Switched Reluctance Motor

MODELLING AND CONTROL OF SWITCHED

RELUCTANCE MOTOR

A project report submitted in partial fulfillment for the award of degree of

BACHELOR OF TECHNOLOGYIN

ELECTRICAL AND ELECTRONICS ENGINEERING

SUBMITTED BY

KANDIPATI RAJANI (07391A0217)

PRIYATAM AVINASH NAMBURI (07391A0232)

SHAIK MASTANBI (07391A0256)

KOPPULA RAVI CHAITANYA (08395A0203)

Under the Esteemed guidance of

Mr.P.V.S.Sobhan M.E

Associate Professor

Department of Electrical & Electronics EngineeringVIGNAN’S ENGINEERING COLLEGE

NAAC ‘A’ Grade, NBA Accredited, ISO Certified(Affiliated to Jawaharlal Nehru Technological University, Kakinada, A.P.)

VADLAMUDI, GUNTUR, 522213, A.P.2007-2011

VIGNAN’S ENGINEERING COLLEGEVadlamudi, Guntur 522213

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

CERTIFICATE

This is to certify that the project work titled “MODELLING AND

CONTROL OF SWITCHED RELUCTANCE MOTOR” by

KANDIPATI RAJANI (07391A0217), PRIYATAM AVINASH

NAMBURI (07391A0232), SHAIK MASTANBI (07391A0256),

KOPPULA RAVI CHAITANYA (08395A0203) during the academic

year 2010-2011 under the guidance of P.V.S.Sobhan is submitted in

partial fulfillment for the award of the degree of Bachelor of

Technology in Electrical & Electronics Engineering.

Mr.P.V.S.Sobhan Dr.G.R.K.Murthy

Project Guide Head of Department Department of Electrical and Electronics Department of Electrical and Engineering Electronics Engineering

ACKNOWLEDGEMENT

I express my profound sense of gratitude and sincere thanks to

Mr. P.V.S.Sobhan M.E Associate Professor, Department of Electrical

and Electronics Engineering, for initiating me into this work and

guiding me in the successful completion of this project

I express my thanks to Dr.G.R.K Murthy Head of the

Department of Electrical and Electronics Engineering, providing all the

facilities in the Department..

We wish to express our profound gratitude and appreciation to

our principal V.Madhusudhan Rao for extending the official support

for the progress of the project.

I take this opportunity to thanks all the people who aided me in

the completion of the project work, directly or indirectly, for their

continuous encouragement and extended services

Finally, I would like to thanks my parents, for their support and

encouragement, which helped me to complete this project with full

enthusiasm.

KANDIPATI RAJANI (07391A0217) PRIYATAM AVINASH NAMBURI (07391A0232) SHAIK MASTANBI (07391A0256) KOPPULA RAVI CHAITANYA (08395A0203)

TABLE OF CONTENTS

LIST OF FIGURES i

ABSTRACT iii

Chapter 1: Introduction

1.1 Introduction 01

1.2 SRM Controller 01

1.3 Organization of Thesis 02

Chapter 2: Principle of Operation of the Switched Reluctance Motor

2.1 Introduction 03

2.2 Construction of Switched Reluctance Motor 03

2.3 Types of SRM 05

2.4 Advantages and Disadvanatges of SRM 06

2.5 Applications of SRM 07

2.6 Elementary Operation of the Switched Reluctance Motor 08

2.7 Principle of Operation of the Swtiched Reluctance Motor 09

2.8 The Relationship Between Inductance and Rotor Position (NON LINEAR ANALYSIS) 12

Chapter 3: Converters For SRM Drives

3.1 Power Converter Topology 19

3.2 Converter Configurations 20

3.3 Asymmetric Bridge Converter 21

Chapter 4: Modelling and Control of SRM

4.1 Mathematical Model 25

4.2 PID controller 27

4.3 General Block Diagram 29

4.4 Block Diagram of Traditional Feedback Control 29

Chapter 5: Simulation and Result Analysis

5.1 Switched Reluctance Motor Specifications 30

5.2Results 31

CONCLUSION 42

REFERENCES 43

LIST OF FIGURES

Figures 2.1 Switched Reluctance Motor Configuration

(a) One tooth per pole

(b) Two tooth per pole

Figure 2.2 Type of SRM

Figure 2.3 Operation of SRM

Figure 2.4 Solenoid and its characteristics

(a)A Solenoid

(b)Flux Vs MMF characteristics

Figure 2.5 Derivation of Inductance Vs rotor position from rotor and stator Pole arcs for an unsaturated SRM

(a)Basis rotor position definition in a two pole SRM

(b)Inductance profile

Figure 3.1 Classification of Converter based on their configuration

Figure 3.2 asymmetric converters for SRM with freewheeling and Regeneration capability

Figure 3.3 Operational waveforms of asymmetric bridge converter

Figure 4.1 Single phase equivalent circuit of SRM

Figure 4.2 Structure of PID controller

Figure 4.3 General Block diagram

Figure 4.4 Block diagram of traditional feedback control

Figure 5.1 MATLAB/simulink model of SRM

Figure 5.2 output speed tracking reference speed

1

Figure 5.3 Stator winding phase Inductance

Figure 5.4 Stator winding phase Inductance (Magnified view)

Figure 5.5 Stator winding 3-phase current

Figure 5.6 Stator winding 3-phase current (Magnified view)

