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Induction MachineSpeed Control

Master Thesis in ElectronicsAugust 30th, 2007

By

Lars-Gran Andersson

[email protected] UniversityDepartment of Computer Science and Electronics

SupervisorMagnus Jansson

Bombardier Transportation

Company SupervisorLars Hrnlund

LSI Svenska AB

ExaminerMikael Ekstrm

Mlardalen UniversityDepartment of Computer Science and Electronics
mailto:[email protected]:[email protected]

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Department of Computer Science and Electronics Page 2 of 28

Abstract

This thesis work finds and presents an alternative method of motor speed control to the

voltage control method currently used by LSI Svenska AB, the constant Volt/Hertz method

with sinusoidal Pulse With Modulation (PWM) and shows the advantages and disadvantages

that is possible to achieve with this new method compared with the currently used method.

Acknowledgement

I really appreciate the guidance and support given by my supervisor Magnus Jansson and

my company supervisor Lars Hrnlund they have been quite dynamic through out my thesis

work and contributed with quite invaluable ideas which really helped me to progress I

acknowledge the Department of Computer Science and Electronics for providing enough

resources to help me complete this thesis work.

Last but not the least I am thankful to my loved ones, my friends and colleagues who

supported me during my time at Mlardalen University.

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Induction Machine Speed Control

Lars-Gran Andersson Mlardalen University

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Table of Contents

1 Introduction..............................................................................................................................5

1.1 Background.......................................................................................................................5

2 Theoretical Background...........................................................................................................5

2.1 AC motor market..............................................................................................................5

2.2 Induction motor theoretical basics....................................................................................5

2.2.1 Dynamical model.......................................................................................................5

2.2.2 Power performance....................................................................................................6

2.3 Speed control systems for Induction Motors....................................................................8

3 Analysis of problem.................................................................................................................9

3.1 Comparison current new method.................................................................................9

3.1.1 Properties method currently used...............................................................................93.1.2 New method requirements.........................................................................................9

3.2 Model / method ..............................................................................................................10

3.2.1 Creating a schematic in Pspice.................................................................................10

3.2.2 Studying different control techniques......................................................................10

4 Solution..................................................................................................................................11

4.1 Deciding what model to be used.....................................................................................11

4.1.1 Three-phase voltage source inverters with sinusoidal PWM...................................12

4.2 Building a model.............................................................................................................16

4.2.1 Simulation with Simulink / Matlab..........................................................................16

4.3 Analysis of results...........................................................................................................21

4.4 Future work.....................................................................................................................214.4.1 Implementation with Digital Signal Processor (DSP).............................................21

5 Summary and conclusions.....................................................................................................22

6 References..............................................................................................................................23

7 Appendix................................................................................................................................24

7.1 Simulink model...............................................................................................................24

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List of figures

Figure 1. Per phase equivalent circuit of polyphase Induction Machine....................................6

Figure 2. Power flow in an induction motor...............................................................................8

Figure 3. Typical motor torque - load characteristic...................................................................8

Figure 4. Schematic LSI speed regulator..................................................................................10

Figure 5. 3-phase inverter.........................................................................................................11

Figure 6. Three-phase inverter VLL/Vd as a function of ma....................................................15

Figure 7. Three-phase sinusoidal PWM waveforms and harmonic spectrum..........................15

Figure 8. Voltage - frequency relation Induction Machine.......................................................16

Figure 9. Induction machine.....................................................................................................18

Figure 10. Dynamic T-equivalent circuit for the induction motor............................................19

Figure 11. 3-phase PWM converter with DC-link....................................................................19

Figure 12. Simulation of Induction Machine start....................................................................21

Figure 13. Main Simulink model..............................................................................................24

Figure 14. Discrete PWM Generator 4 pulses..........................................................................24

Figure 15. IGBT Bridge............................................................................................................25

Figure 16. Three-Phase Induction Machine (IM main)............................................................25

Figure 17. IM Sub. 1.................................................................................................................26

Figure 18. IM Sub. 2.................................................................................................................26

Figure 19. IM Sub. 3.................................................................................................................27

Figure 20. IM Sub. 3.1..............................................................................................................27

Figure 21. IM Sub. 3.2..............................................................................................................28

