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Direct Torque Control of Induction Motor

TABLE OF CONTENTS

TABLE OF CONTENTS i

ABSTRACT iii

LIST OF SYMBOLS v

LIST OF FIGURES vii

LIST OF TABLES ix

1. LITERATURE SURVEY 1

2. INTRODUCTION 3

3. INDUCTION MACHINE MODEL 7

3.1CIRCUIT MODEL OF A THREE PHASE INDUCTION MACHINE

7

3.2 DYNAMIC d-q MODEL 9

3.3 AXES TRANSFORMATION 10

3.4 SYNCHRONOUSLY RATATING REFERENCE FRAME-DYNAMIC MODEL 14

3.5 STATIONARY FRAME DYNAMIC MODEL 20

3.6 DYNAMIC MODEL STATE SPACE EQUATIONS 21

4. FIELD ORIENTED CONTROL 25

4.1 DIRECT FIELD ORIENTED CURRENT CONTROL

27

4.2 INDIRECT FIELD ORIENTATION METHODS

30

5. COMPARISON OF VARIABLE SPEED DRIVES 32

5.1 DC MOTOR DRIVES

32

5.1.1 FEATURES

32

5.1.2 ADVANTAGES

33

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5.1.3 DRAWBACKS

33

5.2 AC DRIVES-INTRODUCTION

34

5.2.1 AC DRIVES-FREQUENCY CONTROL USING PWM

34

5.2.1.1 FEATURES 34

5.2.1.2 ADVANTAGES 35

5.2.1.3 DRAWBACKS 35

5.2.2 AC DRIVES-FLUX VECTOR CONTROL USING PWM 36

5.2.2.1 FEATURES 36

5.2.2.2 ADVANTAGES 37

5.2.2.3 DRAWBACKS 37

5.2.3 AC DRIVES- DIRECT TORQUE CONTROL 38

5.2.3.1 CONTROLLING VARIABLES 38

5.3 COMPARIAON OF VARIABLE SPEED DRIVES

39

6 DIRECT TORQUE CONTROL(DTC) 41

6.1 TORQUE EXPRESSIONS WITH STATOR AND ROTOR FLUXES41

6.2 CONTROL STRATEGY OF DTC

43

6.3 SIMULATION USING MATLAB

47

SUMMARY 56

CONCLUSION 58

REFERENCES 59

APPENDIX-A 61

APPENDIX-B 65

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ABSTRACT

At present, induction motors are the dominant drives in various industries around the

world, owing to their rugged construction and easy maintenance. However, it is quitecumbersome to control an induction motor because of its poor dynamic response in

comparison to the DC motor drives. Consequent to the painstaking research put in by

Power Electronic engineers around the globe, the dynamic response of an induction motor

is brought on par to that of a separately excited DC motor drive.

Earlier, scalar controlled drives such as a simple V/Hz control is used to control the

induction motor. While this method is simple to implement, it results in a poor dynamicresponse of the torque developed by the motor. In 1971, Blaschke had shown that it is, in

principle, possible to derive a DC-motor like response from an induction motor by resorting

to the Vector control. The central theme of vector control is to decouple the stator current

of the induction motor into two orthogonal components and is to control these two

components individually so as to achieve an independent control of flux and torque of the

induction motor. Though this method imparts a much better elegance to the dynamics of

induction motors, it required a very complex processing of signals. Interest in theimplementation of vector control was renewed with the advancements in technology, such

as Digital Signal Processors, as they facilitated an easy and flexible control.

However, the vector control is still very complex to implement. This motivated

engineers to look for alternative solutions for an enhanced performance with a little

computational overhead on the digital control platform. As a consequence of the

perseverant efforts of various research engineers, an improvised scalar method known as

Direct Torque Control (DTC) was invented. This method considerably alleviates the

computational burden on the control platform while giving a performance which is

comparable to that of a vector controlled drive.

With the DTC scheme employing a Voltage Source Inverter (VSI), it is possible to

control directly the stator flux linkage and the electromagnetic torque by the optimum

selection of inverter switching vectors. The selection of inverter switching vector is made

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to restrict the flux and torque errors within the respective flux and torque hysteresis bands.

This achieves a fast torque response, low inverter switching frequency and low harmonic

losses. The modeling and simulation of an induction motor drive employing DTC is

performed and the results are reported.

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LIST OF SYMBOLS

SUBSCRIPTS:-

a, b,c => for respective phase sequence components.

s, r => for respective stator and rotor quantities.

e.g. asv is Phase a voltage of stator winding.

q ,d => For respective quadrature and direct axis components.

e.g. qri is quadrature axis component if rotor current.

0 => For Zero-sequence components.

e.g. sv0 Is the zero-sequence of the stator current.

l => For leakage quantity.

e.g. lsL leakage inductance of stator winding.

em => For electromagnetic.

e.g. Tem is the electromagnetic torque developed by the machine.

sl => slip quantity.

e.g sl is the slip speed of the induction motor.b => For base quantities.

e.g. Ib is the base current.

m => For the magnetizing quantity.

e.g. Lsl is the stator leakage inductance.

SUPERSCRIPTS:-

s => For these quantities in stationary reference frame.

e.g .s

qrv is the quadrature axis component rotor voltage in stationary

reference frame.

r => For the quantities in rotor reference frame.

e.g.r

dsi is the direct axis component stator current in rotor reference frame.

e => For the quantities in synchronously rotating reference frame.

e.g eqsv is the quadrature axis component stator voltage in

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Synchronously rotating reference frame.

(dash) => For the rotor quantities referred to stationary side.

e.g.e

dri'

is the direct axis component stator current in

Synchronously rotating reference frame as referred to stator side.

* (star) => For the reference input quantity in simulation.

e.g. *bm is the reference speed input in the simulation of indirect vector

control drive.

abc => For the matrix notation of any a,b,c phase quantities.

e.g.abc

sv is the column matrix vector of the phase voltages respective a, b, c

Windings.

qd0 => For the matrix notation of any q,d,0 axis quantities.

e.g.0qd

ri is the column matrix vector of the respective q,d,0 axis currents

windings.

SYMBOLS:-

V: - Voltage in Volts

i :- Current in Ampere

z :- Impedance in Ohm

r :- Resistance in Ohm

:- Flux linkages in Wb.turn

L :- Inductance in Henry

x :- Reactance in Ohms

:- Flux linkages in Volts

:- Angular speed in rad / sec

T :- Torque in Nm

Pin :- Power in Watts

p :- Differential operator.

P :- No. of Poles.

n :- stator to rotor turns ratio.

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LIST OF FIGURES

FIGURE 3-1: PER PHASE EQUIVALENT CIRCUIT OF INDUCTION MOTOR 8

FIGURE 3-1: (A) COUPLING EFFECT IN THREE-PHASE STATOR AND ROTOR WINDINGS OF

MOTOR (B) EQUIVALENT TWO-PHASE MACHINE 9

FIGURE 3-2: STATIONARY FRAME A~B~C TO DS~QS AXES TRANSFORMATION 11

FIGURE 3-3: STATIONARY FRAME DS - QS TO SYNCHRONOUSLY ROTATING FRAME DE - QE

TRANSFORMATION 13

FIGURE 3-4: DYNAMIC DE -QE EQUIVALENT CIRCUITS OF MACHINE (A) QE AXIS

CIRCUIT, (B) DE AXIS CIRCUIT

16FIGURE 3-5: COMPLEX SYNCHRONOUS FRAME DQS EQUIVALENT CIRCUIT

17

FIGURE 3-6: FLUX AND CURRENT VECTORS DE - QE FRAME 19

FIGURE 3-7: SYNCHRONOUSLY ROTATING FRAME MACHINE MODELS WITH INPUT

VOLTAGE AND OUTPUT CURRENT TRANSFORMATIONS 19

FIGURE 3-8: DS QS EQUIVALENT CIRCUITS 20

FIGURE 3-9: COMPLEX STATIONARY FRAMES WITH DQS EQUIVALENT CIRCUITS 22

FIGURE 4-10:PROPERLY ORIENTED QD SYNCHRONOUSLY REFERENCE 27

FIGURE 4-11: DIRECT FIELD-ORIENTED CONTROL OF A CURRENT REGULATED PWM

INVERTER INDUCTION MOTOR DRIVE. 28

FIGURE 4-12: INDIRECT FIELD-ORIENTED CONTROL OF A CURRENT REGULATED

INDUCTION MOTOR DRIVE

31

FIGURE 5-1: CONTROL LOOP OF A DC MOTOR DRIVE 32

FIGURE 5-2: CONTROL LOOP OF AN AC DRIVE WITH FREQUENCY CONTROL 34FIGURE 5-3: CONTROL LOOP OF AC DRIVE WITH FLUX VECTOR CONTROL 36

