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A DSP BASED VARIABLE-SPEED INDUCTION MOTOR DRIVE

FOR A REVOLVING STAGE

by

YONG ZHANG

B. A. Sc., Huazhong University of Science and Technology, WH, China, 1992

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCE

in

THE FACULTY OF GRADUATE STUDIES

(Electrical and Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

December 2007

Yong Zhang, 2007


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ii

Abstract

Variable speed drive technology has advanced dramatically in the last 10 years

with the advent of new power devices. In this study, a three phase induction motor drive

using Insulated Gate Bipolar Transistors (IGBT) at the inverter power stage is introduced

to implement speed and position control for the revolving stage in the Frederic Wood

Theatre

This thesis presents a solution to control a 3-phase induction motor using the Texas

Instruments (TI) Digital Signal Processor (DSP) TMS320F2407A. The use of this DSP

yields enhanced operations, fewer system components, lower system cost and increased

efficiency. The control algorithm is based on the constant volts-per-hertz principle

because the exact speed control is not needed. Reflective object sensors which are

mounted on concrete frame are used to detect accurate edge position of revolving stage.

The sinusoidal voltage waveforms are generated by the DSP using the space vector

modulation technique.

In order to satisfy some operating conditions for safe and agreeable operation, a

look-up table, which is used to give command voltage and speed signals in software, is

applied to limit the maximum speed and acceleration of the revolving stage. Meanwhile,

a boost voltage signal is added at the low frequency areas to make the motor produce

maximum output torque when starting.

A test prototype is then built to validate the performance. Several tests are

implemented into the IGBT drive to explore the reason for unacceptable oscillations in

IGBTs gate control signals. Improvement methods in hardware layout are suggested for

the final design.


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Table of Contents

Abstract ...........................................................................................................ii

Table of Contents .............................................................................................iii

List of Tables ....................................................................................................vi

List of Figures .................................................................................................vii

Acknowledgements .......................................................................................... X

Chapter 1 Introduction.....................................................................................1

1.1 Overview of the Current System......................................................................................... 1

1.2 Advantages of an Induction Motor in Variable Speed Application..................................... 2

1.3 Thesis Motivation and Objective ........................................................................................ 3

Chapter 2 Principles of Stage Mechanic System and V/Hz Control .............4

2.1 Elementary Principles of Mechanics................................................................................... 4

2.2 Safe Riding Conditions ....................................................................................................... 5

2.3 Induction Machines............................................................................................................. 8

2.3.1 Torque production ................................................................................................... 8

2.3.2 Equivalent circuit .................................................................................................... 9

2.3.3 Variable-voltage operation .................................................................................... 12

2.3.4 Variable-speed operation....................................................................................... 13

2.3.5 Constant Volts/Hz operation.................................................................................. 13

2.4 Open Loop Volts/Hz Control with Voltage-Fed Inverter................................................... 15

Chapter 3 Hardware Implementation ............................................................17

3.1 Introduction of System...................................................................................................... 17

3.2 Three-Phase Rectifiers ...................................................................................................... 18

3.2.1 Thermistor............................................................................................................. 18

3.2.2 The DC bus bulk capacitor.................................................................................... 19

3.3 Three-Phase Bridge Inverter .............................................................................................20


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3.3.1 The basic IGBT drive principle............................................................................. 21

3.3.2 Maintaining dv/dt noise immunity........................................................................ 22

3.3.3 The applied IGBT drive ........................................................................................ 24

3.3.4 DC-DC converters................................................................................................. 25

3.3.5 Drives input resistors............................................................................................ 26

3.3.6 Gate resistors......................................................................................................... 26

3.3.6.1 Turn-on resistors............................................................................................. 26

3.3.6.2 Turn-off resistors............................................................................................ 29

3.3.6.3 Minimal switching loss constraint.................................................................. 31

3.4 Energy Dissipation Subsystem.......................................................................................... 33

3.5 Over Current Protection.................................................................................................... 37

Chapter 4 Software Implementation .............................................................39

4.1 Approaches of SV_PWM Signals:.................................................................................... 39

4.2 Implementation-Open-Loop Speed Control for 3-Phase AC Induction Motor ................. 41

4.2.1 Overview............................................................................................................... 41

4.2.2 Initialization module description........................................................................... 43

4.2.3 Interrupt module description................................................................................. 43

4.2.4 Generation of sine and cosine ............................................................................... 44

4.2.5 Space vector pulse width modulation.................................................................... 45

4.2.5.1 Expression of the 3 phase voltages (phase to neutral).................................... 46

4.2.5.2 Application to the static power bridge ........................................................... 47

4.2.5.3 Expression of the stator voltages in the (, ) frame ..................................... 48

4.2.5.4 Projection of the stator reference voltage Vs ................................................. 50

4.2.5.5 Space vector algorithm................................................................................... 53

4.3 Voltage Per Hertz Algorithm............................................................................................. 56

4.4 Frequency Command Module........................................................................................... 58

4.5 Deadtime Setting............................................................................................................... 59

4.6 Look-Up Tables................................................................................................................. 59


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4.7 Execution Time ................................................................................................................. 60

Chapter 5 Experimental Results....................................................................62

5.1 Noise Studies of Gate Signals ........................................................................................... 62

5.2 Analysis of the Running Revolve...................................................................................... 63

5.3 Gate Resistor Studies with Different Drives ..................................................................... 67

5.3.1 Gate signal with flyback transformer as power supplies....................................... 69

5.3.2 Gate signals with battery as power supplies.......................................................... 71

5.3.3 IGBTs gate signal with commercial drives .......................................................... 72

5.3.4 Improved drive circuits and corresponding gate signals ....................................... 74

5.4 Collector-Emitter Surge Voltage ....................................................................................... 75

5.5 Deadtime Analysis ............................................................................................................77

Chapter 6 Conclusion and Future Work.......................................................80

6.1 Conclusion ...................................................................................................................... 80

6.2 Future Work ...................................................................................................................... 81

References.........................................................................................................82

Appendix A: Estimation of Moment of Inertia of the Stage ........................ 83

Appendix B: Induction Motor Parameter Estimation.....................................84

Appendix C: Clarke and Park Transformation................................................87


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vi

List of Tables

Table3.1 Features of the IGBT gate drive ............................................................................................. 25

Table3.2 Turn-on gate resistor sizing by tsw constraint ........................................................................ 28

Table3.3 Turn-on gate resistor sizing by dVout/dt constraint ................................................................ 29

Table3.4 Turn-off gate resistor sizing.................................................................................................... 30

Table3.5 Gate voltage spike induced by high dv/dt .............................................................................. 32

Table3.6 Component list for the IGBT gate drive ................................................................................. 32

Table 4.1 Power bridge output voltages (VAO, VBO, VCO)................................................................ 48

Table 4.2 Power bridge output voltages (VAN, VBN, VCN)................................................................ 49

Table 4.3 Stator voltages ....................................................................................................................... 50

Table 4.4 Relationship between sector and P ........................................................................................ 53

Table 4.5 Assigning the right duty cycle to the right motor phase ........................................................ 54

Table 4.6 State Sequence....................................................................................................................... 55

Table 4.7 Look-up tables used in the program ...................................................................................... 60

Table 5. 1 Features of the BG2B universal gate drive........................................................................... 74

Table a.1 Calculation of the moment of inertia of the stage .................................................................. 83

Table b.1 Nameplate data of the induction machine ............................................................................. 84


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vii

List of Figures

Figure 2. 1 Rotating object and its block diagram representation........................................................... 5

Figure 2. 2 Force analyses for variable speed revolution........................................................................ 6

Figure 2. 3 Angular acceleration versus angular speed........................................................................... 7

Figure 2. 4 Per phase equivalent circuit of induction motor ................................................................... 9

Figure 2. 5 Approximate Per phase equivalent circuit of induction motor ........................................... 10

Figure 2. 6 Torque-speed curves at variable frequency ........................................................................ 12

Figure 2. 7 Torque-speed curves with variable stator voltage............................................................... 13