List of tables

Table 1. Harmonics of VLL for a large and odd mf (mf a multiple of 3).................................14

Table 2. Comparison of Adjustable Frequency Drives.............................................................20

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1 Introduction

1.1 Background

The method for Induction Machine (IM) speed control currently used by LSI Svenska AB

in Falun is limited to a maximum of four amperes current delivered to the motor due to

excessive heat build up inside the speed control unit housing. They would like to increase the

maximum allowed current of the speed control unit up to sixteen amperes thereby making it

possible to sell their products to a wider range of customers with different needs for example

control of pumps and more powerful fans, so here it is important to minimize the losses

created in the machine/motor. If possible they would also want to decrease the number of

steps (time) needed in the production line for each unit.

2 Theoretical Background

2.1 AC motor market

Market analysis shows that most of all industrial motor applications uses AC induction

motors. The reasons for this include high robustness, reliability, low price and high efficiency,

> 90% is preferred in order to reduce costs of operation and to maximize long term profit

gains for the user. However, the use of induction motors also has its disadvantages, these lie

mostly in its difficult controllability, due to its complex mathematical model, its non linear

behavior during saturation effect and the electrical parameter oscillation which depends on the

physical influence of the temperature.

2.2 Induction motor theoretical basics

2.2.1 Dynamical model

In the stationary reference frame (-coordinates), the dynamic model of a 3-phase

induction motor can be described as

vbi

jaa

jaais

s

r

s

r

r

r

s

dt

d

+

+

=

02221

1211

(2.1)

where:

Lb

aL

a

LL

La

L

Ra

s

s

rr

m

rrs

m

rs

s

1

1

1

2221

1211

=

==

=

=

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Rs , Rr: stator, rotor resistance per phase respectivelyLs , Lr : stator, rotor inductance per phase respectively

Lm : magnetizing inductance per phaser : rotor angular speedr : rotor time constant (=Lr / Rr)

:Lm / Ls Lr : leakage constant (= 1 Lm2 / Ls Lr)

The input and state variables are as follows,

stator current : is = is + j isstator voltage : vs = vs + j vsrotor flux : r= r + j r

2.2.2 Power performance

Figure 1. Per phase equivalent circuit of polyphase Induction Machine

Where:

U1 = stator terminal voltageE1 = stator emf generated by resultant air-gap fluxR1 = stator effective resistanceX1 = stator leakage reactanceRm = iron core-loss resistanceXm =magnetizing reactanceR'2 = rotor effective resistance referred to stator

X'2 = rotor leakage reactance referred to statorurb = e.m.f due to the saturable iron bridges in the rotor slotsI0 = sum of magnetizing I0Xand core-loss I0R current componentsI1 = stator currentI2 = rotor current referred to stator

Some of the important steady-state performance characteristics of a polyphase induction

motor include the variation of current, speed, and losses as the load-torque requirements

change, and the starting and maximum torque. Performance calculations can be made from

the equivalent circuit. All calculations can be made on a per-phase basis, assuming balancedoperation of the machine. Total quantities can be obtained by using an appropriate

multiplying factor.

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The equivalent circuit of (Fig. 1), is usually employed for the analysis. The core losses, most

of which occur in the stator, as well as friction, windage, and stray-load losses are included in

efficiency calculations. The power-flow diagram for an induction motor is given in (Fig. 2), inwhich m1 is the number of stator phases, 1is the power-factor angle between U1andI1, 2 isthe power-factor angle betweenE1andI2, Tis the internal electromagnetic torque developed,sis the synchronous angular velocity in mechanical radians per second, and mis the actualmechanical rotor speed given by s(1 - S).

The total powerPg in watts transferred across the air gap from the stator is the differencebetween the electrical power inputPiand the stator copper loss.Pgis thus the total rotor inputpower, which is dissipated in the resistanceR2/ Sofeach phase so that

( ) sg TSRImP =='

22

1 '2 (2.2)

where T is the internal electromagnetic torque developed by the machine, and s is thesynchronous angular velocity in mechanical radians per second. Subtracting the total rotor

copper loss, which is m1(I2)2R2=SPg, from (Eq. 2.2) for Pg, we get the internal mechanicalpower developed:

( ) ( ) ( )SS

TS RImPP mgm

===1'

21

'

2

2

1 (2.3)

This much power is absorbed by a resistance ofR2(1-S)/S, which corresponds to the load.From (Eq. 2.3), we can see that, of the total power delivered to the rotor, the fraction (1-S) is

converted to mechanical power and the fraction S is dissipated as rotor copper loss. We can

conclude then that an induction motor operating at high slip values will be inefficient.