FIGURE 5-4: CONTROL LOOP OF AN AC DRIVE USING DTC 38

FIGURE 5-5: CONTROL LOOP OF A DC DRIVE 39

FIGURE 5-6: CONTROL LOOP WITH FREQUENCY CONTROL 39

FIGURE 5-7: CONTROL LOOP WITH FLUX VECTOR CONTROL 39

FIGURE 5-8: CONTROL LOOP OF AN AC DRIVE USING DTC 39

FIGURE 6-13:STATOR FLUX, ROTOR FLUX, AND STATOR CURRENT VECTORS ON DS-QS

PLANE (STATOR RESISTANCE NEGLECTED) 42

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FIGURE 6-2: DIRECT TORQUE AND FLUX CONTROL BLOCK DIAGRAM. 44

FIGURE 6-3: (A) TRAJECTORY OF STATOR FLUX VECTOR IN DTC CONTROL, (B) INVERTER

VOLTAGE VECTORS. 45

FIGURE 6-5 TO 6-22 SIMULATION RESULTS 49

FIGURES B-1 TO B-13: SIMULINK BLOCKS 62

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LIST OF TABLES

TABLE 5-1: COMPARISON OF CONTROL VARIABLES 40

TABLE 6-1: SWITCHING TABLE OF INVERTER VOLTAGE VECTORS 46

TABLE 6-2: FLUX AND TORQUE VARIATIONS DUE TO APPLIED VOLTAGE VECTOR IN

(ARROW INDICATES MAGNITUDE AND DIRECTION) 46

TABLE 6-3: BEHAVIOR OF EACH STATE JUST IN THE FIRST ZONE FOR THE CLASSICAL DTC

AND THE MODIFIED DTC 48

TABLE 6-4: THE M_DTC LOOK UP TABLE FOR ALL ITS SIX SECTORS 49

TABLE 6-5: BEHAVIOR OF EACH STATE JUST IN THE FIRST ZONE FOR THE CLASSICAL DTCAND THE MODIFIED DTC 50

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1. LITERATURE SURVEY

Most of the industrial motor applications use AC induction motors. The reasons forthis include high robustness, reliability, low price and high efficiency. Industries have many

applications, where variable operating speed is a prime requirement. Principal benefits of

variable speed drives in industrial applications are that they allow the drive speed and

torque to be adjusted to suit the process requirements. In many applications, operating the

plant at a reduced speed when full output is not needed produces a further important

benefit: energy savings and reduced cost. Plant wear and hence, maintenance requirements,

are also minimized by operation at reduced speed. The various methods of speed controlof squirrel cage induction motor through semiconductor devices are given in [1, 2 and 4] as

under:

1. Scalar control.

2. Vector control (Field-Oriented Control, FOC).

3. Direct Torque Control (DTC).

4. Fuzzy based control.

Constant voltage/hertz control is one of the popular methods for speed control ofinduction motor. This aims at maintaining the same terminal voltage to frequency ratio so

as to give nearly constant flux over wide range of speed variation. In this control scheme,

the performance of machine improves in the steady state only, but the transient response is

poor. More over Constant voltage/hertz control keeps the stator flux linkage constant in

steady state with out maintaining decoupling between the flux and torque [1].

In 1971, Blaschke propose a scheme which aims as the control of an induction

motor like a separately excited dc motor, called field oriented control, vector control, or

Trans vector control [4]. In this scheme the induction motor analyzed from a synchronously

rotating reference frame where all fundamental variables appears to be dc ones. The torque

and flux component of currents are identified and controlled independently to achieve good

dynamic response [4]. However there is a necessity of transforming the variables in the

synchronously rotating reference frame to stator reference frame to affect the control of

actual currents/voltages [4]. This transformation contains transcendental functions like sine

cosine and also introduces computational complexity into the system. Additionally the

transformation also needs the approximate flux vector angle, where is either calculated slip

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angle and measured rotor angle as indirect vector control or by estimating the flux angle

directly by employing a flux observer as in direct vector control. Thus the accuracy of the

vector control governed by the accuracy with which flux angle is calculated and the rotating

reference frame variables are transformed into the stator variables [4].

Recently advanced control strategies for PWM inverter fed induction motor drives

have been developed based on the space vector approach, where the induction motor can be

directly and independently controlled with out any co-ordination transformation. One of the

emerging methods in this perspective is the direct torque and flux control. In DTFC, the

motor torque and the flux are calculated from the primary variables, and they are controlled

directly and independently by selecting optimum inverter switch modes. This selection is

made so as to restrict the errors of flux and torque with in hysteresis bands. This control

results in quick torque response in the transient operation and improvement in the steady

state efficiency. [5]



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2. INTRODUCTION

The history of electrical motors goes back as far as 1820, when Hans ChristianOersted discovered the magnetic effect of an electric current. One year later, Michael

Faraday discovered the electromagnetic rotation and built the first primitive D.C. motor.

Faraday went on to discover electromagnetic induction in 1831, but it was not until 1883

that Tesla invented the A.C. asynchronous motor.

Currently, the main types of electric motors are still te same, DC, AC asynchronous

and synchronous, all based on Oested, Faraday and Teslas theories developed and

discovered more than a hundred years ago.Since its invention, the AC asynchronous motor, also names induction motor has

become the most widespread electrical motor in use today.

These facts are due to the induction motors advantages over the rest of the motors.

The main advantage is that induction motors do not require an electrical connection

between stationary and rotating parts of the motor. Therefore, they do not need any

mechanical commutator (brushes), leading to the fact that they are maintenance free

motors. Induction motors also have low weight and inertia, high efficiency and a highoverload capability. Therefore, they are cheaper and more robust, and less proves to any

failure at high speeds. Furthermore, the motor can work in explosive environments because

no sparks are produced.

Taking into account all the advantages outlined above, induction motors must be

considered the perfect electrical to mechanical energy converter. However, mechanical

energy is more than often required at variable speeds, where the speed control system is not

a trivial matter.

The only effective way of producing an infinitely variable induction motor speed

drive is to supply the induction motor with the three phase voltages of variable frequency

and variable amplitude. A variable frequency is required because the rotor speed depends

on the speed of the rotating magnetic field provided by the stator. A variable voltage is

required because the motor impedance reduces at low frequencies and consequently the

current has to be limited by means of reducing the supply voltages.

Before the days of power electronics, a limited speed control of induction motor

was achieved by switching the three-stator windings from delta connection to star



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connection, allowing the voltage at the motor windings to be reduced. Induction motors

also available with more than three stator windings to allow a change of the number of pole

pairs. However, a motor with several windings is more expensive because more than three

connections to the motor are needed and only certain discrete speeds are available. Another

alternative method of speed control can be realized by means of a wound rotor induction

motor, where the rotor winding ends are brought out to slip rings. However, this method

obviously removes most of the advantages of induction motors and it also introduces

additional losses. By connecting resistors or reactance in series with the stator windings of

the induction motors, poor performance is achieved.

At that time the above described methods were the only ones available to control

the speed of induction motors, whereas infinitely variable speed drives with good

performances for DC motors already existed. These drives not only permitted the operation

in four quadrants but also covered a wide power range. Moreover, they had a good

efficiency, and with a suitable control even a good dynamic response. However, its main

drawback was the compulsory requirement of brushes.

With the enormous advances made in semiconductor technology during the last 20

years, the required conditions for developing a proper induction motor drive are present.

These conditions can be divided mainly in two groups:

1. The decreasing cost and improved performance in power electronic switching

devices.

2. The possibility of implementing complex algorithms in the new microprocessors.

However, one precondition had to be made, which was the development of suitable

methods to control the speed of induction motors, because in contrast to its mechanical

simplicity their complexity regarding their mathematical structure (multivariable and non-

linear) is not a trivial matter.It is in this field, that considerable research effort is devoted. The aim being to find

even simpler methods of speed control for induction machines one method, which is

popular at the moment, is Direct Torque Control.

Historically, several controllers have been developed:

Scalar controllers: Despite the fact that Voltage-Frequency (V/f) is the simplest

controller, it is the most widespread, being in the majority of the industrial

applications. It is known as a scalar control and acts by imposing a constant relationbetween voltage and frequency. The structure is very simple and it is normally used



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without speed feedback. However, this controller does not achieve a good accuracy

in both speed and torque responses, mainly due to the fact that the stator flux and

torque are not directly controlled. Even though, as long as the parameters are

identified, the accuracy in the speed can be 2% (expect in a very low speed), and the

dynamic response can be approximately around 50ms.

Vector controllers: In these types of controllers, there are control loops for

controlling both the torque and the flux. The most widespread controllers of this

type are the ones that use vector transform such as either Park or Ku. Its accuracy

can reach values such as 0.5% regarding the speed and 2% regarding the torque,

even when at standstill. The main disadvantages are the huge computational

capability required and the compulsory good identification of the motor parameters.

Field Acceleration method: This method is based on maintaining the amplitude and

the phase of the stator current constant, whilst avoiding electromagnetic transients.

