Induction motor modelling and applications report

INDUCTION MOTOR MODELING AND APPLICATIONS

Dept of Electrical and Electronics 1

Chapter-1

1. INTRODUCTION

In domestic application or industry, motion control is required everywhere. The systems

that are employed for this purpose are called drives. Such a system, if makes use of electric

motors is known as an electrical drive. In electrical drives, use of various sensors and control

algorithms is done to control the speed of the motor using suitable speed control methods. The interest for motor controller has been constantly rising during the last years. The fact

that the rotor speed is not measured, but estimated has several important benefits especially

related to higher robustness, lower cost and lower sensitivity to noise. The drawbacks are lower

speed range and a higher computational effort.

Because of advances in solid state power devices and microprocessors, variable speed

AC Induction motors powered by switching power converters are becoming more and more

popular. Switching power converters offer an easy way to regulate both the frequency and

magnitude of the voltage and current applied to a motor. As a result much higher efficiency

and performance can be achieved by these motor drives with less generated noises.

The most common principle of this kind is the constant voltage/frequency (V/Hz)

principle which requires the magnitude and frequency of the voltage applied to the stator of a

motor maintain a constant ratio. By doing this, the magnitude of the magnetic field in the stator

is kept at an approximately constant level throughout the operating range. When transient

response is critical, switching power converters also allow easy control of transient voltage and

current applied to the motor to achieve faster dynamic response.

1.1 Faradays laws of electromagnetic induction

1.1.1First law:

When the magnetic flux linking a conductor or coil changes an e.m.f is induced in it.

1.1.2 Second law:

The magnitude of induced e.m.f in a coil is equal to the rate of change of magnetic flux

linkages.

1.1.3 Lenz’s law:

The induced current will flow in such a direction so as to oppose the cause that product



The induction machine is used in wide variety of applications as a means of

converting electric power to mechanical power. Pump steel mill, hoist drives, household

applications are few applications of induction machines. Induction motors are most

commonly used as they offer better performance than other ac motors.

In this chapter, the development of the model of a three-phase induction motor is

examined starting with how the induction motor operates. The derivation of the dynamic

equations, describing the motor is explained. The transformation theory, which simplifies the

analysis of the induction motor, is discussed. The steady state equations for the induction

motor are obtained. The basic principles of the operation of a three phase inverter are

explained, following which the operation of a three phase inverter feeding a induction

machine is explained with some simulation results.

1.2 Basic Principle of Operation of Three-Phase Induction Machine

The operating principle of the induction motor can be briefly explained as, when

balanced three phase voltages displaced in time from each other by angular intervals of 120is

applied to a stator having three phase windings displaced in space by 120electrical, a rotating

magnetic field is produced. This rotating magnetic field has a uniform strength and rotates at

the supply frequency, the rotor that was assumed to be standstill until then, has

electromagnetic forces induced in it. As the rotor windings are short circuited, currents start

circulating in them, producing a reaction. As known from Lenz’s law, the reaction is to

counter the source of the rotor currents. These currents would become zero when the rotor

starts rotating in the same direction as that of the rotating magnetic field, and with the same

strength. Thus the rotor starts rotating trying to catch up with the rotating magnetic field.

When the differential speed between these two become zeros then the rotor currents will be

zero, there will be no emf resulting in zero torque production. Depending on the shaft load

the rotor will always settle at a speed ωr , which is less than the supply frequency. This

differential speed is called the slip speed.



Chapter-2

2. LITERATURE REVIEW

Many papers have discussed about different modeling based on different reference

frame theories. Few discussed the application like control of speed, Torque, Flux etc. Our

goal is to detect the fault and virtual flux measurement.

