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LIBRARY
Michigan State
University

This is to certify that the
dissertation entitled

A NOVEL POLE-CHANGING INDUCTION MOTOR DRIVE

presented by

JOHN WILLIAM KELLY

has been accepted towards fulfillment
of the requirements for the

Doctoral degree in Electrical Enflteering

 

 

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DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5/08 K:lProj/Acc&Pres/C IRC/DateDue. indd

A NOVEL CONTROL SCHEME FOR A POLE-CHANGING
INDUCTION MOTOR DRIVE

By

John William Kelly

A DISSERTATION

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Electrical Engineering

2007

ABSTRACT

A NOVEL CONTROL SCHEME FOR A POLE-CHANGIN G
INDUCTION MOTOR DRIVE

By

John William Kelly

For applications, such as the propulsion of a hybrid vehicle, a novel pole-changing in-
duction motor drive is proposed. A pole-changing control scheme which allows continuously
operation and torque production over the drive’s entire speed/torque range was developed.
The scheme is based on the concept of the pole-changing machine being simultaneously op-
erated as two independent motors. From the nine stator winding machine, the two possible
configurations are, the 9-phase/4-pole and 3-phase/12-pole motors.

For 9-phase operation, a generalized scheme for n-phase Space Vector PWM was devel-
oped. For field oriented control, a unique coordinate transformation from a 9-phase symmet-
rical system to an orthogonal system was developed. The inverse transformation also was

developed based on the constraints which minimized core and winding losses

© 2007
John William Kelly
All Rights Reserved

To my parents, William and Patricia Kelly

iv

ACKNOWLEDGMENTS

I would like to express my gratitude and thanks to my advisor Professor Elias Strangas for
his guidance, encouragement, and support. I would also like to thank Professor Feng Pang,
Hassan Khalil, John Miller, and Ranjan Mukheijee for their time and effort in being part of
my committee.

I would like to extend special thanks to those at Ford Motor Company’s Research Labora-
tories who helped make this research possible. Also, I would like to thank my colleague Wes
Zanardelli and Mike Degner for their support. I would also like to thank the members of the
department whose help was much appreciated, including Brain Wright, Roxanne Peacock and
Sheryl Hulet.

Finally, I owe special thanks to my parents, William and Patricia Kelly, whose support,

prayers and encouragement helped make my graduate studies possible.

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

1 Introduction

3

1.1
1.2
1.3

1.4

Motivation and Objectives ...........................
Previous Work: Starter-Alternator Machine ..................
Pole-changing Machines ............................
1.3.1 Multi-Stator Windings .........................
1.3.2 Reconfigurable Stator Winding ....................
Objectives and Thesis Outline .........................

Nine Leg Inverter

2.1
2.2

2.3

2.4

Introduction ...................................
Analysis of a N inc-Leg Inverter ........................
2.2.1 Load Circuit Analysis .........................
2.2.2 n-Step Inverter Operation .......................
2.2.3 Inverter Switching Efficiency .....................
2.2.4 Harmonic Content ...........................
Extension of Space Vector Theory to n Phases .................
2.3.1 Three Phase Space-Vectors .......................
2.3.2 Nine Phase Space-Vector ........................
Space-Vector PWM implementation ......................
2.4.1 Three-Phase Space-Vector PWM ....................
2.4.2 Extension of three-phase SVPWM to n-Phase SVPWM .......
2.4.3 Proposed n-phase SVPWM Techniques ................
2.4.4 Low Order Harmonic Injection .....................
2.4.5 SVPWM Using Maximum Subsets ..................
2.4.6 Modified SVPWM With Adjusted Vzm ................
2.4.7 Conclusions ...............................

Analysis of the Experimental Pole-Changing Induction Machine

3.1
3.2

3.3

Introduction ...................................
Three Possible Stator Winding Configurations .................
3.2.1 3-phase 12-pole Configuration .....................
3.2.2 3phase-4pole Configuration ......................
3.2.3 9-phase 4—pole Configuration ......................
3.2.4 Comparison Between the 3 configurations ...............
Steady State Model Development ........................
3.3.1 Equivalent Rotor Circuit of an Induction Motor ............

vi

vii

viii

(It-#WUJNr-II-I

00°“

10
11
13
13
14
14
15
17
17
18
21
22
22
23
24

26
26
27
28
32
35
38
39
39

3.3.2 Equivalent Circuit of an Induction Motor ...............
3.3.3 Equivalent Circuit Per-Phase Parameters ................
3.3.4 Calculated Parameters .........................

