Report srm

7/30/2019 Report srm

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MODELING AND STIMULATION OF SWITCHED

RELUCTANCE MOTOR

By

Anurag Choudhary

Avanish Kr. Verma

Abhinav Kumar

Pankaj Kumar

Submitted to the department of Electrical & Electronics

in partial ful fillment of the requirements

for the degree of

Bachelor of Technology

In

Electrical & Electronics

Vishveshwarya institute of engg & tech

G.B. Technical University

April, 2013


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DECLARATION

We hereby declared that the submission is my own work and that, to the best of my

knowledge and belief, its contain no material previously published or written by any other

person nor material which to a substantial extent has been accepted for the award of any other

degree or diploma of the university or other institute higher learning except where due

acknowledgment has been made in the text.

Signature

Name -

Date

Signature

Name -

Roll. No.-

Date

SignatureName

Roll. No. -

Date

Signature

Name -

Roll. No.-

Date


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CERTIFICATE

This is to certify the project report entitled Modeling & Stimulation Of Switched

Reluctance Motor, which is submitted by, name in partial fulfillment for the award of

degree B. Tech in Department of Electrical & Electronics of G.B. Technical University, is a

record of the candidate own worked carried out by him under my/our supervision. The matter

embodied is the thesis is original and has not been submitted for the award of any degree.

Date Supervisor

( )


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ACKNOWLEDGEMENT

It gives us a great sense of pleasure to present the report of the B. Tech project under taken

during B. Tech final year we owe special depth of gratitude to Mr Puneet Dixit, Department

of Electrical & Electronic, Vishweshwarya Institute Of Engineering & Technology, G.B.

Nagar for his constant support and guidance throughout the course of our work. His sincerity,

thoroughness and perseverance have been a constant source of inspiration for us. It is only his

cognizant efforts that our endeavors have seen light of the day.

We also take the opportunity to acknowledge the contribution of Head of Department Prof.

H.C. Sharma, of Electrical & Electronics, Vishweshwarya Institute Of Engineering &

Technology, G.B. Nagar for his full support and assistance during the development of the

project.

We also do not like to miss the opportunity to acknowledge the contribution of all faculty

members of the department for their kind assistance and cooperation during the development

of our project. Last but not the least we acknowledge our friends for their contribution in the

completion of the project.

Signature: Signature:

Name: Name:

Roll. No.: Roll. No.:

Date: Date:

Signature: Signature:

Name: Name:

Roll. No.: Roll. No.:

Date: Date:


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TABLE OF CONTENTS

LIST OF FIGURESABSTRACT

Chapter 1: Introduction1.1 Introduction1.2 SRM Controller1.3 Organization of ThesisChapter 2: Principle of Operation of the Switched Reluctance Motor2.1 Introduction2.2 Construction of Switched Reluctance Motor

2.3 Types of SRM2.4 Advantages and Disadvantages of SRM2.5 Applications of SRM2.6 Elementary Operation of the Switched Reluctance Motor

2.7 Principle of Operation of the Switched Reluctance Motor

2.8 The Relationship Between Inductance and Rotor Position

Chapter 3: Converters For SRM Drives3.1 Power Converter Topology3.2 Converter Configurations3.3 Asymmetric Bridge Converter

Chapter 4: Modelling and Control of SRM4.1 Mathematical Model4.2 PID controller4.3 General Block Diagram4.4 Block Diagram of Traditional Feedback Control

Chapter 5: Simulation and Result Analysis5.1 Switched Reluctance Motor Specifications5.2 ResultsCONCLUSIONREFERENCES


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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 rotorPosition 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 basedon 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

Figure 5.3 Stator winding phase Inductance

Figure 5.4 Stator winding phase Inductance


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Figure 5.5 Stator winding 3-phase current

Figure 5.6 Stator winding 3-phase current

Figure 5.7 Electromagnetic torque developed

Figure 5.8 Electromagnetic torque developed

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 for

low reference speed

Figure 5.12 Stator winding 3-phase current for

low reference speed

Figure 5.13 Stator winding 3-phase current for low

reference speed

Figure 5.14 Electromagnetic torque developed for low

reference speed

Figure 5.15 Electromagnetic torque developed 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 at0.75sec and 10N-m at 1.5sec

Figure 5.19 Output speed before and after applying loads of

5 N-m at1.7sec and 10N-m at 2.0sec

Figure 5.20 Output speed tracking variable reference

speeds for low speeds


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Figure 5.21 Output speed tracking variable reference speeds

for high speed


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ABSTRACT

Now a days, switched reluctance motors (SRMs) attract more and more attention. The

switched reluctance motor consist 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

non linear 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.