The various methods of speed control of 3-ph Induction motor are as under:

1. Pole Changing

2. Variable Supply Frequency

3. Variable rotor resistance control

4. Variable supply voltage control

5. Constant V/f control

6. Slip recovery

7. Vector Control

In parameter estimation, one tries to derive a parametric description for an object, a

physical process, or an event. If the situation involves two parameters, the estimation seems

to boil down to solving two equations with two unknowns. However, the situation is more

complex because measurements always come with uncertainties. Usually, the application not

only requires an estimate of the parameters, but also an assessment of the uncertainty of that

estimate. The situation is even more complicated because some prior knowledge must be

used to resolve the ambiguity of the solution. The prior knowledge can also be used to reduce

the uncertainty of the final estimate. In order to improve the accuracy of the estimate the

engineer can increase the number of (independent) measurements to obtain an over

determined system of equations. In order to reduce the cost of the sensory system, the

engineer can also decrease the number of measurements leaving us with fewer measurements

than parameters. The system of equations is underdetermined then, but estimation is still

possible if enough prior knowledge exists, or if the parameters are related to each other. In

either case, the engineer is interested in the uncertainty of the estimate.



In state estimation, one tries to do either of the following – either assigning a class

label, or deriving a parametric (real-valued) description – but for processes which vary in

time or space. There is a fundamental difference between the problems of classification and

parameter estimation on the one hand, and state estimation on the other hand. This is the

ordering in time (or space) in state estimation, which is absent from classification and

parameter estimation. When no ordering in the data is assumed, the data can be processed in

any order. In time series, ordering in time is essential for the process. This results in a

fundamental difference in the treatment of the data. In the discrete case, the states have

discrete values (classes or labels) that are usually drawn from a finite set. An example of such

a set is the alarm stages in a safety system (e.g. ‘safe’, ‘pre-alarm’, ‘red alert’, etc.). Other

examples of discrete state estimation are speech recognition, printed or handwritten text

recognition and the recognition of the operating modes of a machine.



Chapter-3

3. METHODOLOGY

Fig 3.1 Basic Block Diagram of Induction Motor Control Mechanism

The basic block diagram as shown above assumes that all controlled system

parameters are known. However, some system parameters are generally not known a priori,

and may even be varying in normal operating conditions. In particular, the stator and the rotor

resistances are sensitive to the magnitude of the currents, and thus undergo wide variations in

the presence of speed reference and load torque changes.

To maintain the control performance at the desired level despite changing operating

conditions, the speed controller may need to be reinforced with a parameter adaptation

capability. Another limitation of the control strategy is that all state variables are assumed to

be accessible through measurements. However, reliable and cheap sensors are only available

for stator currents and voltages. Flux sensors are generally not available on machines because

of their high implementation cost and maintenance complexity. Mechanical sensors (for

speed and, more rarely, torque measurements) are common, but also entail reliability issues

and extra maintenance costs due to physical contact with rotor. Therefore, state observers are

attractive to obtain online estimates of the states based only on electric measurements. Sensor

less controllers involving online state estimation using observers are commonly referred to as

output-feedback controllers.



Before going to analyze any machine it is very much important to obtain the machine

in terms of equivalent mathematical equations. The dynamic model of the 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 two sets of windings, one on the stator

and the other in the rotor. The induction motor model can be developed from the fundamental

electrical and mechanical equations. Assuming ds-qs are oriented at θ angles, then the

corresponding voltages Vds and Vqs can be resolved in to as-bs-cs components and can be

represented in matrix form with reference to stationary reference frame.



Chapter-4

4. TRIPHASE INDUCTION MOTOR MODELING

The problem of controlling induction motors is not a simple issue due to the

multivariable and highly nonlinear nature of these machines. Besides, some of their

parameters are time varying and some of their state variables are not accessible to

measurements. These problems are generally dealt with using model-based control

approaches, that is, the controller or the observer design relies upon a given model that is

supposed to accurately describe the machine of interest.

Control-oriented modeling of induction motors has first been accomplished by

considering simplified assumptions, for example, linear magnetic characteristic and constant

(or slowly varying) rotor speed. Then, the obtained models turn out to be linear and of quite

limited use. More accurate nonlinear models, describing well the induction motor operating

at nonconstant rotor speed, have been developed later. Furthermore, these nonlinear models

proved to be tractable and thus have been widely used in control design.