Figure 5.7 Electromagnetic torque developed

Figure 5.8 Electromagnetic torque developed (Magnified view)

Figure 5.9 Output speed tracking reference speed for low reference speed

Figure 5.10 Stator winding phase Inductance for low reference speed

Figure 5.11 Stator winding phase Inductance (Magnified view) for low reference speed

Figure 5.12 Stator winding 3-phase current for low reference speed

Figure 5.13 Stator winding 3-phase current (Magnified view) for low reference speed

Figure 5.14 Electromagnetic torque developed for low reference speed

Figure 5.15 Electromagnetic torque developed (Magnified view) for low reference speed

Figure 5.16 Output speed tracking reference speed before and after applying Load of 10 N-m at 1sec for reference speed 200rpm

Figure 5.17 Output speed tracking reference speed before and after applying Load of 10 N-m at 1.5sec for reference speed 200rpm

Figure 5.18 Output speed before and after applying loads of 5 N-m at 0.75sec and 10N-m at 1.5sec

Figure 5.19 Output speed before and after applying loads of 5 N-m at 1.7sec and 10N-m at 2.0sec

Figure 5.20 Output speed tracking variable reference speeds for low speeds

Figure 5.21 Output speed tracking variable reference speeds for high speeds

2

ABSTRACT

Nowadays, switched reluctance motors (SRMs) attract more and more attention. The

switched reluctance motor consists a salient pole stator with concentrated coils, and a salient

pole rotor, which has no conductors or magnets. Simplicity makes the SRM inexpensive and

reliable, and together with its high speed capacity and high torque to inertia ratio, makes it a

superior choice in different applications.

The motor's double salient structure makes its magnetic characteristics highly

nonlinear and the flux linkage is also a nonlinear function of stator currents as well as rotor

position. All these make the control of the SRM a tough challenging.

This work briefly describes the constructional features, principle of operation,

applications and mathematical model of the switched reluctance motor.

The aim of this project work is to design a conventional PI controller for a 6/4 SRM

using MATLAB/SIMULINK. The effectiveness of the designed controller is to be analyzed

by comparing the responses (speed) with and without controller under different load

conditions

3

VIGNAN’S ENGINEERING COLLEGE

1. INTRODUCTION

1.1 INTRODUCTION

Switched Reluctance (SR) motors are relatively new additions to a group of well-

established variable-speed electrical motors. The major difference that distinguishes them

from other conventional drives is simple, low cost, and rugged constructions. The simplicity

of the mechanism is the result of their torque production principle, so called variable

reluctance principle. SRM produce torque without any permanent magnets and with no

concentrated windings on their shaft. This unique torque production principle allows SRM to

have the benefits of reliability and capability of four-quadrant operation in a wide speed

range. Other advantages of SRM are also known to be the high torque-to-inertia ratios and

high torque-to-power ratios. These attractive features have led SRM to be potential

candidates for applications in industrial and commercial markets.

Despite the simple mechanism and attractive capabilities, SRM have some

limitations. Unlike other conventional electrical machines, they cannot operate directly from

main AC or DC supply and require current-pulse signals for proper torque production.

Hence, they require an power electronic controller that regulates commutation of coi1

excitations and the waveform of current signals. Another drawback of SRM is that their

dynamics are inherently nonlinear due to their magnetic characteristics depending on both the

shaft angle and current magnitudes, and thus, in order to design controllers with desired

stability properties, one has to resort to somewhat complicated nonlinear control tools.

Furthermore, the nonlinearities cannot be neglected because in practice the machines are

operated at high current levels (where saturation of core material occurs), so as to maximize

their torque density.

1.2 SRM CONTROLLER

Besides guaranteed stability, it is desirable for SRM controllers to have features such

as parameter insensitivity, quick precise dynamic responses, and rapid recovery from load

disturbances. Traditionally, SRMs are controlled by the combination of a conventional PI

controller and switching controllers. The traditional control scheme is sensitive to variations

MODELLING AND CONTROL OF SWITCHED RELUCTANCE MOTOR 1


in plant parameters and operating conditions. Hence, there have been demands for rigorous

nonlinear control design methods for SRM to meet the performance criteria.

The objectives of this work are as follows:

• To study and analyze the principle and operation of srm

• To obtain the mathematical model of srm

• To design a PI controller for speed controller

1.3 ORGANIZATION OF THE THESIS

The presentation is organized as follows.

Chapter 1: This chapter introduces the SRM and explains the need of the controller

Chapter 2: This chapter briefly describes the constructional features, the principle of

operation and also applications of SRM

Chapter 3: This chapter explains the need for converter, various types and basic converter

operation of SRM

Chapter 4: This chapter gives the details of the mathematical modeling and design of PI

controller for SRM

Chapter 5: This chapter deals with the simulation of the SRM using MATLAB / SIMULINK

and comparision of results (speed responses) with and without PI controller.



2. PRINCIPLE OF OPERATION OF THE SWITCHED RELUCTANCE MOTOR

2.1 INTRODUCTION

The switched reluctance motor (SRM) drives for industrial applications are of recent

origin. Since 1969, a variable reluctance motor has been proposed for variable speed

applications. The origin of this motor can be traced back to 1842, but the “reinvention” has

been possible due to the advent of inexpensive, high-power switching devices. Even though

this machine is a type of synchronous machine, it has certain novel features.