Figure 2. 8 Torque-speed curves with constant voltage/frequency ratio............................................... 14

Figure 2. 9 Torque-speed curves with low-speed voltage boost, constant voltage/frequency ratio...... 15

Figure 2. 10 Open loop volts/Hz speed control with voltage-fed inverter ............................................ 16

Figure 3. 1 Revolve system of the stage................................................................................................ 17

Figure 3. 2 Three-phase rectifiers ......................................................................................................... 18

Figure 3. 3 DC bus voltage curve.......................................................................................................... 19

Figure 3. 4 One leg of a three phase inverter ........................................................................................ 21

Figure 3. 5 Basic IGBT drive circuit..................................................................................................... 22

Figure 3. 6 Gate signal oscillation countermeasure .............................................................................. 23

Figure 3. 7 Noise shielding of opto-couplers........................................................................................ 23

Figure 3. 8 Additional dv/dt immunity of negative bias turn-off voltage ............................................. 24

Figure 3. 9 IGBT turn-on sequence....................................................................................................... 27

Figure 3. 10 RGon sizing ......................................................................................................................27

Figure 3. 11 Current paths when Low Side is off and High Side turns on............................................ 30

Figure 3. 12 Separate gate current paths for turning-on and turning-off............................................... 31

Figure 3. 13 IGBT gate drive schematic ............................................................................................... 33

Figure 3. 14 Current paths for (a) Operation mode of motoring(b) Operation mode of generating..... 34

Figure 3. 15 Application speed, torque and power profiles .................................................................. 36

Figure 3. 16 over current censoring circuit ........................................................................................... 37


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Figure 3. 17 Current scaling for short circuit protection....................................................................... 38

Figure 4. 1 Program flow chart ............................................................................................................. 42

Figure 4. 2 Software flowchart and timing ........................................................................................... 44

Figure 4. 3 Sin, Cos calculation using the sine look-up table ............................................................... 45

Figure 4. 4 Phase equilibrate system..................................................................................................... 46

Figure 4. 5 Power bridge....................................................................................................................... 47

Figure 4. 6 Stator voltages .................................................................................................................... 49

Figure 4. 7 Projection of the reference voltage vector .......................................................................... 51

Figure 4. 8 Sector 1 PWM patterns and duty cycles ............................................................................. 55

Figure 4. 9 Voltage versus frequency ................................................................................................... 56

Figure 4. 10 Speed waveform of accurate position control................................................................... 58

Figure 4. 11 Command frequency censoring hardware ........................................................................ 58

Figure 4. 12 Command frequency scale translation.............................................................................. 59

Figure 4. 13 Execution time of V/Hz control routine............................................................................ 60

Figure 5. 1 Gate signal, low side with different DC bus link voltage ................................................... 62

Figure 5. 2 Phase and line voltage reference waveforms with SVP...................................................... 63

Figure 5. 3 The tested stage with 1500kg unbalanced loads................................................................. 64

Figure 5. 4 Motor current curves under different running conditions................................................... 65

Figure 5. 5 Gate signals......................................................................................................................... 67

Figure 5. 6 Basic gate charge waveforms ............................................................................................. 68

Figure 5. 7 The practical realization of the prototype ........................................................................... 69

Figure 5. 8 The schematic diagram of the flyback transformer ............................................................ 70

Figure 5. 9 Gate signal with flyback transformer as power source of the drive.................................... 71

Figure 5. 10 A group of batteries as power supply for IGBT drives..................................................... 71

Figure 5. 11 Gate signal with batteries as power source of the drive.................................................... 72

Figure 5. 12 The commercial drive ....................................................................................................... 72

Figure 5. 13 The gate signals with commercial drives.......................................................................... 73

Figure 5. 14 DSP embedded in PCB board with commercial drives .................................................... 74


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Figure 5. 15 The gate signal curve with improved hardware layout ..................................................... 75

Figure 5. 16 Gate and Collector-emitter voltage curves ....................................................................... 76

Figure 5. 17 The layout of capacitors be mounted on bus bar .............................................................. 77

Figure 5. 18 The Collector-Emitter voltage curve with the new layout................................................ 77

Figure 5. 19 Current waveforms with different command frequency, deadtime=2s .......................... 78

Figure 5. 20 Current waveforms with different command frequency, deadtime=1.4s ....................... 79

Figure 1 Stator current in the stationary reference frame and its relationship with a,b,and c stationary

reference frame .......................................................................................................................87

Figure 2 Stator current in the d,q rotating reference frame and its relationship with, stationary

reference frame .......................................................................................................................89


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Acknowledgements

I wish to express my deepest gratitude to my supervisor, Dr. William G. Dunford,

for his support, advice and guidance throughout the course of my research.

Numerous interactions with my colleges Weidong Xiao, Kenneth Wicks, Yan LI

and Amir Rassuily have as well inspired me throughout my graduate study. In particular,

I would like to express my thanks to Qiang Han who shared with me his experience and

optimism in software and hardware setup.

Thanks are extended to Mr. Jay Henrickson, the technical manager of the theatre,

for providing necessary facilities and assistance throughout this process.

Finally, I am expressing my sincerest gratitude to my parents and my wife for their

love and support during my studies.


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Chapter 1 Introduction

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1.Chapter 1

Introduction

1.1 Overview of the Current System

The Frederic Wood Theatre is located at the north end of The University of British

Columbia (UBC). The original construction was built in 1963 and designed by

Thompson, Berwick and Pratt. The building exterior is textured concrete with relief to the

concrete walls coming from the landscape and the glazed entrance. This building is

named after Frederic Wood, Founder of the UBC Players Club, as a tribute to his major

contribution to the development of theatre in British Columbia.

During the past 50 years, numerous shows, conferences and other actions have

been held at the theatre. Nowadays, it is still busy to be a platform to operate various

theatre programs, which make it possible to interact among students, scholars and guest

artists. As the heart of a theatre, the stage serves as a space for actors. As is necessary in a

drama, sceneries are required to be changed according to the mood, and rotary stage can

serve a performance to the need of scenery change. There is a round revolver, with

27-feet diameter, in the Frederic Wood Theatre. This revolver is driven by a 3-hp Direct

Current (DC) motor via a steel cable coupled the motor and the stage. The old control

panel has three speed control option buttons and one bi-direction rotated knob to supply a

coarse control approach. Position alignments in the scenery change are based on the

operators experience. However, because the scenery setting differs from time to time,

and so does the number of actors, this operation becomes complex and uncertain even to

a veteran operator. Consequently, an automatic stage drive and control system is

desirable.


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1.2 Advantages of an Induction Motor in Variable Speed

Application

Judged in terms of fitness for purpose coupled with simplicity, the induction motor

must rank alongside the screw thread as one of mankinds best inversions [1]. The

induction motor (IM) has dominated a number of fixed-speed applications because of its

reliability and low maintenance operation compared to DC motors. But, speed control had

been one of the obvious shortcomings which impeded IM applications in some industrial

fields, such as hydraulics. On the contrary, controlling the speed of a brushed DC motor

is simple. The higher the armature voltage, the faster the rotation. This relationship is

linear to the motor's maximum speed. In addition, most industrial DC motors will operate

reliably over a speed range of about 20:1 -- down to about 5-7% of base speed. This is

much better performance than comparable AC motors.

However, in the last two decades, with the evolution of power semiconductor

devices and power electronic converters, the IM is also well established in the

controlled-speed arena. High performance Digital Signal Processor (DSP)s introduction

makes complicated control algorithms, such as flux vector control, available, which

means that Alternating Current (AC) motors can be applied to accurate motor speed

control as DC motor. Meanwhile, an AC induction motor, compared with a DC motor, is

relatively inexpensive, since the windings consist of metal bars which are cast into steel

laminations that make up the remainder of the rotor and the stator windings can easily be

inserted in slots in stator laminations. An induction motor, at least the cage variety, has no

brushes, no moving parts other than the rotor, and virtually no maintenance. As a result,

AC motors are progressively replacing DC machines in variable-speed applications.