4.1 Induction Motors—A Concise Description

Triphase induction motors are classified in two main categories: squirrel cage and

wound rotor. For both types of machine, a three-phase equivalent circuit is associated to the

stator and to the rotor. By Faraday’s and Lenz’s Laws, the stator carrying a sinusoidal current

of pulsation s generates a rotating magnetic field. Then, induced currents are generated in

the rotor bars. The induced currents tend to oppose the flux variation in the rotor coils

resulting in a mechanical torque applied on the rotor. Then, the rotor starts turning at a speed

m and the rotor currents oscillating at the pulsation r = s − mp . The electromagnetic

torque is proportional to the pulsation r . It vanishes whenever the rotor current pulsation is

zero. This is called synchronization. In normal operation, torque generation is necessarily

accompanied by a difference r between the stator pulsation s and the rotor speed mp .

This difference is called slip pulsation and constitutes an image of the torque.



4.2 Triphase Induction Motor Modeling

4.2.1 Modeling Assumptions

1. Linearity: The fluxes and the corresponding induced currents are proportional, that is, all

self- and mutual inductances are constant.

2. All iron losses are neglected.

3. The machine air gap is constant, smooth, and symmetric.

4. The stator and the rotor windings present a symmetrical structure providing the induction

machine with a three-phase equivalent circuit (equation 4.3).

The machine triphase structure entails a sinusoidal spacial distribution of

magnetomotive force (MMF) in the air gap and three-phase currents in the stator and rotor

currents whenever the stator voltage is three-phase.

4.2.2 Tri-Phase Induction Motor Modeling

The modeling process consists of applying the electromagnetic laws to the different

windings and the motion equations to the rotor carrying the load. The application of the

electromagnetic laws yields six voltage equations and six flux equations.

Voltages Equations

. 4.1sabc s sabc sabc

dv R i

dt

. 4.2rabc r rabc rabc

dv R i

dt

Flux Equations

. 4.3

.

sabc os sabc osr rabc

rabc os rabc osr sabc

L i M i

L i M i

4.4

In the above expressions, the following notations are used:

; ; . 4.5

;

sa sa sa

sabc sb sabc sb sabc sb

sc sc sc

ra ra

rabc rb rabc rb

rc rc

v i

v v i i

v i

v i

v v i i

v i

; . 4.6

ra

rabc rb

rc



That is, the tri-phase quantities , , , , , andsabc sabc sabc rabc rabc rabcv i v i denote the stator

and the rotor voltages, currents, and fluxes. The subscripts s and r refer to the stator and the

rotor, respectively. Similarly, the indices a, b, and c refer to the three phases.

A direct consequence of the machine perfect symmetry is that all resistance and

inductance matrices are symmetric, that is,

0 0 0 0

0 0 , 0 0 , 4.7

0 0 0 0

,

s r

s s r r

s r

os os os or or or

os os os os or or or or

os os os or or or

R R

R R R R

R R

l M M l M M

L M l M L M l M

M M l M M l

, 4.8

where sR and rR are the stator and the rotor resistances, osl and orl are the self-inductances,

osM is the mutual inductance between two stator phases, and orM is the mutual inductance

between two rotor phases. Also, an immediate consequence of the working assumptions

(Section 4.2.1), is that the various mutual inductances between the rotor and the stator are

sinusoidal functions of the rotor position θ. Specifically, one has

2 4cos cos cos

3 3

4 2cos cos cos , 4.9

3 3

4 2cos cos cos

3 3

osr o

p p p

M M p p p

p p p

where p designates the number of pole-pairs and oM denotes the maximal mutual inductance

between the stator phase and the rotor phase.

Mechanical Equations

The torque of the motor in qd0 space is given by:

Where P= No of poles

( )r

m l

dJ

dt

3( )

2 2em qr dr dr qr

PT i i

3( )

2 2ds qs qs ds

Pi i



where = load torque

4.2.3 Park Transformations

The key idea is that the MMF, created by a physical three-phase system, can be

equivalently created by a fictive two-phase system involving two orthogonal windings

(Figure 4.2).

The three-phase current system , ,a b ci i i traversing 1n turns and two-phase current

system ,d qi i , traversing 2n turns are said to be equivalent if they produce the same air-gap

MMF.

The MMF created by , ,a b ci i i has the following components:

a 1 a 1 1ε =n i , ε =n i , ε =n i .b b c c

Similarly, the components of the MMF due to ,d qi i are the following:

2 2ε =n i , ε =n i .d d q q

Referring to Figure 2.4, the MMF due to , ,a b ci i i is represented by the vector , which is

a vector sum of the three MMF vectors , ,a b c Figure 4.4 illustrates the projection of

the vector along two orthogonal axes referred to direct axis d and quadrature axis q.