2.2 CONSTRUCTION OF SWITCHED RELUCTANCE MOTOR

SRMs are made up of laminated stator and rotor cores with Ns=2mq poles on the

stator and Nr poles on the rotor. The number of phases is m and each phase is made up of

concentrated coils place on 2q stator poles. Most favored configuration amongst many more

options are 6/4 three phase and 8/6 four phase SRM’s as shown in the figure 2.1(a).

These two configurations correspond to q=1(one pair of stator poles (and coils) per

phase) but q may be equal to 2, 3 when, for the three phase machine, we obtain 12/8 or 18/12

topologies applied either for low speed high torque direct drives or for high speed stator

generator systems for aircraft. The stator and rotor pole angles βs and βr are, in general,

almost equal to each other to avoid zero torque zones.

It has wound field coils of a dc motor for its stator windings and has no coils or

magnets on its rotor. Both the stator and rotor have salient poles, hence the machine is

referred to as a doubly salient machine. Such a typical machine is shown in Figure 2.1(a),

and a modified version with two teeth per pole is shown in Figure 2.1(b).



Figure 2.1 Switched reluctance motor configurations. (a) One tooth per pole. (b) Two teeth per pole

(12/10 poles).



The rotor is aligned whenever diametrically opposite stator poles are excited. In a

magnetic circuit, the rotating member prefers to come to the minimum reluctance position at

the instance of excitation. While two rotor poles are aligned to the two stator poles, another

set of rotor poles is out of alignment with respect to a different set of stator poles. Then, this

set of stator poles is excited to bring the rotor poles into alignment. Likewise, by sequentially

switching the currents into the stator windings, the rotor is rotated. The movement of the

rotor, hence the production of torque and power, involves switching of currents into stator

windings when there is a variation of reluctance; therefore, this variable speed motor drive is

referred to as a switched reluctance motor drive.

2.3 TYPES OF SRM

Figure 2.2 Types of SRM



2.4 ADVANTAGES AND DISADVANATGES OF SRM

2.4.1 Advantages

The SRM possess a few unique features that makes it a vigorous competitor to

existing AC and DC motors in various adjustable-speed drive and servo applications. The

advantages of an SRM can be summarized as follows:

• Machine construction is simple and low-cost because of the absence of rotor winding

and permanent magnets.

• Bidirectional currents are not necessary, which facilitates the reduction of the

number of power switches in certain applications.

• The bulk of the losses appears in the stator, which is relatively easier to cool.

• The torque–speed characteristics of the motor can be modified to the application

requirement more easily during the design stage than in the case of induction and PM

machines.

• The starting torque can be very high without the problem of excessive in-rush current

due to its higher self-inductance.

• The maximum permissible rotor temperature is higher, since there are no permanent

magnets.

• There is low rotor inertia and a high torque/inertia ratio.

• Extremely high speeds with a wide constant power region are possible.

• There are independent stator phases, which do not prevent drive operation in the case

of loss of one or more phases.

2.4.2 Disadvantages

The SRM also comes with a few disadvantages among which torque ripple and

acoustic noise are the most critical. The higher torque ripple also causes the ripple current in

the DC supply to be quite large, necessitating a large filter capacitor. The doubly salient

structure of the SRM also causes higher acoustic noise compared with other machines.

The absence of permanent magnets imposes the burden of excitation on the stator

windings and converter, which increases the converter KVA requirement. Compared with

PM brushless machines, the per unit stator copper losses will be higher, reducing the



efficiency and torque per ampere. However, the maximum speed at constant power is not

limited by the fixed magnet flux as in the PM machine, and, hence, an extended constant

power region of operation is possible in SRMs.

2.5 APPLICATIONS OF SRM

The simple motor structure and inexpensive power electronic requirement have made

the SRM an attractive alternative to both AC and DC machines in adjustable-speed drives.

Few of such applications are listed below.

• General purpose industrial drives;

• Application-specific drives: compressors, fans, pumps, centrifuges;

• Domestic drives: food processors, washing machines, vacuum cleaners;

• Electric vehicle application;

• Aircraft applications;

• Servo-drive.

Below are some specific real world applications.

• CompAir Broomwade Limited uses switched reluctance motors in some of its

variable speed compressors.

• Besam AB uses switched reluctance motors in its Besam EMD 3000 sliding door

operating system

• Smallfry utilises a compact SRM in its “next generation of food processors”.

• SR Drives Manufacturing Ltd manufactures switched reluctance motors for use in

hazardous environments such as mines.

• Automotive applications such as power steering.



2.6 ELEMENTARY OPERATION OF THE SWITCHED RELUCTANCE

MOTOR

Consider that the rotor poles r1 and r1′ and stator poles c and c′ are aligned. Apply a

current to phase a with the current direction as shown in Figure 2.3(a). A flux is established

through stator poles a and a ′and rotor poles r2 and r2′ which tends to pull the rotor poles r2

and r2′ toward the stator poles a and a’, respectively. When they are aligned, the stator current

of phase a is turned off and the corresponding situation is shown in Figure 2.3(b). Now the

stator winding b is excited, pulling r1 and r1′ toward b and b′, in a clockwise direction.

Likewise, energization of the c phase winding results in the alignment of r2 and r2′ with c and

c′, respectively. Hence, it takes three phase energizations in sequence to move the rotor by 900

and one revolution of rotor movement is effected by switching currents in each phase as

many times as there are number of rotor poles. The switching of currents in the sequence acb

results in the reversal of rotor rotation is seen with the aid of Figures 2.3(a) and (b).