Therefore, the equations used can be simplified saving the vector transformation,

which occurs in vector controllers. This technique has achieved some computational

reduction, thus overcoming the main problem with vector controllers and allowing

this method to become an important alternative to vector controllers.

Direct Torque Control (DTC) has emerged over the last decade to become one possible

alternative to the well-known Vector Control of Induction machines. Its main characteristic

is the good performance, obtaining results as good as the classical vector control but with

several advantages based on its simpler structure and control diagram.

DTC is said to be one of the future ways of controlling the induction machine in four

quadrants. In DTC it is possible to control directly the stator flux and the torque by

selecting the appropriate inverter state.

DTC main features are as follows:

Direct control of flux and torque.

Indirect control of stator currents and voltages.

Approximately sinusoidal stator fluxes and stator currents.

High dynamic performance even at stand still.

The main advantages of DTC are:



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Absence of co-ordinate transforms.

Absence of voltage modular block, as well as other controllers such as PID for

motor flux and torque.

Minimal torque response time, even better than the vector controllers.

However, some disadvantages are also present such as:

Possible problems during starting.

Requirement of torque and flux estimators, implying the consequent parameters

identification. .

Inherent torque and stator flux ripple.

Initially the theory of induction machine model is given. The understanding of this

model is mandatory to understand both the control strategies (i.e. FOC and DTC). The

theoretical details of vector control .This part will elaborately discuss the Vector control.

After this, comparison of variable speed drives is given. The analysis of Direct

Torque Control (DTC) strategy will take place. Then all these are followed by summary.

Finally the conclusion of all work is given.



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3. INDUCTION MACHINE MODEL

The steady-state model and equivalent circuit are useful for studying the performanceof machine in steady state. This implies that all electrical transients are neglected during

load changes and stator frequency variations. Such variations arise in applications involving

variable-speed drives. The dynamic model considers the instantaneous effects of varying

voltages/currents, stator frequency and torque disturbances. The dynamic model of

induction motor is derived by using a two-phase motor in direct and quadrature axes. This

approach is desirable because of the conceptual simplicity obtained with the two sets of the

windings, one on the stator and the other on the rotor.The equivalence between the three-phase and two-phase machine models is derived

from the simple observation, and this approach is suitable for extending it to model an n-

phase machine by means of a two phase machine. The concept of power invariance is

introduced: the power must be equal in the three-phase machine and its equivalent two-

phase model. The required transformation in voltages, currents, or flux linkages, is derived

in generalized way. The reference frames are chosen to arbitrary and particular cases such

as stationary, rotor, and synchronous reference frames, are simple instances of the generalcase. Derivations for electromagnetic torque involving the currents and flux linkages are

given. The space-phasor model is derived is derived from the dynamic model in direct and

quadrature axes. The space-phasor model powerfully evokes the similarity and equivalence

between the induction machines and DC machines from the modeling and control points of

view.

3.1 CIRCUIT MODEL OF A THREE PHASE INDUCTION MACHINE

(EQUIVALENT CIRCUIT)

A simple per phase equivalent circuit model of an induction motor is very

important tool for the analysis and performance prediction at steady-state condition. The

Figure 3.1 shows the development of a per phase transformer-like equivalent circuit. The

synchronous rotating air gap flux generates a counter emf (CEMF) Vm, which is then

converted to slip voltage mr nSVV = in rotor phase, where n = rotor-to stator turns ratio

and S = per unit slip. The stator terminal voltage V s differs from voltage Vm by the drops

in stator resistance Rs and stator leakage inductance Lls. The excitation current I0 consists of



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two components: a core loss component Ic=Vm/Rm and a magnetizing component

Im=Vm/eLm, where Rm = equivalent resistance for core loss and Lm = magnetizing

inductance.

Figure 3-14: Per phase equivalent circuit of induction motor

The rotor-induced voltage'rV causes rotor current 'rI at slip frequency sl ,which is

limited by the rotor resistance'rR and the leakage reactance

'lrslL .The stator current Is

consists of excitation component I 0 and the rotor-reflected current rI .Figure 3.1(b) shows

the equivalent circuit with respect to the stator, where I r is given as

''

2'

lrslr

mrr

LjR

SVnnII

+==

''lrslr

m

LjR

V

+=

and parameters Rr (R'r/ n

2) and Llr (=L'lr/n

2) are referred to the stator. At standstill, S=1,

and therefore, Figure 3.1(b) corresponds to the short-circuited transformer Equivalent

circuit. At synchronous speed, S=0, current I r =0 and the machine takes excitation current

I0 only. At any sub synchronous speed, 0 lreL ) parameter.



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3.2 DYNAMIC d-q MODEL

The following assumptions are made to derive the dynamic model:

(i) uniform air gap;

(ii) balanced rotor and stator windings, with sinusoidal distributed mmf;(iii) inductance vs. rotor position in sinusoidal; and

(iv) Saturation and parameter changes are neglected

The dynamic performance of an ac machine is somewhat complex because the

three-phase rotor windings move with respect to the three-phase stator windings as shown

in Figure 3.2(a).

Figure 3-15: (a) Coupling effect in three-phase stator and rotor windings of motor,(b) Equivalent two-

phase machine

Basically, it can be looked on as a transformer with a moving secondary, where the

coupling coefficients between the stator and rotor phases change continuously with the

change of rotor position r correspond to rotor direct and quadrature axes. The machine

model can be described by differential equations with time-varying mutual inductances, but

such a model tends to be very complex. Note that a three-phase machine can be represented

by an equivalent two-phase machine as shown in Figure 3.2(b), where ds

~qs

correspond to stator direct and quadrature axes, and d r~q r

Although it is somewhat simple, the problem of time-varying parameters still

remains. R.H. Park, in the 1920s, proposed a new theory of electric machine analysis to

solve this problem. He formulated a change of variables which, in effect, replaced the

variables (voltages, currents and flux linkages) associated with the stator windings of a

synchronous machine with variables associated with fictitious windings rotating with the

rotor at synchronous speed. Essentially, he transformed or referred, the stator variables to a

synchronously rotating reference frame fixed in the rotor. With such a transformation



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(called Parks transformation), he showed that all the time-varying inductances that occur

due to an electric circuit in relative motion and electric circuits with varying magnetic

reluctances can be eliminated. Later, in the 1930s, H. C. Stanley showed that time- varying

inductances in the voltage equations of an induction machine due to electric circuits in

relative motion can be eliminated by transforming the rotor variables to variables

associated with fictitious stationary windings. In this case, the rotor variables are

transformed to a stationary reference frame fixed on the stator. Later, G. Kron proposed a

transformation of both stator and rotor variables to a synchronously rotating reference

frame that moves with the rotating magnetic field. D. S. Brereton proposed a transformation

of stator variables to a rotating reference frame that is fixed on the rotor. In fact, it was

shown later by Krause and Thomas that time-varying inductances can be eliminated by

referring the stator and rotor variables to a common reference frame which may rotate at

any speed (arbitrary reference frame).

3.3 AXES TRANSFORMATION

Consider a symmetrical three-phase induction machine with stationary as-bs-cs axes

at 2/3-angle apart, as shown in Figure 3.3. Our goal is to transform the three-phasestationary reference frame (as bs cs) variables into two-phase stationary reference frame

(ds~qs) variables and then transform these to synchronously rotating reference frame

(de~qe), and vice-versa.



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Figure 3-16: Stationary frame a~b~c to ds~qs axes transformation

Assume that the deqe. Axes are oriented at angle, as shown in Figure 3.3. The voltages

s

dsV ands

qsV can be resolved into as bs cs components and can be represented in thematrix form as

cs

bs

as

V

V

V

=

++

1)120sin()120cos(

1)120sin()120cos(

1sincos

00

00

s

os

s

ds

s

qs

V

V

V

(3.1)

The corresponding inverse relation is

s

os

sds

s

qs

V

V

V

= 3

2

+

+

5.05.05.0)120sin()120sin(sin

)120cos()120cos(cos

00

00

cs

bs

as

V

V

V

(3.2)

Where sosV is added as the zero sequence component, which may or may not be present.

