator and rotor poles' respectively' andmN r is

the number of stro.es per revolution

The benefit of an SR machine with fewer phases is that it re0uires simpler commutation

control and fewer electrical components @n the other hand' an SR machine with more phases

has a smaller stro.e an#le and' conse0uently' its tor0ue output is smoother n #eneral' one"phase

machines re0uire assists for initial rotation in motorin# operation' and two"phase machines

re0uire non"symmetric rotor poles Machines with three or more phases with symmetric

#eometry can start motion from any initial rotor position n many applications' three or four"

phase machines are preferred because of their overall simplicity and cost n this research' a

re#ular 87% four"phase SR machine is studied as a typical eample

2.2 (rinci!e of Tor)ue (roduction

/i.e many other electrical machines' an SR machine is an ener#y converter that ta.es

electrical ener#y and produces mechanical ener#y in motorin# operation' and vice versa in

#eneratin# operation The ener#y is stored in the rna#netic field created by the phase windin#s

and is echan#ed between the electrical and the mechanical subsystems n the followin#' the

process of tor0ue production in an SR machine is described

9hen a phase is ecited by applyin# a volta#e across its concentrated coil' the current in

the coil creates a ma#netic flu throu#h its stator poles The ma#netic flu flows throu#h the pair

of nearest rotor poles' travels in the rotor and stator steel' and closes a ma#netic circuit' as shown

in ,i#ure 3 n a ma#netic circuit' there eists ma#netic reluctance t is analo#ous to resistance

in an electrical circuit and depends on the ma#netic permeability of the material that the fluflows throu#h n the case of an SR machine' the reluctance in the air #ap between the stator and

rotor poles is very lar#e compared to that in steel


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#igure 2.3 Ma#netic circuit in an SR machine

onse0uently' the total reluctance of the ma#netic circuit can be well approimated by

the reluctance of the air #ap ?ecause of the doubly salient #eometry of an SR machine' the

distance between the stator and rotor poles chan#es as the rotor rotates' and hence the reluctance

of a flu path varies as shown in ,i#ure B

#igure 2."


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the stator poles of the phase The reluctance of the flu path is at its minimum in the ali#ned

position and is at its maimum in the unali#ned position

The variable reluctance principle is the tendency of the rotor to ali#n itself to the

minimum reluctance position 9hen a phase is ecited' the pair of nearest rotor poles (part of the

ma#netic circuit) are attracted to ali#n themselves to the ecited stator poles Thus' tor0ue is

produced This principle is different from the rna#netic interaction occurrin# in other electrical

machines' such as permanent ma#net motors and induction motors The tor0ue production in

these other types of motor is based on the attraction between the *orth and South ma#netic poles

of permanent or electrically induced ma#nets *otice that the rotor poles of an SR machine do

not re0uire the eistence of ma#netic poles to produce tor0ue nterestin#ly enou#h' the radial

ma#netic attraction that operates an SR machine can become ten times lar#er than the

circumference forces produced by an induction machine.

*a+ A!igned osition *,+ Una!igned osition

#igure 2.- li#ned and unali#ned positions

n the ali#ned position shown in ,i#ure = there is no tor0ue produced' even when the

phase is ener#i!ed' because the reluctance of the flu path is at its minimum 6ence' it is a stable

e0uilibrium position There is also no tor0ue produced in the unali#ned position because the

stator pole is eactly in the middle of two adAacent rotor poles 6owever' as soon as the rotor is

displaced to either side of the unali#ned position' there appears a tor0ue that displaces it even