Figure 2.3 Operation of an SRM. (a) Phase c aligned. (b) Phase a aligned.



2.7 PRINCIPLE OF OPERATION OF THE SWTICHED RELUCTANCE

MOTOR

The torque production in the switched reluctance motor is explained using the

elementary principle of electromechanical energy conversion in a solenoid, as shown in

Figure 2.4(a). The solenoid has N turns, and when it is excited with a current i the coil sets up

a flux φ.Increasing the excitation current will make the armature move towards the yoke,

which is fixed. The flux vs. magneto motive force (mmf) is plotted for two values of air gap,

x1 and x2, where x1 > x2 and is shown in Figure 2.4(b).The flux vs. mmf characteristics for x1

are linear because the reluctance of the air gap is dominant, making the flux smaller in the

magnetic circuit. The electrical input energy is written as:

∫ ∫∫ ∫ ==== φφφFddiN

dt

dNdtidtieWe .................................. (2.1)

Where e is the induced emf and F is the mmf. This input electrical energy, We is equal to the

sum of energy stored in the coil, Wf , and energy converted into mechanical work, Wm . It is

written as:

mfe WWW += ................................................................................ (2.2)

When no mechanical work is done, as in the case of the armature starting from position x1,

the stored field energy is equal to the input electrical energy given by equation (2.1). This

corresponds to area OBEO in Figure 2.4(b). The complement of the field energy, termed co

energy, is given by area OBAO in Figure 2.4(b) and mathematically expressed as ∫φ dF

.Similarly, for the position x2 of the armature, the field energy corresponds to area OCDO

and the co energy is given by area OCAO. For incremental changes, equation (2.2) is written

as:

mfe WWW δδδ += .................................................................... (2.3)



Figure 2.4 solenoid and its characteristics, (a) A solenoid. (b) Flux v. mmf characteristics.

For a constant excitation of F1 given by the operating point A in Figure 2.4b, the various

energies are derived as:

)()( 211

2

1

1 BCDEBareaFdFWe =−== ∫ φφφδφ

φ.................................... (2.4)

)()(||12

OBEOareaOCDOareaWWW XXfXXff −=−= == δδδ ........

(2.5)

Using Eqs. (2.3) to (2.5), the incremental mechanical energy is derived as:

)(OBCOareaWWW fem =−= δδδ ............................................. (2.6)

and that is the area between the two curves for a given magneto motive force. In the case of a

rotating machine, the incremental mechanical energy in terms of the electromagnetic torque

and change in rotor position is written as:

δθδ em TW = ............................................................................. (2.7)

Where Te is the electromagnetic torque and δθ is the incremental rotor angle. Hence,

the electromagnetic torque is given by:

δθδ m

e

WT = .................................................................................. (2.8)



For the case of constant excitation (i.e., when the mmf is constant), the incremental

mechanical work done is equal to the rate of change of co energy, ′fW which is nothing but

the complement of the field energy. Hence, the incremental mechanical work done is written

as:

′= fm WW δδ ............................................................................. (2.9)

Where

∫ ∫ ∫ ∫ ∫=====′ diiiLdiidiNiNddFW f ),(),()()( θθλφφφ ...................

(2.10)

Where the inductance, L, and flux linkages, λ, are functions of the rotor position and

current. This change in co energy occurs between two rotor positions, θ2 and θ1. Hence, the

air gap torque in terms of the co energy represented as a function of rotor position and

current is

tconsiffm

e

iWWWT tan|

),(=

′=

′==

δθθδ

δθδ

δθδ ....................................... (2.11)

If the inductance is linearly varying with rotor position for a given current, which in

general is not the case in practice, then the torque can be derived as:

2

),( 2i

d

idLTe θ

θ= ......................................................................... (2.12)

Where

tconsi

iLiL

d

idL

tan12

12 |),(),(),(

=−−

=θθ

θθθ

θ............................................. (2.13)

and this differential inductance can be considered to be the torque constant expressed in

N.m/A2. It is important to emphasize at this juncture that this is not a constant and that it

varies continuously. This has the implication that the switched reluctance motor will not have

a steady-state equivalent circuit in the sense that the dc and ac motors have.



The following are the implications of equation (2.12)

• The torque is proportional to the square of the current; hence the current can be

unipolar to produce unidirectional torque. Note that this is quite contrary to the case

for ac machines. This unipolar current requirement has a distinct advantage in that

only one power switch is required for control of current in a phase winding. Such a

feature greatly reduces the number of power switches in the converter and thereby

makes the drive economical.

• The torque constant is given by the slope of the inductance vs. rotor position

characteristic. It is understood that the inductance of a stator winding is a function of

both the rotor position and current, thus making it nonlinear. Because of its nonlinear

nature, a simple equivalent circuit development for this motor is not possible.

• Since the torque is proportional to the square of the current, this machine resembles a

dc series motor; hence, it has a good starting torque.

• A generating action is made possible with unipolar current due to its operation on the

negative slope of the inductance profile.

• The direction of rotation can be reversed by changing the sequence of stator

excitation, which is a simple operation.