4 Coordinate "II-ansformation

4. 1 Introduction ...................................
4.2 3-Phase 12-Pole: Park-Clark Coordinate Transformation ...........
4.3 9-Phase 4-Pole: Coordinate Transformation ..................
4.4 Development of Coordinate Transformation ..................
4.5 Pole-Changing Transition 4-pole and 12-pole Operation ............

4.5.1 Simultaneous Realization of £4,734 and idqsn ..............

4.5.2 Simultaneous Extraction of idq34 and idq312 ..............

4.5.3 Example of Extraction of iqu4 and idqm from Four Stator Windings .
4.6 Conclusions ...................................

5 Modeling and Simulations

5.1 Introduction ...................................
5.2 Novel Induction Motor Model .........................
5.2.1 Classical AC Theory: Generalized Reference Frame .........
5.2.2 Inductance Calculation .........................

5.2.3 Machine Model in Stator Reference Frame ..............
5.3 Simulation Results ...............................
5.3.1 Simulation Simulink Model ......................
5.3.2 Model Validation of Pole-changing Machine .............
5.3.3 Instantaneous Pole-changing During Steady State Operation .....
5.3.4 Instantaneous Pole-changing During Acceleration ...........
5.3.5 Gradual Pole-changing .........................
5.4 Conclusions ...................................

6 Experimental Setup: Hardware and Software
6.1 Introduction ...................................
6.2 Hardware Setup .................................
6.2.1 Inverter .................................

6.2.2 FPGA/ADC Interface ..........................
6.3 Software .....................................
6.4 Power ......................................

7 Control of the Pole-Changing Motor
7.1 Introduction ...................................
7.2 Review of Rotor Flux Oriented Control (R-FOC) of Induction Motors . . . .
7.2.1 Current Loops .............................
7.2.2 Performance Results of the 12-pole and 4-pole Motor .........
7.2.3 Experimental Results of 4-2 Coordinate Transformation .......

vii

41
44
48

55
55
56
57
58
6O
61
61
63
63

65
65
66
66
67
70
7 1.
72
72
74
74
77
79

82
82
83
83
83
86
87

89
89
90
91
94
96

7.3 Simultaneous Operation of 12/4-pole Motor .................. 99

7.3.1 Dual FOC ................................ 100

7.3.2 Experimental Results: Controlling idq4 and idQlQ ........... 102

7.4 Pole-Changing Transition: Flux Control .................... 105
7.5 Possible Implementation Strategy for Novel Pole-changing Control in a Vehicle 107

8 Conclusions 110
8.1 Accomplishments ................................ 110

8.2 Future Work ................................... 111
BIBLIOGRAPHY 113

viii

2.1
2.2

3.1
3.2
3.3
3.4
3.5

LIST OF TABLES

Equivalent Circuit Comparison ......................... 1 1
Harmonic Content of 18-step mode Voltage Waveforms ............ 14
Locked-Rotor Test 4-pole/9-phase ....................... 46
Locked-Rotor Test 12-pole/3-phase ....................... 47
Measured Parameters .............................. 48
Measured versus Calculated Inductances for 4-pole/9-phase configuration . . 54
Measured versus Calculated Inductances for 12-pole/3-phase configuration . 54

ix

LIST OF FIGURES

1.1 Toroidally wound Induction Machine .......................................................................... 3
1.2 Series connected phase coils resulting in 8-poles ......................................................... 4
1.3 Series-parallel connected phase coils resulting in 4—poles ........................................... 5
2.1 Nine-leg inverter .......................................................................................................... 9
2.2 The four equivalent load configurations of a nine-leg inverter ................................... 10
2.3 Phase voltages of a three-phase inverter ..................................................................... 11

2.4 4-5 eighteen-step operation: gating signals (upper switches)
and the resulting phase voltages ............................................................................ 12

2.5 2-7 eighteen-step operation: gating signals (upper switches)

and one of the resulting phase voltages ................................................................ 13
2.6 Phase voltages of a 3-phase inverter and resultant voltage space-vector ..................... 14
2.7 Nine-phase voltage space-vectors ............................................................................... 15
2.8 Vector addition of voltage phase space-vectors .......................................................... 16
2.9 The four bounding voltage space-vector subsets of a nine-phase system .................... 16
2.10 Three phase Space Vector PWM ............................................................................... 17
2.11 The Space Vector PWM Realization of the vector 1.0ej3 Ozt ..................................... 18
2.12 Vector sequence for the realization of the voltage space vector 1.06j30i ................ 19

2.13 a) Windings of a 3/9 phase machine in 3-phase operation b) 9-phase
operation c) Windings of a conventional 3-phase machine ................................... 20