The total rotational losses including the core losses can be subtracted from Pm to obtainthe mechanical power output Po that is available in mechanical form at the shaft for usefulwork:

morotmo TPPP == (2.4)

The per-unit efficiency of the induction motor is then given by

PP

i

o= (2.5)

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Figure 2. Power flow in an induction motor

2.3 Speed control systems for Induction Motors

The angular speed in rad / s of an induction AC machine mechanical speed is given by

( ) sm s= 1 (2.6)

this shows us that there are two possibilities for speed regulation of an induction motor,

altering the slips (typical < 5%), or the synchronous speed s . When the motor is connected

to mains with constant frequency the speed will be determined by the point of intersectionbetween the motor and the load torque characteristic

Figure 3. Typical motor torque - load characteristic

Ignoring the stator resistance and the magnetizing impedance in the equivalent circuit model

of an induction motor, which is usually a valid approximation for motors, gives a simple

equation for the shaft torque inNm

ssss

TTm

m

ee +=

max2 (2.7)

where the maximal torque and corresponding slip is given by

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X

U

T se

2

132

max= (2.8)

respectively

XRsm

'

2= (2.9)

3 Analysis of problem

3.1 Comparison current new method

Try to find a suitable method making it possible to fulfill the needs of LSI Svenska AB.

3.1.1 Properties method currently used

Benefits: Simple circuit Few components Low component cost Reliable

Disadvantages: Excessive heat build-up

Limited current (due to heat and losses)

Needs extra hardware mounted on the machine

3.1.2 New method requirements

16 A current supplied to the IM Higher starting torque

3-phase output from inverter

Limited power loss (less heat) Must handle EMC Must compile with regulations

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3.2 Model / method

3.2.1 Creating a schematic in Pspice

P 2

2 . 2 M e g

P 1

1 M e g

R 3

1 0 k

R 2

1 0 k

R 1

3 3 0

C 1

1 0 0 n F

C 2

1 5 0 n F

C 4

6 8 n F

L 1

1 . 0 m H

1 2

V 1B 1

1 2

I M

I M

F 2

1 2 8

F 1

6 . 3 A

P1 Potentiometer for speed regulation

P2 Potentiometer for min current adjustment

D 1

V 21 V a c

0 V d c

Figure 4. Schematic LSI speed regulator

3.2.2 Studying different control techniques

VOLTAGE CONTROL (the model used by LSI Svenska AB)Unfortunately this is not an effective control. As the voltage decreases, the torque

decreases (the torque developed in an induction motor is proportional to the square of the

terminal voltage). Practically this is confined to 80-100% control.

FREQUENCY CONTROLThis is by far the most efficient way to control the speed. However, one has to make sure

that the machine does not saturate. Since the flux is proportional to V/f, this control has toassure that the magnitude of the voltage is proportional to the speed. Power electronic circuits

are best suited for this kind of control.

VECTOR CONTROLThe magnetizing current always lags (inductive) the voltage by 90 and the torque

producing current is always in phase with the voltage. In vector control the magnetizing

current (Id) is controlled in one control loop and the torque producing current (Iq) in another.The two vectorsId andIq which are always 90 apart, are then added (vector sum) and sent tothe modulator, which turns the vector information into a rotating PWM modulated 3-phase

system with the correct frequency and voltage. This will reduce torque pulsation and a robust

control with fast dynamic response for the induction motor is achieved.

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CHANGING STATOR POLESFor a stator witch has several independent windings, one can connect them is series for

starting, essentially building N*poles. The speed of the machine will be reduced by the samefactor. As the machine speed increases, one can switch the stator connection to a parallel

connection, hence reducing the amount of poles and hence accelerating the machine. This

method is simple, but can really accommodate only 2 speeds.