2.8 THE RELATIONSHIP BETWEEN INDUCTANCE AND ROTOR

POSITION (NON LINEAR ANALYSIS)

Since the torque characteristics are dependent on the relationship between flux

linkages and rotor position as a function of current, it is worthwhile to conceptualize the

control possibilities and limitations of this motor drive. For example, a typical phase

inductance vs. rotor position is shown in Figure 2.5 for a fixed phase current. The inductance

corresponds to that of a stator-phase coil of the switched reluctance motor neglecting the

fringe effect and saturation. The significant inductance profile changes are determined in

terms of the stator and rotor pole arcs and number of rotor poles. The rotor pole arc is

assumed to be greater than the stator pole arc for this illustration, which is usually the case.

From Figures 2.5(a) and (b), the various angles are derived as:



+−= )(

2

2

11 rs

rPββπθ ............................................................ (2.14a)

sβθθ += 12 ............................................................................. (2.14b)

)(23 sr ββθθ −+= .................................................................. (2.14c)

sβθθ += 34 ............................................................................ (2.14d)

rP

πθθθ 2145 =+= .................................................................... (2.14e)

Where βs and βr are stator and rotor pole arcs, respectively, and Pr is the number of rotor

poles.

Four distinct inductance regions emerge:

FIGURE 2.5 Derivation of inductance vs. rotor position from rotor and stator pole arcs for an

unsaturated switched reluctance machine. (a) Basic rotor position definition in a two pole SRM.

(b) Inductance profile.



1. 0 − θ1 and θ4 − θ5: The stator and rotor poles are not overlapping in this region

and the flux is predominantly determined by the air path, thus making the

inductance minimum and almost a constant. Hence, these regions do not

contribute to torque production. The inductance in this region is known as

unaligned inductance, Lu.

2. θ1 − θ2: Poles overlap, so the flux path is mainly through stator and rotor

laminations. This increases the inductance with the rotor position, giving it a

positive slope. A current impressed in the winding during this region produces a

positive (i.e., motoring) torque. This region comes to an end when the overlap

of poles is complete.

3. θ2 − θ3: During this period, movement of rotor pole does not alter the complete

overlap of the stator pole and does not change the dominant flux path. This has

the effect of keeping the inductance maximum and constant, and this inductance

is known as aligned inductance, La. As there is no change in the inductance in

this region, torque generation is zero even when a current is present in this

interval. In spite of this fact, it serves a useful function by providing time for the

stator current to come to zero or lower levels when it is commutated, thus

preventing negative torque generation for part of the time if the current has been

decaying in the negative slope region of the inductance.

4. θ3 − θ4: The rotor pole is moving away from overlapping the stator pole in this

region. This is very much similar to the θ1 − θ2 region, but it has decreasing

inductance and increasing rotor position contributing to a negative slope of the

inductance region. The operation of the machine in this region results in

negative torque (i.e., generation of electrical energy from mechanical input to

the switched reluctance machine).

It is not possible to achieve the ideal inductance profiles shown in Figure 2.5 in an

actual motor due to saturation. Saturation causes the inductance profile to curve near the top

and thus reduces the torque constant. Hence, saturating the machine beyond a point produces

a diminishing return on torque and power output.



ALIGNED INDUCTANCE AND UNALIGNED INDUCTANCE

Let LA be the aligned inductance of a coil/Phase and LU be the unaligned inductance

of the coil / phase. βs and βr are stator and rotor pole arcs, respectively. Let us assume that βr

> βs and LA >LU.

CASE I: When θ=00

Axis of the stator pole is in alignment with the stator pole as shown in the figure below.

Therefore the inductance of the coil is LA, because the stator reference axis and rotor

reference axis are in alignment. At this position flux linkage of phase winding of stator has

maximum value and hence inductance of phase winding has maximum value for given

current.



CASE II: When 2

sr ββθ −=

The rotor reference axis makes angular displacement of 2

sr ββθ −= stator reference axis

one edge of rotor pole is along the edge of stator pole. At this position reluctance is

minimum. Then the inductance of the coil continues to be LA. When θ varies from 0 to

2sr ββ −

. At this position also L=LA.

CASE III: When 2

sr ββθ +=

Pole pitch of the rotor = rN

π2

Half the pole pitch of the rotor =rN

π Assume

r

sr

N

πββθ <+

=2

In this position, the flux pattern is such that the flux linkages / unit current of the stator is less

than the previous case but not minimum. Therefore L < LA and L > LU.


LU < L < LA22

srsr ββθββ +<<−


At

CASE IV: When rN

πθ =

For r

sr

N

πθββ≤≤

+2


L=Lu


CASE V: When 2

sr ββθ += after

rN

π(or)

2

2 sr

rN

ββπθ +−= as far as the rotor pole is

considered. After which stator pole comes under the influence of the rotor pole 2. Now the

inductance variation is from LU to LA as the rotor pole moves towards so as to cover the stator

pole.



3. CONVERTERS FOR SRM DRIVES

3.1 POWER CONVERTER TOPOLOGY

As indicated by its name, phase-to-phase switching in the SRM drive must be

precisely timed with rotor position to obtain smooth rotation and the optimal torque output.

Rotor position feedback, or the so-called "sensor less" feedback method, is needed for proper

control. It is well known that this phase-to-phase switching is realized by power

semiconductors. The so-called power converter topology refers to different circuit structures

by power semiconductors, which can meet the SRM's switching operation mode requirement.

It is well known that the power converter topology has great influence on the SRM's

performance.

There are many researches on power converter topology for the SRM drive.