We have considered voltage as the variable. The current and flux linkages can be

transformed by similar equations. It is convenient to set = 0, so that the q s axis is

aligned with the as-axis. Ignoring the zero sequence components, the transformation

relations can be simplified as

s

qsas VV = (3.3)



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sds

s

qsbs VVV 2

3

2

1= (3.4)

sds

s

qscs VVV 2

3

2

1+= (3.5)

And inversely

ascsbsass

qs VVVVV == 31

3

1

3

2(3.6)

csbss

ds VVV3

1

3

1+= (3.7)

Figure 3.4 shows the synchronously rotating de- q e, which rotate at synchronous speed e

with respect to the ds-qs axes and the angle .tee = the two-phase de- q s windings are

transformed into the hypothetical windings mounted on the de-qe axes. The voltages on the

ds-qs axes can be converted (or resolved) into the de-qe frame as follows:

es

dse

s

qsqs VVV sincos = (3.8)

es

dse

s

qsds VVV cossin += (3.9)

For convenience, the superscript e has been dropped from now on from the

synchronously rotating frame parameters. Again, resolving the rotating frame parameters

into a stationary frame, the relations are

edseqss

qs VVV sincos += (3.10)

edseqss

ds VVV cossin += (3.11)

As an example, assume that the three-phase stator voltages are sinusoidal and balanced, and

are given by

)cos( += tVV emas (3.12)

)32cos( += tVV embs (3.13)

)3

2cos(

++= tVV emcs (3.14)

Substituting Equations (3.12) - (3.14) in (3.6) - (3.7) yields

)cos( += tVV ems

qs (3.15)

)sin( += tVV ems

ds (3.16)

Again, substituting Equations (3.8) - (3.9) in (3.15) - (3.16), we get



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cosmqs VV = (3.17)

sinmds VV = (3.18)

Figure 3-17: Stationary frame ds - qs to synchronously rotating frame de - qe transformation

Equations (3.15) - (3.16) show thats

qsV ands

dsV are balanced, two-phase voltages of equal

peak values and the latter is at /2 angle phase lead with respect to the other component.

Equations (3.17) - (3.18) verify that sinusoidal variables in a stationary frame appear as dc

quantities in a synchronously rotating reference frame. Note that the stator variables are not

necessarily balanced sinusoidal waves. In fact, they can be any arbitrary time functions.

The variables in a reference frame can be combined and represented by a complex space

vector (or phasor). For example, from Equations (3.15) - (3.16),

[ ]

)(2

)sin()cos(

+=

=

+++=

==

e

ee

j

s

tjj

m

eem

s

ds

s

qs

s

qds

eV

eV

tjtV

jVVVV

(3.19)

Which indicates that the vectorV rotates counter-clockwise at speed e from the initial (t

= 0) angle of to the qe - axis. Equation (3.19) also indicates that for a sinusoidal



23/79


variable, the vector magnitude is the peak value ( mV ) which is 2 times the rms phasor

magnitude (Vs).The qe -de components can also be combined into a vector form:

ee jjs

dssqs

e

s

dse

s

qse

s

dse

s

qsdsqs

e

qds

eVejVV

VVjVVjVVV

==

+==

)(

)cossin()sincos((3.20)

Or inversely

ej

dsqs

s

ds

s

qs ejVVjVVV+== )( (3.21)

Note that the vector magnitudes in stationary and rotating frames are equal, that is,

22dsqsm VVVV +== (3.22)

The factor eje may be interpreted as a vector rotational operator (defined as a vector rotator

(VR) or unit vector) that converts rotating frame variables into stationary frame variables.

Cose and sine are the Cartesian components of the unit vector. In Equation (3.20), eje is

defined as the inverse vector rotator (VR-1) that converts ds -qs variables into de - qe

variables. The vector V and its components projected on rotating and stationary axes are

shown in Figure 3.4. The as-bs-cs variables can also be expressed in vector form.

Substituting Equations (3.6) (3.7) into (3.19)

[ ]csbsas

csbscsbsas

s

ds

s

qs

VaaVV

VVjVVV

jVVV

2

3

2

31

31

31

31

32

++=

+

=

=

(3.23)

Where a=e j 2 / 3 and a 2 = e -j 2 / 3. The parameters a and a2 can be interpreted as unit

vectors aligned to the respective bs and cs axes of the machine, and the reference axis

also corresponds to the vas - axis. Similar transformations can be made for rotor circuit

variables also.

3.4 SYNCHRONOUSLY ROTATING REFERENCE FRAME - DYNAMIC

MODEL

For the two-phase machine shown in Figure 3.2(b), we need to represent both d s -qs

and dr qrcircuits and their variables in a synchronously rotating de -qe frame. We can write

the following stator circuit equations:

s

qs

s

qss

s

qs

dt

dIRV += (3.24)



24/79


s

ds

s

dss

s

dsdt

dIRV += (3.25)

Wheres

qs ands

ds are q- axis and d-axis stator flux linkages, respectively. When these

equations are converted to de

-qe

frame, the following equations can be written:

dseqsqssqsdt

dIRV ++= (3.26)

qsedsdssdsdt

dIRV += (3.27)

Where all the variables are in rotating form the last term in Equations (3.26) and (3.27)

can be defined as speed emf due to rotation of the axes, that is, when e =0, the equations

revert to stationary form. Note that the flux linkages in the de and qe axes induce emf in the

de and qe axes, respectively, with /2 angle lead.

If the rotor is not moving, that is, 0=r , the rotor equations for a doubly fed wound-rotor

machine will be similar to Equations (3.26) - (3.27):

dreqrqrrqrdt

diRV ++= (3.28)

qredrdrrdrdt

diRV += (3.29)

where all the variables and parameters are referred to the stator. Since the rotor actually

moves at speed r , the d - q axes fixed on the rotor move at a speed e - r relative to the

synchronously rotating frame. Therefore, in de qe frame, the rotor equations should be

modified.

drreqrqrrqrdt

diRV )( ++= (3.30)

qrredrdrrdr

dt

diRV )( += (3.31)

Figure 3.5 shows the de -qe dynamic model equivalent circuits that satisfy Equations (3.26) -

(3.27) and (3.30) - (3.31). A special advantage of the d e -qe dynamic model of the machine

is that all the sinusoidal variables in stationary frame appear as dc quantities in synchronous

frame. The flux linkage expressions in terms of the currents can be written from Figure 3.5

as follows:

)( qrqsmqslsqs iiLiL ++= (3.32)

)( qrqsmqrlrqr iiLiL ++= (3.33)



25/79


)( qrqsmqm iiL += (3.34)

Figure

3-18:

Dynamic de -qe equivalent circuits of machine (a) qe axis circuit, (b) de axis circuit

)( drdsmdslsds iiLiL ++= (3.35)

)( drdsmdrlrdr iiLiL ++= (3.36)

)( drdsmdm iiL += (3.37)

Combining the above expressions with Equations (3.26), (3.27), (3.30) and (3.31), the

electrical transient model in terms of voltages and currents can be given in matrix form as

++

++

=

dr

qr

ds

qs

rrrremmre

rrerrmrem

mmessse

memsess

dr

qr

ds

qs

i

i

i

i

SLRLSLL

LSLRLSL

SLLSLRL

LSLLSLR

V

V

V

V

)()(

)()(

(3.38).

where S is the Laplace operator. For a singly fed machine, such as a cage motor, V rq =

Vdr= 0.

If the speedr

is considered constant (infinite inertia load), the electrical dynamics of

the machine are given by a fourth-order linear system. Then, knowing the inputs v sq , v sd

and e , the currents iqs, ids, iqr and idr can be solved from Equation (3.38). If the machine is

fed by current source, iqs, ids and e are independent. Then, the dependent variables v sq, v sd,

iqr and idr can be solved from Equation (3.38).

The speed r in Equation (3.38) cannot normally be treated as a constant. It can be

related to the torques as



26/79


dt

dJ

PT

dt

dJTT rL

mLe

2+=+= (3.39)

Where TL = load torque, J = rotor inertia, and m = mechanical speed.

Often, for compact representation, the machine model and equivalent circuits are expressedin complex form. Multiplying Equation (3.27) by j and adding with Equation (3.26) gives

)()()( dsqsedsqsdsqssdsqs jjjdt

djiiRjVV ++= (3.40)

Or

qdsreqdsqdssqds jdt

diRV )( ++= (3.41)

Where vqds, iqds, etc. are complex vectors (the superscript e has been omitted). Similarly, the

rotor equations (3.30)-(3.31) can be combined to represent

qdrreqdrqdrrqdr jdt

diRV )( ++= (3.42)

Figure 3.6 shows the complex equivalent circuit in rotating frame where vqdr=0. Note that

the steady-state equations can always be derived by substituting the time derivative

components to zero. Therefore from Equations (3.41) - (3.42), the steady-state equations

can be derived as

sesss jIRV += (3.43)

rerr jIS

R+=0 (3.44)

where the complex vectors have been substituted by the corresponding rms phasors. These

equations satisfy the steadystate equivalent circuit shown in Figure 3.1 if the parameter Rm

is neglected. We know that

sin

22

3rme I

PT

= (3.45)

Figure 3-19: Complex synchronous frame dqs equivalent circuit



27/79


From Equation (3.45), the torque can be generally expressed in the vector form as

rme IxP

T

=

22

3(3.46)

Resolving the variables into de qe components, as shown in Figure 3.7

drqmqrdme IiP

T

=

22

3(3.47)

Some other torque expressions can be derived easily as follows:

dsqmqsdme IiP

T

=

22

3(3.48)

dsqsqsdse IiP

T

=

22

3(3.49)