3( )

2 2m dr qs qr ds

PL i i i i

l



Figure 4.1 Triphase system , ,a b ci i i and its equivalent two-phase system ,d qi i . Both systems create

the same MMF

The obtained components, andd q , are given by the following expression:

2 4cos cos cos

3 3

2 4sin sin sin

3 3

a

d

b

q

c

(4.12)

The system (4.12) is clearly noninvertible as it involves a non-square matrix. This is

overcome by adding a third equation associated with a fictive MMF denoted o . The new

variable is defined to be proportional to the homopolar component of the triphase , ,a b c

Specifically, one has o o a b cK for some proportional constant oK to be defined

later. To the fictive MMF o is associated a fictive current, denoted oi , referred to

homopolar. Accordingly, one has 2o on i



Replacing in equation (4.12) the MMFs by the corresponding currents one gets the

following relation between the three-phase current , ,a b ci i i (traversing 1n turns) and the

equivalent two-phase current ,d qi i (traversing 2n turns):

1

2

2 4cos cos cos

3 3

2 4sin sin sin .

3 3

d a

q b

o c

o o o

i in

i in

i iK K K

(4.13)

As the fictive current oi is not physically involved in the creation of the MMF, its orientation

can be chosen arbitrarily. For convenience, the homopolar axis is let to be orthogonal to the

plane qd . To complete the transformation (4.13), it remains to assign values to 1

2

n

n and oK .

4.2.4 Park Transformation Preserving Amplitudes

The interest, Park transformation has lately regained is mainly due to the considerable

progress made in the digital computer technology and in the power electronic component

technology. The spectacular advances achieved in these fields have made it possible to

implement real-time applications involving the construction and manipulation of the Park

transformation. The original Park transformation is defined by equation (2.13) letting the free

parameters (i.e., 1

2

n

nand oK ) be chosen to meet

The following requirements:

1. The homopolar current oi coincides with the arithmetic mean value of the currents

, ,a b ci i i .

2. The components of the two-phase current ,d qi i have the same amplitude as those of the

triphase current , ,a b ci i i , that is, current amplitude is preserved by the Park transformation.

The first requirement leads to the following double equality:

1

2

1.

3o a b c o a b c

ni i i i K i i i

n

These yields,



1

2

1.

3o

nK

n (4.14)

The amplitude preservation requirement immediately entails the following expressions:

2 4cos , cos , cos ,

3 3

cos , sin .

a m b m c m

d m q m

i t I t i t I t i t I t

i t I t i t I t

(4.15)

On the other hand, one gets from equation (2.13) that

1 1

2 2

3 3cos , sin . 4.16

2 2d m q m

n ni t I t i t I t

n n

Comparing equations (2.15) and (2.16) gives, using (2.14):

1

2

2 1K .

3 2o

nand

n (4.17)

Using (4.17), it follows from (4.13) that the (amplitude preservation-based) Park

transformation dqo abci P i is entirely characterized by the following matrix:

2 4cos cos cos

3 3

2 2 4sin sin sin . 4.18

3 3 3

1 1 1

2 2 2

P

The inverse transformation, that is, 1

abc dqoi P i , is characterized by the inverse

Park matrix,

1

cos sin 1

2 2cos sin 1 .

3 3

4 4cos sin 1

3 3

P

(4.19)

The particular value, ψ = 0, yields the so-called Clarke matrices



1

1 1 11 1 0

2 2 2

2 3 3 2 1 3 10 , . 4.20

3 2 2 3 2 2 2

1 1 1 1 3 1

2 2 2 2 2 2

C C

4.2.5 Two-Phase Models of Induction Motors

Equations (4.1)–(4.4), and (4.10) get simplified by applying the Park transformation defined

by the matrix (4.27). Roughly, all mathematical relationships initially expressed in terms of

the triphase frame (a, b, c) are rewritten in terms of (d, q, o). The perfect symmetry of the

induction motor implies that the sum of the currents carried by the rotor and the sum of those

carried by the stator are both null. Then, the corresponding homopolar currents (i.e. the

components along the axis o) are null . It turns out that, in the new frame (d, q), the initial

electromagnetic system (4.1), and (4.2), consisting of six equations, boils down to a simpler

system, consisting of only four equations.