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1.INTRODUCTION1.1 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

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

e reluctance principle. SRM produce torque without any permanent magnets and with non-

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 potentialcandidatesfor applications in industrial and commercial

markets.Despite the simple mechanism and attractive capabilities, SRM have somelimitations

. 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 coi1excitati

ons 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

desiredstability 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 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.


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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 operatio

n 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 SRMChapter 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 SWITCHEDRELUCTANCE MOTOR

2.1 INTRODUCTION

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

recentorigin. 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 reinventionhas 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 favoured configuration amongst many more options are

6/4 three phase and 8/6 four phase SRMs as shown in the figure 2.1(a).These twoconfigurations 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 18/12topologies applied

either for low speed high torque direct drives or for high speed stator generator systems for

aircraft. The stator and rotor pole angles s and rare, in general, almost equal to each otherto 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).


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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 sequentiallyswitching 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


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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 ofan SRM can be summarized as follows:

Machine construction is simple and low-cost because of the absence of rotor winding andpermanent magnets.

Bidirectional currents are not necessary, which facilitates the reduction of thenumber ofpower switches in certain applications.

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

The torquespeed characteristics of the motor can be modified to the applicationrequirement 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 toits higher self-inductance.

The maximum permissible rotor temperature is higher, since there are no permanentmagnets.

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


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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 lossof one or more phases.

2.4.2 Disadvantages

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

Comp Air Broom wade Limited uses switched reluctance motors in some of its variablespeed compressors.

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

Smallfry utilisesa compact SRM in its next generation of food processors.

SR Drives Manufacturing Ltd manufactures switched reluctance motors for use inhazardous environments such as mines.


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Automotive applications such as power steering.

2.6 ELEMENTARY OPERATION OF THE SWITCHED

RELUCTANCEMOTOR

Consider that the rotor poles r1 and r1 and stator poles c and c are aligned. Apply a currentto 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 r2toward 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 cand c, respectively. Hence, it takes three phase energizations in sequence to move therotor by 90 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 thesequence acb results in the reversal of rotor rotation is seen with the aid of Figures 2.3(a) and

(b

2.7 PRINCIPLE OF OPERATION OF THE SWTICHED

RELUCTANCE MOTOR

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

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 .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


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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:

We=eidt = idt

= Nid= Fd(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 intomechanical work, Wm. It is written as:

= + ....................................... (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 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:

= + ................................................. (2.3)

Fig 2.4 Solenoid and its characteristics (a) A Solenoid (b) Flux vs mmf characteristics

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

energies are derived as:

= d=( =area(BCDEB)..(2.4)

( ((2.5)

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

(..(2.6)


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

arotating machine, the incremental mechanical energy in terms of the electromagnetic

torqueand change in rotor position is written as:.................................................................(2.7)

Where Te is the electromagnetic torque and is the incremental rotor angle. Hence,theelectromagnetic torque is given by:

.(2.8)

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

mechanical work done is equal to rate of change of co energy, Wf Which is nothing but thecomplement of the field energy. Hence, the incremental mechanical work done is written as:

(2.9)

Where

( ( ..(2.10)

Where the inductance L, and flux linkage,are function of rotor position and current.This

change in co energy occurs between two rotor positions,2&1. Hence the air gap torque interms of the co energy represented as a function of rotor position and current is

(

(2.11)

If the inductance is linearly varying with rotor positin for a given current, which in general isnot the case in practice, then the torque can be derived as:

(

( ..(2.12)

Where

(

((

| .(2.13)

and this differential inductance can be considered to be torque constant expressed in N.m/A.it is important to this juncture that this is not a constant and 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)

T h e to rq u e i s p ro p o r t io n a l to th e sq u are o f th e cu r ren t ; h en ce th ec u r r en t c a n b e 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 ofpower swi tch es in the converter and ther eb y makes the drive economical.


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The torque constant is given by the the slope of the inductance vs. rotor positioncharacteristic. 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 resemblesadc 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 of can be reversed by changing the seqenuence ofstator excitation, which is a simple operation.

2.8 The relationship between Inductance & Rotor Position

(NON LINEAR ANALYSIS)

Since the torque characteristics are dependent on the relationship between flux linkage

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

possibilities and limitations in this motor drive. For ex. A typical phase inductance vs.

rotor position is shown in fig. 2.5 for a fixed phase current. The inductance corresponds

to that of a stator phase coil of the SRM neglecting the fringe effect and saturation. The

significant inductance profile changes the determined in terms of the stator & rotor polearcs & 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 figure 2.5(a)&(b), the various angle are derived as:

( (2.14a)

.. (2.14b)

( (2.14c) .(2.14d)

.(2.14e)

Where & are stator and rotor pole arcs, respectively and is the number of rotor poles.

