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CHAPTER 1

INTRODUCTION


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Introduction

Till recently, in applications variable speed operation was required, only DC motors were

used due to the ease, which with one could control them. Separately excited DC motors

were particularly popular in applications where fast torque response was required.

However DC motors have some generic disadvantages like

requirement of periodic maintenance, unstable in explosive or corrosive environments due to sparking problem commutation is difficult high currents and voltages, and hence its use is use is

limited to low power, low speed motors

These problems can be overcome by using Induction Motors that have a simple and

rugged structure. Further, they have a lower weight to output power ratio compared to

their DC counterparts.

1.1. Vector Control of Induction Motor

The idea behind the vector control or field oriented control is to control the

Induction Motors in the similar for DC motor control .The flux and torque, in the case of

DC machines, can be controlled independently controlling the field and armature currents

respectively. It is because of this inherent decoupling between the flux and the armature

currents; one is able to achieve very good torque dynamics from DC machines. Unlike

DC machines, there is no inherent decoupling between the flux and the torque producing

components of the stator current in AC machines. Therefore, achieving good torque

dynamics in AC machines is not easy. However, nowadays field orientation control or

vector control techniques have been employed, which result in good torque dynamics of

AC motors.


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1.2. Sensorless Vector Control of Induction Motor

Today, vector controlled induction motor has been established as the core servo-

drive system for industry applications, and has been widely applied almost in all

industrial fields. However, in some applications, the necessity of the speed sensor for

vector control may become the defect of the ,or make the users hesitate to apply this

excellent drive to their systems. The effort of engineers has solved this difficulty, and the

vector control of induction motor can be now implemented without speed sensor.

Hereafter, this implementation is briefly named as sensorless control.

Induction Motor drives without shaft sensor, sensorless drives, are increasingly

applied in many industrial processes involving lower cost and higher performance

specifications. To achieve sensorless control requires either flux measurement using flux

sensors, flux estimation, or speed identification. it is worthy of note that both voltage and

current sensors are required for the implementation of flux estimation and speed

identification.

1.3. Sensorless Vector Control of Induction Motor at Zero Frequency

The sensorless drive at low speed and in the regenerating operation still remains

an unsolved problem . For the stable sensorless control at low speed including zero

frequency, a new control scheme using secondary speed-emf estimation was presented in

this dissertation work, instead of the flux or excitation current. Especially at zero stator

frequency, the secondary speed emf is estimated under fluctuated reference of the

secondary flux to assure the stability of the estimation, and the stable sensorless drive is

realized.


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CHAPTER 2

MOTOR CONTROL STRATERGIES


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Motor control stratergies

2.2.1. Direct field oriented control

In this mode of control the flux measurement can be made using either the hall

sensors or the stator search (sense) coils. If the stator coils are used, then the voltage

sensed from the coils will have to be integrated to obtain the air gap flux linkages. The

measured air flux linkage components are used to calculate the required (rotor, stator or

air gap) flux linkage space phasor magnitude and position V. The value ofV thus

computed is used to align the arbitrary axis along the flux linkage space phasor to achieve

decoupled control of the torque and flux producing components of the stator current and

space phasor.

The flux sensing devices are placed in the air gap of the machine, which will

determine the air gap flux space phasor. Any other flux space phasor can be calculated as

it has an algebraic relationship with the air gap flux space phasor. The air gap flux sensed

by either hall-effect devices or stator search coils suffer from the disadvantage that a

specially constructed induction motor is required. Further, hall sensors are very sensitive

to temperature and mechanical vibrations and the flux signal is distorted by large slot

harmonics that can not be filtered effectively because their frequency varies with motor

speed. In the case of stator search (sense) coils, they are placed in the wedges close to the

stator slots to sense the rate of change of air flux. The induced voltage in the search coil

is proportional to the rate of change of flux. This induced voltage has to be integrated to

obtain the air gap flux. At low speeds below about 1HZ, the induced voltage will be

significantly low which would give rise to in accurate flux sensing due to presence of

comparable amplitudes of noise and disturbances in a practical system. As an alternative,

indirect flux estimation techniques are preferred as explained in the next sub-section.


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2.2.2. Indirect field oriented control:

In an Indirect Field Oriented Control (IFOC) a flux estimator is used to estimate the

required flux linkage space phasor magnitude and angular positiona

U . The shaft position

is usually needed for estimating flux linkage space phasor position. If the shaft transducer

is a position encoder, then the position informationr

U can be directly used. But if the

shaft transducer is a speed transducer like a tacho, then speed has to be integrated to

obtain the shaft position. In the case of shaft transducer being a position encoder, the

speed feedback is obtained by differentiating the shaft position information.

Indirect sensing of flux space phasors give a more versatile drive system that can

be used with standard commercial motors, but this approach would generally result in a

more complex control system. Since it is generally desirable to have a scheme which is

applicable for all induction motors, the indirect field oriented has emerged as the more

popular method. In the indirect method of field orientation the flux linkage space phasor

is estimated from the motor model as will be discussed in next section. As a consequence

all indirect methods are sensitive to variations in some machine parameter like the stator

or rotor time constants. For example, in the rotor flux oriented control, the indirect rotor

flux estimator is sensitive to the rotor time constant Xr, of the motor. In the case of stator

flux oriented control, the indirect stator flux estimator is sensitive to the stator time

constant of the motor. In the air gap flux oriented control, the indirect air gap flux

estimator is sensitive to both the stator and the rotor time constants. Therefore, if the

value of the motor parameter varies, the desired decoupled of the flux and the torque

components of the stator current space phasor is not achieved and this leads to

deterioration in the dynamic behavior of the drive system.

2.3 Sensorless ControlSensorless control is another extension to the FOC algorithm that allows

induction motors to operate without the need for mechanical speed Sensorless control

is another extension to the FOC algorithm that allows induction motors to operate


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without the need for mechanical speed sensors. These sensors are notoriously prone to

breakage so removing them not only reduces the cost and size of the motor but improves

the drives long term accuracy and reliability. This is particularly important if the motor

is being used in a harsh, inaccessible environment such as an oil well.

Instead of physically measuring certain values control engineers can calculate

them from a systems state variables. This is known as the state space modeling approach

and is a powerful method for analyzing and controlling complex non-linear systems with

multiple inputs and outputs. In high performance sensorless motor drives the two main

control techniques used are open loop estimators and closed loop observers. In early

literature the terms observer and estimator are often used interchangeably however most

recent papers define estimators as devices that use a model to predict the speed using the

phase currents and voltages as state variables. Observers also use a model to estimate

values, however these estimates are improved by an error feedback compensator that

measures the difference between the estimated and actual values. The predicted value of

speed is then used by the FOC to adjust the PWM waveform in exactly the same way as

an actual measured value.


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CHAPTER 3

DYANAMIC MODEL OF INDUCTION MOTOR


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Dyanamic model of IM

3.1. Introduction

In developing the dynamic model of the induction motor, the following assumptions

will be made without affecting the validity of the model.

y The motor has symmetrical three phase windings.y The mmf wave is sinusoidally distributed in space.y The stator and rotor iron have infinite permeability.y Skin effect and core losses are neglected.y The motor is operating in the linear region of B-H characteristic.

In order to understand and analyze vector control, the dynamic model of the

induction motor is necessary. It has been found that the dynamic model equations

developed on a rotating reference frame is easier to describe the characteristics of

induction motors. It is the objective of this chapter is to derive and explain induction

motor model in relatively simple terms by using the concept of space vectors and d-q

variables. It will be shown that when we choose a synchronous reference frame in which

rotor flux lies on the d-axis, dynamic equations of the induction motor is simplified and

analogous to a DC motor. Traditionally in analysis and design of induction motors, the

per-phase equivalent circuit of induction motors shown in Fig. 3.1 has been widely

used. In the circuit, Rs (Rr) is the stator (rotor) resistance and Lm is called the

magnetizing inductance of the motor. Note that stator (rotor) inductance Ls (Lr) is defined

by

Ls = Lls + Lm, Lr= Llr+ Lm (3.1)

where Lls(Lrs) is the stator (rotor) leakage inductance. Also note that in this equivalent

circuit, all rotor parameters and variables are not actual quantities but are quantities

referred to the stator . Parameters of the circuit are determined from no-load test and

locked rotor test. It is also known that induction motors do not rotate synchronously to

the excitation frequency. At rated load, the speed of induction motors is slightly (about 2


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-7% slip in many cases) less than the synchronous speed. If the excitation frequency

injected into the stator ise

[ and the actual speed converted into electrical frequency unit

isr

[ , slip s is defined by

s = (e

[ r

[ )/e

[ =sl

[ /e

[ (3.2)

andsl

[ is called the slip frequency which is the frequency of the actual rotor current. In

the steady-state AC circuit, current and voltage phasors are used and they are denoted by

the underline. In Fig. 3.1, power consumption in the stator is interpreted as Is2Rs, while

Ir2Rr/s represents both power consumption in the rotor and the mechanical output

(torque). By subtracting rotor loss Ir2Rr from Ir

2Rr/s, produced torque (mechanical power

divided by the shaft speed) is given by

Te = ir2Rr(P/2) (1-s) / (swr) = ir

2Rr[ P / (2we )], (3.3)

where P is the number of poles. Although the per-phase equivalent circuit is useful in

analyzing and predicting steady-state performance, it is not applicable to explain dynamic

performance of the induction motor.