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further and attracts it towards the net ali#ned position 6ence' the unali#ned position is an

unstable e0uilibrium position onse0uently' tor0ue is produced in the direction from any

unali#ned position to the net ali#ned position Since the rotor poles are identical around the

rotor' the tor0ue production is periodic @ne period from an unali#ned position to the net

unali#ned position is called the rotor pole"pitch' ' in radians and #iven by

τ =2 π

N r

The rotor pole"pitch of an 87% SR machine is %&o' and the maimum tor0ue !one' where

positive tor0ue can be produced in one period' is 3&o ?y successfully ecitin# the phases in

se0uence' a continuous tor0ue is produced ;nli.e other electrical machines' the direction of

rotation in an SR machine does not depend on the direction of ma#netic flu and' hence' does not

depend on the direction of phase current This unipolar characteristic of phase current allows

simple desi#n of electrical circuits' described in the net section

2.3&!ectrica! %ardare

SR machines utili!e power converter switchin# circuits for the commutation of phase

ecitation The most common confi#uration of a switchin# circuit is shown in ,i#ure % n

#eneral' a switchin# circuit for an SR machine is simple because of the unipolar (not alternatin#)

characteristic of its flu"lin.a#e and phase current

#igure 2./ Typical confi#uration of power converter

Since the direction of rotation does not depend on the si#ns of flu"lin.a#e and phase

current' a switchin# circuit of an SR machine is desi#ned so that the current in the ecitation coil


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flows only in one direction n the followin#' we illustrate the main re0uirements that a switchin#

circuit for an SR machine must satisfy

SR machines cannot operate directly from an or D mains volta#e supply because

inputs to their phase windin#s must be current pulses power converter must supply unipolar

current pulses from a D volta#e source' precisely at desired rotor positions t must also

re#ulate the ma#nitude and even waveform of the current in order to satisfy the re0uirements of

tor0ue and speed control and ensure safe operation of the motor and the power transistors

,inally' it must be able to supply pulses of reverse volta#e for de"fluin#' ie' forcin# the phase

current to !ero in order to avoid reverse tor0ue at certain rotor positions

The desirable type of power converter has separate switches for each phase so that all

phases are virtually independent of each other The switchin# circuit considered in this research

has the confi#uration in ,i#ure % The ecitation coil in each phase is connected to one

common D volta#e source (or a rectified supply) throu#h a transistor switch on each end

The circuit has two freewheelin# diodes to provide the unipolar characteristic of phase current

,i#ure E shows the current flow in the switchin# circuit for one phase under different switchin#

conditions 9hen both

*a+ 0102 on *,+ D1D2 on *c+ 02D2 on

#igure 2. urrent dynamics in a switchin# circuit

switchesQ

1 andQ

2 are turned on (,i#ure E(a))' a constant volta#e is applied to the

ecitation coil' and the current starts to increase The ener#y is stored in the ma#netic field and

converted to mechanical ener#y 9hen both switches are turned off (,i#ure E(b))' the


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freewheelin# diodes D1 and

D2 allow the eistin# current in the coil to .eep flowin# in

the same direction

6owever' the reverse volta#e applied to the ecitation coi1 forces the current to decrease

The unused ener#y in the ma#netic field is sent bac. to the volta#e supply as seen in the

direction of the current 9hen only one switchQ2

is turned on (,i#ure E(c))' the stored

ener#y is dissipated by the phase resistance and the bac. emf developed in the coil' and thus' the

phase current slowly decreases f the initial current is !ero in ,i#ure E(c)' then the current will

remain !ero because there is no volta#e applied across the coil The switches are turned on and

off to control a desired current level for each phase

2."Stator Inductance

The tor0ue characteristics of switched reluctance motor are dependent on the relationship

between the stator flu lin.a#es and the rotor position as a function of the stator current

typical phase inductance vs rotor position is shown in ,i#8 for a fied phase current The

inductance corresponds to that of a stator"phase coil of the motor ne#lectin# the frin#e effect and

saturation The si#nificant inductance profile chan#es are determined in terms of the stator and

rotor arcs and number of rotor poles The various an#les 45 are derived as:

βs+ βr2 π

P r−¿ (2.1a)

θ1=1

2¿

θ2=θ1+ βs (2.1b)

θ3=θ2+( βr− βs ) (2.1c)