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1.3 Thesis Motivation and Objective

The objective of this thesis is to clarify the practical approaches needed to set up a

Digital Signal Processor (DSP)-based variable-speed drive to realize accurate speed and

position control. The specific objectives include:

To find safe operation areas for the stage

To build a three phase rectifier

To develop a variable-speed drive

To generate a DSP program with the assembly language

To test the prototype to determine characteristics related to above theoretical

analysis

The thesis is organized into six chapters. Chapter 1 gives a brief introduction of the

current stage system and outlines the objectives of this thesis. In Chapter 2, some basic

principles of mechanics and IM variable-speed control are reviewed and a safe operation

area for the stage is proposed. Chapter 3 is focused on hardware setup for a variable-

speed IM drive. Chapter 4 will be dealing with software implementation. Some design

illustration concerning software is presented. Selective experimental results are included

in Chapter 5. The last chapter concludes the design and the implementation and proposes

some work needed to be done in the future.


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Chapter 2 Principles of the Stage Mechanic System and V/Hz Control

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2.Chapter 2

Principles of Stage Mechanic System andV/Hz Control

2.1 Elementary Principles of Mechanics

In the stage and its drive system, both mechanical and electromagnetic energies

exist and there is the exchange between the two types of energies. Since the whole system

involves mechanical and electrical engineering, it is necessary to recall some basic

concepts and laws related to mechanics. The most general equation to describe rotational

motion is:

M L

dT T J

dt

= (2-1)

where . )MT N m is the electrical torque and . )LT N m the load torque, ( / )rad s is the

angular speed, 2. )J kg m is the overall moment of inertia of the rotating mass about the

axis of rotation. As speed is the derivative of the shaft position, we have

2

2M L

d dT T J J

dt dt

= = (2-2)

where2

2

d d

dt dt

= = (2-3)

2( / )rad s is the angular acceleration.

The rotational system can be considered as a second-order differential equation,

with the input as the driving torque and the load torque and the output as speed and

position [2]. The following diagram, Figure 2. 1 describes such a mechanical system with

a lumped mass.


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LM TT

Figure 2. 1 Rotating object and its block diagram representation

2.2 Safe Riding Conditions

Before proceeding to the system design, we have to find a way to decide what the

maximum angular speed max and maximum angular acceleration max should be since

they associate with the safety for actors on-board. We can divide the safety problem into

two levels, mechanically safe and physiologically safe. For mechanical safety, the

maximum angular speed max and maximum angular acceleration max should be

within the range such that motors and the stage can stand. In addition, slippage in the

cable coupled gear box and the stage should be taken into account while the maximum

angular acceleration max is chosen. For physiological safety, max and max should

be within the range that those on-board can stand and have no dizziness or fear caused by

the motion of the stage.

Rotating along the shaft is a typical movement for the stage. The angular speed of

the stage can be changed in the acceleration/deceleration period. So does the angular

acceleration/deceleration. Therefore the motion of the stage is a varying-speed

varying-acceleration revolution. If an object is rotating with a varying speed, its

acceleration can be divided into two components, a radial/centripetal acceleration that

changes the direction of the angular speed, and a tangential acceleration that changes the

magnitude of the angular speed. Figure 2. 2 [3]shows the forces and accelerations applied

to a person standing on a stage.


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TTF ,

CCF ,

ffF ,

LL ,

Figure 2. 2 Force analyses for variable speed revolution

Assume the stage is rotating at an angular speed L and an angular

acceleration L . fF and represent the force applied to the person and the actual

acceleration for the person respectively. fF (the same to f ) can be divided into two

components, cF in the normal direction and tF in the tangential direction. Recall

2

C C LF ma m r = = (2-4)

T T LF ma m r = = (2-5)

with m being the mass of the person and r being the rotational radius of the person.

From (2.4) and (2.5) we have

2 2 4 2

f C T L LF F F mr = + = + (2-6)

F , subscripted with f referring to friction, is actually a friction acting as the force to

keep the person moving with the stage simultaneously. The maximum of the friction is

given by

,maxf sF mg= (2-7)

where s is the coefficient of static friction between the stage and persons shoes and


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g is the acceleration due to gravity. For safety reasons, the inequality

,maxf fF F (2-8)

must be satisfied to prevent slip from happening. Substitute (2.6) and (2.7) into (2.8) and

eliminate m results in

4 2

s L Lg r + (2-9)

or 4 2 sL Lg

r

+ (2-10)

the most serious case, in terms of r, happens when people stand at the edge of the stage,

thus /s g r reaches its minimum /s g R with R (13.5fts) the radius of the stage.

Under this condition, Figure 2. 3 [3]shows the relationship of maximum angular

acceleration versus speed with different friction coefficients. Safe operation states are

those points bordered by the curves and the y axis.

0 0.2 0.4 0.6 0.8 1 1.2

-1

-0.5

0

0.5

1

L (rad/s)

L

(rad/s2)

s=0.1

s

=0.2

s=0.3

s=0.4

s=0.5

Figure 2. 3 Safe angular acceleration versus angular speed, radius is R

From the figure it can be concluded that in low to medium speed area,

acceleration/deceleration can be chosen in a relative big area under safe operation


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condition. However, as speed increases, allowable acceleration/deceleration decreases

dramatically. In the following practical design, it is desirable to maintain the operation

area of the stage in the middle left area shown in Figure 2. 3. According experience from

the old system, the comfortable speedmax

is limited at 1.42 rpm (0.1495 /rad s ) and

max should be less than 0.052( / )rad s

2.3 Induction Machines

Among all types of ac machines, the induction machine, particularly the cage type,

is most commonly used in industry. These machines are very economical, rugged, and

reliable, and are available in the ranges of fractional horse power (FHP) to

multi-megawatt capacity [4]. In the following two sections, the principle of torque

production is introduced and per phase equivalent circuits are used to figure out the

expression of relationship between IMs torque and speed.

2.3.1 Torque production

If a IMs rotor is initially stationary, its conductor will be subjected to a sweeping

magnetic field, produced by stators current, inducing current in the short-circuit rotor

with same frequency. The interaction of air gap flux and rotor Magnetomotive force

(mmf) produces torque. At synchronous speed, the rotor can not have any induced

currents and; therefore, torque can not be produced. At any other speed, there will be a

difference between the rotating field (synchronous) speed and the shaft speed, which is

called slip speed. The slip speed will induce current and torque in the rotor. The rotor will

move in the same diction as that of the rotating magnetic field to reduce the induced

current. We define slip as:

e r e r sl

e e e

N Ns

N

= = = (2-11)

where e = stator supply frequency / )r s , r = rotor electrical speed / )r s , and


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sl = slip frequency / )r s . The rotor mechanical speed is (2 / ) ( / )m rP r s = , where

P = number of poles of the machine. The rotor current is induced at slip frequency.

Since the rotor is moving at speed r and it current wave is moving at speed sl

relative to the rotor, the rotor mmf wave moves at the same speed as that of the air gap

flux wave the torque expression [4] can be derived as

sin2

e p p

PT lrB F

=

(2-12)

where P = number of poles, l = axial length of the machine, r= machine radius,

PB = peak value of air gap flux density, PF = peak value of rotormmf , and is

defined as the torque angle

2.3.2 Equivalent circuit

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

important tool for analysis and performance prediction under steady-state conditions.

Figure 2. 4shows the development of a per phase transformer-like equivalent circuit.