Fig. 3.1 Conventional Per-phase Equivalent Circuit


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3.2. Dynamic Model in Space Vector Form

In an induction motor, the 3-phase stator windings are designed to produce

sinusoidally distributed mmf in space along the airgap periphery. Assuming uniform

airgap and neglecting the effects of slot harmonics, distribution of magnetic flux will also

be sinusoidal. It is also assumed that the neutral connection of the machine is open so that

phase voltages, currents and flux linkages are always balanced and there are no zero

phase sequence component in the system. For such machines, the notation in terms of the

space vector is very useful. For 3-phase induction motors, the space vector Yss

of the

stator voltage, current and flux linkage is defined from its phase quantities by

Yss

= (2/3) (Ya + kYb + k2Yc ), (3.4)

where k = exp(j 2/3). The above transform is reversible and each phase quantities can

be calculated from the space vector by,

Ia = Re (Y s ), Ib = Re (k2Ys ), Ic = Re (kY s ). (3.5)

For a sinusoidal 3-phase quantity of constant rms value, the corresponding space

vector is a constant-magnitude vector rotating at the frequency of the sinusoid with

respect to the fixed (stationary) reference frame. Note that the space vector is at vector

angle 0 when

A-phase signal (Ya) is at its sinusoidal peak value in steady-state. With space vectornotation, voltage equations on the stator and rotor circuits of induction motors are,

vs

= Rs is

+ ps (3.6)

vr = Rrir + pr = 0 (3.7)

It is very convenient to transform actual rotor variables (Vr, ir, r) from Eq.

3.7 on a rotor reference frame into a new variables ( Vr, ir

, r

) on a stator reference

frame as in the derivation of conventional steady-state equivalent circuit. The Space

Vector diagram for induction motor is shown in fig 3.2 Let the stator to rotor winding

turn ratio be n and the angular position of the rotor be r, and define

ir

= (1/n) exp(jr) ir, r

= n exp(j r) r (3.8)


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VS

is iqs

ids

ir

1

a r

fig.3.2 Space Vector diagram for induction motor

Also, by defining referred rotor impedances as Rr = n2Rr, etc., we have

vs = Rs is + ps (3.9)

0 = Rr irs

+ (p jr) r (3.10)

Where r= pr, is the speed of the motor in electrical frequency unit and

s

= Lsis

+ Lmir (3.11)

r

= Lmis

+ Lrir (3.12)

The above 4 equations (Eq. 3.9 - 3.12) constitute a dynamic model of the induction motor

on a stationary (stator) reference frame in space vector form. These model equations may

be simplified by eliminating flux linkages as

vs

= (Rs + Lsp) is+ Lm pir

(3.13)

0 = (Rr+ Lr(p jr)) ir

+ Lm (p jr) is

(3.14)

Stator axis

Rotor axis

Arbitrary axis


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From the equations. 3.13-3.14, the dynamic equivalent circuit model on a stationary

reference frame can be drawn as in Fig. 3.3.

Fig. 3.3.Dynamic Equivalent Circuit on a Stationary Reference Frame

For steady-state operation with excitation frequency e, p in Eq. 3.13-3.14 may be

replaced by je and after some algebraic manipulation, we get

vs

= (Rs + jeLs ) is

+ Lm pir (3.15)

0 = (Rr/ s + jeLr) ir

+ je Lm is

. (3.16)

which exactly describes the conventional steady-state equivalent circuit of Fig. 3.1.

Now, the previous procedure can be generalized so that the dynamic model is

described on an arbitrary reference frame rotating at a speed a, where Eq. 3.15 -3.16 is a

special case with a,= 0 . To do that, define the new space vector on the arbitrary frame

as

Ya

= exp(- j a)Ys (3.17)

and reconstruct all the model equations in terms of the new space vectors. In the arbitrary

reference frame, Eqs. 3.6-3.8 are modified to


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vsa

= (Rs + Ls p) isa

+ Lm pira

+ j a sa

(3.18)

0 = (Rr+ Lrp) ira

+ Lm p Isa

+ j (a -sl) ra (3.19)

With new flux linkage equations defined by,

sa

= Ls isa

+ Lm ira (3.20)

ra

= Lm isa

+ Lrira (3.21)

By substituting Eqs. 3.20-3.21 into Eqs. 3.14-3.15, we have

vsa

= ((Rs + Ls (p + a)) isa

+ Lm (p + ja )ira

(3.22)

0 = ((Rr+ Lr(p + ja jr) ira

+ Lm (p + ja - jr)isa

(3.23)

where eliminated flux linkage variables are eliminated.

Normalized equivalent circuit on a arbitrarily rotating frame based on Eq. 3.18-

3.23 is shown in Fig. 3.4. Now, depending on a specific choice of a, many forms of

dynamic equivalent circuit can be established. Among them, the synchronous frame form

can be obtained by choosing a = e. This form is very useful in describing the concept

of vector control of induction motors as well as of PM synchronous motors because at

this rotating frame, space vector is not rotating, but fixed and have a constant magnitude

in steady-state. Since space vectors in the synchronous frame will frequently be used,

they are denoted without any superscript indicating the type of frame. Another possible

reference frame used in vector control is the rotor reference frame by choosing a = o

which is , in fact, the reverse step of Eq. 3.8 with n =1.

Dynamic Equivalent Circuit on an Arbitrary Reference Frame Rotating at a.


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3. 3.D-QEquivalent Circuit

In many cases, analysis of induction motors with space vector model is

complicated due to the the fact that we have to deal with variables of complex numbers.

For any space vectorY, define two real quantities Sq and Sdas,

S= Sq+ j Sd (3.24)

In other words, Sq = Re (S) and Sd = Im (S). Fig. 3.5 illustrates the relationship

between d-q axis and complex plane on a rotating frame with respect to stationary a-b-c

frame. Note that d- and q-axes are defined on a rotating reference frame at the speed of a= pa with respect to fixed a-b-c frame.

Definition of d-axis and q-axis on an arbitrary reference frame

With the above Eq. 3.22-3.23 can be written the following 4 equations of real variables

( ) ds qsa a a a a

ds s s s a m dr a m qrv R p i i p i i[ [! (3.25)

( )a a a a a

qs s s qs s a ds m qr a m drv R pL i L i pL i L i[ [! (3.26)

0 ( )qs ds

a a a a

r s dr sl m m sl r qrR pL i L i pL i L i[ [! (2.27)

0 ( )ds qs

a a a a

r s qr sl m m sl r drR pL i L i pL i L i[ [! (2.28)


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The above 4 equations are expressed in a matrix form as follows:

ds

qsqs

aa

ds s s s a a

aa

s a s s a

a sl r s sl r

dr

asl sl r r qr

iv p p

ip pvp p io

p p io

[ [

[ [[ [

[ [

- - -

(3.29)

where sl a r[ [ [! 3.29a

For future reference, the above matrix equation simplified for popular reference

frames in analysis and design of vector control will be introduced. For stationary

reference frame, by substituting a = 0, the above equation is reduced to

0 0

0 0=

0

0

ds s s

ds

s s qsqs

r r s r r dr

r

r r r qr

v p p i

p p iv

p p i

p p i

E E

EE

E

E

[ [

[ [

- - -

(3.30)

Some implementation of vector control drive includes calculation in rotor reference

frame (frame is attached to the rotor rotating at r ). In this case, we can substitute all a

in Eq. (3.29) by r, which makes simplified rotor voltage equations. Moreover, for

synchronous frame, we have

e eds s s s e m e m ds

ees e s s e m m qsqs

e

m sl m r s sl r dr

e

sl m m sl r r qr

v p p i

p p iv

p p io

p p io

[ [

[ [

[ [

[ [

- - -

(3.31)


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As mentioned before, each variable (voltage, current or flux linkage) in the synchronous

frame is stationary and fixed to a constant magnitude in steady-state. Based on Eq. 3.4,

dynamic d-q equivalent circuit is shown in Fig. 3.2.