θ4=θ3+ βs (2.1d)

θ5=θ4+θ1=2π

N r(2.1e)


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where βs and

βr are the stator and rotor pole arcs' respectively' in most case β r> βs '

and N r is the number of rotor poles

,our distinct inductance re#ions emer#e:

1 0−θ1∧θ4−θ5 : The stator and rotor poles are not overlap' and the inductance is

minimum and almost a constant 6ence' these re#ions do not contribute to tor0ue

production

θ1−θ2: +oles overlap' so that the flu path is mainly throu#h the stator and rotor

laminations This increases the inductance with the rotor position and #ives it a positive

slope current impressed in the windin# durin# this re#ion produces a positive tor0ue

This re#ion comes to an end when the overlap of poles is complete3

θ2−θ3: Durin# this period' movement of rotor pole does not alter the complete overlap

of the stator pole This has the effect of .eepin# the inductance maimum and constant

Therefore' tor0ue #eneration is !ero n spite of this fact' it serves a useful function by

providin# time for the stator current to come to !ero or lower levels when it is

commutated' thus preventin# ne#ative tor0ue #eneration in the ne#ative slope re#ion of

the inductance

B θ3−θ4 : The rotor pole is movin# away from overlappin# the stator pole in this re#ion

and the inductance decreases' ma.in# a ne#ative slope of the inductance re#ion The

operation of the machine in this re#ion results in ne#ative tor0ue


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*a+

*,+

#igure 2. nductance vs rotor position

t is not possible to achieve the ideal inductance profile shown in ,i#ure 8 in an actual

motor due to saturation Saturation causes the inductance profile to curve near the top and thus

reduces the tor0ue constant ,or rectan#ular currents' it can be seen that the motorin# tor0ue is

produced for a short duration in pulsed form' resultin# in a lar#e tor0ue ripple 45

This can create problems of increased audible noise' fati#ue of the shaft' and possiblespeed oscillations 6owever' the tor0ue ripples can be minimi!ed by desi#nin# the machine such

that the inductance profiles of two succeedin# phases overlap durin# the endin# of one and the

be#innin# of the other n turn' this re0uires the correct choice of number of stator and rotor poles

and their pole arcs n alternative techni0ue to reduce the tor0ue ripples is to shape the current


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2.-&)uiva!ent Circuit

An elementary equivalent circuit for the SRM can be derived neglecting

the mutual inductance between the phases as follows. The applied voltage to

a phase is equal to the sum of the resistive voltage drop and the rate of the

ux linages !"# and is given as$

V = R si+dλ(θ , i)

dt (2.2)

where Rs is the resistance per phase and λ is the flu lin.a#e per phase #iven by:

λ= L (θ , i ) . i(2.3)

where L is the inductance dependent on the rotor position and phase current The phase

volta#e e0uation' then' is

v= R s i+d { L (i , θ ) i}

dt = Rs i+ L (i ,θ )

di

dt +i

dθ

dt .dL(i , θ)

dθ

¿ Rs i+ L (i ,θ ) didt + dL (i , θ )dθ ωmi (2.4)

n this e0uation' the three terms on the ri#ht"hand side represent the resistive volta#e drop'

inductive volta#e drop' and induced emf' respectively' and the result is similar to the series

ecited dc motor volta#e e0uation The induced emf'e

' is obtained as:

e=dL(i ,θ)

dθ ω

m

i= K b

ωm

i(2.5)

where K b may be construed as an emf constant similar to that of the dc series ecited

machine and is #iven here as:


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K b=dL(i , θ)

dθ (2.6)

*ote that the emf constant is dependent on operatin# point and is obtained with constant current

at the point ,rom the volta#e e0uation and the induced emf epression' the e0uivalent circuit for

one phase of the SRM is derived and shown in ,i#ure $

#igure 2.4 Sin#le"phase e0uivalent circuit of the SRM

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Intorduction to Switched Reluctance Motor