Figure 2. 4 Per phase equivalent circuit of induction motor

The various power expressions can be written form the equivalent circuit ofFigure

2. 4as follows:

Input power: sin2

e p p

PT lrB F

=

(2-13)


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Stator copper loss: 23ls s sP I R= (2-14)

Core loss:23 m

lc

m

VP

R= (2-15)

Power across air gap:2

3 rg rR

P I S= (2-16)

Rotor copper loss: 23lr r r

P I R= (2-17)

Output power: 21

3o g lr r r s

P P P I RS

= = (2-18)

Since the output power is the produce of developed torque Te and speed m, Te can

be expressed as

0 2 23 1

3 2

r

e r r r m m e

P RS p

T I R I S s

= = = (2-19)

The equivalent circuit ofFigure 2. 4can be simplified to that shown in Figure 2. 5 ,

where the core loss resistor mR has been dropped and the magnetizing inductance mL

has been shifted to the input. This approximation is easily justified for an integral

horsepower machine, where

( )s e ls e m R j L L +


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( ) ( )2 22/

sr

s r e ls lr

VI

R R S L L=

+ + +(2-21)

substituting Equation (2-21) in (2-19) yields

( ) ( )

2

2 223 2 /

sre

e s r e ls lr

VRP

T S R R S L L

= + + + (2-22)

A further simplification of the equivalent circuit of Figure 2.6 can be made by

neglecting the stator parameters sR and lsL . This assumption is not unreasonable for an

integral horsepower machine, particularly if the speed is typically above 10 percent [4].

Then, the equation (2-22) can be simplified as

2

2 2 23 2s sl r

ee r sl lr

VP R

T R L

= + (2-23)

where sl es = . The air gap flux can be given by

s

m

e

V

= (2-24)

in a low-slip region, (2-23) can be approximated as

( )21

3

2e m sl

r

PT

R

=

(2-25)

where2 2 2

r sl lr R L>> . Equation (2-25) is critical for following analysis because it

indicated that at constant flux, the torque is proportional to slip frequency, or at constant

slip frequency, torque is proportional to flux.


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2.3.4 Variable-speed operation

If the stator frequency of a machine is increased beyond the rated value, but the

voltage is constant, the torque-speed cures derived from Equation (2-22) can be plotted as

shown in Figure 2. 7. The air gap flux and rotor current decrease while the frequency

increases and corresponding developed torque also decreases. The breakdown torque as a

function of slip (at constant frequency) can be derived by differentiating Equation (2-23)

as

2

2 2 23

2s slm r

em

e r slm lr

VP RT

R L

= + (2-26)

where /slm r lr R L = is the slip frequency at maximum torque. The equation show that

2

em eT = constant

0 1 2 3

0.5

1

Frequency (e/

b) pu

Torque

(Te

/Tem

)pu

Teme

2

=constant

Rated cruve

Tem

Figure 2. 7 Torque-speed curves with variable stator voltage

2.3.5 Constant Volts/Hz operation

If an attempt is made to reduce the supply frequency at the rated supply voltage, the

air gap flux m will tend to saturate, causing excessive stator current. Therefore, the

region below the rated frequency should be accompanied by the proportional reduction of


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stator voltage so as to maintain the air gap flux constant. This relationship can be

expressed by Equation (2-24) as well. Figure 2. 8 shows the plot of torque-speed curves at

/Volt Hz = constant. Note that the breakdown torque emT given by Equation (2-26)

remains approximately valid, except in the low frequency region where the effect of

stator resistance in reducing the flux becomes very pronounced. It is clear from Figure 2.

8 that the starting torque at the minimum frequency is much less than the breakdown

torque at higher frequencies, and this could be a problem for loads which require a high

starting torque. For example, the starting torque for the stages revolve is quite high. The

additional stator voltage can be compensated to restore emT value, as shown in Figure 2.

9.

0.5 10

0.5

1

Frequency (e/b) pu

Torque(Te

/Tem

)pu

Vs/e=constant

Rated cruve

Maximum torque

Figure 2. 8 Torque-speed curves with constant voltage/frequency ratio

If the air gap flux of the machine is kept constant in the constant torque region, as

indicated in Figure 2. 9, it can be shown that the torque sensitivity per ampere of stator

current is high, permitting fast transient response of the drive with stator current control.

In variable-frequency, variable-voltage operation of a drive system, the machine usually

has low slip characteristics, giving high efficiency. With low-frequency voltage boosting,

the machine can always be started at maximum torque, as shown in Figure 2. 9. The


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absence of high starting current in a direct-start drive reduces stress and therefore

improves the effective life of the machine.

0.5 10

0.5

1

Frequency (e/b) pu

Torque(Te

/Tem

)pu

Vs/e=constant

Rated cruve

Maximum torque

Figure 2. 9 Torque-speed curves with low-speed voltage boost, constant voltage/frequency ratio

2.4 Open Loop Volts/Hz Control with Voltage-Fed Inverter

The open loop volts/Hz control of an induction motor is by far the most popular

method of speed control because of its simplicity, and there types of motors are widely

used in industry [4]. Traditionally, the induction motors have been used with power

supplies at constant frequency for constant speed applications. For adjustable speed

applications, variable voltage and variable frequency is prevalent. The simple principle is

to keep state flux ( /s s eV = ) constant by changing voltage with proportional to

frequency. Figure 2. 10 shows the block diagram of the /Volt Hz speed control method.

The power circuit consists of a diode rectifier with three phase AC supply, LC filter, and

PWM voltage-fed inverter. The frequency command *e is the control signal because it

is approximately equal to speed r , neglecting the small slip frequency sl of the

machine. Based on /Volt Hz control theory which has been motioned in the above


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16

section, the phase voltage command *sV can be generated from frequency command be

the gain factor G, as shown, So that the flux s remains constant. If the stator resistance

and leakage inductance of the machine are neglected, the flux will also correspond to the

air gap flux m or rotor flux r . At low speed areas, the stator resistance become

significant and absorbs the major amount of the stator voltage, thus weakening the flux.

Therefore, the boost voltage boostV is added to compensate flux to keep it equal to rated

flux and corresponding full torque become available at low frequency. The *e signal

is integrated to generate the angle signal *e , and the corresponding sinusoidal phase

voltages ( *aV , *bV , *cV ) are generated by the expressions shown in the figure. Then

PWM controllers which is embedded in DSP can generate control signals to drive the

inverter. Detailed description of hardware and software for this control topology will be

given in chapter3 and chapter 4 respectively.

* 2 sina s e

V V =

* 22 sin

3

c s eV V

= +

* 22 sin3

b s eV V

=

Figure 2. 10 Open loop volts/Hz speed control with voltage-fed inverter


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Chapter 3 Hardware Implementation

17

3.Chapter 3

Hardware ImplementationBased on the theory has been discussed in chapter 2, a practical variable-speed

drive will be built for experimental result. In this chapter, emphasis will be given on how

to choose components and put them together to form a prototype of IM variable-speed

drive.

3.1 Introduction of System

The drive system of the stage can be depicted in

Figure 3. 1. It includes an AC-DC rectifier, a DC-AC inverter, a DSP, an induction

motor and other accessorial components. It works based on popular AC-DC-AC

topology. Following discussion will one by one explain above components.

Figure 3. 1 Revolve system of the stage


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18

3.2 Three-Phase Rectifiers

In order to obtain the essential DC bus voltage for the inverter, a three-phase diode

bridge rectifier (Figure 3. 2) was applied in this application. A six pulse full bridge

rectifier will produce 325V DC bus voltage while input AC line to line voltage is 230V.

Figure 3. 2Three-phase rectifiers

3.2.1 Thermistor

A thermistor is installed to avoid high inrush current and voltage ringing whenconnecting the capacitors to the input network. When current begins to flow through

resistor and charge capacitors, the voltage difference between the power source and

capacitor is almost equal to 325V, which will produce big current in the circuit loop. This

current could be so high that it is in excess of capacitors rating current and damage

capacitors permanently. The thermistor has biggest resistance value of 5 ohms at 25

degree centigrade. It will be helpful in limiting starting charge current to 65A in a short

time. With the process of charging capacitors, thermistors resistance will drop

dramatically with the increase of its temperature. Finally, it reaches 0.082ohms, which

brings very small power dissipation in the steady state. In other words, the thermistor can

be considered as a short circuit and without any voltage drop on it in the steady state.


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19

3.2.2 The DC bus bulk capacitor

Sizing of the capacitor represents a tradeoff. For a given load, a larger capacitor

will reduce ripple but will cost more and will create higher peak currents in the supply

feeding it. In Figure 3. 3, the voltage waveform of capacitors is depicted to calculate

corresponding capacitance value.