Fig. 3.4 D-axis equivalent circuit on a arbitrary frame

Fig. 3.5Q-axis equivalent circuit on a arbitrary frame

Expression for the Electromagnetic Torque

The electro magnetic torque Te can be expressed in terms of the stator, rotor or air gap

flux linkages as follows:

ird

vqs

isd

Lr ([a-[r) qrP RrRs [a qsP Ls

Lm

drP

vds

irq

vqr

i Lr ([a-[m) drP RrRs -[a dsP Ls

mL

qrP qsP vqs


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32 2

mPe dr qs qr ds

r

Li i

LX P P ! - (3.32)

32 2

P

e ds qs qs dsi iX P P ! - (3.33)

32 2

P

e md qs mq dsi iX P P ! - (3.34)

3.4. Sensorless vector controller model based on Secondary Speed

Emf on Secondary Speed Emf

3.4.1. Induction Motor Model Based on Secondary Speed Emf

The voltage equation of Induction Motor is rewritten as follows:

stator voltage equation:

+ + ps s s s sv i [P P (3.35)

rotor voltage equation:

0 + + pr r sl r i r[ P P (3.36)

Stator flux equation:

=Ls s s m r i L iP (3.37)

rotor flux equation:

+r m s r r i iP (3.38)

Substituting the equations (3. 37) & (3.38) into voltage equations, equations (3.35) &

(3.36) can be written as follows:


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( ( )) + ( +p)s s s s m rv p i i[ [ (3.39)

0 ( + ( ) + (p+ )r sl r m sl s

p i i[ [ (3.40)

From the equations (3.37) & (3.38) d-axis and d-axis flux linkage equations can be

written as follows:

+ds s ds m dr

i iP (3.41)

=Lqs s qs m qri L iP (3.42)

=Ldr m ds r dr

i L iP (3.43)

+qr m qs r qri iP (3.44)

Separating the d-axis and q-axis voltages, the voltage equations becomes as follows

= R

R

ds dss s s e m e m

qsqs s e s s e m m

drm sl m r s sl r

qrsl m sl r r

v iR pL L pL L

iv L R pL L pL

ipL L pL Lo

iL pLm L pLo

[ [

[ [

[ [[ [

- - -

(3.45)

The secondary fluxes ,d qJ J and the corresponding excitation currents ,d qi iJ J are in (3.47)

and (3.48)

Here

,dr d

q r q

P J

P J

!

! (3.45)


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Therefore, the equations (3.41-3.44) becomes

d ds dr d

m r m

q qs qr q

i i i

L L Li i i

J

J

J

J

! ! - - - - (3.46)

d ds drr

q qs qrm

i i i

i i i

J

J

!

- - - (3.47)

The vectors of the stator voltage sv , stator current si , rotor current ri ,the secondary flux J

and the secondary excitation current iJ, in (3.44),(3.46) and (3.47) are as follows:

Letds

s

qs

vv

v

!

- ,

ds

s

qs

ii

i

!

- ,

dr

r

qr

ii

i

!

- (3.48)

,d dq q

ii

iJ

J

J

JJ

J

! !

- -

from equations (3.45)-(3.48), the vector representation of the voltage equation using the

secondary excitation current iJ

is obtained in the following equation (3.49)

2 2

2 22 2

( )

0( / ) { ( / ) }

m ms e e

sr rs

m mr m r r m r sl

r r

p I J p I J iv

iI p I J

W W

J

[ [

[

! - - -

(3.49)


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where , ,L I JW

areasfollows

2

1 0 0 1,

0 1 1 0

ms

r

LL L

L

I J

W !

! !

- -

(3.50)

Fig3.6 equivalent circuit of the IM

Fig3.6 shows the equivalent circuit of the induction motor based on (3.49). Since the

secondary flux J and the excitation current iJ

are indefinite at the angular frequency

0e[ !

,the sensorless algorithm based on JoriJ can not assure the stable operation in the

low speed region. To solve this problem, the authors propose a new algorithm based on

the

Secondary speed emf er ,is defined as follows

2

mr r

r

Le J i

LJ[! (3.51)

2

2

mr q

dr r

qr mr d

r

Li

e L

e Li

L

J

J

[

[

! -

-

(3.52)


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The Secondary speed emf er, leads excitation current iJ by the angle of / 2T , and

the magnitude is proportional to the rotor speed r[ .therefore, the exact estimation of the

secondary peed emf er is leads to the estimation of the secondary flux position and the

rotor speed. From equations (3.49) and (3.50), the voltage equation using the secondary

peed emf er , is obtained in the following equation (3.53)

2={(R ) } ( / ) ( )s s s r m r s r v p I J i R L L i i eJW [W

(3.53)

For the equation (3.53) the space vector diagram is shown the following fig 3.9

fig 3.7 space vector diagram of the IM

3.4.2. Estimation of Secondary Speed Emf

The Secondary Speed Emf re is estimated by assuming the error between the actual

excitation current iJ and its reference*

iJ is small enough, that is


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*

*

*0

d

q

i Ii i

i

J J

J J

J

! !

- - ;

(3.54)

The fig3.8 shows theSecondary Speed Emf re estimation system. Since the actual

Fig 3.8Speed Emf estimation

position of d-q axis is unknown in the controller, the sensorless algorithm is based on the

estimated position of dc-qc axis. Equation (3.53) for the actual motor is effective even on

the dc-qc axis frame. Since the only difference between the actual motor model is

secondary speed emf rMe on the dc-qc axis frame in the controller is defined as follows.

rMd

rM

rMq

ee

e

!

- (3.55)

The motor model is given in (3.56) by replacing the actual secondary speed emf erM in

(3.53)

2= -(R ) ( / ) ( )s s s e s r m r s r p i v I J i R L L i i eJW [ W (3.56)


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The model voltage sMp iW is given in (3.54) can be calculated from the know

values*, , ( )s sv i i iJ J! and re .On the otherhand, the actual voltage sp iW across the

leakage inductance can be obtained by calculating the current difference between the

detected stator currents si at the two adjusting sampling points.

The estimation error re between the actual emf re in the equation and the model

emf re in eq (3.53) is represented by using the voltage difference sp iW across the

leakage inductance between the actual motor and model as follows

r r rM e e e( !

s sp i p iW W! (3.57)

From the relation between re( and sp iW( in the above equation, the model emf rMe can

be estimated in by the following equation by using the estimation gain KJ

r

se K p i dtJ W! ( (3.58)

0

0

dK

K K

J

JJ

! - (3.59)

From the (3.56) and (3.58), the transfer function from re to re( can be

obtained as follows;

1( )r re sI K seJ

( ! (3.60)

0

0

ddr dr

qr qr

q

s

s Ke e

e es

s K

J

J

( ! (- -

-

(3.61)

The time constants for the convergence of the secondary speed emf errorsdre( and qre(

In( 3.61) are given by1

qKJ

and1

dKJ

, respectively


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3.5. Sensorless Control System Configuration

isd

- d-controller

ids*

+

iqs* +

_ q-controller

iqs

iaisq -

isd ib - ic

wr*+

+ -

-wre +

pLisMd -

pLisMd pLisMq+

wsl*+

pLisMq wre +

+M

erMd+

M

erMq

wre

Fig.3.9 Schematic Block Diagram of Sensorless Vector Control System

Decoupling

network

vd*e

iM

vq*

2-Ph3-Ph

Sinusoidal

PWM

Voltagesource

Inverter

AC toDC

3-PhAC

IM

3-Ph2-Ph

sL

sL

M

odel

Speed

emf

Estimato

r

Flux position

com

Speed

E timat

speed controller

LrLm

2id

*

Rr

Lr id*

1/s

vq*

*


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3.5.1 Estimation of the rotor speed re[ :

From the relation in (3.52) speed qre , the estimated rotor speed re[ is obtained in the

following eq (3.62) using the estimated q component r

qe in the r

e and the exciting

current reference *diJ .

2 *

rre rMq

m d

Le

L iJ

[ !(3.62)

From the rotor speed error between the rotor speed reference*

r[ and the estimated rotor

speed re[ ,the torque ref*

X is determined through the PI controller. From the relation in

eq (5.75) between the motor torqueX and the stator current qsi under the condition that

the q-axis component of the excitation current diJ equals to zero, the reference of the q-

axis current *qsi is the determined in (3.64)

T qsK iX ! (3.63)

* *1qs

T

i

K

X! ,2

*mT d

r

LK i

LJ

! (3.64)

3.5.2Estimation of slip angular speed:

The voltage equation of the IM is

2 2

2 22 2

(R )

0( / ) { ( / ) }

m ms e e

sr rs

m mr m r r m r sl

r r

L Lp I J p I J

iL Lv

iL LR L L I R L L p I J

L L

J

W W[ [

[

! - - -

(3.65)


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27

From the second row of the equation (3.65), one can be written as follows:

2 22 2

1 0 1 0 0 1( / ) { ( / ) } 0

0 1 0 1 1 0 0

ds m mr m r r m r sl

qs r r

i IL LR L L R L L p

i L L

J[

! - - - - -

(3.66)

Simplifying the above equation, yields:

2 22 2

0( / ) { ( / ) } 0

0

ds m mr m r r m r sl

qs r r

i IL LR L L R L L p

i IL L

J

J

[

! - - -

(3.67)

The second row of the equation (3.67), yields

2 22 * 2 *

22 * *

( / ) { ( / ) }0 0

( / ) 0

m mr m r qs r m r sl d

r r

mr m r qs s l d

r

L L R L L i R L L p i

L L

L R L L i i

L

J

J

[

[

!