2.14 Four phase voltages of a 9-phase load generated by a 9-phase

SVPWM scheme ........................................................................................................ 21
2.15 Voltage space—vector realization using vectors from 45 max subset

and zero vectors ......................................................................................................... 22
2.16 Switching schemes for adjacent sector regions .......................................................... 24
2.17 The vector sequence for realizing Vzero .................................................................... 25

3.1 The coil arrangements and applied voltages for the 3 motor configurations .............. 27

3.2 Coil arrangement, b) winding density n and c) resulting mmf F ................................. 28
3.3 The Fourier Series Approx (k = 100; 1) of Winding Density ..................................... 29
3.4 The Fourier series Approx (k = 100; 1) of the air-gap mmf ........................................ 30
3.5 Instantaneous air-gap mmf and b) resulting Fourier Transform ................................. 31
3.6 3-D Fourier transform with respect to time and stator position .................................. 32
3.7 Coils arrangement, b) winding density n and c) resulting mmf F ................................ 32
3.8 The Fourier Series Approx (k = 1; 100) of the winding density ................................. 33
3.9 The Fourier Series Approx (k = 1; 100) of the air-gap mmf ....................................... 33
3.10 Instantaneous air-gap mmf and b) resulting Fourier Transform ................................ 34
3.11 3-D Fourier Transform with respect to time and stator position ............................... 35
3.12 Coils arrangement, b) winding density n and c) resulting mmf F .............................. 35
3.13 Fourier Series (k = 1; 100) of the winding density ..................................................... 36
3.14 Fourier Series (k = 100) of the air-gap mmf 9phase-4pole ...................................... 36
3.15 Instantaneous Stator Air-Gap MMF and b) Fourier Transform ................................. 37
3.16 3-D FFT of the 9-phase/4-pole configuration ........................................................... 38
3.17 Comparison of the fundamental air-gap mmf ........................................................... 39
3.18 Stator and Rotor Magnetic Fields ............................................................................... 40
3.19 Per Phase Equivalent Model ....................................................................................... 42
3.20 No-Load Equivalent Model ........................................................................................ 42
3.21 Locked-Rotor Equivalent Model ................................................................................ 43
3.22 The phase voltage and current: (a) 12pole-3phase (b) 4pole-9phase ........................ 44
3.23 The Magnetization Curve for the 4pole-9phase Motor ............................................. 45
3.24 The Magnetization Curve for the 12pole-3phase Motor ........................................... 45

xi

3.25 Total, Real Power and pf from Locked-Rotor 12pole-3phase .................................. 47
3.26 Slot and End-tum Flux Leakage ................................................................................ 48
3.27 Slot Geometry a) stator slot b) rotor slot .................................................................... 49

3.28 Stator Top Flux Leakage a) Single Conductor b) Conductor

Bundle model c) Dimension of actual conductor bundle ........................................ 51
3.29 Rotor Ring a) Leakage Flux b) Dimension ............................................................... 52
4.1 9-phase symmetrical components ................................................................................. 58
4.2 Three 3-phase axes reference frames with stationary currents .................................... 59
4.3 Example of decoupling idq3 and idq9 from 4 stator windings ................................... 63
5.1 Stator Winding Conductor Density for a 4-pole and 12-pole Induction Motor. ......... 67
5.2 Location of one of the nine stator windings ................................................................. 68
5.3 Conductor Density of one of the nine stator windings ................................................. 68

5.4 Conductor density waveform resulting from the first four terms

of the Fourier series. ..................................................................................................... 69
5.5 Experimental Induction Motor Model: Two Sets of Applied Voltages ....................... 72
5.6 Comparison of Speed and Torque During Free Acceleration ...................................... 73

5.7 Open-loop, Speed-torque characteristics: Comparison of Experimental
and Simulation Results ................................................................................................ 73

5.8 Pole-Changing from 6-pole to 2-pole at t=3seconds ................................................... 75

5.9 Pole-Changing fiom 6-pole to 2-pole when speed reaches 118
radians per second ........................................................................................................ 76

5.10 Comparison of Speed, Torque and Current for different voltage

combinations ............................................................................................................... 78
5.11 Flux Distribution: Flux 2D ......................................................................................... 80
6.1 Overall Experimental Setup ........................................................................................ 83
6.2 Overall Experimental Setup ........................................................................................ 83

xii

6.3 9-1eg Inverter ................................................................................................................ 84