As mentioned earlier, the angle ψ in (4.27) is a free parameter assuming several

possible choices. This entails several variants of the two-coordinate frame (d, q). The two

most common in the literature are the following:

• The fixed reference frame (α, β), connected to the stator.

• The rotating reference frame (d, q), linked to, for example, the rotor flux or the stator

current.

The passage from the triphase frame (a, b, c) to the fixed (α, β) frame is accomplished

by choosing the transformation angle ψ, in the transformation matrix (4.25), as follows:

• Set ψ = 0, for the transformation of the stator variables.

• Set ψ = θ, for the transformation of the rotor variables.

The passage from the triphase frame (a, b, c) to the rotating frame (d, q) is

accomplished by choosing the transformation angle ψ as follows:

• Set ψ = s , for the transformation of stator variables.

• Set ψ = r = s − θ, for the transformation of the rotor variables.



Figure 4.2 Angles between electric frames

4.2.6 Electric Equations in d-q Coordinates

Following the above rules, the passage from the tri-phase frame (a, b, c) to the (d, q) frame

necessitates the following transformations of the electric variables (Figure 4.2):

, , , 4.29sd sd sd

s sabc s sabc s sabc

sq sq sq

v iP v P i P

v i

, , . 4.30rd rd rd

r rabc r rabc r rabc

rq rq rq

v iP v P i P

v i

Applying the transformations (4.29) and (4.30) to the induction machine equations (4.1)

and (4.2), yields the following (d, q) equations:



, 4.31

,

sdsd s sd s sq

sq

sq s sq s sd

dv R i

dt

dv R i

dt

4.32

( ) , 4.33

(

rdrd r rd s r rq

rq

rq r rq s

dv R i

dt

dv R i

dt

) , 4.34r rd

Where, , .ss m

d d

dt dt

4.2.7 Flux Equations in d-q Coordinates

Similarly, the passage from the triphase frame (a, b, c) to the (d, q) frame necessitates the

following transformations of the fluxes:

4.35

4.36

sdq s sabc

rdq r rabc

P

P

Using the flux-current expressions (4.3) and (4.4), the couple of equations (4.35) and (4.36)

develops as follows:

At the stator:

,sdq s s sabc s rabcP L i P Lm i

Which implies, using (4.29)

1 1

. sdq s s s sdq s r rdqP L P i P Lm P i

At the rotor, one has

,rdq r r rabc r sabcP L i P Lm i

Which implies, due to (4.30)

The obtained flux equations in the (d, q) frame can be given the more compact forms

1 1

. rdq r r r rdq r s sdqP L P i P Lm P i



, , sdq s sdq rdq rdq r rdq sdqL i Lm i L i Lm i

With, sL Stator inductance;

rL Rotor inductance;

Lm Mutual inductance between the stator and rotor windings.

From above equations

4.3 d-q voltage equations

Stator winding abc voltage equations

(4.34)

Where, Pd

dt

d-q transformation matrix

( 4.35)

(4.36)

(4.37)

[ ][ ] [ ]

[ ][ ] [ ]

sabcsabc s sabc

rabcrabc r rabc

dV R i

dt

dV R i

dt

[ ] [ ]

[ ] [ ]

sdq s sdq sr rdq

rdq r rdq sr sdq

L i M i

L i M i

V Pabc abc abc abc

s s s sr i

2 2cos cos cos

3 3

2 2Tdq sin sin sin

3 3

1 1 1

2 2 2

1

sin cos 0

2 2sin cos 0 P

3 3

2 2sin cos 0

3 3

dqo dqo

s dqo s

dT

dt

1 1

V P dqo dqo abc dqo

s dqo dqo s dqo s dqo sT T T r T i

1

P dqo

dqo sT



Substituting above equation (4.37) in (4.36) voltage equation we can get

(4.38)

Similarly, for rotor

0 1 0

1 0 0 P

0 0 0

dqo dqo dqo dqo dqo

r r r r r rV r i

(4.39)