!(3.68)

Replacing the qsi , diJ with*

di

J, *qsi in the q-axis component in the second row of the

equation (3.68) becomes

2 22 * 2 *( / ) { ( / ) }0 0m mr m r qs r m r sl d

r r

L LR L L i R L L p i

L LJ[ ! (3.69)

ie.

22 * *( / ) 0m

r m r qs sl d

r

L R L L i i

LJ[ ! (3.70)

From the (3.70) slip can be calculated in the equation (3.71)

* *

*

rsl qs

r d

R iL iJ

[ ! (3.71)

By adding the estimated speed re[ to the slip angular speed reference*

sl[ , the angular

speed e[ is determined as follows:


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28

*

e sl r e[ [ [! (3.72)

On the otherhand, the d-axis component of the estimated speed emf r de represents the

position estimation error U( between the actual position U and estimated positionM

U as

shown in fig 3.10. By using equations(3.52) and (3.54), the estimation error U( can be

obtained in (3.73) under approximation of tan U( ; = U(

2*m

rMd rMq d

r

Le e tan i

LJU [ U! ( (; (3.73)

Fig 3.10 Estimated axis (dc-qc) and speed emf

From the relation in the equation in (3.73), the position compensation term MU( can be

calculated in (3.74) by using the compensation gain KU

2 *

rM rMd

m d

L K e dt

L iU

J

U( ! (3.74)

The estimated axis positionM

U is given in equation (3.75)

M e MdtU [ U! ( (3.75)

According to (3.73) & (3.74), the compensation system of the axis position error is

shown in fig 3.11.the transfer function of the position estimation error U( is obtainedfrom fig 3.11 as follows;

( / )es

ss K

U

U U [( !

(3.76)


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29

Fig 3.11compensation system of axis position error

The time constant for the convergence of the position estimation error U( is1

KU

.

Under the constant secondary excitation current iJ (= IJ ), the d-axis stator current

reference *sdi is the constant value IJ in (3.54) and q-axis stator current reference*

qsi is

given in (3.64).Using the current control errors between the *qsi ,*

dsi and the detected

currents ,qs dsi i , the compensation voltages*

dv( and*

qv( for stator current are calculated

through PI controllers as shown in fig 3.11. These compensation voltages *dv( and*

qv(

are the compensation terms of voltage drop ( )s sp iW across stator resistance and the

leakage inductance.

3.5.3Calculation of decoupling terms:

Replacing * *,d qv v( ( , dIJ , qsI with ( )s sp iW ,*

dIJ ,*

qsI in the first row of (3.65), the

voltage references are*

dsv and*

qsv obtained as follows;

ie.

2 2

{( ) } { }m ms s e s er r

L Lv p I J i p I J iL L

JW W[ [! (3.77)


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30

2 2

* * * *

** * * 2 2

0( )

( ) 0

m me

r rs eds ds qs d

ds eqs qs ds m mse

r r

L Lp

L Lpv I I I

Ipv I I L Lp

L L

J

J

[W W[

W W[[

! - - - - - - - - -

(3.78)

2* * * *( ) mds s ds e qs d

r

Lv p I I p I

LJW W[! (3.79)

2* * * *

( ) mqs s qs e ds e dr

Lv p I I I

LJW W[ [! (3.80)

2* * * *mds ds e qs d

r

Lv v i p i

LJ[ W! ( (3.81)

* *

ds ds dov v v! ( (3.82)

2* *

0m

d e qs d

r

Lv i p i

LJ[ W! (3.83)

2* * * *mqs ds e ds d

r

Lv v i i

LJ[ W! ( (3.84)

* *

qs qs qov v v! ( (3.85)

2* *m

qo e ds d

r

Lv i i

LJ[ W! (3.86)

where 0dv , qov are the decoupling terms

3.6. Sensorless Control at Zero Frequency

Fig3.12. Vector Diagram at Zero Angular Frequency


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31

Fig 3.63 shows the vector diagram based on (3.54) at zero angular frequency of e[ , at

zero angular frequency of e[ , the secondary speed emf re in (3.51) can be modified by

using slip

equation and the second row of (3.49)

22( ) ( )m mr r r s

r r

L Le J i R i i

L LJ J[! ! (3.87)

From equation (3.87), the secondary speed emf re and the term2( ) ( )m

r s

r

LR i i

LJ

are

canceled out each other. In this case, the voltage equation (3.52) results in only the

voltage drop across the stator resistance as follows;

r s se R i! (3.88)

Since the term of the secondary speed emf re is not included in equation (3.88),

the estimation of secondary speed emf re is impossible. For the estimation of the

secondary speed emf re at zero angular frequency, the sinusoidal component with the

amplitude IJ

( and the angular frequency d[ is super imposed to secondary excitation

current reference *diJ as follows ;

*

*

*sin

0

d d

q

i I I tii

J J J

J

J

[ ( ! ! - -

(3.89)

Fig.3.13 Vector Diagram under Fluctuating Excitation


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32

in (3.89).since re and2( ) ( )m r s

r

LR i i

LJ

terms are not canceled out, the stable

estimation of re is possible. Since the motor control is realized at the stator side, the

stator current reference to obtain the fluctuating excitation current iJ

in (3.89) is needed.

By substituting (3.89) into the second row in (3.49),the d-axis stator current reference *ds

i

is obtained as follows;

* *(1 )rsd d

r

Li i

RJ

!

21 ( ) sin( )d rd d

r

Li t

R

J J

[[ U! ( (3.90)

Where,1tan ( )d r

d

r

L

R

[U !


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33

CHAPTER 4

BLOCK SCHEMATIC OF SENSORLESS VECTOR

CONTROL


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34

4.1. Introduction

The purpose this section is to discuss the basic steps involved in the development

of simulation blocks for the Sensorless Vector Control of the induction motor. All the

simulation blocks are developed in MATLAB6.1/SIMULINK.This Schematic of

Sensorless Vector Control of IM Drive System consist of the following basic parts:

a. Induction Motor Drivesb. Three phase to two-phase transformation (a, b, c to , )c. Stator to synchronous reference frame transformation (E,F d,q)d. Sensorless vector control algorithme. Decoupling Networkf. d-q to a, b, c transformation(Two Phase to three phase transformation)g. Sine-Triangle PWM of Three Phase Inverters

In the practical implementation of the Sensorless Vector Controlofthe induction

motor is fed from a voltage source inverter with fast current control loops. This approach

is used in high performance induction motor servo drives for Machine tool, Rotary press,

Storrer, Pressor and Winder applications. Sensorless vector controlled induction motor

has been used widely used from the standpoints of cost, size and reliability.

In field oriented control system, the induction motor behaves like a dc machine

under both steady state and transient conditions. Consequently, similar drive control

strategies can be employed. Below base speed, the magnetizing current of the induction

motor representing the rotor flux magnitude is maintained constant at its maximum

possible value to achieve constant torque operation. Above base speed, the flux is

reduced thereby giving the field-weakening region or the constant horse power region of

operation. In Sensorless vector controlled induction motor speed is estimated from the q

axis component of the secondary speed emf in the synchronous reference frame


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35

A typical Sensorless vector controlled drive system consists of an induction motor,

which is driven by a voltage source inverter, speed controller ,current controller , speed

e.m.f estimator, flux position estimator, speed estimator and Park & Clark

transformations

4.2. Induction Motor Drives

Power electronic devices known as motor drives are used to operate AC motors at

frequencies other than that of the supply. These consist of two main sections, a controller

to set the operating frequency and a three-phase inverter to generate the required

sinusoidal three-phase system from a DC bus voltage. The model of the Induction Motor

is developed as per the equations which is shown in fig 4.1

4.3 Three phase to two-phase transformation (a, b, c to , )

Mode

of the Induction Motor

6

vq s

5

vd s4

we r

3

T e2

iq s

1

id s

0 w

1

sth

1

J.s+B

speed

v a

v b

v c

th

v qs

v ds

abc--dqs

2 /pW e r

ids

iqs

lam qr

lam dr

Te

Torque

v qs

iqs

w

v ds

ids

lamda ds

lamda qs

Stator Fluxes

iqr

idr

w

wr

lam qr

lam dr

Rotor fluxes

lam ds

lam qs

lam dr

lam qr

ids

iqs

idr

iqr

Current s

4

T l

3vcn

2

vb n

1

va n


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36

The three stator currents isa, isb andiscthat are measured, are first transformed to

an equivalent two-phase system (isand is) because the induction motor is represented as

equivalent two-phase machine. The three- phase to two-phase transformation (3-2) is

carried out in the stator reference frame.

This transformation is a general transformation that can be applied to any variable of

the induction motor like the stator voltages, stator currents, flux linkages etc.

1 1

3 3

1 0 0

0

a

b

c

ii

ii

i

E

F

!

(4.1)

The block for the three phase to two-phase transformation (a, b, c to ,) is developed

as per the equation(4.1) which is shown in fig 4.2.