Four distinct inductance regions emerge:


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FIGURE 2.5 Derivation of inductance vs. rotor position from rotor and stator pole arcs foran unsaturated SRM.(a) basic rotor position definition in a two pole SRM. (b) Inductance

profile.

1.0 and : The stator and rotor poles are not overlapping in this regionan d t h ef lu x i s p red o min an t ly d e te rmin ed b y th e a i r p a th , th u s mak in g

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

co n t r ib u te to to rq u e p ro d u c t io n . T h e in d u c tan ce in th i s r eg io n i s k n o wn

a s unaligned inductance, .

2. : Po les o v er l ap , so th e f lu x p a th i s ma in ly th ro u g h s t a to r an drotor 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

overlapof poles are complete.

3.: During this period, movement of rotor pole does not alter the complete overlap ofthe stator pole and does not change the dominant flux path. This has the effect of keeping the

inductance maximum and constant, and this inductanceis known as aligned inductance,

. 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


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serves a useful function by providing time for thestator current to come to zero or

l o we r l ev e ls wh e n i t i s c om mu t at ed , th us preventing negative torque generation

for part of the time if the current has been decaying in the negative slope region of the

inductance.4. : The rotor pole is moving away from overlapping the stator pole in this region.This is very much similar to the region, but it has decreasing inductance andincreasing rotor position contributing to a negative slope of the in du ct an ce r e gi on . Th eoper at ion o f the mach ine in th is reg ion resu l t s 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 & UNALIGNED INDUCTANCE

Let be the aligned inductance of a coil/Phase and be the unaligned inductanceof the coil / phase. nd are stator and rotor pole arcs, respectively. Let us assumethat > and >;

CASE 1: When

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

inductance of coil is , because the stator reference axis and rotor reference axisare in alignment. At this position flux linkage of phase winding of stator has

maximum value & hence inductance of phase winding has maximum value forgiven current.


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CASE 2: When

The rotor reference axis makes angular displacement of stator reference axisone edge of rotor pole is along the edge of stator pole. At this position reluctance is

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

.

At this position also L=.

CASE 3: When

Pole pitch of rotor =

Half the pole pitch of rotor =

Assume

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

previous case but not minimum. Therefore L


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&

CASE 4: When =

For

L=


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CASE 5: When after

(

as far as the pole is

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

inductance variation is from as the rotor pole moves towards so as to cover the statorpole.

CHAPTER 3


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CONVERTERS FOR SRM DRIVES

3.1 POWER CONVERTER TOPOLOGY

As in d ica ted b y i t s n ame , p h ase - to -p h ase swi tch in g in SRM d r iv e

mu s t b e p rec i se ly t imed wi th ro to r p o s i t io n to o b ta in smo o th

ro ta t io n & o p t imal to rq u e o u tp u t . Ro to r p o s i t io n feed b ack , o r so

c a l l e d se nso r l e s s f eed b ack , i s n eed ed fo r p o wer semico n d u c to r s .T h e so -ca l l ed p o wer co n v er t e r to p o lo g y re fe r s to d i f f e ren t c i r cu i t

s t ru c tu res b y p o wer semico n d u c to r s , wh ich can mee t th e SRMs sw i t ch in g o p era t io n mo d e req u i remen t . I t i s we l l k n o wn th a t p o wer

co n v er t e r to p o lo g y h as g rea t in f lu en ce o n th e SRMs p er fo rman ce .

T h ere a re man y resea rch es o n p o wer co n v er t e r to p o lo g y fo r SRM d r iv e . Gen era l ly sp eak in g , th e re a re two main c l asses :

in d ep en d en t & d ep en d en t s t ru c tu re , acco rd in g to th e c r i t e r io n

wh e th er i t mak es th e co n t ro l b e tween ex c i t ed p h ases in d ep en d en t

o r n o t . In mo s t cases , t h e d ep en d en t s t ru c tu re to p o lo g y n eed s l e s s

p o wer s em ic on d u c t o r s t h an in d ep e nde n t s t r u c t u r e . Al s o , a no t h er

k ey d i f f e ren ce b e tween th em i s th a t th ey h av e d i f f e ren t d wel l

an g le r eq u i remen t s . E sp ec ia l ly fo r th e d ep en d en t s t ru c tu res , t h e re

a re ce r t a in l im i ta t io n s o n th e d wel l an g les fo r p ro p er mo to r

co n t ro l . T h ese l im i ta t io n s d i rec t ly a f fec t th e co mmu ta t io n s t r a t eg y ,

wh ich i s th e main reaso n wh y th e co n v er t e r to p o lo g y h as

co n s id e rab le in f lu en ce o n SRMs p er fo rman ce .