Generally speaking, there are two main classes: independent and dependent structure,

according to the criterion whether it makes the control between the successive excited phases

independent or not. In most cases, the dependent structure topology needs less power

semiconductors than the independent structures. Also, another key difference between them

is that they have different dwell angle requirements. Especially for the dependent structures,

there are certain limitations on the dwell angles for proper motor control. These limitations

directly affect the commutation strategy, which is the main reason why the converter

topology has considerable influence on the SRM's performance.

Since the torque in SRM drives is independent of the excitation current polarity, the

SRM drives require only one switch per phase winding. This is contrary to the ac motor

drives where at least two switches per phase are required for current control. Moreover, the

windings are not in series with the switches in ac motor drives, leading to irreparable damage

in shoot-through faults. The SRM drives always have a phase winding in series with a

switch.

In case of a shoot-through fault, the inductance of the winding limits the rate of rise in

current and provides time to initiate protective relaying to isolate the faults. The phases of the



SRM are independent and, in case of one winding failure, uninterrupted operation of the

motor drive operation is possible, although with reduced power output.

3.2 CONVERTER CONFIGURATIONS

The mutual coupling between phases is negligible in SRMs. This gives complete

independence to each phase winding for control and torque generation. While this feature is

advantageous, a lack of mutual coupling requires a careful handling of the stored magnetic

field energy. The magnetic field energy has to be provided with a path during commutation

of a phase; otherwise, it will result in excessive voltage across the windings and hence on the

power semiconductor switches leading to their failure. The manner in which this energy is

handled gives way to unique but numerous converter topologies for SRM drives. The energy

could be freewheeled, partially converting it to mechanical/electrical energy and partially

dissipating it in the machine windings. Another option is to return it to the dc source either by

electronic or electromagnetic means. All of these options have given way to power converter

topologies with q, (q+1), 1.5q, and 2q switch topologies, where q is the number of machine

phases.

3.2.1 Classification of Converter Configurations



Figure 3.1 Classifications of Converter Configurations

3.3 ASYMMETRIC BRIDGE CONVERTER

Figure 3.2a shows the asymmetric bridge converter considering only one phase of the

SRM. The rest of the phases are similarly connected. Turning on switches T1 and T2 will

circulate a current in phase A of the SRM. If the current rises above the commanded value,

T1 and T2 are turned off. The energy stored in the motor winding of phase A will keep the

current in the same direction until it is depleted. Hence, diodes D1 and D2 will become

forward biased leading to recharging of the source. That will decrease the current, rapidly

bringing it below the commanded value. This operation is explained with the waveforms of

Figure 3.2(b).

Assuming that a current of magnitude Ip is desired during the positive inductance

slope for motoring action, the A -phase current command is generated with a linear

inductance profile. Here, phase advancing both at the beginning and during commutation are

neglected. The current command *ai is enforced with a current feedback loop where it is

compared with the phase current, ia. The current error is presumed to be processed through a

hysteresis controller with a current window of i∆ .When the current error exceeds i∆− , the

switchesT1 and T2 are turned off simultaneously.

Hysteresis current controller is considered here due to its simplicity in concept and

implementation. At that time, diodes, D1 and D2 take over the current and complete the path

through the dc source.



Figure 3.2 (a) Asymmetric converter for SRM with freewheeling and regeneration capability.

Note that the voltage of phase A is then negative and will equal the source voltage,

Vdc. During this interval, the energy stored in the machine inductance is sent to the source,

thus exchanging energy between the load and source repeatedly in one cycle of a phase

current. After the initial startup, during turn-on and turn-off of T1 and T2, the machine phase

winding experiences twice the rate of change of dc link voltage, resulting in a higher

deterioration of the insulation. This control strategy (strategy I) hence puts more ripples into

the dc link capacitor, thus reducing its life and also increasing the switching losses of the

power switches due to frequent switching necessitated by energy exchange. These can be

ameliorated with an alternate switching strategy.



Figure 3.2 (b) Operational waveforms of the asymmetric bridge converter (strategy I);

(c) Operational waveforms of the asymmetric bridge converter (strategy II).

The energy stored in the phase A can be effectively circulated in itself by turning off,

say, T2 only (strategy II). In that case, the current will continue to flow through T1, phase A,

and D1, the latter having forward biased soon after T2 is turned off. The voltage across the

winding becomes zero if the diode and transistor voltage drops are neglected as shown in

Figure 3.2c. That will take the phase current from iI P ∆+ to iI P ∆− in a time greater than

had it been forced against the source voltage using the previous strategy. This particular fact

reduces the switching frequency and hence the switching losses.



When the current command goes to zero, both T1 and T2 are turned off

simultaneously. During this interval, the voltage across the winding is −Vdc as long as D1 and

D2 conduct (i.e., until ia goes to zero) and thereafter the winding voltage is zero. The voltage

across T2 during its off time and when T1 is on is equal to the source voltage, Vdc. Hence, the

power switches and diodes have to be rated to a minimum of source voltage at least. The

current ratings of the switches are equal to or less than qI P by interchanging the off times

between T1 and T2 in one cycle of phase conduction.

Similarly, the current rating of the diodes can be evaluated. While such a self-

circulation will keep the current going for a longer time compared to recharging the source

voltage, it has the advantage of converting the stored energy to useful mechanical work.

While this form of control can be used for current control, the recharging of the source is

advantageous when the current has to be turned off rapidly.

Such an instance arises when the inductance profile becomes flat or is starting to have

a negative slope. Any further conduction of current in such regions entails a loss of energy or

production of negative torque, thus reducing the average motoring torque. Note that this

converter requires two transistors and two diodes for each phase, resembling the conventional

ac motor drives.