>

2

Ibet

1

ia l

1 /sqrt(3)

1 /sqrt(3)/1

1/ sqrt(3)

1 /sqrt(3)

3

ic n

2

ia n

1

ib n

Fig 4.2 Block diagram for the Three Phase To Two-Phase Transformation (a, b, c to E,F)


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37

4.4. Stator to synchronous reference frame transformation (E,F d,q)

The two-phase stator currents that are in the stator reference frame are

transformed to a synchronous reference frame. The choice of the synchronous

reference frame is dependent on the flux along which the orientation is to be

performed. If the arbitratory is oriented along the rotor flux linkage space phasor,

then the synchronous reference frame would be the rotor flux reference frame and if

the arbitrary axis is to be oriented along the stator flux linkage space phasor, then the

synchronous reference would be the stator flux reference frame etc. If the angle V,

represents the instantaneous position of the synchronous reference frame along which

the arbitrary axis is aligned, then the transformation from the stator to synchronous

reference frame. The inputs to this block are is , is and the rotor flux positionV. The

outputs of this block are isdand isq.

cos sin

sin cos

ds

qs

i i

i i

E

F

V V

V V

! (4.2)

The block diagram for the (E,F d,q) transformation is developed as per the

equation(4.2) which is shown in fig 4.3

fig 4.3. PARK TRASFORMATION(2Ph-->2Ph)

2

iq s

1

id s

sin

sin

cos

cos

Ibet*sin(th)

Ibet*cos(th)

Ial*sin(th)

Ial*cos(th)

3

theta

2

ib t

1

ia l


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38

4.5. Sensorless vector control algorithm

y Estimation of Secondary Speed Emf:y The magnitude of theSecondary Speed Emf can be estimated for Sensorless

Vector control is in equation in (4.3)

rM se K p i dt

JW! ( (4.3)

The block diagram is developedfor the Secondary Speed Emf Estimation as per the

equation(4.3) which is shown in the following fig.

!

2

e rM q

1

e rM d

K* u

i * p d e l i d q s

uK p h i

K p h i

1

s

I n t e g ra t o r 1

m

2

P s i g d l i q s

1

P s i g d l i d s

Fig4.4. Secondary Speed Emf Estimation Model

y Estimation of Rotor Speed re[ Rotor speed can be calculated using the following eq (4.4) which simulation block is

shown in the following fig4.5

2 *

rre rMq

m d

Le

L iJ[ ! (4.4)

SPEED ESTIMATOR

1

Wre

Lr/(M ^2)

ErM q*Lr/M ^2

u(1)/u(2)

(Lr/(M 2*Ip hidref))*erM q

2

erM q

1

Iphidref


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39

Fig4.5. Estimation of Rotor Speed re[ Model

y Estimation of slip *sl[ :Slip angular speed *sl[ can be calculated using the following eq (4.5) which simulation

block is shown in the following fig4.6* *

*

rs l qs

r d

Ri

L iJ

[ ! (4.5)

"

# $ %

& '

#

&

( #

'

) $

0

1

1

Ws

u(1)/u(2)

Rr/LR*idsref/ Iphdref

Rr/(Lr)

Ga i n2

Iphiref

1

iqsref

Fig4.6.Block diagram forEstimation of slip *sl[

Synchronous speed can be calculated using the following equation (4.6)

*e sl r e[ [ [! (4.6)

y Estimation of flux position compensation:

The flux position compensation term is estimated using the following equation

2 *

rM rMd

m d

LK e dt

L iU

J

U( ! , which simulation block is in the following fig


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40

Position Estimator

1

delt at hM

-K -

Lr/(M ^2*iphdref)1

1

s

Int egrat or

u( 1) /u( 2)

Fc n

2

Iphidref

1

erM d

Fig4.6.1. Model for Estimation of flux position compensation

The estimated axis position MU is given in eq (4.7)

M e MdtU [ U! ( (4.7)

where2 *

rM rMd

m d

LK e dt

L iU

J

U( !

4.6. Speed and Current Controllers

The reference speed refis compared with the estimated speed re which is

estimated from equation (3.62). The speed error is passed through a zero steady state

error controller like a PI controller to obtain the command value for the quadrature

component of the stator current *qsi (i.e. Torque reference*

X ), in the synchronous

reference frame.

The reference for the direct current *dsi , of the stator current space phasor in the

case of the vector control can be a constant value up to base speed operation of the motor.

For the operation of the motor above the base speed, the *dsi is decreases in such a manner

to maintain the power constant i.e. by weakening the field. The command values *dsi and

*

qsi are compared with the feedback values of the stator currents ids and iqs in the

synchronous reference frame. The current errors thus obtained are passed through PI

controllers which form the current controllers of the drive system.


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41

In feed back control systems a controller may be introduced to modify the error

signal and to achieve better control action. The introduction of controllers will modify the

transient response and steady state error of the system.

The simulation blocks for the speed and current controllers are shown in following figs

4.7,4.8&4.9

speed-controller

1

out_1

1

s

sat=70

T re flS um

Kps

Kps

Kis

1/ T i1

spe e d error

Fig4.7. Model for speed controller

d-controller

1

De lVqsrefvsqre fl

1

s

sat=12 0

S um

Kp

P

Ki

1 /T i1

dc- e rror

Fig4.8. Model for d- controller


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42

q_controller

1

de l Vqsrefvsdre fl

1

s

sat

Ki

ki

S um

Kp

KP

1

qerrr

Fig4.9.Model for q- controller

y Calculation of the d-axis stator current reference *dsi The d-axis stator current reference *dsi is calculated as for the equation (3.90)

which simulation block is shown in fig 4.10

CALCULATION OF Iqsref

1

iqsref

Lr / (M ^ 2 )

Lr / (M ^ 2 * i phdr e f)

u ( 1 ) / u ( 2 )

(Lr * T re f)/ (Lm ^ 2 * I p hi dr e f)2

I p h i d r e f

1

T ref

Fig4.10.Model for *dsi

y Calculation of the *d

iJ

:

The reference magnetizing current *diJ is calculated as for the equation (3.89)

which simulation block is shown in fig 4.11

CALCULATION O F Iphidref at ZERO FREQUENCY

1

Iphidref

0

delIphi

Product2Product1

5

Iphi

sin(u )

Fcn

wd

Constant

Clock

Fig4.10.Mdel for *diJ


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43

4.7. Decoupling Network:

It can be noted that under proper vector control, the stator current components ids

and iqs decoupled, and hence the outputs of the current controllers can be used as

command values for the current source inverter. However, in the case of the voltage

source inverter, the stator voltage command values Vds and Vqs are not decoupled.

Hence, decoupling networks are necessary to generate Vdsref and Vqsref in the

synchronous reference frame, if a voltage source inverter is used. In the present work,

voltage source inverter is used to drive the induction motor. Therefore, suitable

decoupling terms will have to be incorporated to the outputs of the current controllers.

As discussed in the earlier, the d-axis stator circuit loop has a coupling term

(2

* *me qs d

r

Li p i

L

J[ W )from the quadrature axis and the q-axis stator circuit loop has a

coupling term (2

* *m

e ds d

r

Li i

LJ

[ W )from the direct axis. If the coupling terms are not

compensated, then the torque and the flux components of the stator current will not be

decoupled. Therefore, feed forward terms, Vdo for d-axis voltage compensation and vqo

for q-axis voltage compensation, must be added to the output of the current controllers.

Vdo and Vqo are given by :

2

* *

0m

d e qs d

r

Lv i p i

LJ

[ W! and2

* *mqo e ds d

r

Lv i i

LJ

[ W! respectively

(4.8)

The feed forward terms, Vdo for d-axis voltage compensation and vqo for q-axis

voltage compensation are estimated based on equaion (4.8) in the sensorless vector

control model simulation block diagram which block diagram is shown fig4.11


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44

Fig4.11.Modelforse

nsorlessvectorcontrolmodel

vsref

vsref

vsref

psigmadlis

SENSORLESS VECTOR CONTRO

2

pLi

pLi

0

zero

K* u

vs

K* u

is

K* u

e rM

sigma

We

Rs

Rs1K* u

Rs

Product2

Product1

u

u

u

u

u

K* u

M atrix

Ga in3

m

(M /Lr) 2*R r

Constant1

0

Cons

0

0

8

iphidref

7

erM q

6

erM d

5we

4

iq s

3

id s

2

vdsref

1

vqsref


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45

4.8. d-q to a, b, c transformation(Two Phase to three phase

transformation)

The vdsref and vqsref thus obtained in the synchronous reference frame are first

converted into two phase stator reference frame and then to three phase stator

reference using the following transformations .Using the general variable x ,the

transformations are given by

d,q to ,E F transformation:

cos sin

sin cos

d

q

x x

x x

E

F

V V

V V

!

- - - (4.10)

1 0

1 3

2 2

1 3

2 2

a

b

c

xx

xx

x

E

F

! - -

(4.11)

The three reference voltages thus obtained after the transformations are used as

reference in pulse width modulator to obtain the switching pattern for the inverter

switches.