ROTOR RESISTANCEAs seen for the starting, one can insert a variable resistance in the rotor (slip rings) and

hence cause the developed torque to vary, hence control the speed.

DOUBLY FED MOTORA special application can be to inject a current in the rotor. Hence the air gap flux will

depend upon the difference of frequency between stator and rotor currents, and therefore thespeed can be varied by varying the rotor frequency.

KRAMER CIRCUITWith the method of variable resistor in the rotor circuit, a lot of power is dissipated in this

additional resistor. With the Kramer method, one takes the rotor windings, and feed a 3-phase

rectifier. This DC voltage is then fed through an inverter back to the source. Here only the

component losses are accounted for. The excess power not transformed in mechanical torque

will be fed back to the source.

4 Solution4.1 Deciding what model to be used

The most frequently used three-phase inverter circuit consists of three legs, one for each

phase, as shown in (Fig. 5). The output of each leg, for example VAN (with respect to thenegative dc bus), depends only on Vdand the switch status the output voltage is independentof the output load current since one of the two switches in a leg is always on at any instant.

Here, I ignore the blanking time required in practical circuits by assuming the switches to be

ideal. Therefore, the inverter output voltage is independent of the direction of the load current.

Figure 5. 3-phase inverter

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4.1.1 Three-phase voltage source inverters with sinusoidal PWM

Most motors are designed to for sine wave AC supply and the inverter output should be asnear to sinusoidal as possible. It is therefore best to choose the control wave with sine shape

to give a PWM pattern in which the pulse width is sinudosially modulated throughout the half

cycle. Pulse-width-modulated three-phase inverters shape and control the three-phase output

voltages in magnitude and frequency with an essentially constant input voltage Vd. To obtainbalanced three-phase output voltages in a three-phase PWM inverter, the same triangular

voltage waveform is compared with three sinusoidal control voltages that are 120 out of

phase, as shown in (Fig. 7) (which is drawn for modulation factormf = 15).

f

f

m controltri

f

= (4.1)

It should also be noted from (Fig. 7b)that an identical amount of average DC componentis present in the output voltages VANand VBN, which are measured with respect to the negativeDC bus. These dc components are canceled out in the line-to-line voltages, for example in VABshown in (Fig. 7b).

In a three-phase inverter, only the harmonics in the line-to-line voltages are of concern.

The harmonics in the output of any one of the legs, for example VANin (Fig. 7b), only the oddharmonics exist as sidebands, centered around mfand its multiples, provided mfis odd. Only

considering the harmonic at mf (the same applies to its odd multiples), the phase differencebetween the mfharmonic in VAN and VBNis (120 mf). This phase difference will be equivalent tozero (a multiple of 360) ifmf is odd and a multiple of 3. As a consequence, the harmonic atmfis suppressed in the line-to-line voltage VAB, The same argument applies in the suppressionof harmonics at the odd multiples ofmfifmfis chosen to be an odd multiple of 3 (where thereason for choosing mfto be an odd multiple of 3 is to keep mfodd and, hence, eliminate evenharmonics). Thus, some of the dominant harmonics in the one-leg inverter can be eliminated

from the line-to-line voltage of a three-phase inverter.

Sinusoidal PWM considerations are summarized as follows:

1. Small mf (mf 21): To eliminate the even harmonics, a synchronized PWM should be

used and mfshould be an odd integer. Moreover, mfshould be a multiple of 3 to cancelout the most dominant harmonics in the line-to-line voltage.2. Large mf (mf > 21): The amplitudes of subharmonics due to asynchronous PWM are

small at large values of mf. Therefore, at large values of mf the asynchronous PWMcan be used where frequency of the triangular waveform is kept constant, whereas the

frequency of vcontrol varies, resulting in noninteger values of mf (so long as they arelarge). However, if the inverter is supplying a load such as an ac motor, the

subharmonics at zero or close to zero frequency, even though small in amplitude, will

result in large currents that will be highly undesirable. Therefore, the asynchronous

PWM should be avoided.