Electrolytic capacitors are used to smooth the dc bus voltage. Its capacitance can be

found from the formula:

min 2 2

max min

2

( )

in

rect

PC

V V f=

(3-1)

where Pin is the load power in watts,rect

f is the ripple frequency, maxV is the maximum

dc voltage and minV is the minimum dc voltage [5].

Figure 3. 3 DC bus voltage curve

In practical realization, a three phase 230V AC input is connected to the input of

the rectifier. The peak voltage value of input is as follows:

max 2 325LLV V V= =

assume min max96% 312V V V= = ; WPin 2235745*3 == ; for three phase rectifier

6 60 360rect

f Hz= = . Then


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20

min 2 2 2 2

max min

2 2 22351499

( ) (325 312 ) 360

in

rect

PC F

V V f

= = =

tc, the charging time, can be calculated as

1 min1

maxcos ( ) cos (0.96)

7532 2 60

c

in

V

Vt S

f

= = =

(3-2)

and discharging time tDC is

1 1753 2

360 DC c

rect

t t mSf

= = = (3-3)

the average charging current is given by

max min 325 3121499 26753

C

c c

V VV I C C At t = = = = (3-4)

According to the calculation, at least a 1500F capacitor should be employed to

maintain the dc bus ripple within 4% or less. The capacitor should also can stand 26A

charging current.

3.3 Three-Phase Bridge Inverter

Figure 3. 4 shows a leg which includes high side and low side IGBT modules,

drivers and DC-DC converters of the three-phase bridge inverter. In the following

paragraphs, the detailed discussion will be focused on all components of this inverter.


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21

N/C1

ANODE2

CATHODE3

N/C4

Vcc8

V07

V06

VEE5

HCPL-1R3

180R

3.8KR6

3.8KR5

10uFC5

10uFC2

+5

R1

180RVin-1

Q1IGBT-N

R91.0K

VCC

10uF

C1

N/C1

ANODE2

CATHODE3

N/C4

Vcc8

V07

V06

VEE5

HCPL-2

R2

180RVin-2

Q2IGBT-N

+Vin1

-Vout4

+Vout6

-Vin2

COM5

*1

VASD1-S5-D15-SIP

R4

180R

3.8KR8

3.8K

R7

10uFC6

10uF

C4

+5

R101.0K

10uFC3

+Vin1

-Vout4

+Vout6

-Vin2

COM5

*2

VASD1-S5-D15-SIP

Phase A

Negative side of DC bus link

Figure 3. 4 One leg of a three phase inverter

3.3.1 The basic IGBT drive principle

Figure 3. 5 illustrates a basic IGBT gate drive circuit, which converts logic level

control signals into appropriate voltage and current that can drive the IGBT power


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22

module reliably and efficiently [6]. The conversion is performed by a pair of bipolar

transistors alternately connecting the IGBTs gate to the appropriate on (Von) and off

(Voff) voltages. The gate resistor is selected to generate a proper peak current charging or

discharging the IGBTs gate. The optocoupler provides isolation between the high power

component and control signal to avoid potential damage to the digital controller.

3.3.2 Maintaining dv/dt noise immunity

The IGBT gate drive circuits are subjected to high common mode /dv dt noise

produced by the fast switching, high voltage and high current IGBT power modules. To

maintain the immunity to the high /dv dt noise is critical for the drive circuit to function

normally in an offensive environment.

Figure 3. 5 Basic IGBT drive circuit

If the wiring between the drive circuit and the IGBT is long, the IGBT may be in a

malfunction due to gate signal oscillation or induced noise. A countermeasure for this is

shown in Figure 3.6. In order to avoid this situation, some points should be taken into

account as follows:

a) Make the drive circuit wiring as short as possible and finely twist the gate and

emitter wiring.

b) Increase RG. However, pay attention to switching time and switching loss

c) Separate the gate wiring and IGBT control circuit wiring as much as possible,


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23

and set the layout so that they cross each other

d) Do not bundle together the gate wiring or other phases

Drive circuit

Stray inductance

RG

RGE

LS

Figure 3. 6 Gate signal oscillation countermeasure

In this circuit, RGE is installed to prevent IGBT from being destroyed if gate circuit

is bad or if the gate circuit is not operating and a voltage is applied to the power circuit

Figure 3. 7 Noise shielding of opto-couplers

Furthermore, an optocoupler which is built in IGBTs drive is used to prevent high

common mode /dv dt. The immunity is normally achieved by adding shields between the

primary and secondary side of the opto-coupler (Figure 3. 7).

In addition, a larger series gate resistance is desirable to help reduce transient

voltage during turn-off switching. Unfortunately, in most cases the series gate resistance

must be increased substantially to have any significant impact on the turn-off fall time.

Usually, such an increase in series gate resistance will result in poor /dv dt noise

immunity and excessive switching losses. It is usually better to reduce transient voltages

with improved power circuit layout or snubber designs. There are detailed discussions

about how to find a right way to build /dv dt noise immunity in this application circuit

in Chapter 5.


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Figure 3. 8 Additional dv/dt immunity of negative bias turn-off voltage

Finally, a substantial negative bias is used for IGBT drive, which provides

additional /dv dt immunity and reduces turn-off losses. The additional margin to absorb

"real" collector-gate capacitance coupled reverse transfer charge during high /dv dt,

with respect to the gate-emitter "turn-on" threshold voltage, is a significant reliability

improvement, particularly when switching peak (fault) current, coincident with a high

dc-bus voltage (Figure 3. 8).

3.3.3 The applied IGBT drive

The gate drive used in the prototype, HCPL-3120, is a high-current output IGBT

gate drive with built-in opto-coupler. Its main parameters are given in Table 3.1.

The current and voltage supplied by HCPL-3120 make it ideally suited for directly

driving IGBTs with ratings up to 1200V/100A. In this drive, IRs IGBTs (IRG40C50UD)

are used as power switches. Their rating current is 27A at 100oC and rating voltage is

600V. The switching frequency is 10 kHz. From HCPL-3120 datasheet, it is easy to draw

a conclusion that this drive is suitable for designated IGBTs. The HCPL-3120 contains an

under-voltage lockout (UVLO) feature that is designed to protect the IGBT under fault

conditions which cause the HCPL-3120 supply voltage (equivalent to the fully- charged

IGBT gate voltage) to drop below a level necessary to keep the IGBT in a low resistance

state. When the HCPL-3120 output is in the high state and the supply voltage drops


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25

below the VUVLO- threshold, the opto-coupler output will go into the low state with a

typical delay. When the HCPL-3120 output is in the low state and the supply voltage rises

above the HCPL-3120 V UVLO+ threshold, the opto-coupler output will go into the high

state with a typical delay.

Feature Specification Description

Peak output current 2.0 A

Common-mode rejection 15 kV/s Vcm = 1.5 kV

Input voltage Vcc 15 30 V

UVLO Threshold Vuvlo+ 11-13.5 V

UVLO Threshold Vuvlo- 9.5 12 V Hysteresis

Maximum switch frequency 2 MHz

Isolation 630 V peak

Table3.1 Features of the IGBT gate drive

3.3.4 DC-DC converters

A dc-dc converter (VASD1-SIP-S5-D15-SIP) is chosen to provide the isolated

15V power to the IGBT drive. The converter can provide 1kV dc voltage isolation

across its input and output that is high enough in this application. The output isolated

power is 1 w. A resistor has to be connected to the output of the converter which needs a

minimum of 10% loading to maintain a reliable and fully-performed output. In order to

confirm that converter can provide enough power to drive, a 3.8k resistor is chosen as

the load resistor. The corresponding power dissipation is:

2 2300.12

2 7600

VP W

R= = (3-5)

Approximate 0.9W output power could be used by IGBTs drive.


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26

3.3.5 Drives input resistors

To provide enough current to drive LED in HCPL-3120, a appropriate resistor has

to be installed between output of DSP and input of HCPL. The operating condition of this

LED diode is:

Current: 7~16mA

Voltage: 0.8V

the following equation is employed to calculate essential resistance

3

3.3 0.8178 180

14 10IN

Rx

= = (3-6)

3.3.6 Gate resistors

There are numerous methods to size IGBTs gate resistors. Here some of them

which are applied by industries will be illustrated. More accurate resistance values can be

found by practical tests depending on the different emphasis of switching loss, switching

time and slope of /dv dt.