The block diagram for d,q to ,E F transformation and ,E F a,b,c are developed as

per the equation s(4.10) &(4.11) whose simulation block diagram is shown in the fig4.11


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46

Invpark_TF(2-Ph-->2-Ph)

2

valsref

1

vbtaref

sin

sin

cos

cos Vqsref*costheta

Vdsref*sintheta

Product4

Product1

3

theta

2

vdsref

1

vqsref

InvclarkTF(2Ph-->3Ph)

3

vcref

2

vbref

1

varef

. 8 66

sqrt(3)/2

-.5

-.5

2

valsref

1

vbtsref

Fig4.11.Model for d,q ,E F transformation and ,E F a,b,c

4.9. Sine-Triangle PWM of Three Phase Inverters

Although the basic MOSFET circuitry for an inverter may seem simple,

accurately switching these devices provides a number of challenges for the power

electronics engineer. The most common switching technique is called Pulse Width

Modulation (PWM) which involves applying voltages to the gates of the six MOSFETS

at different times for varying durations to produce the desired output waveform. In Figure

4.12, Q1 to Q6 represents the six MOSFETS and a,a,b,b,c,c represent the respective


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47

control signals. In practice each switching leg may consist of more than two MOSFETs

in order to reduce switching losses by paralleling the on resistance.

Figure 4.12 - Basic Three-Phase Voltage Source Inverter

In the following equations logic values that are equal to 1 when the MOSFET is

on and 0 represent the control signals when it is off. In AC induction motor control when

the upper MOSFET is switched on i.e. a,b,c is 1 the corresponding lower MOSFET is

switched off i.e. a,b,c = 0. Using complementary signals to drive the upper and lowerMOSFETS prevents vertical conduction providing that the control signals dont overlap.

From the states of a,b,c the phase voltages connected to the motor winding can be

calculated using the following matrix representation:

Knowing the phase voltage for a given switching state is important for the

technique known as sine triangle Pulse Width Modulation which will be discussed in

detail in section 4.9.

(4.12)


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48

Sinusoidal Pulse Width Modulator

One commonly used PWM scheme is called carrier based modulation. This uses a

carrier frequency usually between 10 to 20 kHz to produce positive and negative pulses

of varying frequency and varying width. The pulse width and spacing is arranged so that

their weighted average produces a sine wave. The sine-triangle PWM model is shown in

fig4.12

Sintriangle Pulse Width Modulated nverter

3

V cn

2

V bn

1

V a n

Tga

Tgb

Tgc

Va n

Vb n

Vc n

Three P hase V oltage Source Inverter

Varef

Vbref

Vcref

Tga

Tgb

Tgc

Sintriangle Pulse Width M odulator3 Vcref

2 Vbref

1 Varef

Sintriangle Pulse Width Modulator

3

T gc

2

T gb

1

T ga

Rel ay 3

Rel ay 2

Re l ay 1

6 0 * 2 1

Fsw

Ac

F s wCwav e

CARRI ER WAVE

3 0 0

Ac

3 Vcref

2 Vbref

1 Var ef

Fig4.13. model for sine-triangle PWM

Fig4.14.Shows sine-triangle PWM Inverter model


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49

Three Phase Voltage S ource Inverter

3

V cn

2

V b n

1

V a n

1 /3

V zs

1 7 5

Vdc /2

V co

V b o

V a o

3

T g c

2

T g b

1

T g a

Fig4.14.1. Model for sine-triangle PWM Inverter

In sine-triangle PWM a triangular carrier waveform of frequency fs establishes the

inverter switching frequency. This is compared with three sinusoidal control voltages that

comprise the three phase system. The output of the comparators produces the switching

scheme used to turn particular inverter MOSFETS on or off. These three control voltages

have the same frequency as the desired output sine wave which, is commonly referred to

as the modulating frequency, fm. The modulation ratio is equal to mf= fm/fs. The value of

mf should be an odd integer and preferably a multiple of three in order to cancel out the

most dominant harmonics as these are responsible for converter losses. One limitation of

the sine triangle method is that it only allows for a limited modulation index, so it doesnt

fully use the DC bus. The modulation index can be increased by using distorted

waveforms that contain only triplen (multiples of three) harmonics. These form zero

sequence systems where the harmonics cancel out resulting in no iron losses .It is

discussed in detail in the following section.

To obtain balanced 3-phase output voltages from the 3-phase PWM inverter, the

same triangular voltage waveform is compared with three sinusoidal control voltages that

are 1200

out of phase, as shown in the fig 4.15. The comparison of V control with

triangular wave form results in the following logic signals to control the switches in legs

A,B,C.


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If Va ref > Vtri , Vao =2

d cV

else Vao = -2

d cV

If Vbref > Vtri , Vbo = 2d cV

else Vbo = -2

d cV

If Vcref > Vtri , Vco =2

d cV

Else Vao = -2

d cV

0 0.002 0.004 0 .006 0 .008 0 .01 0 .012 0 .014 0 .016 0.018 -300

-200

-100

0

100

200

300

Time t in sec

3-Ph

RefVoltages

Fig 4.15. Reference voltages and carrier wave forms

The common mode voltage is given in (4.19)

i.e. 1

3no ao bo coV V V V ! (4.19)

The output phase voltages can be calculated by subtracting the common mode voltage

from the pole voltages.

a n a o n oV V V! (4.20)


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b n b o n oV V V! (4.21)

c n c o n oV V V! (4.22)

The pole voltages are shown in fig 4.16 ,phase voltage Van is shown in fig 4.17 and line-

line voltage Vab is shown in fig 4.18

0 0 .0 02 0 .0 04 0 .0 06 0 .0 08 0 .0 1 0 .0 12 0 .0 14 0 .0 16 0 .0 18 -200

0

20 0

Vao

0 0 .0 02 0 .0 04 0 .0 06 0 .0 08 0 .0 1 0 .0 12 0 .0 14 0 .0 16 0 .0 18 -200

0

20 0

Vbo

0 0 .0 02 0 .0 04 0 .0 06 0 .0 08 0 .0 1 0 .0 12 0 .0 14 0 .0 16 0 .0 18 -200

0

20 0

time t in sec

Vco

-Vdc/2

+Vdc/2

Fig4.16. Pole voltages Vao,Vbo and Vco Waveforms

0 0 . 0 0 2 0 . 0 0 4 0 . 0 0 6 0 . 0 0 8 0 . 0 1 0 . 0 1 2 0 . 0 1 4 0 . 0 1 6 0 . 0 1 8 -2 50

-2 0 0

-1 50

-1 0 0

-5 0

0

50

1 0 0

1 50

2 0 0

2 50

tim e t in s e c

phase

voltage

V

an

V a n

Fig 4.17 Phase

voltage Van Waveform


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0 0 .0 02 0 .00 4 0 .0 06 0 .0 08 0 .0 1 0 .01 2 0 .0 14 0 .0 16 0 .0 18 -400

-300

-200

-100

0

100

200

300

400

time in sec

L-L

Volt

ge

Vab

V ab

V dc

-Vdc

Fig 4.18 line-line voltage Vab Waveform

These 3-phase voltages will now be fed to the induction motor. In the 3- phase

inverters, only the harmonics in the line-to-line voltages are concerned. The harmonics in

the output (Van) of any one of the legs are identical to the harmonics in Vao, where only

the odd harmonics exist as side bands , centered around m f and its multiples, provided mf

is odd.. only considering the harmonics at mf ( the same applies to its odd multiples), the

phase difference between the mf harmonic in Van and Vbn is (120mf)0

. This phase

difference will be equivalent to zero (a multiple of 3600 ) if mf is odd and a multiple of 3.

As a consequence, the harmonic at mf is suppressed, in the line-to-line voltage Vab . The

same argument applies in the suppression of harmonics at the odd multiples of mf , if mf

is chosen to be an odd multiple of 3 ( where the reason for choosing mf to be odd

multiple of 3 is to keep mfodd and hence, eliminate even harmonics ). Thus some of the

dominating harmonics in the one-leg inverter can be eliminated from the line-to line

voltage of a 3 phase inverters.

In the linear modulation (ma e 1.0) the fundamental frequency component in

the output voltage varies linearly with the amplitude modulation ratio ma. The peakvalue of fundamental frequency component in one of the inverter legs is

(van)1 = ma v vd/2


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53

For low values of mf (mf e 21) to eliminate the even harmonics, a

synchronized PWM (mf be an integer) should be used and mf should be an odd integer.

Moreover, mfshould be a multiple of 3 to cancel out the most dominant harmonics in the

line to line voltage. The reason for using the synchronous PWM inverter is that the

asynchronous PWM (where mf is not an integer) results in sub harmonics (of

fundamental frequency) that are very undesirable in most applications.