3. Overmodulation (ma > 1.0): Regardless of the value ofmf, the conditions pertinent to asmall mfshould be observed.

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Modulation Index

The average output voltage can be affected by changing the modulation index, defined asvoltage ratio between the fundamental of the control wave to the fundamental of the non-

modulated carrier wave as ma modulation index (fig. 7a)

VV

mtri

control

a)1(

)1(= (4.2)

Linear Modulation (ma< 1.0)

In the linear region (ma < 1.0), the fundamental-frequency component in the outputvoltage varies linearly with the amplitude modulation ratio ma (fig. 6).The peak value of the

fundamental frequency component in volts in one of the inverter legs is

2)(

1

VmV daAN = (4.3)

Therefore, the line-to-line rms voltage at the fundamental frequency, due to 120 phase

displacement between phase voltages (ma 1.0), can be written as

VmVmVV dadaLL AN 612.0223

2

3)(

1== (4.4)

The harmonic content for the phase to phase voltage will be strongly dependent on the

modulation index ma. A Fourier analysis on the output phase-to-phase waveform and ingeneral the harmonic spectra will be given from

+

=

= 2cos

2sin

4

1

md

h

mn

nn

nVA (4.5a)

+

=

= 2sin

2sin

4

1

md

h

mn

nn

nVB (4.5b)

With n=kmf mk= 1, 2, 3, ... and m can be odd or even. These rms harmonic voltages arelisted in Table 1 below.

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maf

0.2 0.4 0.6 0.8 1.0

1 0.122 0.245 0.367 0.490 0.612mf 2 0.010 0.037 0.080 0.135 0.195mf 4 0.005 0.011

2mf 1 0.116 0.200 0.227 0.192 0.1112mf 5 0.008 0.0203mf 2 0.027 0.085 0.124 0.108 0.0383mf 4 0.007 0.029 0.064 0.0964mf 1 0.100 0.096 0.005 0.064 0.0424mf 5 0.021 0.051 0.0734mf 7 0.010 0.030

Table 1. Harmonics ofVLL for a large and odd mf (mfa multiple of 3)

Overmodulation (ma> 1.0)

In PWM overmodulation, the peak of the control voltage is allowed to exceed the peak of

the triangular waveform. Unlike the linear region, in this mode of operation the fundamental-

frequency voltage magnitude does not increase proportionally with mu. This is shown in Fig.3, where the rms value of the fundamental-frequency line-to-line voltage VLL is plotted as afunction ofma. Similar to a single-phase PWM, for sufficiently large values ofma, the PWMdegenerates into a square-wave inverter waveform. This results in the maximum value ofVLLequal to 0.78 Vd(fig. 6).

In the overmodulation region compared to the region with ma < 1.0, more sidebandharmonics appear centered around the frequencies of harmonics mf and its multiples.However, the dominant harmonics may not have as large amplitude as with ma < 1.0.Therefore, the power loss in the load due to the harmonic frequencies may not be as big in the

overmodulation region as the presence of additional sideband harmonics would suggest.

Depending on the nature of the load and on the switching frequency, the loss due to these

harmonics in overmodulation may be even less than those in the linear region of the PWM.

Disadvantages with sinusoidal PWM

The biggest disadvantages with sinusoidal PWM are that the liner range is relatively

small. There are many ways to extend it

A third harmonic is added to the sine wave to make the waveform more flat topped.Adding a third harmonic does not constitute a problem as the third harmonic and

multiples thereby will not been seen in the line-to-line voltage.

The sine wave is replaced by a trapezoid or staircase wave to a flat top reference wave. The carrier wave is only applied during the first and last 60 intervals per half cycle,

e.g. 0 to 60 and 120 to 180.

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Figure 6. Three-phase inverter VLL/Vdas a function ofma

Figure 7. Three-phase sinusoidal PWM waveforms and harmonic spectrum

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To me the frequency control model with flux proportional to V/fand voltage proportionalto the speed seems to bee the best solution. Building a solution with a rectifier, a DC link with

LP-filter and a three-phase Pulse With Modulated (PWM) inverter feeding the motor. At firsttesting this approach with a computer model built in Simulink (Matlab) making simulations of

the solution possible.