3.3.6.1Turn-on resistors

By properly sizing the gate resistors the switching speed of the output IGBT can be

controlled [7]. Some basic rules are given below for sizing the gate resistors to obtain

desired switching time. The switching timesw

t is defined as the time spent to reach the

end of the plateau voltage, as shown in Figure 3. 9. *GE

V indicates the plateau voltage;

GCQ and

GEQ indicate the gate to collector and gate to emitter charge respectively.


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27

Figure 3. 9 IGBT turn-on sequence

Depending on Figure 3. 10, to obtain the desired switching time, the gate resistance

can be sized by:

GC GE avg

sw

Q QI

t

+= (3-7)

and

-CC GE TOT

avg

V VR

I= (3-8)

wherePTOT DR Gon

R R R= +

GonR = gate on-resistor

PDRR = driver equivalent on-resistance

Figure 3. 10 RGon sizing

Table3.2 shows the calculation process to size the turn-on gate resistor driven by


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swt constraint.

Reference Description IRG4PC50UD

GEQ Gate Emitter charge (turn-on) 25 nC

GCQ Gate Collector Charge (turn-on) 61 nC

swt Switching Time 500 ns

sw

GEGC

avgt

QQI

+= Average Charging Current 172 mA

*

GEV Gate Plateau Voltage 6 V

avg

GECC

TOTI

VVR*= Equivalent Output Resistance of

the Gate Driver52

DRpR Driver Equivalent on-resistance 0

DRpTOTGon RRR = Gate On-resistance 52

Table3.2 Turn-on gate resistor sizing by tswconstraint

Turn-on gate resistor can also be sized to control output slope /outdV dt . Although

the output voltage has a non-linear behavior, the maximum output slope can be

approximated by

avgout

RESoff

IdV

dt C= (3-9)

inserting the expression yielding Iavg and rearranging:

-CC GE TOT

outRESoff

V VR

dVCdt

= (3-10)

The calculation of this kind of constraint is given in Table 3.3.


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29


dt

dVout

Output Voltage Slope 5 V/ns

RESoffC Reverse Transfer Capacitance

(off-state)52 pF

RESoff

out

avg Cdt

dVI =

Average Charging Current 260 mA

*

geV Gate Plateau Voltage 6 V

avg

geCC

TOTI

VVR

*=

Equivalent Output Resistance

of the Gate Driver

34

DRpR Driver Equivalent on-resistance 0

DRpTOTGon RRR = Gate On-resistance 34

Table3.3 Turn-on gate resistor sizing by dVout/dt constraint

3.3.6.2Turn-off resistors

The worst condition in calculating the turn-off resistor is when the collector of the

IGBT in the off state is forced to commutate by the turn-on of the companion IGBT [7].

In that case, a parasitic current throughRESoff

C will be induced by the high /dv dtof the

output node. If the voltage drop at the gate exceeds the threshold voltage of the IGBT, the

device may be turned on by itself, which will cause cross conduction for the whole leg. If

no negative bias voltage is used, condition

( )out

th ge Goff DRn RESoff

dVV V R R C dt> = + (3-11)

must be verified to avoid spurious turn-on. Rearrange (3-11)

thGoff DRn

RESoff

VR R

dVC

dt

<

(3-12)


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30

Figure 3. 11 Current paths when Low Side is off and High Side turns on

Figure 3. 12 shows the current induced by the high /dv dt of the output node,

where IESC is the input capacitance, and RESoffC is the reverse transfer capacitance. An

example of calculating the turn-off gate resistor is given in Table 3.4


dt

dVout

Output Voltage Slop 5 V/ns

RESoffC

Reverse Transfer Capacitance

(off-state)52 pF

thV Gate Threshold Voltage 6 V

TOTR

Equivalent Output Resistance of the

Gate Driver23

DRnR Driver Equivalent off-resistance 0

DRnTOTGoff RRR = Gate Off-resistance 23

Table3.4 Turn-off gate resistor sizing

Apart from the methods mentioned above, another way to avoid the spurious

turn-on is to use negative bias voltage for the off state. For the negative bias voltage of

-15V, the actual gate voltage under the extreme condition will be -11V as maximum


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31

during the off state, which is quite far from the threshold voltage of the IGBT. In the

prototype, a -15V negative bias voltage is connected to VEE, which provide enough

margin to avoid spurious turn-on by the parasitic current.

3.3.6.3Minimal switching loss constraint

There is a dilemma of how to choose proper resistance for gate resistor from

turn-on and turn-off gate resistors. Figure 3. 13 shows a way to resolve this problem by

employing a diode, which enables the gate resistor to be a different resistance depending

on on or off state; however, another simple and practical way is introduced by

calculating the gate resistor from drive side to minimize IGBT Switching Losses.

Figure 3. 13 Separate gate current paths for turning-on and turning-off

From equation (3.12) [8], a new value of gate resistance is obtained.

( ) 15 ( 15) 211

2.5

CC EE OL

OLPEAK

V V VRg

I A = = (3-13)

where VOL is low level output voltage at the peak current of 2.5A. Table 4.7 gives the

verification for the IGBT used in the prototype.

The above-described methods for sizing gate resistors are intended to approximate

phenomena of turn-on and turn-off switching time and switching losses of power IGBTs.

More accurate sizing may rely on more precise IGBT modeling and parasitic components

dependant on the layout and connection of the circuit. In the prototype, thanks to a big

error from stray inductance of wires which are used to connect drives and IGBTs, an

180 resistor has been installed to avoid dramatic oscillation in VGE. In chapter 5, a

detailed experimental study related to the gate resistor will be made.


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32


RESoffC Reverse Transfer Capacitance

(off-state)52 pF

IESC Input Capacitance 4000 pF

ceV Collector Voltage 300 V

geV Gate Voltage 3.9 V

thV Gate Threshold Voltage 3 - 6 V

Table3.5 Gate voltage spike induced by high dv/dt

Other components used in the gate drive are listed in Table 3.6.

Reference Name Type Description

U1 Dc/dc power supply VASD1-S5-D15 5V/15V

U2 Gate drive IC HCPL3120With built-in

opto-coupler

RIN Resistor 180

RG Gate resistor 180

R1 Resistor 1k

R2,R3 Resistor 3.8k

C1,C2,C3 Capacitor 10 F electrolytic

Table3.6 Component list for the IGBT gate drive

The per-phase IGBT drive schematic is shown in Figure 3. 14.


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Figure 3. 14 IGBT gate drive schematic

3.4 Energy Dissipation Subsystem

When an induction motors rotor is turning slower than the synchronous speed set

by the drives output power, the motor is transforming electrical energy obtained from the

drive into mechanical energy available at the drive shaft of the motor. This process is

referred to as motoring. When the rotor is turning faster than the synchronous speed set

by the drives output power, the motor is transforming mechanical energy available at the

drive shaft of the motor into electrical energy that can be transferred back to the drive.

This process is referred to as regeneration

Most AC PWM drives convert AC power from the fixed frequency utility grid into

DC power by means of a diode rectifier bridge or controlled SCR bridge before it is

inverted into variable frequency AC power. Diode and SCR bridges are cost effective, but

can only handle power in the motoring direction. Therefore, if the motor is regenerating,

the bridge cannot conduct the necessary negative DC current; the DC bus voltage will


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34

increase and cause an over-voltage fault at the drive. More complex bridge configurations

use SCRs or transistors that can transform DC regenerative electrical power into fixed

frequency utility electrical energy. This process is known as line regeneration.

A more cost effective solution can be provided by allowing the drive to feed the

regenerated electrical power to a resistor which transforms it into thermal energy. This

process is referred to as dynamic braking. In the prototype, a braking resistor is applied to

avoid high voltage in DC bus link during the regeneration of motor. The detailed method

on how to calculate resistance of this resistor is explained as follows.