)(22

3qrdsdrqsme iiiiL

PT

= (3.50

)(22

3drqrqrdre Ii

PT

= (3.51)

Equations (3.38), (3.39), and (3.50) give the complete model of the electro-mechanical

dynamics of an induction machine in synchronous frame. The composite system is of the

fifth order and nonlinearity of the model is evident. Figure 3.8 shows the block diagram of

the machine model along with input voltage and output current transformation



28/79

Figure 3-20: Flux and current vectors de - qe frame

Figure 3-21: Synchronously rotating frame machine models with input voltage and output current

transformations


29/79

3.5 STATIONARY FRAME DYNAMIC MODEL

The dynamic machine model in the stationary frame can be derived by

substituting 0=e in the Equation (3.38) or in (3.26), (3.27), (3.30) and (3.31).The

corresponding stationary frame equations are given as

s

qs

s

qss

s

qsdt

diRV += (3.52)

s

ds

s

dss

s

dsdt

diRV += (3.53)

s

drr

s

qr

s

qrrdt

diR +=0 (3.54)

s

qrr

s

dr

s

drr dt

d

iR ++=0 (3.55)

(a) qs circuit (b) ds circuit

Figure 3-22: ds qs equivalent circuits

Where vqr =vdr=0. Figure 3.9 shows the corresponding equivalent circuits. As mentioned

before, in the stationary frame, the variables appear as sine waves in steady state with

sinusoidal inputs. The torque equations (3.47) - (3.51) can also be written with the

corresponding variables in stationary frame as

s

dr

s

qm

s

qr

s

dme iiP

T = 223

(3.56)


30/79

s

ds

s

qm

s

qs

s

dme iiP

T

=

22

3(3.57)

s

ds

s

qs

s

qs

s

dse iiP

T

=

22

3(3.58)

)(22

3 sqr

s

ds

s

dr

s

dsme iiiiLP

T

= (3.59)

)(22

3 sdr

s

qr

s

qr

s

dre iiP

T

= (3.60)

Equations (3.24) - (3.25) and (3.54) - (3.55) can easily be continued to derive the complex

model as

s

qds

s

qdss

s

qds dt

d

iRV += (3.61)

s

qdrr

s

qdr

s

qdsr jdt

diR +=0 (3.62)

s

ds

s

qs

s

qds jVVV = ,s

ds

s

qs

s

qds j = ,s

ds

s

qs

s

qds jiii = ,s

dr

s

qr

s

qdr j = etc. The complex

equivalent circuit in stationary frame is shown in Figure 3.10(a). Often, a per phase

equivalent circuit with CEMF ( rr ) and sinusoidal variables is described in the form of

Figure 3.10(b) omitting the parameter Lm.

3.6 DYNAMIC MODEL STATE SPACE EQUATIONS

The dynamic machine model in state-space format is important for transient analysis,

particularly for computer simulation study. Although the rotating frame model is

generally preferred the stationary frame model can also be used. The electrical variables in

the model can be chosen as fluxes, currents or a mixture of both. In this section, we will

derive state space equations of the machine in rotating frame with flux linkages as the main

variables.Lets define the flux linkage variables as follows:

qsbqsF = (3.63)

qrbqrF = (3.64)

dsbdsF = (3.65)

drbdrF = (3.66)

Where b = base frequency of the machine.


31/79

Figure 3-23: Complex stationary frames with dqs equivalent circuits

Substituting the above relations in (3.26) - (3.27) and (3.30) - (3.31), we can write

dsb

eqs

bqssqs

Fdt

dFiRv

++=

1

(3.67)

qs

b

eds

b

dssds Fdt

dFiRv

++=

1(3.68)

dr

b

reqr

b

qrr Fdt

dFiR

)(10

++= (3.69)

qr

b

redr

b

drr Fdt

dFiR

)(10

++= (3.70)

where it is assumed that vqr = vdr = 0.

Multiplying equations (3.32) - (3.37) by b on both sides, the flux linkage expressions can

be written as

)( qrqsmqslsqsbqs iiXiXF ++== (3.71)

)( qrqsmqrlrb iiXiXrFr ++== (3.72)

)( qrqsmqmbqm iiXF +== (3.73)

)( drdsmdslsdsbds iiXiXF ++== (3.74)


32/79

)( drdsmdrlrdrbdr iiXiXF ++== (3.75)

)( drdsmdmbdm iiXF +== (3.76)

Where X ls = b Lls, X lr= b Llr, and Xm = b Lm, or

qmqslsqs FiXF += (3.77)

qmqrlrqr FiXF += (3.78)

dmdslsds FiXF += (3.79)

dmdrlrdr FiXF += (3.80)

From Equations (3.77) - (3.80) the currents can be expressed in terms of the flux linkages

as

ls

qmqs

qsX

FFi = (3.81)

lr

qmqr

qrX

FFi

= (3.82)

ls

dmdsds

X

FFi

= (3.83)

lr

dmdrdr

X

FFi

= (3.84)

Substituting Equations (3.81) - (3.84) in (3.77) - (3.78), respectively, the Fqm expression is

given as

+

=

lr

qmqr

ls

qmqs

mqmX

FF

X

FFXF (3.85)

Or

+=

lr

qr

ls

qs

mqm

X

F

X

FXF 1 (3.86)

Where

++

=

lrlsm

m

XXX

X111

11

(3.87)

Similar derivation can be made for Fdm as follows

+=

lr

dr

ls

dsmdm

X

F

X

FXF 1 (3.88)


33/79

Substituting the current equations (3.81) - (3.84) into the voltage equations (3.67) - (3.70)

ds

b

eqs

b

qmqs

ls

sqs F

dt

dFFF

X

Rv

++=

1)( (3.89)

qs

b

eds

b

dmds

ls

sds F

dtdFFF

XRv

+= 1)( (3.90)

dr

b

reqr

b

qmqr

lr

r Fdt

dFFF

X

R

)(1)(0

++= (3.91)

qr

b

redr

b

dmdr

lr

r Fdt

dFFF

X

R

)(1)(0

++= (3.92)

which can be expressed in state-space form as

= )( qmqs

ls

sds

b

eqsb

qs FFXRFv

dtdF

(3.93)

+= )( dmds

ls

sqs

b

edsb

ds FFX

RFv

dt

dF

(3.94)

+

= )(

)(qmqr

lr

rdr

b

reb

qrFF

X

RF

dt

dF

(3.95)

+

= )(

)(dmdr

lr

rqr

b

reb

dr FF

X

RF

dt

dF

(3.96)

finally, from equation (3.49)

)(1

22

3dsqsqsds

b

e iFiFP

T

=

(3.97)

Equations (3.93) - (3.97), describe the complete model in state-space form where

,,, qrdsqs FFF and drF are the state variables.


34/79

4. FIELD-ORIENTED CONTROL

In a dc machine, the axes of the armature and field windings are usually orthogonal toone another. The mmfs established by currents in these windings will also be orthogonal. If

iron saturation is ignored, the orthogonal fields produce no net interaction effect on one

another. The developed torque may be expressed as,

Nm)( afaem IIkT = (4.1)

Where ka is a constant coefficient, (If), the field flux, and Ia, the armature current.

Here the torque angle is naturally 900, flux may be controlled by adjusting the field current,

If and torque may be controlled independently of flux by adjusting the armature current, Ia.

Since the time constant of the armature circuit is usually much smaller than that of the field

winding, controlling torque by changing armature current is quicker than changing If, or

both.

In general, torque control of a three-phase induction machine is not straight forward

as that of a dc machine because of the interactions between the stator and rotor fields whose

orientation are not held spatially at 900 but vary with operating condition. The field of the

rotor winding in an induction machine may be likened to that of a field winding of a dc

machine, except that it being induced is not independently controllable. With sinusoidal

excitation, the rotor field rotates at synchronous speed. If we were to select a synchronously

rotating qd0 frame whose d-axis is aligned with the rotor field, the q-component of the rotor

field,e

qr

' in the chosen reference frame would be zero, that is

Wb.turn0''' =+= eqrre

qsm

e

qr iLiL (4.2)

'' e

qs

r

me

qr iL

Li = (4.3)

Withe

qr

' zero, the first equation in (4.1) for the developed torque reduces to

Nm22

3 '' eqr

e

drem iP

T = (4.4)

Substituting fore

qri'

using equation (4.3), (4.4) can be written in desired form of,


35/79

Nm22

3 '''

e

qr

e

dr

r

mem i

L

LPT = (4.5)

Which shows that if the rotor flux linkage,e

qr

' is not disturbed, the torque can be

independently controlled by adjusting the stator q-component current,e

qsi .