6.4 FPGA/ADC PWM Functionality Block Diagram ....................................................... 85
6.5 Sofiware Organization .................................................................................................. 87
6.6 Experimental Setup Power Diagram ............................................................................ 88
7.1 Stator, Rotor and Flux currents .................................................................................... 90
7.2 Simple Current Control Loop ....................................................................................... 92
7.3 Iq Current Control Loop with Anti-windup ................................................................. 93
7.4 Magnetizing current imr and Rotor Flux Model .......................................................... 94
7.5 12-pole and 4-pole id Control ...................................................................................... 95
7.6 Id frequency response (between 60-70Hz ) .................................................................. 96
7.7 Motor performance: Speed Response .......................................................................... 97
7.8 4-2 Coordinate Transformation ................................................................................... 98

7.9 Reduced Coordinate Transformation: Orthogonal Stator

Current Component to and ib ...................................................................................... 99
7.10 Dual 12-pole and 4-pole Reference Frames .............................................................. 100
7.11 Dual machine control scheme .................................................................................... 102
7.12 Torque, id4, step command ........................................................................................ 103
7.13 4-pole and 12-pole alternating torque commands resulting in

constant shaft torque ................................................................................................... 104
7.14 qu12 vs qu4 ............................................................................................................. 105
7.15 Pole-changing control scheme .................................................................................... 105
7.16 Gradually adjusting id4 and id12 ............................................................................... 106
7.17 Constant torque and power regions ............................................................................ 107
7.18 Control States with field weakening .......................................................................... 108

xiii

7.19 Speed comparison (simulation): 4pole operation, instantaneous
pole change, controlled pole change ......................................................................... 109

7.20 Torque Comparison (simulation): 3) 4pole operation b) instantaneous
pole change 12 to 4 c) controlled pole change .......................................................... 109

xiv

CHAPTER 1

Introduction

1.1 Motivation and Objectives

This work is an extension of work conducted on the development of a toroidally wound,
pole reconfigurable induction machine. Ford Motor Company designed this machine to be
the starter/alternator for 42Volt passenger vehicles. The unique machine has nine separately
wound, equally distributed stator windings each attached to a terminal of a 9-leg inverter. This
system allows for grouping coils into two different arrangements resulting in a motor with two
possible pole numbers. In addition, to being used for the starter/alternator application, this
system can be utilized as an induction motor drive with extended capability.

For applications such as propulsion, extended speed/torque capabilities of the drive system
are desirable. Increased starting torque allows for faster acceleration, while increase speed
allows for higher cruising velocity. Typically, these enhanced capabilities are achieved with
conventional electric motors with the addition of a mechanical transmission and or motor
field weakening control. This is at the cost of overall efficiency due to increased weight and
gear inefficiency. Likewise, field weakening decreases efficiency with an increase in winding
losses.

The starter/alternator was designed for high starting torque and high speeds; however,
it was not designed for continuous operation over its extended speed/torque range. Pole-

changing was to occur once the windings had been de-energized. The objective of the work

presented here is to develop a pole-changing control scheme for the existing starter/alternator,
resulting in a drive system that can operate continuously and supply torque over its entire

speed/torque range.

1.2 Previous Work: Starter-Alternator Machine

A toroidally wound, pole-phase modulated induction machine was designed by Miller and
Ostovic [16],[15] for vehicle altemator/starter applications. The integrated starter-generator
design was in response to the proposed 42V ISO standard for passenger automobiles [5].
Mounted directly to the internal combustion motor, the toroidal design was intended to meet
the strict space constraints of the engine compartment. The volume of a toroidally wound
machine is smaller than an equivalently rated lap wound motor, due to the elimination of end
turns.

However, there are two significant drawbacks to using the toroidal design: 1) poor stator
winding thermal dissipation and, 2) flux leakage to the housing. Since the stator windings
are wrapped around the stator, there is no direct, metal to metal, thermal path from the stator
to the housing. Therefore, the stator was designed to have wide mounting tabs that not only
secured the stator to the housing, but created equally spaced, low resistance thermal paths
around the motor. In addition, the space between the stator windings and housing was filled
with a special thermal conductive resin from Dow Corning. Finally, the housing contained
a water jacket. At first, the housing was made of steel. However, the steel was replaced by
aluminium, significantly reducing the flux leakage to the housing, figure 1.1. The machine was
designed to operate as a 3-phase/4-pole alternator and a 3-phase/12-pole starter. Depending
on the application, the stator coils were grouped accordingly by a 9-leg inverter. Changing the
number of poles of a machine by changing the number of applied phases is called pole-phase
modulation (PPM) [16]. In chapter 3, the machine design is presented in detail.

Extensive work was conducted by Stefanovic [23]: l) implementation of PPM 2) the study
of transient effects occurring during motor-generator transition, 3) evaluation of stability of a

PPM system in regards to sub-harmonics resulting from phase imbalances, and 4) analysis of

 

Figure 1.1: Toroidally wound Induction Machine.

offset and sensor error.