4. MODELLING AND CONTROL OF SRM

4.1 MATHEMATICAL MODEL

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 flux linkages and is given as:

dt

idiRV S

),(θλ+= ..................................................................... (4.1)

Where Rs is the resistance per phase, and λ the flux linkage per phase given by:

iiL ),(θλ= .......................................................................................

(4.2)

Where L is the inductance dependent on the rotor position and phase current. Then, the phase

voltage is:

id

idL

dt

diiLiR

d

idL

dt

di

dt

diiLiR

dt

iidLiRV

mS

SS

ωθθθ

θθθθθ

),(),(

),(),(

),(

++=

++=+=.......................

(4.3)

In this equation, the three terms on the right-hand side represent the resistive voltage

drop, inductive voltage drop and induced emf, respectively. The induced emf, e, is expressed

as:

iKid

idLe mbm ωω

θθ == ),(

........................................................... (4.4)

Multiplying both sides of the equation (4.3) with the current gives the instantaneous power.

22 ),(),( i

d

idL

dt

diiiLiRViP mSi ω

θθθ ++== ....................................(4.5)



The energy stored by an inductor is given by

2

2

1iLW = ................................................................................ (4.6)

Power in an inductor is given as the change in energy over time. The product rule gives

θθω

θ d

idiL

d

dLi

d

idiL

dt

dLiiL

dt

dPL +=+=

= 222

2

1

2

1

2

1..................

(4.7)

Using the law of conservation of energy the mechanical power can be found by

subtracting the power loss due to the winding resistance and the inductor. Subtracting

equation (4.7) and Ri2 from equation (4.5) will give

2),(

2

1i

d

idLP mi ω

θθ= .............................................................. ...........

(4.8)

Hence, the induced voltage contains information about the rotor position. This property can

be exploited for position feedback without a shaft sensor. With constant current, (4.4) is linked to

both increase in magnetic field energy and produced mechanical power. In unsaturated conditions,

both terms equal each other, and torque can be expressed as:

θθ

d

idLiT

),(

2

2

= ......................................................................... (4.9)

When 0>θd

dL the torque is positive and electrical power is converted into mechanical

output (motoring), while when 0<θd

dL the torque is negative and mechanical power is converted

into electrical power (generating). Note that the produced torque is independent of the direction of the

current, since i2 always positive. With the machine driven in saturation, although (4.9) being no

longer valid, these conclusions remain true.

Fig.4.1 illustrates the equivalent circuit for one phase of the SRM.



Figure 4.1 Single phase equivalent circuit of SRM

4.2 PID CONTROLLER

It is well known that a conventional proportional integral-derivative (P1D) type

controller is most widely used in industry due to its simple control structure, easy of design

and inexpensive cost. PID Controller was regarded as the standard control structures of the

classical control theory and fuzzy controllers positioned themselves as a counterpart of

classical PID controllers. More than 90% of the control loops were of the PID type. The PID

Controller formulas are simple and can be easily adopted corresponding to different

controlled plant.

A PID controller attempts to correct the error between a measured variable and a

desired variable by calculating and then outputting a corrective action that can adjust the

process accordingly. The general structure of PID Controller is as shown in the fig.4.2.

Figure 4.2. Structure PID Controller



A standard PID controller is also known as the “three-term” controller, whose

transfer function is generally written in the ideal form as

)1

1( sTsT

KG di

PID ++= …………………………………………………….. (4.10)

Where

K is the proportional gain

Ti is the integral time constant

Td is the derivative time constant

The following are the three-term functionalities:

• The proportional term is providing an overall control action proportional to the error

signal through the all-pass gain factor. A proportional gain (K) will have the effect of

reducing the rise time and will reduce, but never eliminate, the steady state error.

• The integral term is reducing steady-state errors through low-frequency compensation

by an integrator. The Integral term determines the reaction based on the sum of recent

errors

• The derivative term is improving transient response through high-frequency

compensation by a differentiator. The Derivative term determines the reaction to the

rate at which the error has been changing.

Effects of each of controllers K, K d, and Ki on a closed-loop system are

summarized in the table 4.1shown below. Change one of these variables can change the

effect of the other two variables.

Gain/Effects Rise Time Overshoot Settling Time S-S Error

K Decrease Increase Small Change Decrease

Ki Decrease Increase Increase Eliminate

Kd Small Change Decrease Decrease Small Change



Table 4.1 Effects of each of controllers K, Kd, and Ki on a closed-loop system


wref

TL


4.3 GENERAL BLOCK DIAGRAM

Figure 4.3 General block diagram.

4.4 BLOCK DIAGRAM OF TRADITIONAL FEEDBACK CONTROL

Figure 4.4 Block diagram of traditional feedback control



5. SIMULATION AND RESULT ANALYSIS

The simulation of the SRM using MATLAB/SIMULINK and comparision of the

results with and without PI controller is dealt in this chapter.

5.1 SWITCHED RELUCTANCE MOTOR SPECIFICATIONS:

Stator resistance : 0.01 Ohm/phase

Inertia : 0.0082 Kg.m2

Friction : 0.01N m s

Initial speed : 0 rad/sec

Position : 0 rad

Unaligned Inductance : 0.7mH

Aligned Inductance : 20mH

Maximum Current : 450A

Maximum Flux Linkage : 0.486 weber-turn

The SRM with PI controller is simulated using MATLAB/Simulink as shown in fig 5.1

Fig 5.1 The SRM with PI controller is simulated using MATLAB/Simulink



5.2 RESULTS

Case (i): When the reference speed is high i.e ωr= 4000rpm and at no load i.e TL= 0.