Fore

qr

' to remain unchanged at zero,e

qrp' must be zero, in which case, the q-axis

voltage equation of the rotor winding with no applied rotor voltages reduces to

V)( ''''' edrree

qr

e

qrr

e

qr pirv ++= (4.6)

In other words, the slip speed must satisfy

secelect.rad/'

''

e

dr

e

qrrre

ir

= (4.7)

Also, if 'edr is to remain unchanged,e

drp' must be zero too. Using this condition and that

ofe

qr

' being zero in the d-axis rotor voltage equation, we will obtain the condition that edri'

must be zero, that is

V)( ''''' eqrree

dr

e

drr

e

dr pirv ++= (4.8)

And, when edri' is zero, edsm

e

dr iL=' . Substituting this into equation (4.7) and using (4.3), we

obtain the following relationship between slip speed and the ratio of the stator qdcurrent

components for the d-axis of the synchronously rotating frame to be aligned with the rotor

field:

secelect.rad/'

'

e

ds

e

qs

r

rre

i

i

L

r= (4.9)


36/79

Figure 4-24:Properly oriented qd synchronously reference

In practice, the magnitude of rotor flux can be adjusted by controlling edsi , and the

orientation of the d-axis to the rotor field can be maintained by keeping either slip speed ore

qsi in accordance to equation (4.9). With proper field orientation, the dynamic of'e

dr will

be confined to the d-axis and is determined by the rotor circuit time constant. This can be

seen from equation (4.8) with edri' replaced by '' )/( r

e

dsm

e

dr LiL , that is,

rnWb.tu''

'' e

ds

rr

mre

dr ipLr

Lr

+= (4.9)

Field-oriented control schemes for the induction machine are referred to as the directtype

when the angle, , shown in Figure 4.1, is being determined directly as with the case of

direct air gap flux measurement or as the indirect type when the rotor angle is being

determined from surrogate measures, such as slip speed.

4.1 DIRECT FIELD-ORIENTED CURRENT CONTROL

Figure 4.2 shows a direct field oriented control scheme for torque control using acurrent-regulated pwm inverter. For field orientation, controlling stator current is more


37/79

direct than controlling stator voltage; the later approach must allow for the additional

effects of stator transient inductances. With adequate dc bus voltage and fast switching

devices, direct control of stator current can be readily achieved. The direct method relies on

the sensing of air gap flux, using specially fitted search coils or Hall-effect devices. The

drift in the integrator associated with the search coil is especially problematic at very low

frequencies. Hall devices are also temperature-sensitive and fragile.

Figure 4-25: Direct field-oriented control of a current regulated pwm inverter induction motor drive.

The measured flux in the air gap is the resultant mutual flux. It is not the same as

the flux linking the rotor winding, whose angle, , is the desired angle for field orientation.

But, as shown by the expression below, in conjunction with the measured stator current, we

can determine the value of and the magnitude of the rotor flux. The measured abc

currents are first transformed to the stationary qdcurrents using,

)(3

1

A3

1

3

1

3

2

csbsas

s

ds

csbsas

s

qs

iiii

iiii

+=+= (4.10)

Adding and subtracting as

qslriL'

term to the right-hand side, the rotor q-axis flux linkage in

the stationary reference frame may be expressed as

nWb.tur)()( ''''' sqrlrms

qslrlrm

s

qr iLLiLLL +++= (4.11)


38/79

Sinces

mq is equal to )('s

qr

s

qsm iiL + , we can determines

qr

' from the measured quantities,

that is

''

' sqslr

smq

m

lrsqr iL

L

L= (4.12)

Similarly, sdr' can be determined from

Wb.turn''

' s

dslr

s

md

m

lrs

dr iLL

L= (4.13)

Using sqr' and s

dr' computed from equations (4.13) and (4.14), we can determine the

cosine and sine of by the following geometrical relations that are deducible from Figure

4.2:

sin

2

cos

cos2

sin

'

'

'

'

s

r

s

qr

s

r

s

dr

==

==

(4.14)

Where,

2'2''' s

qr

s

dr

s

r

e

r +== (4.15)

The above computations from equations (4.11) to (4.16) are performed inside the

field orientation block shown in the middle of Figure 4.2. The calculated value ofe

r

' is fed

back to the input of the flux controller regulating air gap flux. Inside the torque calculation

block , the calculated values of er' and

e

qsi are used in equation (4.5) to estimate the value

of the torque developed by the machine, and the estimated torque is fed back to the input of

the torque controller.

The respective output of the torque and flux controllers are the command value

*eqsi and

*e

dsi , in the field-oriented rotor reference frame. Inside the qdabc transformation

block are the following transformations from qde to qds and qds to balanced abc:


39/79

**

***

***

cossin

Asincos

s

qsas

e

ds

e

qs

s

ds

e

ds

e

qs

s

qs

iiiii

iii

=+=

+=

(4.16)

***

***

2

3

2

1

2

3

2

1

s

ds

s

qscs

s

ds

s

qsbs

iii

iii

=

=(4.17)

4.2 INDIRECT FIELD-ORIENTATION METHODS

For very low-speed operations and for position type control, the use of flux sensing

that relies on integration which has a tendency to drift may not be acceptable. A commonly

used alternative is indirect field orientation, which does not rely on the measurement of air

gap flux, but uses the condition in equations (4.5), (4.9) and (4.10) to

Satisfy the condition for proper orientation. Torque can be controlled by regulatinge

qsi and

slip speed, (e- r). Rotor flux can be controlled by regulating edsi . Given some desired

level of rotor flux, '*r , the desired value of

*e

dsi may be obtained from

rnWb.tu*

''

''* e

ds

rr

mrdr i

pLr

Lr

+= (4.18)

For the desired torque of*

emT at the given level of rotor flux the desired value of

*e

qsi in accordance with equation (4.5) is,

Nm22

3 **''

* e

qs

e

dr

r

m

emi

L

LPT = (4.19)

It has been shown that when properly oriented, edri' is zero and edsm

e

dr iL=' ; thus the slip

speed relation of equation (4.9) can also be written as

secelect.rad/*

*

'

'*

2 e

ds

e

qs

r

r

re i

i

L

r

== (4.20)


40/79

The above conditions, if satisfied, ensure the decoupling of the rotor voltage

equations. To what extent this decoupling is actually achieved will depend on accuracy of

motor parameters used. Since the values of rotor resistance and magnetizing inductance are

known to vary somewhat more than the other parameters, on-line parameter adaptive

techniques are often employed to tune the value of these parameters used in an indirect

field-oriented controller to ensure proper operation.

Figure 4-26:Indirect field-oriented control of a current regulated induction motor drive

Figure 4.3 shows an indirect field-oriented control scheme for a current controlled pwm

induction motor drive. The field orientation, , is the sum of the rotor angle from the

position sensor r, and the angle 2, from integrating the slip speed. If orthogonal outputs of

the form cosr and sinr are available from the shaft encoder, the values of cos and sin

can be generated from the following trigonometric identities:

sincoscossin)sin(sinsinsincoscos)cos(cos

222

222

rrr

rrr

=+==+= (4.21)

In simulation, the value of cos2 and sin2 may be generated from a variable-frequency

oscillator.


41/79


42/79

5. COMPARISON OF VARIABLE SPEED DRIVES

5.1 DC MOTOR DRIVES:

Figure 5-1 Control loop of a DC Motor Drive

5.1.1. FEATURES:

Field orientation via mechanical commutator

Controlling variables are Armature Current and Field Current, measured

DIRECTLY from

the motor.

Torque control is direct

In a DC motor, the magnetic field is created by the current through the field winding inthe stator. This field is always at right angles to the field created by the armature winding.

This condition, known as field orientation, is needed to generate maximum torque. The

commutator-brush assembly ensures this condition is maintained regardless of the rotor

position once field orientation is achieved; the DC motors torque is easily controlled by

varying the armature current and by keeping the magnetizing current constant. The

advantage of DC drives is that speed and torque the two main concerns of the end-user -

are controlled directly through armature current: that is the torque is the inner control loopand the speed is the outer control loop. (see figure1.)


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5.1.2. ADVANTAGES:

Accurate and fast torque control

High dynamic speed response

Simple to control

Initially, DC drives were used for variable speed control because they could easily

achieve a good torque and speed response with high accuracy.

A DC machine is able to produce a torque that is:

Direct - the motor torque is proportional to the armature current: the torque can

thus be controlled directly and accurately.

Rapid - torque control is fast; the drive system can have a very high dynamic

speed response. Torque can be changed instantaneously if the motor is fed from an ideal

current source. A voltage fed drive still has a fast response, since this is determined only by

the rotors electrical time constant (i.e. the total inductance and resistance in the armature

circuit)

Simple - field orientation is achieved using a simple mechanical device called a

commutator/brush assembly. Hence, there is no need for complex electronic control

circuitry, which would increase the cost of the motor controller.

5.1.3. DRAWBACKS:

Reduced motor reliability

Regular maintenance

Motor costly to purchase

Needs encoder for feedback

The main drawback of this technique is the reduced reliability of the DC motor; the

fact that brushes and commutators wear down and need regular servicing; that DC motors

can be costly to purchase; and that they require encoders for speed and position feedback.