Where,

4.4 Voltage equation: The stator and rotor voltage equations after d-q transformation can be given as follows.

( )

( )

sdsd s sd s sq

sq

sq s sq s sd

rq

rd r rd s r rq

rq

rq r rq s r rd

dV R i

dt

dV R i

dt

dV R i

dt

dV R i

dt

(4.37)

Where,

4.5 Current equations

Substituting above equations (4.37) we can derive these current equations for rotor

and stator d-q axis

Stator d-q currents

(4.38)

, Synchronous Speed and , Synchronous Speedss m

d d

dt dt

1[ ]

[ ]

sd sd rd s sd ssr s sq sr rq

s s s s

sq sq s sq rqsr ss sd sr rd

s s s s

di V di R iM L i M i

dt L L dt L L

di V R i diML i M i

dt L L L dt L

0 1 0

1 0 0 P

0 0 0

dqo dqo dqo dqo dqo

s s s s sV r i

1 0 0

0 1 0

0 0 1

dqo

s sr r

d

dt



Rotor d-q currents

( )[ ]

( )[ ]

rd rd sr sd s rrrd r rq sr sq

r r r r

rq rq r rq sqsr s rr rd sr sd

r r r r

di V M diRi L i M i

dt L L L dt L

di V R i diML i M i

dt L L L dt L

(4.39)

4.6 Efficiency

The relationship between input power and output power can be derived as follows.

Shaft power output o e rP

Mechanical power developed P ( )md o rF

Rotor copper loss P1

rc md

sP

s

Input to motor P P P Pi md rc sc

Hence, the expression for efficiency is given by,

% Efficiency= P

100Pi

o

(4.40)

4.7 Power factor

The expression for power factor for an Induction motor is given by,

Power factor

22

r

R

R sX

where, 2r r rX f L (4.41)

120

rr

N Pf

4.8 Flux equations

Similarly, the direct axis and quadrature axis flux equations are given by,

qs s qs m qr

ds s ds m dr

qr s qr m qs

dr s dr m ds

L i L i

L i L i

L i L i

L i L i

(4.42)



4.9 Speed and Slip

The relationship between rotor speed and torque is given by,

P

( )2J

r e l ( 4.43)

Hence the, slip‘s’ can be given by,

e r

e

s

(4.44)



Chapter-5

5. Simulation

Using mathematical modeling discussed in previous chapter, the blocks are built in

Simulink software to realize the derived mathematical equations. In the following section we

briefly discuss about each block.

5.1 Park transformation

A 3- phase ac supply is converted into 2 ph d-q co-ordinates as shown.(reference eq 4.20)

Fig. 5.1 Park’s transformation blocks

5.2 Speed and slip blocks

The speed and slip can be calculated from the following blocks shown.(eq 4.43 and 4.44 )

Fig. 5.2.Speed and slip blocks



5.3 Current calculations

From above current stator d axis equations

1

[ ]sd sd rd s sd ssr s sq sr rq

s s s s

di V di R iM L i M i

dt L L dt L L

Similarly all the currents can be calculated using this basic block

Fig. 5.3 Current block for isd

5.4 Power factor block

From the rotor speed output and slip, the power factor can be calculated as follows, ( eq 4.41)

Fig. 5.4.1 Power Factor block



Fig 5.4.2 Power factor block with effect of variation of temperature

5.5 Torque block

Using d-q currents and mutual inductance, torque is calculated where load torque put

on motor which is in positive or negative quantity for sudden increase or sudden decrease of

load and some friction is also considered.

Fig. 5.5 torque block



5.6 Inverse parks transformation

3 ph ac quantities can be re-obtain from d-q quantities by using inverse park transformations.