Figure 8. Voltage - frequency relation Induction Machine

4.2 Building a model

4.2.1 Simulation with Simulink / Matlab

4.2.1.1 Dynamic model for the IM

Let us first consider the stator circuit. The resistance Rsof the stator winding is (for allpractical purposes) equal in all three phases. From the law of induction it follows that the part

of the stator voltage which is not dissipated in the stator resistance will build up a flux in the

stator winding. Hence, with vss as the stator voltage space vector, the following relation musthold:

0=dt

ds

ss

ss

s

s iRv (4.6)

where iss and ss are the space vectors for stator current and stator flux linkage respectively.The rotor circuit, with winding resistanceRr, can be treated in a similar way. Suppose that the

rotor is observed from a coordinate system (rotor coordinates) which rotates with the samespeed as the rotorr. Let us denote rotor coordinates with superscript "r". As the coordinate

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system is rotor-fixed, there will be no induced voltage due to the rotation, so the same relation

as for the stator must hold, but with s r:

0=dt

dr

rs

sr

r

r iRv (4.7)

Here vrr, irr and rr are the rotor voltage, current, and flux space vectors respectively. But therotor winding is short-circuited, so vrr = 0. Now, let us transform irr and rr to stationarycoordinates. This is a transformation using the rotor position r= rdt:

r

r

js

r

r

r

js

r eiei rr == , (4.8)

Equation (4.7) is transformed as

0

0

00

=

=

=

dtdj

dt

dj

dt

d

s

rs

rr

s

rr

s

r

j

s

r

j

r

s

r

j

r

s

r

j

s

r

j

r

iR

eeieR

eieR

r

rr

r

r

(4.9)

The induction motor is thus described by the following equations:

)(

)(

rotorjdt

d

statordt

d

iR

iRv

s

rr

s

rr

s

r

s

ss

s

s

s

s

=

=

(4.10)

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Figure 9. Induction machine

Let us now find a relation between the stator and rotor flux linkages. The rotor winding isreferred to the stator, i.e., the rotor winding is represented by coils in the and directions,cf. (Fig. 9). Assuming linear magnetic conditions, the air gap flux s can then be expressed as

iiiiLs

r

s

s

s

m

s

mm

s

+== ,

(4.11)

where Lmis the mutual inductance between the stator and the rotor, which is also called themagnetizing inductance, and ims, is the magnetizing current. The stator flux is the sum of theair gap flux and the stator leakage flux, the latter which under linear magnetic conditions is

proportional to the stator current only. Similar reasoning for the rotor flux yields

iLiL

iLiL

s

rrl

s

mm

s

r

s

ssl

s

mm

s

s

+=

+=

(4.12)

where Lsl and Lrl are the stator and rotor leakage inductances, respectively. The leakageinductances are typically 10% ofLmor less. Alternatively, withLs = Lm + LslandLr = Lm + Lrtas the stator and rotor self-inductances, respectively, the relations can be expressed as

iLiL

iLiL

s

rr

s

sm

s

r

s

rm

s

ss

s

s

+=

+=

(4.13)

Combining (4.12) with (4.10), assuming constant inductances, yields

0

0

=

=

dt

d

dt

d

dt

d

dt

d

iLiLiRj

iLiLiRvs

mm

s

rrl

s

rr

s

rr

s

mm

s

ssl

s

ss

s

s

(4.14)

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These equations describe the dynamic equivalent circuitdepicted in (Fig. 10). As there arethree inductances configured in a T, this is known as the T-equivalent circuit.

Figure 10. Dynamic T-equivalent circuit for the induction motor

4.2.1.2 Simulink model

I developed an AC/AC converter with DC-link in Simulink / Matlab (Appendix 7.1) with

a diode rectifier and a 3-phase PWM inverter controlling both the frequency and magnitude of

the voltage output. The induction machine model was based on the equations of the dynamic

induction machine model. For generation of PWM pulses the technique shown in Fig. (7.a-b)

was used comparing sinusoidal control voltage (at the desired output frequency and

proportional to the output voltage magnitude) with a triangular waveform at a selected

switching frequency.

Figure 11. 3-phase PWM converter with DC-link

The harmonics in the output voltage appears as sidebands of the switching frequency and

its multiples in a PWM inverter. Therefore a high switching frequency results in an essentially

sinusoidal current (plus a superimposed small ripple at a high frequency) in the motor.