While a DC drive produces an easily controlled torque from zero to base speed and beyond,

the motors mechanics are more complex and require regular maintenance.

5.2 AC DRIVES INTRODUCTION:


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Small size

Robust

Simple in design

Light and compact

Low maintenance

Low cost

The evolution of AC variable speed drive technology has been partly driven by the

desire to emulate the performance of the DC drive, such as fast torque response and speed

accuracy, while utilizing the advantages offered by the standard AC motor.

5.2.1. AC DRIVES FREQUENCY CONTROL USING PWM:

Figure 5-2 Control loop of an AC Drive with frequency control using PWM

5.2.1.1. FEATURES:

Controlling variables are Voltage and Frequency

Simulation of variable AC sine wave using modulator

Flux provided with constant V/f ratio

Open-loop drive

Load dictates torque level

Unlike a DC drive, the AC drive frequency control technique uses parametersgenerated outside of the motor as controlling variables, namely voltage and frequency. Both


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voltage and frequency reference are fed into a modulator which simulates an AC sine wave

and feeds this to the motors stator windings. This technique is called Pulse Width

Modulation (PWM) and utilizes the fact that there is a diode rectifier towards the mains and

the intermediate DC voltage is kept constant. The inverter controls the motor in the form of

a PWM pulse train dictating both the voltage and frequency. Significantly, this method

does not use a feedback device which takes speed or position measurements from the

motors shaft and feeds these back into the control loop. Such an arrangement, without a

feedback device, is called an open-loop drive.

5.2.1.2. ADVANTAGES:

Low cost

No feedback device required simple.

Because there is no feedback device, the controlling principle offers a low cost and

simple solution to controlling economical AC induction motors. This type of drive is

suitable for applications which do not require high levels of accuracy or precision, such as

pumps and fans.

5.2.1.3. DRAWBACKS:

Field orientation not used

Motor status ignored

Torque is not controlled

Delaying modulator used

With this technique, sometimes known as Scalar Control, field orientation of themotor is not used. Instead, frequency and voltage are the main control variables and are

applied to the stator windings. The status of the rotor is ignored, meaning that no speed or

position signal is fed back. Therefore, torque cannot be controlled with any degree of

accuracy. Furthermore, the technique uses a modulator which basically slows down

communication between the incoming voltage and frequency signals and the need for the

motor to respond to this changing signal.

5.2.2. AC DRIVES - FLUX VECTOR CONTROL USING PWM:


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Figure 5-3 Control loop of an AC Drive with flux vector control using PWM

5.2.2.1 FEATURES:

Field-oriented control - simulates DC drive

Motor electrical characteristics are simulated - Motor Model

Closed-loop drive

Torque controlled INDIRECTLY

To emulate the magnetic operating conditions of a DC motor, i.e. to perform the

field orientation process, the flux-vector drive needs to know the spatial angular position of

the rotor flux inside the AC induction motor. With flux vector PWM drives, field

orientation is achieved by electronic means rather than the mechanical commutator/ brush

assembly of the DC motor. Firstly, information about the rotor status is obtained by feeding

back rotor speed and angular position relative to the stator field by means of a pulse

encoder. A drive that uses speed encoders is referred to as a closed-loop drive. Also the

motors electrical characteristics are mathematically modeled with microprocessors used to

process the data. The electronic controller of a flux-vector drive creates electrical quantities

such as voltage, current and frequency, which are the controlling variables, and feeds these

through a modulator to the AC induction motor. Torque, therefore, is controlled

INDIRECTLY.


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5.2.2.2. ADVANTAGES:

Good torque response

Accurate speed control

Full torque at zero speed

Performance approaching DC drive

Flux vector control achieves full torque at zero speed, giving it a performance very

close to that of a DC drive.

5.2.2.3. DRAWBACKS:

Feedback is needed

Costly

Modulator needed

To achieve a high level of torque response and speed accuracy, a feedback device is

required. This can be costly and also adds complexity to the traditional simple AC

induction motor. Also, a modulator is used, which slows down communication between the

incoming voltage and frequency signals and the need for the motor to respond to this

changing signal. Although the motor is mechanically simple, the drive is electrically

complex.

5.2.3. AC DRIVES - DIRECT TORQUE CONTROL:


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Figure 5-4 Control loop of an AC Drive using DTC

5.2.3.1. CONTROLLING VARIABLES:

With the revolutionary DTC technology developed by ABB, field orientation is

achieved without feedback using advanced motor theory to calculate the motor torque

directly and without using modulation. The controlling variables are motor magnetizing

flux and motor torque. With DTC there is no modulator and no requirement for a

tachometer or position encoder to feed back the speed or position of the motor shaft.

DTC uses the fastest digital signal processing hardware available and a more

advanced mathematical understanding of how a motor works. The result is a drive with a

torque response that is typically 10 times faster than any AC or DC drive. The dynamic

speed accuracy of DTC drives will be 8 times better than any open loop AC drives and

comparable to a DC drive that is using feedback.

5.3 COMPARISON OF VARIABLE SPEED DRIVES:


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Let us now take a closer look at each of these control blocks and spot a few differences.

Figure 5-5 Control loop of a DC Drive

Figure 5-6 Control loop with frequency control

Figure 5-7 Control loop with flux vector control

Figure 5-8 Control loop of an AC Drive using DTC

The first observation is the similarity between the control block of the DC drive

(Figure 5-5) and that of DTC (Figure 5-8). Both are using motor parameters to directly


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control torque. But DTC has added benefits including no feedback device are used; all the

benefits of an AC motor and no external excitation is needed.

Table 5-1 Comparison of control variables

As can be seen from Table 5-1, both DC drives and DTC drives use actual motor

parameters to control torque and speed. Thus, the dynamic performance is fast and easy.Also with DTC, for most applications, no tachometer or encoder is needed to feed back a

speed or position signal. Comparing DTC (Figure 5-8) with the two other AC drive control

blocks (Figures 5-6 & 5-7) shows up several differences, the main one being that no

modulator is required with DTC. With PWM AC drives, the controlling variables are

frequency and voltage which need to go through several stages before being applied to the

motor. Thus, with PWM drives control is handled inside the electronic controller and not

inside the motor.


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6. DIRECT TORQUE CONTROL (DTC)

In addition to vector control systems, instantaneous torque control yielding fast torqueresponse can also be obtained by employing direct torque control. Direct torque control was

developed more than a decade ago by Japanese and German researchers (Takahashi and

Noguchi 1984, 1985; Depenbrock 1985). Drives with direct torque control (DTC) are being

shown at great interest, since ABB has recently introduced a direct-torque controlled

induction motor drive, which according to ABB can work even at zero speed. This is a very

significant industrial contribution, and it has been stated by ABB that direct-torque control

(DTC) is the latest a.c. motor control method developed by ABB (Tiitien 1996). It isexpected that other manufacturer will also release their DTC drives and further

developments are underway for speed-sensor less and artificial intelligence based

implementations.

In a DTC drive, flux linkage and electromagnetic torque are controlled directly

independently by the selection of optimum inverter switching modes. The selection is made

to restrict the flux linkages and electromagnetic torque errors within the respective flux and

torque hysteresis bands, to obtain fast torque response, low inverter switching frequencyand low harmonic losses. The required optimal switching vectors can be selected by using

so-called optimum switching-voltage vector look-up table. This can be obtained by simple

physical considerations involving the position of the stator-flux linkage space vector, the

available switching vectors, and the required torque flux linkage.

6.1 TORQUE EXPRESSIONS WITH STATOR AND ROTOR FLUXES

The torque expression for induction machine can be expressed in vector form as,

22

3sse I

PT

= (6.1)

wheres

ds

s

qss j = ands

ds

s

qss jiiI = . In this equation, sI is to be replaced by

rotor flux r . In the complex form, s and r can be expressed as function of currents as,

rmsss ILIL += (6.2)

smrrr ILIL += (6.3)


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Eliminating rI from equation (6.2), we get

' ssrr

ms IL

L

L+= (6.4)

where2'

mrss LLLL = . The corresponding expression of sI is

1

'' r

sr

ms

s

sLL

L

LI = (6.5)

Substituting equation (6.5) in (6.1)and simplifying yields

sr

sr

me

LL

LPT

'22

3

= (6.6.)

That is, the magnitude torque is

sin22

3'

srsr

me

LL

LPT

= (6.7)

Figure 6-27:Stator flux, rotor flux, and stator current vectors on d s-qsplane

(stator resistance neglected)

where is the angle between the fluxes. Figure 6.1 shows the phasor (or vector) diagram

for equation (6.6), indicating the vectors s , r , and sI for positive developed torque.