During the braking period, the kinetic energy of the stage system will be reverted to

electric energy through the induction machine, which is shown in Figure 3. 15[3]. The

braking branch includes a voltage-controlled IGBT and a power resistor connected in

series to the dc bus. The IGBT switch will be closed and connect the braking resistor to

the dc bus when the dc voltage exceeds a threshold. The control circuit disconnects the

braking resistor when the dc voltage drops back to normal level.

Figure 3. 15 Current paths for (a) Operation mode of motoring

(b) Operation mode of generating

In order to find the resistance, following information should be gathered:


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a) Required decelerate time

b) Motor inertial and load inertia in kg-m2

c) Gear ratio

d) Motor shaft speed, torque and power profile of the drive application

Figure 3. 16 shows typical application profiles for speed, torque and power. The

following variables are defined forFigure 3. 15

( )W t = Motor shaft speed in radians per second (rps)

N= Motor shaft speed in Revolutions Per Minute (RPM)

( )T t = Motor shaft torque in Newton-meters

( )P t = Motor shaft power in watts

b = Rated angular rotational speed (rad/s)

0 = Angular rotational speed less than b (can equal 0) (rad/s)

bP = Motor shaft peak regenerative power in watts

Determine value of equation variables [9]

Step 1 Total Inertia

2( )T m L J J GR J = + (3-14)

where:

TJ = Total inertial reflected to the motor shaft (kg.m2)

mJ = Motor inertia (kg.m2)

GR = Gear ratio for any gear between motor and load

LJ = Load inertia (kg.m2)

2

20.14950.011 34000 0.107 .89

T J kg m

= + =


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37

dV =DC bus voltage (150V)

2150804

28db

R = =

From above calculation, it is obvious that the regenerating power is small.

Consequently, the braking resistor becomes large under designated voltage condition. The

reason for this is that it takes 30 second to decelerate maximum speed to zero. In order to

keep actors feel comfortable, the stage runs at a low speed (maximum 42 seconds per

revolution). Limited acceleration/deceleration speed is applied to avoid jerks for the sake

of riding safety and convertibility. The total deceleration time from permitted maximum

to zero is 30 seconds. Under this condition, most power is dissipated as IGBT switching

loss and stage friction loss. Some power is regenerated to charge the bus bulk capacitors

to make their voltage increase; however, the voltage rise is still in the inverters rating

area in this prototype. In the practical measurement, the maximum voltage rise is 5 Volts

at DC bus 150V and fast drop to 150V with the completion of deceleration. Therefore, no

braking resistors are installed in the prototype. In the future, a braking resistor could be

mounted next to motor to ensure the inverter to work stably in deceleration of the motor.

3.5 Over Current Protection

port1

GND

R105.6K

R9

10k

C7

104

C6

104

+15V

-15V

R1110K

I_protection

C8102

A3.3V

3

21

8

4

U17A

OP284_1Ia_IN

13

2

D2

A3.3V

R8

15K 5

67

U17B

Comment: OP284_1

R13

10K

R1212K

Figure 3. 17 over current censoring circuit

In Figure 3. 17, two operational amplifiers (Op amp) are employed to implement


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38

two tasks. The first one is used to scale input voltage to -1.5V~1.5V by a coefficient of

0.25. The second one will bring 1.5v offset, which scale output voltage to 0~3.3V.

Depending on input signal from current voltage transducer and anticipating trip current,

the coefficient could be modified by change R9 and R10 resistance. Figure 3. 18 gives

detailed explanation for current scaling.

Anticipating fault current Input of censoring circuit First Op-amp

Current sensor

60A(pk)

-6V

6V

coefficient

1.5V

0

-1.5V

offset

3.0V

0

Second Op-amp DSP

931

0

A/D

x0.25x0.1 +1.5V

Figure 3. 18 Current scaling for short circuit protection

After A/D conversion, a digital offset should be added in the program. Its value is

-931/2., herein the number 931 corresponds to 3V where 1024 corresponds to 3.3V in

DSPs A/D conversion. The next step is to figure out absolute value of this signal and

compare with threshold 450, which corresponds to 58A. If the input signal is larger than

threshold, it means that the short circuit happens in the main circuit and DSP will disable

all PWM outputs to shut down the inverter right away. In a commercial IGBT module, a

fault signal pin will produce fault signal when IGBTs internal circuit is exposed to

abnormalities such as over-voltage and over-current. This pin can be connected to DSP

PdpintA or Pdpint B pin. When fault signal pin carry a falling edge signal, Pdpint will be

enabled and put PWM output pins in the high-impedance state, which prevents IGBT

module from being damaged by over current and voltage.


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Chapter 4 Software Implementation

39

4.Chapter 4

Software ImplementationRelated hardware such as the inverter, driving circuits and DC link has been

described in chapter 3. Here, a software setup to implement control algorithm will be

posted. All description and discussion of the software are based on TIs (Texas

Instruments) DSP 320F-2407A CPU. A program flow chart will be presented with a

detailed explanation of crucial points to achieve the design objective.

4.1 Approaches of SV_PWM Signals:

In order to control a three-phase AC induction motor, one needs a three phase

inverter with the required DC link and driving circuits, and a digital processor that

supplies the PWM signals based on a selected control algorithm. In this chapter, we focus

on algorithm and software implementation issues.

A 3-phase AC induction motor control algorithm based on the discussed

constant /V Hz principle and the space vector PWM technique generally

contains the following steps:

Configure the timers and compare units to generate symmetric PWM outputs;

Input desired speed, use it as the command speed;

Obtain the magnitude of reference voltage vectorout

U (command voltage)

based on /V Hz profile;

Obtain the phase ofout

U based on command frequency;

Determine which sectorout

U is in;

Decomposeout

U to obtain T1, T2 and T0;


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Determine the switching pattern or sequence to be used and load the calculated

compare values into the corresponding compare registers.

The above procedure assumes that the digital signal processor has all the needed

timers and compare units with associated PWM outputs. This is true in the case of

TMS320F -2407A. The major features of the TMS320F2407A include:

TMS320F-2407A CPU core with 25nS instruction cycle time;

544 words of on-chip data/program memory, 32K words of on-chip program

ROM or Flash EEPROM, 64K words of program, 64Kwords of data and 64K words of

I/O space of address reach;

Sixteen multiplexed analog inputs 10-bit ADC core with built-in Sample and

Hold (S/H) and fast conversion time (S/H + Conversion): 375 ns

PLL, Watchdog Timer, SCI, SPI, and 41 multiplexed I/O pins;

Event Manager featuring

Two general-purpose (GP) timers;

a) Three general-purpose up and up/down timers, each with a 16-bit compare unit

capable of generating one independent PWM output;

b) Pulse-width modulation (PWM) circuits that include space vector PWM

circuits, dead-band generation units, and output logic;

c) Three 16-bit simple compare units capable of generating 4 independent PWM

outputs;

d) Three capture units

e) Quadrature encoder pulse (QEP) circuit;

TMS320F2407A has the necessary features to allow easy implementation of

different motor control algorithms and PWM techniques. For the application here, the

following set up is needed for the generation of PWM outputs:

GP Timer 1 is configured in continuous-up/down mode to generate symmetric

PWM. The three full compare units are configured in PWM mode to generate

six complementary PWM outputs.


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Once the above items are completed, all that is needed to generate the required

PWM outputs is for the application code to update the compare values based

on the discussed principle and PWM techniques.

4.2 Implementation-Open-Loop Speed Control for 3-Phase

AC Induction Motor

There are two major issues that must be resolved to implement the discussed

principle and PWM technique. One is how to generate or represent the revolving

reference voltage vector Uout given the command frequency and magnitude of the

reference voltage vector. The other is the determination of the switching pattern based on

this reference voltage vector.

4.2.1 Overview

The major features of this implementation are 16-bit integration to obtain the

frequency of the reference voltage vector, frequency-based table look-up magnitude of

the reference voltage, frequency-based table look-up SIN and COS functions, projection

of the reference voltage from _d q to _ axis, update of compare units for PWM

channel toggling sequence. GP Timer 1 is used as the time base for PWM output

generation with the Full Compare Units. The flow chart of this implementation is

illustrated in Figure 4. 1

An ADC channel is used to input the speed command. In this application, the

accuracy of speed response is not a concern. Therefore, open-loop speed control is

implemented.