Since the ripple current through the dc bus capacitor is at the switching frequency, the

input dc source impedance seen by the inverter would be smaller at higher switching:frequencies. Therefore, a small value of capacitance suffices in PWM inverters, but this

capacitor must be able to carry the ripple current. A small capacitance across the diode

rectifier also results in a better input current waveform drawn from the utility source.

However, care should be taken in not letting the voltage ripple in the dc bus voltage become

too large, which would cause additional harmonics in the voltage applied to the motor.

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In a PWM inverter output voltage, since the harmonics are at a high frequency, the ripple

in the motor current is usually small due to high leakage reactances at these frequencies. Since

these high-frequency voltage harmonics can have as high or even higher amplitude compared

to the fundamental-frequency component, the iron losses (eddy current and hysteresis in thestator and the rotor iron) dominate. In fact, the total losses due to harmonics may even be

higher with a PWM inverter than with a square-wave inverter. This comparison would of

course depend on the motor design class, magnetic material property, and switching

frequency. Because of these additional harmonic losses, it is generally recommended that a

standard motor with a 5-10% higher power rating be used.

In a PWM drive, the pulsating torqueses developed are small in amplitude and are at high

frequencies (compared to the fundamental). Therefore, as shown in (Eq. 4.10), they produce

little speed pulsations because of the motor inertia.

inertiafrequencyrippleletorquerippofamplitudekespeedripplofAmplitude

= (4.10)

Parameter PWM Square Wave CSIInput power factor + - - -Torque pulsation ++ - -

Multi motor capability + + -Regeneration - - ++Short-circuit protection - - ++Open-circuit protection + + -

Ability to handle undersizedmotor

+ + -

Ability to handle oversized motor - - -Efficiency at low speeds - + +Size and weight + + - -

Ride-trough capability + - -Table 2. Comparison of Adjustable Frequency Drives

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4.2.1.3 Simulation results

Figure 12. Simulation of Induction Machine start

4.3 Analysis of results

The volt hertz (V/f) Pulse-Width-Modulation model seems to fulfill perhaps not all butmost of the requirement stated earlier in this document (3.1.2). Making an increase in the

current supplied to the induction machine up to 16 amperes possible without big losses in the

speed controller, thereby decreasing heat inside the enclosure. The 3-phase output gives abetter feed to the induction machine without extra components needed on the motor and also

produces a higher starting torque and reduced speed pulsation amplitude.

4.4 Future work

4.4.1 Implementation with Digital Signal Processor (DSP)

Traditionally motor control was designed with analog components; they are easy to

design and can be implemented with relatively inexpensive components. However, there are

several drawbacks with analog systems. Aging and temperature can bring about component

variation causing the system to need regular adjustment, as the parts count increase the

reliability of the system decreases. Analog components raise tolerance issues and upgrades aredifficult as the design is hardwired. Digital systems offer improvements over analog

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designs. Drift is eliminated since most functions are performed digitally, upgrades can easily

be made in software and part count is also reduced since digital systems can handle several

functions on chip.

Digital Signal Processors go on further to provide high speed, high resolution and sensor

less algorithms in order to reduce system costs. Providing a more precise control to achieve

better consumption or radiation performances often means performing more calculations, the

use of some 1-cycle multiplication & addition instructions included in a DSP speeds-up

calculations.

Generally fixed point DSPs are preferred for motor control for two reasons. Firstly, fixed

point DSPs cost much less than the floating point DSPs. Secondly, for most application a

dynamic range of 16 bits is enough. If and when needed, the dynamic range can be increased

in a fixed-point processor by doing floating-point calculations in software.

5 Summary and conclusionsIt seem to me that switching from volt control to frequency control (volt / hertz)

method would make it possible to achieve the increase in current supplied to the induction

motor requested by LSI Svenska AB without excessive heat buildup inside the speed

controller housing. 3-phase output from the PWM inverter will reduce speed pulsation and

produce a higher starting torque making it possible to reduce the size of the motor. There will

be no need for manual adjustment of each unit, but the component cost and technical

complicity are going in the wrong direction.

For the future Digital Signal Processors may be the best solution providing high speed,

high resolution and sensor less algorithms in order to reduce system costs. Upgrades can

easily be made in software and part count is also reduced since digital systems can handle

several functions on chip.