Fig. 5.6 inverse parks transformation block

Motor ratings

The induction motor chosen for the simulation studies has the following parameters 20 hp,

460V, 50Hz, 3 Induction motor with the following equivalent circuit parameters

Table.1: induction motor parameter table

Parameters Values

No of poles 4

Reference speed 500 rpm

Stator resistance 0.087 Ω

Rotor resistance 0.187 Ω

Inductance of motor 0.04 H

Inductance of stator 0.0425 H

Inductance of rotor 0.043 H

Friction 10

Stator copper loss 700 W

Temperature coefficient 3.9*10-3 Ω /oC



5.7 Simulation Results

Results of simulations are obtained under normal operating conditions

Fig. 5.7.1 Torque characteristics

Fig. 5.7.2 Speed characteristics



Fig. 5.7.3 Variation of Efficiency w.r.t Time

Fig. 5.7.4 Variation of Power Factor w.r.t Time

Fig. 5.7.5 Variation of Slip w.r.t Time



Fig. 5.7.6 Variation of Torque developed w.r.t Time

Fig. 5.7.7 Variation of Slip w.r.t Torque



Fig. 5.7.8 Variation of Speed w.r.t Torque

Fig. 5.7.9 Variation of rotor currents w.r.t time



Fig. 5.7.10 Variation of Flux w.r.t Time

Fig. 5.7.11 Variation of currents w.r.t Time



Chapter 6

6. Application

The mathematical modeling of Induction motor can be used for various control and

estimation applications. We consider the application of fault detection and analysis of effect

of temperature variation on Induction motor parameters.

1) Fault detection

Firstly, we discuss the application of fault detection in which a sudden load is applied for

very short duration of time, when Induction motor is at steady state. Then its effect on torque,

speed, current, slip, and flux are observed.

The basic principle of fault detection is to compare the Induction motor system parameters

continuously with the standard reference values for that particular operating condition.

When, any of the parameter exceeds the limit, the fault is identified.

The following simulation results show that, the load is applied for duration of 1 second. The

effect is observed in terms of a sudden change in toque and speed.

Fig. 6.1 Torque characteristics

Fig. 6.2 Speed characteristics



Fig. 6.3 Characteristics d-q axis currents

Fig. 6.4 Variation Rotor Current of time

Fig. 6.5 Variaton of Flux w.r.t Time



Fig 6.6 Variation of power factor

It can be observed that, from graph 6.1 the torque curve deviates from its stable path towards

unstable path when a sudden load is applied. Also, the speed reaches beyond the reference

value. Hence, as a consequence, the Induction motor rotor current increases rapidly. By

comparing the currents with reference (Fig 5.7.11) the fault can be identified.

2) Analysis of effect of temperature variation on Induction motor parameters.

As rotor conductors are having finite resistance, the heat is produced when current flows

continuously through windings. Thus, the effect of change in temperature can be observed

immediately on, change in resistance of the windings. This causes change in currents, fluxes,

and power factor. Analysis is carried out to investigate the effect of change in temperature on

Induction motor parameters. The resistance is made to increase along with increase in

temperature. And its consequent effect is observed on above mentioned parameters.

Fig. 6.6 Variation of Torque w.r.t Time



Fig. 6.7 Variation of Speed w.r.t Time

Fig. 6.8 Variation of Power Factor w.r.t Time

Fig. 6.10 Variation of Flux w.r.t Time



Fig. 6.11 Variation of currents w.r.t Time

From the above observations, it can be concluded that, there is a considerable change

in the rotor current and flux. Also the power factor changes significantly when there occurs a

temperature change in the system.



Chapter 7

7. Conclusion and Future Scope

In this approach, implementation of modular Simulink model for induction machine

simulation has been introduced. Unlike most other induction machine model

implementations, with this model, the user has access to all the internal variables for getting

an insight into the machine operation. Any machine control algorithm can be simulated in the

Simulink environment with this model, without actually using sensors. Individual parameter

equations are solved in each block. The operation of the model is to simulate dynamic model

of induction motor with torque, speed, power factor, slip, efficiency, flux with variation in

load and temperature.

A block model approach was used in the construction of the motor model that allows

all motor parameters to be easily accessed for monitoring and comparison purposes. The

model can be used to study the dynamic behavior of the induction motor, or can be used in

various motor-drive topologies with minor modifications. New subsystems can be added to

the model presented to implement various types of control schemes.

Finally, the analysis made in the project work is extremely helpful from design

prospective.

Future scope:

1) Controller can be designed to obtain desired speed automatically with changing

loading conditions.

2) Kalman Estimator can be designed for accurate estimation applications.

3) Hardware implementation can be done.

Induction motor modelling and applications report

Engineering