1.3 Pole-changing Machines

There are two predominant techniques for changing the number of poles for an induction
machine. The first technique requires a specially-designed reconfigurable stator winding. The
number of poles is changed by rearranging the coils of the winding. The second technique
also requires an unconventional machine, one with two stator windings. One winding is used

for low speed operation, while the other winding is used for high speed operation.

1.3.1 Multi-Stator Windings

For multi—stator induction machines, the simplest mode of operation is energizing one winding
set at a time. The windings are spaced to achieve the desired pole number. However, Osama
and Lipo showed that increased efficiency and copper utilization can be achieved by energiz-
ing both winding sets simultaneously, [18]. This dual stator winding induction machine can
operate either as a 2-pole or 4-pole machine. The coils of the windings are stacked in the

stator slots, forming a double layer winding distribution. Each of the two 3-phase windings is

controlled by two separate three-phase inverters. For 4-pole operation, the phase sequence for
both inverters is 2'0, 2],, ic. The number of poles is decreased by half, by phase shifting the cur-
rents in one inverter. While the outputs of one inverter remain the same, 2'0, ib, z‘c, the second
inverter output is changed to —i.,, —ic, — 2],. For starting and low speed operation the machine
is configured for 4-poles. Once the break-down torque is reached, the machine is reconfigured

for 2-pole operation.

1.3.2 Reconfigurable Stator Winding

Early pole-changing machines used mechanical contactors to reconfigure the coil arrangement
to obtain the desired pole number [22]. For example, a 2:1 pole ratio is possible with phase
coils that can be rearranged either in parallel or series-parallel connection. Figure 1.2 shows a

winding with its coils connected in series. This arrangement sets up 8 poles around the stator.

 

 

 

 

a, {é—phase-belt C1
C‘ %C C
1 2: . 3 4 C3
- 4: it?” - V+ C4
02
, JJ

 

 

neutral

 

I l
3phase Power

supply

 

 

 

 

Figure 1.2: Series connected phase coils resulting in 8-poles.

Changing the state of the switches rearranges the windings into a 4-pole configuration as
shown in figure 1.3.

The switching changes the number of adjacent coils, effectively changing the length of
the phase-belt. In figure 1.3 there are two adjacent coils within the same phase in the 4-pole
configuration; as a result the phase-belt width is doubled. By doubling the phase-belt width,
the number of poles is reduced by half.

A second technique for reconfiguring the stator windings, by Rawcliffe and J ayawant [21],

adjusts the phase-belt by a factor of three. This specially designed 3:1 pole induction machine

a; ge-phase-belt

C C‘ §C C
- 1 fi- -§ 3++ 4- C1 CZ
v 1 p 5 C3 C4

‘1 ‘1... “ ‘V

l l
3phase Power

supply

 

 

 

 

 

 

 

 

 

 

 

Figure 1.3: Series-parallel connected phase coils resulting in 4-poles.

has 18 leads, with 9 equally spaced phase windings. Arranging the 9 windings in a series-
delta configuration results in a 2-pole machine. The phase-belt span for this arrangement is 60
electrical degrees. The number of poles for this machine can be switched from two to six by
adjusting the phase-belt from 60 to 20 electrical degrees, which is accomplished by arranging

the windings in a series-wye pattern.

1.4 Objectives and Thesis Outline

The overall objective of this work is the development of a drive control scheme which re-
sults in continuous operation and smooth torque production during pole-changing, utilizing
the starter/alternator motor and inverter. This is accomplished by controlling the induction
machine as two motors, a 3-phase/12-pole and a 9—phase/4pole motor. Energized by the
same stator windings, both motors operate independently and simultaneously during the pole-
changing transition. To realize this novel pole-changing control scheme several obstacles have
to be overcome. In chapters 2 through 6 these obstacles are detailed, and novel solutions are
presented.

One of the first challenges is developing a Pulse Width Modulation (PWM) inverter switch-
ing scheme for 9-phase operation of the motor. Very little research has been conducted on sys-
tems with more than three phases. In chapter 2, the conventional 3-phase Space Vector Pulse

Width Modulation (SVPWM) switching scheme is extended for 9-phase systems. A gener-

 

alized SVPWM algorithm is also developed for n-phase systems. In addition, an analysis is
conducted on the operation of the 9-leg inverter of the starter/alternator system, resulting in all
512 switching states. By choosing switching states that result in lower switching losses, sev-
eral modified 9-phase Space Vector Pulse Width Modulation (SVPWM) switching schemes
are developed.