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CHAPTER 5

SIMULATED RESULTS AND CONCLUSIONS


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5.1. Description of proposed Scheme

Fig 5.1 shows the simulated schematic simulation block diagram for Sensorless

Vector Control of induction motor drive system, whose specifications and the parameters

of sensorless control scheme are shown in Appendix A.

The system consists of an induction motor which is driven by a voltage source

inverter. The dc-link to the inverter is obtained from the output of ac-dc converter which

is fed from the three phase mains. The inverter switching is controlled by the speed and

current controllers as shown in fig 5.1

The ac-dc converter consists of a three phase bridge rectifier followed by a

capacitor which output is fed to the three phase voltage source inverter. The control

signals for the inverter switches are obtained form the sine triangle modulator block. The

six power switches output are three phase pulse modulated voltages which are fed to the

induction motor. The three phase stator currents ias,ibs and ics are measured(sensed by

using hall effect sensors),are transformed to,

i iE F

in the stationary reference frame ,,ds e qs e

i i

are calculated from,

i iE F

in the synchronous reference(stator flux reference frame) by using

estimated positionm

U .

The voltage across the leakage inductances

pL iW can be obtained by calculating

the current difference between the detected stator currentssi at the two adjacent sampling

points. the model voltage across the leakage inductancesm

pL iW

can be obtained(eq

(3.54)) from the know values *, , ( )s sv i i iJ J! and rMe .The model secondary speed

emf rMe can be estimated(eq (3.58)) by using speed emf estimation gain KJ .

From the d-axis component of the secondary speed emf, flux position compensation term

MU( in equation (3.74), and q-axis component of the secondary speed emf, rotor speed

re[ in equation (3.62), can be estimated.


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Fig5.1Simulatedschematicsim

ulationblockdiagramforSenso

rlessVector

Controlofinductionmotordrivesystem

The

referencespeed

ref

[

iscomparedwiththeestimatedrotorspe

ed

re

[

andthe

speederrorthuspassedthroughaspeedco

ntroller,whichisaPIcontrollerandservesthe

threepurposes-stabilizesthedriveandadjuststhedampingratioatdesire

dvalue,makes

Schematic block diagram of the Sensorless Vector Ccontrol scheme

speed-con troller

softsta rt

q_ c ontroller

d-con troller

Wre f

1

s

W e

delv dsref

Idsref

delv qsref

Iqsref

we

Iphidref

Vqsref

Vdsref

V C D e c oup l

Psigdlids

Psigdliqs

erMd

erMq

Spee d em f Estim a tor

Iphidref

erMqW re

S p e e d E stim a tor

iqsref

Iphidef

W s

S L I P

erMd

Iphidrefde lta thM

Positi on E stim a tor

pL

pL

v qsref

v dsref

idse

iqse

we

erMd

erMq

iphidref

pLiMd

pLiMq

M O DEL

. 1 8 2

.00351s+1

LP Fq

. 1 8 2

.00351s+1

LP Fd

Tref

Iphidrefiqsref

Iqsref

IphidrefIphire f

v qsref

v dsref

the ta

v bta ref

va lsref

Invp a rk_T F

v b

va

I

Idsref

Idsref

2 /p

2 /p


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57

the steady state error close to zero by integral action, and filters out noise gain .The

output of the PI controller is applied to the limiter which sets a torque producing

componentqsref

i .From the torque producing componentqsref

i , slip speedsl

[ can be

estimated using equation (3.71),which is added to the estimated speedre

[ to get the

synchronous speede

[ ,which sets the inverter frequency. The inverter frequency is

adjusted to make the actual speed equal to the reference speed. The reference for the

direct componentdsref

i of stator current space phasor is estimated by using the equation

(3.90).

The command valuesdsref

i andqsref

i are compared with the feedback values of the

stator currents dsei and qsei , which are in the synchronous frame. The current errors thus

obtained passed through a current controllers, which are the PI controllers, which serves

the same three purposes just described. The decoupling terms0, 0d q

v v are calculated from

the equations (3.83)&(3.86) and added to the output of the current

controllers *dsv( and*

qsv( to get stator voltage command values*

dsv ,*

qsv .

The stator voltage command values *dsv ,*

qsv are first converted to two phase stator

reference frame then three phase synchronous reference frame .These three reference

voltages are used as reference signals to a sine triangle pulse width modulator to obtain

the switching pattern for the inverter switches. Finally, the output of the sine triangle

pulse width modulated voltage source inverter is fed to the three phase induction motor.


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5.2. Simulation Results

The fig 5.2 shows the speed response at reference speed Wref = 188.57 rad/sec which

shows that the estimated speedre

[ is coincident with the speedr

[ actual.

0 0 .5 1 1 .5 0

10 0

20 0

Wref

0 0 .5 1 1 .5 -100

0

10 0

20 0

Wre

0 0 .5 1 1 .5 -200

0

20 0

40 0

time(sec)

Wr

Fig.5.2.Speed response vs time

The voltage response Vds, Vqs are shown in fig 5.3 and locus of the voltages Vds and Vqsare shown in fig 5.4.The reference voltages to the PWM modulator are shown in fig 5.5.

Stator voltages van, vbn & vcn are shown in fig 5.6.

1 . 4 1 . 4 1 1 . 4 2 1 . 4 3 1 . 4 4 1 . 4 5 1 . 4 6 1 . 4 7 1 . 4 8 1 . 4 9 1 . 5 - 4 0 0

- 2 0 0

0

2 0 0

4 0 0

t im e ( s e c )

Vd

s

1 . 4 1 . 4 1 1 . 4 2 1 . 4 3 1 . 4 4 1 . 4 5 1 . 4 6 1 . 4 7 1 . 4 8 1 . 4 9 1 . 5 - 4 0 0

- 2 0 0

0

2 0 0

4 0 0

Vqs

V qs ,V ds

fig 5.3 Voltage waveform at steady state


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-400 -300 -200 -100 0 100 200 300 400 -400

-300

-200

-100

0

10 0

20 0

30 0

40 0

Vd s

Vqs

Vds Vs Vqs

fig 5.4 Locus of the voltages Vds and Vqs at steady state

2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5 -400

-200

0

20 0

40 0

tim 2 (sec)

Vbref

2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5 -400

-200

0

20 0

40 0

Varef

volatage response

Fig 5.5 Reference voltages waveforms to the PWM Modulator at steady state


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Stator voltages of the motor are as shown in fig 5.6.

1. 4 1. 41 1. 42 1. 43 1. 44 1. 45 1. 46 1. 47 1. 48 1. 49 1. 5

-200

0

200

Vbn

1. 4 1. 41 1. 42 1. 43 1. 44 1. 45 1. 46 1. 47 1. 48 1. 49 1. 5

-200

0

200

t3

4

5

(6 5 7

)

Vcn

1. 4 1. 41 1. 42 1. 43 1. 44 1. 45 1. 46 1. 47 1. 48 1. 49 1. 5

-200

0

200

Van

Fig 5.6 Stator voltages of the induction motor at steady state

Simulated results at zero frequency are shown in the following figs

0 0. 5 1 1 . 5 2 2. 5 3-60

-40

-20

0

W

8

0 0. 5 1 1 . 5 2 2. 5 30

20

40

60

t@

A B

(C B

c)

W

D

E

0 0. 5 1 1 . 5 2 2. 5 3-50

0

50

100

WF

,WF G

,WH

I

W

D

0 0 . 5 1 1 . 5 2 2 . 5 3-6 0

-4 0

-2 0

0

W

P

Q

0 0 . 5 1 1 . 5 2 2 . 5 30

2 0

4 0

6 0

tR

S

T (U

T c)

W

V

W

0 0 . 5 1 1 . 5 2 2 . 5 3-5 0

0

5 0

10 0

WX

,WX Y

,W` a

W

V

Fig 5.7.Actual motor speedr

[ , estimated rotor speedre

[ and slip speed

sl[ characteristics at zero Frequency


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0 0.5 1 1.5 2 2.5 3-5 0

-4 0

-3 0

-2 0

-1 0

0

Wsl

W sl,W e a t zero frequenb

y

0 0.5 1 1.5 2 2.5 3-1 0

-5

0

5

10

15

We

time(sec)

Fig5.8.The stator angular frequencye

[ andsl

[ characteristics at zero Frequency

0 0.5 1 1.5 2 2.5 3-10

-5

0

5

10q-axis current response at zero frequency

Iqse

0 0.5 1 1.5 2 2.5 3-15

-10

-5

0

time(sec)

Iqsre

f

0 0.5 1 1.5 2 2.5 3-10

-5

0

5

10

Idse

Idse,idseref at Zero frequency

0 0.5 1 1.5 2 2.5 34.5

5

5.5

6

6.5

7

time(sec)

Idseref

Fig.5.9 dq axis currents characteristics at zero Frequency


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0 0 5 1 1 5 2 2 5d

f

0

40

20

0

20

erM

g

h i p

eq

se cr

0 0 5 1 1 5 2 2 5d

f

4

2

0

erM

s

e rMt

u e rMv

Fig 5.10.Estimated speed emf characteristics at zero frequency

The fig 5.7 shows that the estimated speedre

[ is coincident with the actual motor

speedr

[ . The fig 5.8 shows the stator angular frequencye

[ is fluctuating around the

zero with the amplitude of 10r/min and the angular frequency of 2 2d

[ T! v rad /sec.