If the rotor flux remains constant and stator flux is changed incrementally by stator voltage

sV as shown and the corresponding change of angle is , the incremental torque eT

expression is given as

sin22

3'

+

= ssr

sr

me

LL

LPT (6.8)


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6.2 Control Strategy of DTC

The block diagram of direct torque and flux control is shown in Figure 6.5 and Figure

6.6 explains the control strategy. The speed control loop and the flux program as a function

of speed are shown as usual and will not be discussed. The command stator flux*s and

torque *eT magnitudes are compared with the respective estimated values and the errors are

processed through hysteresis-band controllers, as shown. The flux loop controller has two

levels of digital output according to the following relations:

for1 HBEH +>= (6.9)

HBEH

= for1 (6.11)

TeTeTe HBEH


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Figure 6-2: Direct torque and flux control block diagram


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Figure 6-3: (a)Trajectory of stator flux vector in DTC control, (b) Inverter voltage vectors and

corresponding stator flux variation in time t.

The voltage vector table block in Figure 6-2 receives the input signals ,, TeHH and

S(k)and generates the appropriate control voltage vector (switching states) for the inverter

by lookup table, which is shown in table 6.2(the vector sign is deleted). The inverter

voltage vector (six active and two zero states) and a typical s are shown in Figure 6-3(b).

Neglecting the stator resistance of the machine, we can write

)( ssdt

dV = (6.14)

Or

. tVss = (6.15)

Which means that s can be changed incrementally by applying stator voltage sV for time

increment t. The flux increment vector corresponding to each of six inverter voltage

vectors is shown in Figure 6-3(b). The flux in machine is initially established to at zerofrequency (dc) along the trajectory OA shown in Figure 6-3(a). With the rated flux, the

command torque is applied and the*

s vector starts rotating.

Table 6.2 applies the selected voltage vector, which essentially affects both the torque and

flux simultaneously. The flux trajectory segments AB, BC, CD and DE by the respective

voltage vectors 4343 and,,, VVVV are shown in Figure 6-3(a). The total and incremental

torque due to s are explained in figure 6-1. Note that the stator flux vector changes


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quickly by, but the r change is very sluggish due to large time constant T r. Since r is

more filtered, it moves uniformly at frequency e , whereas s movement is jerky. The

average speed of both, however, remains the same in the steady-state condition. Table 6-2

summarizes the flux and torque change (magnitude and direction) for applying the voltage

vectors for the location of s shown in Figure 6-3(b). The flux can be increased by the

621 and,, VVV vectors (vector sign is deleted), whereas it can be decreased by the

543 and,, VVV vectors.

H HTE S(1) S(2) S(3) S(4) S(5) S(6)

1

1 V2 V3 V4 V5 V6 V1

0 V0 V7 V0 V7 V0 V7

-1 V6 V1 V2 V3 V4 V5

-1

1 V3 V4 V5 V6 V1 V2

0 V7 V0 V7 V0 V7 V0

-1 V5 V6 V1 V2 V3 V4

Table6-1: Switching table of inverter voltage vectors

Voltage

vector

V1 V2 V3 V4 V5 V6 V0 or v7

s 0

Te

Table6-2: Flux and Torque variations due to applied voltage vector in

Figure (6-5b) (Arrow indicates magnitude and direction)

Similarly, torque is increased by the 432 and,, VVV Vectors, but decreased by the

651 and,, VVV vectors. The zero vectors (V0 or V7) short-circuit the machine terminals

and keep the flux and torque unaltered. Due to finite resistance (Rs) drop, the torque and

flux will slightly decrease during the short-circuit condition.


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Consider for example, an operation in sector S (2) as shown in Figure 6-3(a), where

at point B, the flux is too high and the torque is too low; that is, 1=H and 1 +=TeH

. From table 6-1, voltage V4 is applied to the inverter, which will generate the trajectory

BC. At point C, 1 +=H and 1 +=TeH and this will generate the V3 vector from the

table. The drive can easily operate in the four quadrants, and speed loop and field-

weakening control can be added, if desired. The torque response of the drive is claimed to

be comparable with that of a vector-controlled drive.

6.3 SIMULATION USING MATLAB

We run the model for typical conditions of reference speed and applied torque

values. Initially we will see the starting transients for the DTC drive at no load condition.

Next we will check out the performance of the machine for the speed reversal

characteristics. Finally we will check out the performance of the DTC drive for load

variations. Lastly the hexagonal flux plot of this typical DTC drive has shown.


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SIMULATION RESULTS:

WHEN LOAD IS APPLIED:

Figure 6-5: stator A phase current Vs time

Figure 6-6: D-axis flux Vs time

Figure 6-7: Q-axis flux Vs time


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Figure 6-8: Stator flux Vs time

Figure 6-9: Vas Vs time

Figure 6-10: Vbs Vs time


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Figure 6-11: Vcs Vs time

Figure 6-12: Hexagonal Flux plot

Figure 6-13: Electromagnetic torque, applied torque Vs Time


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Figure 6-14: speed in rpm Vs Time

Figure 6-15: Command Torque Vs Time


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WHEN SPEED IS REVERSED:

Figure 6-16: Flux plot


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Figure 6-17: Speed Vs time

Figure 6-18: Te, Tapp Vs Time

Figure 6-19: Stator Flux Vs Time


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Figure 6-20: Stator A phase current Vs time

Figure6-21: D-Axis flux Vs Time

Figure6-22: Q-Axis flux Vs Time


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SUMMARY

Flux and torque control mechanism:-FOC scheme uses a d-q co-ordinates frame having the d-axis aligned with the rotor

flux vector that rotates at the stator frequency. This particular situation allows the flux and

torque to be separately controlled by the stator current d-q components. The rotor flux is a

function of the d-axis component of the Stator current. The developed torque is controlled

by the q-axis component of the stator current. The decoupling between the flux and torque

control is achieved only if the accurate rotor position is known. This can be done by the

direct flux sensors or by using flux estimator that computes the rotor flux vector from thestator voltages and currents and/or speed sensor signals.

On the other hand, the direct torque control scheme uses a stationary d-q reference

frame having d-axis aligned with the stator axis. Torque and flux are controlled by the

stator voltage space vector which is defined in the same reference frame. The variation of

the stator flux vector due to application of the stator voltage vector, during a time interval

of t can be given by equation no.6.15 which is as; tVss = . , in which the stator

resistance is neglected. Since the rotor flux changes slowly, the rapid variation of the statorflux space vector produce a variation in the developed torque because of the variation of the

angle between the two vectors.

Controllers:-

FOC scheme is based on the assumption that the motor is fed by a three-phase

current source. Since a voltage-source inverter is used, current controllers are required to

impose the stator currents. To obtain the performance torque control, fast current

controllers such as hysteresis current can be used. In the DTC scheme the torque and fluxare directly controlled by the inverter voltage space vector. Two independent hysteresis

controllers are used to select appropriate stator voltage space vector in order to maintain the

flux and torque between the upper and lower limits. The response time of hysteresis

controller is optimal but the switching frequency is the variable.

Estimated variables:-


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The operation of both FOC and DTC depends on the system variables that are

computed or estimated from the measured quantities. The accuracy of the estimated

variables has a direct influence on the control performance.

On the FOC scheme, the estimated variable is the rotor flux angle () required for

the co-ordinate transformation. The calculation of requires the measured rotor speed and

estimated slip frequency. The slip frequency depends on the rotor time constant and the

estimated rotor flux amplitude. The electrical angle is of first importance in FOC scheme.

A false position of could lead to undesirable coupling between the d and q axis

components and invalidate the FOC scheme. Because is obtained from the integration of

the sum of rotor speed and slip speed, the error is cumulative and additional calculation

could be necessary to correct this error. During transients the rotor flux position may

change and perfect decoupling may be able to be temporarily lost.

In DTC scheme, the estimated quantities are the stator flux and motor torque which

are required for feedback control. The stator flux is calculated from the stator voltage and

current space vectors and the developed torque is calculated from the stator flux and the

stator current space vectors. The accuracy of stator flux depends mostly on the estimation

accuracy of the stator resistance. An error on the stator flux will affect the behavior of both

flux and torque control loops.

Implementation complexity:-

The implementation of the considered schemes can not be accurately compared

because of the many factors that can influence the actual hardware and software

configurations. The calculations in FOC scheme are done in rotating reference frame so that

co-ordinate transformations involving trigonometric functions are required. These

calculations are time consuming tasks.

On the other hand, in DTC system, the calculations are done in stationary reference

frame using space vector notation. There is no calculation involving trigonometric function.


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CONCLUSION

In this dissertation report, main characteristics of direct torque control scheme forinduction motor drives are studied with a view of highlighting the advantages and

disadvantages of direct torque control.

Initially, the model of an induction machine is analyzed with its complete

theoretical details and the required equations. A thorough understanding of this model is

essential to understand DTC scheme in detail.With the DTC scheme employing a Voltage

Source Inverter (VSI), it is possible to control directly the stator flux linkage and the

electromagnetic torque by the optimum selection of inverter switchi

final without mdtc (1)

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