Knowledge of the air-gap flux is pertinent in the pole-changing scheme developed in chap-
ter 7. As a result, the magnetomotive force (MMF) of both the 12-pole/3-phase and 4-pole/9-
phase motors is studied in chapter 3. The MMF harmonic content of both configurations is
presented.

Since the starter/alternator was originally intended a 3-phase system, 9-phase motor pa-
rameters did not exist. In the second part of chapter 3, the motor parameters of both config-
urations are analytically and experimentally determined. These values are used in the control
of the machine in chapter 7.

Rotor Flux Field Orientated Control (R-FOC) is the basis of the novel, drive control
scheme of chapter 7. For conventional R-FOC, machine variables, i.e. current and volt-
ages, are mapped between the symmetrical 3-phase coordinate system and the imaginary-real
coordinate system using Parks Transformation [13]. For electrically balanced systems, the
transformation between the symmetrical 3—phase and 2—phase system is unique. For field ori-
entation control of the 9-phase/4-pole motor, a method for choosing a transformation between
the 9-phase symmetrical and imaginary-real coordinate systems is developed in chapter 4.
With the objective of equalizing the current density around the stator and decreasing wind-
ing loses, a coordinate transformation for the 9-phase/4-pole motor is developed. However,
the real benefit of this transformation is the decoupling of the controls of both motors when
operated simultaneously.

In order to evaluate the drive control scheme and to study torque and current transients dur-
ing pole-changing, an unconventional induction motor plant model is developed. Transients
resulting from pole-changing can not be simulated using classical induction motor modeling.

Instead, in chapter 5, a model is developed using fundamental electromagnetics. The machine

inductances are developed from the Fourier series of the actual, non-sinusoidal, stator winding
distribution.

For validation, a complete drive system, including a field programable gate array (FPGA)
IO/SVPWM processor, was designed and built for this work. Chapter 6 describes the software
architecture, which was also developed for this work.

Finally, chapter 7 details the operation of the newly developed drive. First, current and
speed control are demonstrated for both the 4-pole/9-phase and 12-pole/3-phase motor con-
figurations. The novel drive control scheme presented here is based on controlling the machine
as two independent motors using the same stator windings and producing torque simultane-
ously. The flux and electromagnetic torque produced by both motors are controlled indepen-
dently. During the pole transition, the orthogonal current sets of both the 9-phase/4-pole and
3-phase/12-pole motors are controlled to produce the necessary flux to create a smooth, con-
stant torque and avoid saturation. Both simulated and experimental data are presented. Finally,
an overall torque management strategy is presented. This strategy is used to determine when

and if pole-changing is necessary.

CHAPTER 2

Nine Leg Inverter

2.1 Introduction

The 3-leg inverter is the most commonly used inverter to power AC machines; however, there
are applications where an n-leg, n-phase (n > 3) inverter is needed. One such application is
pole-phase modulation control of an induction motor. Pole-phase modulation can extend the
speed-torque range of an induction motor by adjusting the pole-phase ratio. For example, a
nine-phase, symmetrically wound induction machine can operate as either a four- or twelve-
pole machine. This is accomplished by reconfiguring the nine-leg inverter as either a nine-
phase or a three-phase voltage source [9]. Extended speed-torque range is desired for several
automotive induction motor applications. This chapter will provide a comprehensive analysis
of a multi-leg, multi-phase inverter and propose techniques for its implementation.

First, the n-leg inverter will be examined in terms of the load equivalent circuit during a
27r/n switching period. Unlike the three—phase inverter, which has only one load equivalent
circuit, an n-leg inverter has (n - 1) / 2 load equivalent circuits. Each one of these equivalent
circuits can be operated in a n-step mode to produce a unique discrete AC or ‘stair-step’
voltage waveform. These waveforms differ in terms of harmonic content and magnitude of
the fundamental component. As shown by Holtz [6], the fundamental component of the three-
phase 6-step voltage waveform is 2Vdc / 7r. On the other hand, a nine-phase inverter has four

different such voltage waveforms, with fundamental components of 0.64Vdc, 0.56Vdc, 0.41Vdc,

0.22Vdc.

For most electrical machines, the windings are assumed to be sinusoidally distributed in
the stator. Voltage space-vectors are defined based on the voltages applied to the windings.
For the conventional three-phase inverter, connected to an electrical machine, there are eight
space-vectors possible. For a n-leg, inverter connected to a n-phase machine, there are 2"
possible space-vectors.