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6 References

I. Sadarangani, C., Electrical Machines,Royal Institute of Technology, Stockholm, Sweden, (2000)

II. Mohan N, Undeland, T. M. and Robbins, W. P., Power Electronics,

John Wiley & Sons Inc., USA, (2003)

III. Harnefors, L., Control of Power Electronic Converters and Variable-Speed Drives,

Mlardalen University, Vsters, Sweden, (1999)

IV. Slemon, G. R, Electric Machines and Drives,

Addison-Wesley Publishing Company, USA, (1992)

V. Sarma, M. S, Electrical Machines, Steady-State Theory and Dynamic Performance,

West Publishing Company, USA, (1994)

VI. El-Hawary, M. E, Principled of Electric Machines with Power Electronic App.,

John Wiley & Sons Inc, USA, (2002)

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7 Appendix

7.1 Simulink model

Continuous

powergui

v+-

Vab

Terminator1

TerminatorSelector

Scope

I_Sw1 I_Sw2

Scope

IM

Scope

Fundamental

0

Multimeter

Tr1a

Tr1b

Tr2a

Tr2b

Vd+

A

B

Vd-

IGBT Bridge

5.77e-4*u^2

Fcn

In

Mag

Phase

Discrete

Fourier1

In

Mag

Phase

Discrete

Fourier

Tr1a

Tr1b

Tr2a

Tr2b

Discrete

PWM Generator

4 pulses

DC 400V

C1

Tmis_abc

Te

wr

A

B

C

3 Phase IM

Vab

Is f und.

Vab fund.

I_Sw1 I_Sw2

is_abc

is_abc

Te

wr

Figure 13. Main Simulink model

4

Tr2b

3

Tr2a

2

Tr1b

1

Tr1a

? ? ?

Triangular Wave

Tri

To Workspace5

Sinref

To Workspace4Sine Wave

Sign1

Sign

1

Constant

Figure 14. Discrete PWM Generator 4 pulses

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4 Vd+ 3 Vd-

2 B 1 A

g

CE

IGBT4

g

CE

IGBT3

g

CE

IGBT2

g

CE

IGBT1

D4D3

D2D14

Tr2b

3

Tr2a

2

Tr1b

1

Tr1a

Figure 15. IGBT Bridge

3

w r

2

T e

1

i s _ a b c

3

C

2

B

1

A

v+-

v+-

V s r e

V s i m

T m

i s _ a b

w r

T e

S u b 3

V a b

V b c

V s

S u b 2

i s _ a b c

V a

V b

V c

S u b 1

R e ( u

I m ( u

1

T m

Figure 16. Three-Phase Induction Machine (IM main)

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3

Vc

2

Vb

1

Va

Terminator

s

-+

s

-+

1

is_abc

Figure 17. IM Sub. 1

1

V s

u K

u K

u K 2 / 3

G a i n

f ( u )

f ( u )

f ( u )

2

V b c

1

V a b


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3

Te

2

wr

1

is_abc

rs

rs

rr

rr

p

p

Vsre

isre

rs

Vsim

isim

irre

rr

irim

Tm

J

Out

Sub2

FIs

FI r

is

ir

Te

Sub1

Re

Im

Re

Im

J

J

[Te]

[p]

[firi]

[firr]

[fisi]

[fisr]

[wr]

[firi]

[firr]

[fisi]

[Te]

[wr]

[fisr]

f(u)

f(u)

Re(u)

Im(u)

Re(u)

Im(u)

3

Tm

2

Vsim

1

Vsre


Product4

3

Te

2

ir

1

isProduct5

Product3

Product1

Procuct2

Ls

Ls

Lr

Lr

[p]

f(u)

Fcn1

Divide1

Divide

In1Out1

Conjugate

Im(u)

Lm

f(u)

2

FIr

1

FIs

Figure 20. IM Sub. 3.1

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1

Out

x' = Ax+Bu

y = Cx+Du

[Te]

[p]

[wr]

[firi]

[firr]

[wr]

f(u)

f(u)

f(u)

f(u)

f(u)

10

J

9

Tm

8

irim

7

rr

6

irre

5

isim

4

Vsim

3

rs

2

isre

1Vsre

Figure 21. IM Sub. 3.2

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