The fig 5.10 shows the estimated speed emfrq

e is also fluctuating with the amplitude of

10 % of the average emf and angular frequency ofd

[ .From these results, the stable

sensorless control at zero frequency is realized.


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5.3. Conclusions

In this dissertation work for the stable low speed drive, a new sensorles control

scheme, which is based on the secondary speed emf estimation under fluctuating

excitation current is presented. The sensorles vector control scheme of the induction

motor at low speed region including zero stator frequency can be successfully controlled

regardless of the load and even zero frequency is approached without losing stability.

Constant operation at zero frequency is not possible, but stable crossing is very well

possible, even at a reasonably slow rate.

The proposed drive can compete with a speed-sensor equipped drive if

continuous operation at ac excitation and high load is not required. The simulated

characteristics of the sensorles control scheme were verified using a 4-ploe 2.2kW

induction motor. Even at the zero stator angular frequency, the stable sensorless drive is

realized in the speed range of more than 40 r/min.


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5.4. Further work

All further work is summarized schematically in the following ideas:

Development of fuzzy controllers to achieve better performance. Practical implementation of this sensorless vector control using DSP

controllers (TMS 320 F240, TMS 320 F243).

Try to find suitable parameter adoption schemes for Vector Control undervarious operating conditions.

Application of modern control techniques for design of optimum speedand current controllers for reducing EMI and for increasing energy savings

from the mains.


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APPENDIX: B

INTRODUCTION TO SIMULINK


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INTRODUCTION

In this project MATLAB6.1/SIMULINK software is used for sensorless vector control of

induction motor drive. In past, high-level programming languages such as FORTRAN or

C have been used for carrying out simulations. The writing of source code requires much

greater skill and knowledge on the part of the user. For example, proper integrations

routines must be selected and written, even simple mathematical manipulations have to

be programmed. These programs typically produce results, which must be post-processed

to derive visual impressions. This is a two-step process, and typically results in large files

of data, which must be stored before processing.

Computer simulation plays an important role in the design, analysis, and

evaluation of power electronic converters and their controllers. Designing and developing power electronic circuits without suitable computer simulation is extremely laborious,

error-prone, time-consuming, and expensive. Therefore, it is essential to teach, at the

undergraduate level, power converter modeling and simulation, together with the

dynamic behavior of the converter, using a theoretical framework suited for controller

design and development.

Nowadays, a variety of software tools, such as SPICE, EMTP, SABER,

CASPOC, SIMPLORER, SPECTRE, etc., is available to simulate electrical and

electronic circuits. The most used simulators are SPICE or PSPICE, user-friendly

programs designed to perform analysis of low power analog electronic circuits. Several

power electronics professors have used SPICE to simulate the behavior of power

electronics converters.

SIMULINK is a window-oriented dynamics modeling software package built on

top of the MATLAB numerical workspace. An advantage is that models are entered as

block diagrams with an intuitive graphical interface when the corresponding

mathematical descriptions are available for the target systems. This application is not

difficult to do for basic topologies of dcdc switching converters. Furthermore, a set of

blocks with signal interconnections could be masked as a subsystem for convenience in

the SIMULINK environment. The parameters of masked subsystems are then entered in


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dialog windows and can be changed interactively during a simulation. Simulation results

can be viewed during the simulation via a virtual oscilloscope and then exported to the

MATLAB workspace for subsequent off-line analysis. The SIMULINK modeling

environment provides make construction of simple dynamical systems quite easy. This

construction is also true for the design and verification of feedback controllers for

dynamical systems. If the mathematical way of using Kirchhoffs laws to construct the

corresponding dynamical systems is not favored, the MATLAB environment can also be

used to develop mathematical models from inputoutput data.

MATLAB/SIMULINK software is widely used for the simulation of almost all

types of dynamic systems. This software package is also valuable for teaching and

learning since it provides a series of standard routines and software toolboxes, such as a

control toolbox, system identification blocks, nonlinear control design block set, and

neural networks block set, which enable students to perform system simulation,

identification, and control.

The latest versions of MATLAB/SIMULINK include a Power System Blockset

This toolbox features electrical models of power semiconductors and the most commonly

used power devices (machines, transformers, power lines, voltage sources), and allows

simulation of power systems and power electronics. This package is valuable for

imulating well-known topologies several of which are included as demonstrations, but it

tends to generate too many algebraic loops on more complex or novel power topologies.

These algebraic loops are difficult to handle (because they are inherent to the modeling

method) and are time consuming, often preventing simulation convergence.

Furthermore, this toolbox does not easily allow open-loop or closed-loop

simulation of series associations of power rectifiers, nor does it study the steady and the

transient-states in cases of unbalanced or distorted and/or polluted power supply.

Considering the approach of with PSPICE and SIMPLORER, the authors think that a

system-level simulation, considering only the ideal switching and functional behavior of

power semiconductors, would be desirable for MATLAB/SIMULINK. The system-level


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simulation is fast enough and free of algebraic loops and convergence problems

(SIMULINK has built-in integration methods suited to deal with stiff systems).

Therefore, it could avoid the problems of the Power System Block set mentioned

above. Additionally, the system-level derived models to implement in SIMULINK can be

used for closed-loop controller design, since they are switched state-space models. This

advantage is lost when using the Power System Blockset or SIMPLORER.

Considering the increasing capabilities of MATLAB/SIMULINK for the

simulation of dynamic systems, it is advantageous to adapt the ideal models of

semiconductors and simulation methods presented here for this software since only one

software package is needed. The simulation time is short (a few seconds); an excellent

graphical interface is available with parametric identification of the system and the ability

to choose the numerical integration method and toolboxes for closed-loop control. In

addition, the SIMULINK package offers the benefits of a hierarchical structure and uses

MATLAB as its mathematical engine. If required, the modeling method here proposed

could be adapted to other programs. Since the goal is to teach nonlinear mathematical

modeling and control and the simulation of power converters, this paper shows, in

Section II, how to write system-level models of power electronics circuits. In Section III,

examples of pulse width modulation (PWM) ac/dc and dc/ac power electronic converters

are given.

The simulation models described are quite suitable to study power electronics

converters in drives or other applications whose simulation times are not too long, since

only the ideal behavior of the power switches is considered. This work was initially

developed for research in the area of new topologies for power electronics. However,

further developments allowed its use as a valuable teaching aid. Therefore, this work

presents a new way to teach undergraduate students the dynamic behavior of powerelectronics circuits without cutting down the analytic skills needed to learn and

synthesize power converter controllers. The new method can also be used as verification

of analytical methods, allowing students to check their mathematical work quickly and

use it for power converter behavior and controller development.


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BIBLOGRAPHY

[1] Takaharu Takeshita, Yoshiki Nagatoshi, and Nobuyuki Masti, Sensorles Vector

Control of Induction Motor at Zero Frequency. Power Conversion Conference,

2002. PCC Osaka 2002.Proceedings of the, Volume:2, 2-5Apri 2002 Pages:510 -

515 vol.2

[2] K.Nagasaka, Y.Nagatoshi, T.Takesita, N.Matsui, Sensorles Vector Controlled

Induction Motor Drive at Zero Frequency 2001 National Convention Record

IEEJ,4-115,p.1376.

[3] Y.Nagatoshi, K.Nagasaka, T.Takesita, N.Matsui, Sensorles Vector Control Scheme

of Induction Motor Drive at Zero Frequency 2001 Conference Record of IEEJ,

SPC-01-65.[4] Y.S.Lai, C.N.Lui, K.Y.Luo, C.I.Lee, and C.H.Liu, Sensorless Vector Controllers for

Induction Motor Drives.IEEE CNF 1997

[5] L. Umanand, Modeling & Simulation studies & Digital controller Synthesis for

Vector Controlled A.C. Drives., I.I.Sc, Bangalore, 1994.

[6] Scott Wade, Barry W. Williams, Modeling and Simulation of Induction Motor

Vector Control with Rotor Resistance Identification, IEEE Trans. Power

Electronics, vol.12, no.3, May 1997,pp495-506.

[7] P.Vas, Vector Control ofACMachines. London, U.K: Oxford Univ. Press, 1990.

[8] I. Boldea&Naser, Vector control of AC Drives.

[9] B.K Bose, power Electronics and AC Drives. Englewood cliffs, NJ Prentice-hall,

1986.

[10] G.K.Dubey, Power semiconductor Controlled Drives.

[11] Ned Mohan, Tore M. Undeland, William P. Robbins. Power Electronics

converters, Applications and Drives , John Willy & Sons Ltd, Canada .

[12] Finch, J.W. Atkinson, D.J. General Principles of Vector Control for Induction

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