The implementation of PWM in a multi-leg, multi-phase inverter is examined. In partic-
ular, a generalized implementation method for Space-Vector PWM (SVPWM) is presented
[12],[7]. The theory of Space-Vector PWM and its implementation through the Unified the-
ory [2] are extended to many phases. Additional novel algorithms, particular to multi-phase
machines, are presented and compared.

Throughout this chapter, a nine—leg, nine-phase inverter will be used as a practical example.

In the final section, experimental data from a nine-phase SVPWM system will be presented.

2.2 Analysis of a Nine-Leg Inverter

The nine-leg inverter in figure 2.1 requires eighteen gating signals, gl-g18. The gating com-
bination determines the phase voltage across each of the nine separate loads, which are con-

nected at a point to form a star.

VdJZ‘L
91 g 99
VdJZ-I-
912 916

ib icz id Li: 'fz lg: '11
z Iaz$z 2232 z

 

 

 

 

 

4w.

Figure 2.1: Nine-leg inverter

Depending on the gating pattern, the nine phase loads can form four different equivalent

 

circuits. For example, when the gating pattern is [91, 93, 95, g7, 918, 92, 94, 96, 98] the load
equivalent circuit consists of a group of four parallel impedances in series with a group of five

parallel impedances as shown in Figure 2.2-a.

 

 

 

 

 

 

 

V
a) 4-5 Configuration b) 3-6 Configuration

 

 

 

 

 

 

o) 2-7 Configuration d) 1—8 Configuration

Figure 2.2: The four equivalent load configurations of a nine-leg inverter

Likewise, the 3-6 equivalent circuit configuration shown in figure 2.2-b, is formed by three
parallel impedances in series with a group of six parallel impedances. One of the possible
inverter gating patterns for this case is [91, 93, 95, 916, 918, 92, 94, 98] or, in terms of energized
inverter legs, [11100000] ,where ‘1’ represents the upper switch of the inverter leg closed and
the lower switch open. The other two possibilities are the 2-7 and the 1-8 configuration, figures

2.2-c,d.

2.2.1 Load Circuit Analysis

Table 2.1 shows the equivalent impedance, source current and the maximum phase current for
the four different load circuits. The corresponding quantities for a three-phase inverter were
included for comparison. Of the four possible load circuit configurations, the 4-5 configuration
results in maximum phase current and the smallest ratio of phase current to source current. For
the 1-8 configuration, one inverter leg carries the entire source current, while the other eight

legs carry only 1 / 8th of the total current.

10

 

 

 

 

 

 

 

Configuration Equivalent Equivalent Mithum [Ratio 2
9 phase Impedance Current ase phase max.
- Current / l
inverter total

92 =
4_5 A0 0.452 20 Va%z 5Va%z 025
3-6 lOZ/20 =0.52 18V%Z 6V%Z 0.33
92 =
2_7 /4 0.642 14Vd%z 7V%Z 0.5
- = V V
18 9% 1.1252 3 dc9z 8 dcgz 1.0
3 phase
32 = 6Vd 6V dc .
inverter A 1'52 c 92 AZ 1 0

 

 

 

 

 

 

Table 2.1: Equivalent Circuit Comparison

2.2.2 n-Step Inverter Operation

In a three-phase inverter operating in six-step mode, switching states are changed every sixth
of a cycle. The four potential phase voltage levels are Ith / 3 and 3:2Va;C / 3. The sequence
of the six switching states is such that only one switch changes state. This sequence produces
three phase voltages that are displaced 120°and that appear in ‘stair-step’ shape, as shown in

figure 2.3. For eighteen-step mode, the nine-leg inverter changes switching states every eigh-

 

 

 

 

'Vdc/3 _|—’_i
-2Vd./3

'Vdc/3 i_l—l__i
-2Vdcl3

””3 J Ll,
-2Vd./3

 

Figure 2.3: Phase voltages of a three-phase inverter

11

teenth of a cycle. In order to produce nine symmetrical phase voltages, the nine-leg inverter
is restricted to operate in one of the four configurations during the complete cycle. This is
because a single-level inverter can only produce four different voltage levels during a switch-
ing interval. Each of the four possible load circuit configurations produce only four distinct
voltage levels. For example, the 4-5 configuration results in phase voltage levels of i4/9Vdc
and i5/9Vdc. Figure 2.4 shows the upper gating signals for eighteen-step operation in the 4-5

configuration, along with the resulting nine phase voltages, (Va...V,-).