The major steps involved in this implementation are:

Integrate the command speed to get the phase, theta, of the reference vector;

Determine theta, and use theta based look-up table to obtain SIN(theta) and

COS(theta) and the andcomponents of the reference voltage vector;


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4.2.2 Initialization module description

After a processor reset, the initialization module performs the following tasks:

DSP setup : core, watchdog, clocks, ADC, SCI, general purpose IO, event

manager

Variables initializations : default values

Interrupt source selection and enable

Waiting loop

The waiting loop implemented corresponds to an interruptible communication

between the DSP and a Graphical User Interface. The DSP communicates via its

asynchronous serial port to the COM port of a PC. The user can send commands via this

RS232 link and update variables and flags from the computer.

4.2.3 Interrupt module description

The interrupt module handles the whole V/F algorithm. It is periodically computed

according to a fixed PWM (pulse width modulation) period value. The choice of the

PWM frequency depends on the motor electrical constant L/R. If the PWM frequency is

too low, audible noise can be heard from the motor. Usually, PWM frequencies are in the

range of 20 kHz. In this project, a PWM frequency of 10 kHz has been chosen. In Figure

4. 2 , the sampling period T of 100 s (10kHz) is established by setting the timer period

T1PER to 2000 (PWMPRD=2000). This timer is set in up-down count mode and

generates a periodical interrupt on T1 underflow event. The goal of the interrupt module

is to update the stator voltage reference and to ensure the regulation of rotor mechanical

speed.


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Figure 4. 2 Software flowchart and timing

4.2.4 Generation of sine and cosine

The Park-1

uses the value of the rotor electrical position in order to handle a rotating

frame _d q axis projection in a rotating frame _ axis. The electrical position is

not directly used in this transforms but the sine and cosine values of this electrical

position.

To obtain both sine and cosine from the electrical angle, a sine look-up table has

been implemented. The table contains 256 words to represent sine values of electrical

angles in the range [0;360]. As a result, the resolution one

is limited

to360/ 256 1.40625o= .

e = electrical angle / 360 (with e in the range [0;1FFFh])

e varies from 0 to 8191. As only 256 words are available to represent this range,

e is divided by 32 and stored into the variable index that will be used to address the

lookup table.


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The content of the table row pointed by the index is fetched in indirect addressing

mode via AR5 auxiliary register (Figure 4. 3). This content coded in Q12 is stored in the

variable sin that will be used in the Park-1

transforms.

Note that to get the cosine value of the electrical angle, 90 is added toe

. This

operation corresponds to add 64 (256/4) to the value of index. The result is stored in the

variablecos .

Figure 4. 3 Sin, Cos calculation using the sine look-up table

4.2.5 Space vector pulse width modulationThe Space Vector Modulation is used to generate the voltages applied to the stator

phases. It uses a special scheme to switch the power transistors to generate sinusoidal

currents in the stator phases [10].

This switching scheme comes from the translation of the ( , ) voltage reference

vector into an amount of time of commutation (on/off) for each power transistors. In

order to understand some of the assumptions made in the case of the rectified voltage, a

brief description of three phase systems is described in the following section. .


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4.2.5.1Expression of the 3 phase voltages (phase to neutral)

Previously, the method used to generate a rotating magnetic field was to use three

independent voltage sources that were dephased from 120 degrees from one another.

Figure 4. 4 3-phase equilibrium system

In this standard three-phased system (Figure 4. 4), 3 sinusoidal voltages are applied

to each of the motor phases to generate the sinusoidal currents. These voltages can be

expressed as follows:

2 cos( * )oa eV V t= (4-1)

)3

2*cos(2

= tVV eob (4-2)

42 cos( * )

3oc e

V V t

= (4-3)

In order to calculate the phase to neutral voltages(respectively Van, Vbn, Bcn) from

the applied source voltages( respectively Voa, Vob, Voc), the assumption is made that the

system is equilibrated is made. This leads to the following equations:

1*on oaV V Z I = + (4-4)

2*on obV V Z I = + (4-5)

3*on ocV V Z I = + (4-6)


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then

)(**3 321 IIIZVVVV ocoboaon +++++= ; where 0321 =++ III

As Von is now expressed by a combination of )*cos(2 tVV eoa = the source

voltages the phase to neutral voltage for phase A can be calculated as:

ocoboaoaocoboaoaonVVVVVVVVVVan 3/13/13/2))(3/1( ++=++==

the same calculation is made for the three phases leading to:

1/ 3(2 )an ao bo coV V V V = (4-7)

1/ 3(2 )bn bo co aoV V V V = (4-8)

1/ 3(2 )cn co ao boV V V V = (4-9)

4.2.5.2Application to the static power bridge

In the case of a static power bridge, sinusoidal voltage sources are not used. They

are replaced by 6 power transistors that act as on/off switches to the rectified DC bus

voltage. The goal is to recreate a sinusoidal current in the coils to generate the rotating

field. Owing to the inductive nature of the phases, a pseudo sinusoidal current is created

by modulating the duty cycle of the power switches.

In Figure 4. 5, the power transistors are activated by the signals (a,b,c) and their

complemented values.

Figure 4. 5 Power bridge


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Only eight combinations of the switches are possible with this configuration (Table

4.1). The applied voltages are referenced to the virtual middle point of rectified voltage.

A B C VAO VBO VCO

0 0 0 -VDC/2 - VDC/2 - VDC/2

0 0 1 - VDC/2 - VDC/2 +VDC/2

0 1 0 -VDC/2 +VDC/2 -VDC/2

0 1 1 -VDC/2 +VDC/2 +VDC/2

1 0 0 +VDC/2 -VDC/2 -VDC/2

1 0 1 +VDC/2 -VDC/2 +VDC/2

1 1 0 +VDC/2 +VDC/2 -VDC/2

1 1 1 +VDC/2 +VDC/2 +VDC/2

Table 4.1 Power bridge output voltages (VAO, VBO, VCO)

Because of the equations:

)2(3/1 coboaoan VVVV =

)2(3/1 aocobobn VVVV =

)2(3/1 boaococn VVVV =

It is possible to express each phase to neutral voltages, for every combination of the

power transistors as listed in Table 4.2.

4.2.5.3Expression of the stator voltages in the ( ), frame

This voltage reference is expressed in the ( ), frame. To make the relationship

between the 3 phase voltages (VAN, VBN and VCN) and the voltage reference vector, the 3

phase voltages are also projected in the ( ), frame.


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A B C VAN VBN VCN

0 0 0 0 0 0

0 0 1 - VDC/3 - VDC/3 2VDC/3

0 1 0 - VDC/3 2VDC/3 - VDC/3

0 1 1 -2VDC/3 VDC/3 VDC/3

1 0 0 2VDC/3 - VDC/3 - VDC/3

1 0 1 VDC/3 -2VDC/3 VDC/3

1 1 0 VDC/3 VDC/3 -2VDC/3

1 1 1 0 0 0

Table 4.2 Power bridge output voltages (VAN, VBN, VCN)

The expression of the 3 phase voltages in the ( ), frame is given by the general

Clarke transform equation:

1 11

2 2 2

3 3 30

2 2

AN

s

BN

s

CN

VV

VV

V

=

(4-10)

Since only 8 combinations are possible for the power switches (Table 4.3), SV

andS

V can also take only a finite number of values in the ( ), frame according to the

status of the transistor command signals ( ), ,a b c .

)010(2V

)101(5V

)100(4V)011(3V

)001(1V

)000(0V)111(7V

)110(6V

02

06

01

03

04

05

Figure 4. 6 Stator voltages


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The eight voltage vectors defined by the combination of the switches are

represented in Figure 4. 6.

A B C V V0 0 0 0 0 0V

0 0 1 3

DCV 3

DCV 1

ubc_2008_spring_zhang_yong

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