The fig 5.2 shows that the SRM speed tracks the reference speed without any ripples.

It can be observed that the percentage maximum peak overshoot is below 7.5 and the settling

time is 0.9 sec (for 2% tolerance).This shows that the designed PI controller works

satisfactorily for high speed operation of SRM.

Fig 5.2 Output speed tracking Reference Speed



The fig 5.3 shows that the stator winding phase inductance is a function of angular

position of the rotor .It can be observe that the aligned Inductance is 18 mH and unaligned

Inductance is 0.8 mH

Figure 5.3 The stator winding phase Inductance

Figure 5.4 The stator winding phase Inductance (Magnified view)



Figure 5.5 The stator winding 3-phase current

Figure 5.6 The stator winding 3-phase current (Magnified view)







Case (ii): When the reference speed is low i.e ωr= 200rpm and at no load i.e TL= 0.

The fig 5.9 shows that the SRM speed tracks the reference speed with very low

ripples.It can be observed that the percentage maximum peak overshoot is 0 and the settling

time is 0.5sec.

Figure 5.9 Output speed tracking Reference Speed

From the figures 5.2 and 5.9, it can be observed that the SRM works satisfactorily for

high speed applications.



The fig 5.10 shows that the stator winding phase inductance is a function of angular

position of the rotor .It can be observe that the aligned Inductance is 18 mH and unaligned

Inductance is 0.8 mH

Figure 5.10 The stator winding phase Inductance

Figure 5.11 The stator winding phase Inductance (Magnified view)



Fig 5.12 the stator winding 3-phase current

Figure 5.13 The stator winding 3-phase current (Magnified view)







Case (iii): When the reference speed is low i.e ωr= 200rpm and a load of 10 N-m.

applied at 1sec.

The fig 5.16 shows that the SRM speed tracks the reference speed at 0.5 sec (Settling

time=0.5 sec) before the load is applied at 1sec and it can be observed that the srm speed

tracks the reference speed once again with low ripples.

Figure 5.16 Output speed tracking Reference Speed before and after applied a load of 10N-m at 1sec.

Case (iv): When the reference speed is high i.e. ωr= 4000rpm and a load of 10 N-m.

applied at 1.5sec.

The figure 5.17 shows that the SRM tracks the reference speed at 0.9 sec(2%

tolerance) before the load is applied at 1.5 sec and it can be observed that the SRM tracks the

reference speed once again.

Figure 5.17:Output speed tracking Reference Speed before and after applied a load of 10N- m at 1.5sec



Case (v): When the reference speed is low i.e ωr= 200rpm and a load of 5 N-m.is applied at 0.75sec.and it is increased to 10N-m is applied at 1.5 sec.

The fig 5.18 shows that the SRM speed reaches the reference speed at 0.5 sec before

the different loads are applied at 0.75sec and 1.5sec and it can be observed that the srm speed

reaches the reference speed once again with low ripples.

Figure 5.18 Output speed before and after applied loads of 5N-m at 0.75sec and 10N-m at 1.5sec.

Case (vi): When the reference speed is high i.e ωr= 4000rpm and at load of 5 N-m.is applied at 1.7sec another load of 10N-m applied at 2s.

The fig 5.19 shows that the SRM speed tracks the reference speed at 0.9 sec before

the load is applied at 1.7sec and another load is applied at 2s and it can be observed that the

srm speed tracks the reference speed once again with low ripples.

Figure 5.19 Output speed before and after applied loads of 5N-m at 1.7sec and 10N-m at 2sec.



Case (vii): When the reference speed is low i.e ωr= 100rpm up to 1.5sec and it is increased

to 200 rpm after 1.5sec at no load.

The fig 5.20 shows that the SRM speed tracks the variable reference speeds one at 0.5

sec another at 2sec.

Figure 5.20 Output speed tracking variable Reference Speeds

Case (viii): When the reference speed is high i.e ωr= 2000rpm at 0sec and another 4000rpm

at 1.5sec at no load.

The fig 5.21 shows that the SRM speed tracks the variable reference speeds one at 0.5

sec another at 2.5sec

Figure 5.21 Output speed tracking variable Reference Speeds



CONCLUSIONS

The Switched Reluctance Motor's double salient structure makes its magnetic

characteristics highly nonlinear and the flux linkage is also a nonlinear function of stator

currents as well as rotor position. All these make the control of the SRM a tough challenging.

In This work the constructional features, principle of operation, applications and

mathematical model of the switched reluctance motor briefly described. A conventional PI

controller for a 6/4 SRM using MATLAB/SIMULINK is designed.

From the simulations it is being observed that the torque is developed during change

of inductance. For constant inductance (unaligned position) torque developed is zero. To get

positive torque , voltage should apply during θddL+ region where as negative torque will

develop during θddL− region. Therefore exact switching (turn-on and turn-off angles) is

needed. Simulation helps to get exact switching angles. The simulation results shows that the

designed PI controller performs satisfactorily to track the reference speed for various cases

like no load , constant loads and variable loads at low , high speeds and variable speeds . It is

also observed that the designed PI controller completely eliminates ripples at high speeds.



REFERENCES

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Switched Reluctance Motor