S in ce th e to rq u e in SRM d r iv es i s in d ep en d en t o f th e

ex c i t a t io n cu r ren t p o la r i ty , t h e SRM d r iv es r eq u i re o n ly o n e swi tch

p e r p h as e w i n d in g . T h i s i s co n t r a ry t o th e a c m ot o r d r i v es wh e r e a t

l eas t two swi tch es p e r p h ase a re r eq u i red fo r cu r ren t co n t ro l .

Mo reo v er , t h e w in d in g s a re n o t in se r i e s w i th th e swi tch es in ac

mo to r d r iv es , l ead in g to i r r ep arab le d amag e in sh o o t - th ro u g h

fau l t s . T h e SRM d r iv es a lway s h av e a p h ase w in d in g in se r i e s w i tha swi tch .

In case o f a sh o o t - th ro u g h fau l t , t h e in d u c tan ce o f th e

win d in g l im i t s th e r a t e o f r i se in cu r ren t & p ro v id es t ime to in i t i a t e

p r o t e c t i v e r e l a yi n g t o i so la t e t he f a u l t s . Th e ph a s es o f th e SRM a re

in d ep en d en t an d , in case o f o n e w in d in g fa i lu re , u n in te r ru p ted

o p era t io n o f th e mo to r d r iv e o p era t io n i s p o ss ib le , a l th o u g h wi th

red u ced p o wer o u tp u t .


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3.2 CONVERTER CONFIGURATION

T h e mu tu a l co u p l in g b e tween p h ases i s n eg l ig ib le in SRMs. T h i s

g iv es co mp le te in d ep en d en ce to each p h ase w in d in g fo r co n t ro l

& to rq u e g en era t io n . Wh i le th i s f ea tu re i s ad v an tag eo u s , a l ack

o f mu tu a l co u p l in g req u i res a ca re fu l h an d l in g o f s to redmag n e t i c f i e ld en erg y . T h e mag n e t i c f i e ld en erg y h ad to b e

p ro v id e d wi t h a p a t h du r i n g co mm ut a t i o n o f a ph a s e ; 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.


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3.2.1Classification 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 switchesT1 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 D 1 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 i* a is enforced with a currenfeedback loop where it is

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


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a hysteresis controller with a current window of i .When the current error exceedsi, 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 andregeneration 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 powerswitches due to frequent switching necessitated by energy exchange. These can be ameliorated


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with an alternate switching strategy.

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 T 1, 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 fromIPi to IPI 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.

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

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


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

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

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

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

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

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

between T1 and T2 in one cycle of phaseconduction.

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

circulationwill 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 theinductance profile becomes flat or is starting to have a

negative slope. Any furtherconduction 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 twotransistors and two diodes for each phase, resembling the conventional ac

motor drives.


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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 sumof the resistive voltage drop and the rate of the flux linkages and is given as

((4.1)

WhereRsis the resistanceper phase, and the flux linkage per phase given by:

L(, i)I (4.2)

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

voltage is ( (

(

( +(

(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

( (4.4)

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

( (

.. (4.5)

The energy stored by an inductor is given by

.(4.6)

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

) ..(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

(

..(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,


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

(

..4.9

> 0 the torque is positive and electrical power is converted into mechanical output

(motoring), while when < 0the 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 CONTROLLERIt 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.


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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

( .(4.10)Where

Kis the proportional gain

Ti is the integral time constant

Tdis the derivative time constant

The following are the three-term functionalities:

The proportional term is providing an overall control action proportional to the errorsignal 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 compensationby an integrator. The Integral term determines the reaction based on the sum of recent errors

The derivative term is improving transient response through high-frequencyCompensation 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, Kd, 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.


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4.3 GENERAL BLOCK DIAGRAM

Figure 4.3 General block diagram

4.4BLOCK DIAGRAM OF TRADITIONAL FEEDBACK CONTROL

Figure 4.4 Block diagram of traditional feedback control


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5. SIMULATION AND RESULT ANALYSIS

The simulation of the SRM using MATLAB/SIMULINK and comparison 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-turns

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


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5.2 RESULTS

Case (i): When the reference speed is high i.e = 4000rpm and at no loadi.e = 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.


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Report srm

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