 

 

9111111111onnnnn0n

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PhaseA .l'\.l'LI'\.I‘I.l
930111111111 oooooo
'4V°°’9 LJ'IJ'LI‘LI'I
95 0011111111100000 -5Vdo/9
97 0000011111111100019 P113893 l.rLI'I.l'l.I'I.|
g9000000011111111100 -4VaJ9J_I l
'5VdJ9
.J. .
m1ooooooooo TTTTTTTr :
l
l
i

9131' 00009000011111”

 

Phase I

i

f.

g17111111000000000 T'T‘ -5VdJ9

 

915 TTT ooooooooo‘ TTTT‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.4: 4-5 eighteen-step operation: gating signals(upper switches) and the resulting phase
voltages

Note in figure 2.4, that only one switch changes states between consecutive conduction
intervals. Similarly, the gating signals and resulting phase voltages for 2-7 eighteen-step op-

eration are shown in figure 2.5.

12

g1
g3
95
97
99
911

-2Vdc/ 9

g1

91 5
-7Vdc./9

 

 

917

Figure 2.5: 2-7 eighteen-step operation: gating signals (upper switches) and one of the result-
ing phase voltages

2.2.3 Inverter Switching Efficiency

In the 2-7 mode of operation of figure 2.5, five switches change state between conduction
intervals. For modes 1-8, 3-6 and 4-5, seven, three and one switches, respectively, change
state. An inverter operating continuously in the 4-5 switching set would have greater switching
efficiency than one operating in the 1-8 switching mode. More switches have to change states

to change voltage levels from 1/9Vdc to 8 / 9Vdc than from 4/9Vdc to 5/9Vdc.

2.2.4 Harmonic Content

For a three-phase inverter, switching every sixth of a cycle, the phase voltage has a fundamen—
tal of 2 / 7rVdc. Table 2.2 shows the result of a fundamental magnitude of the waveforms of
figures 2.4 and 2.5.

For a nine-leg inverter operating in eighteen-step mode, the 4-5 switching set waveform
has the highest fundamental content. The 1-8 switching set has the lowest fundamental con-

tent.

13

 

 

 

 

 

 

 

 

 

 

 

 

Configuration Fundamental 3rd order 5‘h Order 7‘“ Order
n=l n=3 n=5 n=7

3 phase 0.6366=2/pi 0 0.1273 0.0909
inverter

Four-Five 0.6366=2/pi 0.2122 0.1273 0.0909
Three-Six 0.5593 0 0.1715 0.2303
Two-Seven 0.4155 0.2122 0.0677 0.2619
One-eight 0.2211 0.2122 0.1951 0.1709

 

Table 2.2: Harmonic Content of 18-step mode Voltage Waveforms
2.3 Extension of Space Vector Theory to 77. Phases

Symmetric time-varying electrical quantities operating on spatially distributed functions (e. g.
windings) give rise to the concept of space-vectors. In an AC machine stator, voltages are
assigned a direction (that of the winding spatial distribution) and their vectorial sum defines

the corresponding voltage space-vector.

2.3.1 Three Phase Space-Vectors

For symmetric three-phase voltages, the resulting space-vector, vs, sweeps a continuous cir-

cular path in the imaginary-real reference frame. It rotates at the frequency of the terminal

lml

 
 

------ -Re

 

Figure 2.6: Phase voltages of a 3-phase inverter and resultant voltage space-vector

voltages. If, however, a three-leg inverter supplies the voltage, there are only six angular po-

sitions the voltage space-vector can take at any instance. The three—leg inverter results in 23

l4

possible space-vector positions. The six non-zero vectors form a hexagon.

2.3.2 Nine Phase Space-Vector

For a nine-phase machine fed by a nine-leg inverter, there are 29 possible voltage space-

vectors. Figure 2.7 shows all the possible positions of the resultant vectors.

 

 

 

 

 

 

 

 

 

 

 

 

 

j0.6Vdc * 1; I 4}
«11 +41 +4. +
' a. a.“ a. a 1* A. a. "he
j0.4Vdc . r . r . . . ¢.
*4 11 "#131319 1* r r_*
_ 1+ #*#rlrfir*# 9"
10.2w.- 1: 1r * “h 1.4-##1## *1, * e e
41 -1 f?! i 41- +
* ¢ 1 2 t t ‘E‘
0 regsage; ; #¢¢¢*¢¢
r t... r a at r
+10 art ‘ 14111 + +
-j0.2 Ve. e e t. ' «t--¢.¢~t#+- WM »- -
e p 1H 44* i i
.1 r a. 91+ he +1..
+ + #1 =14; +1 +
- . ‘1’ .‘l'. . 411* . .‘F. ‘1’
'10-4 We 1' 1* 1r 7 it 7 1r *1- 1'
+ +41 Hr +11
. + + + 41
[0.6Vdc * *-

 

 

 

 

 

 

 

 

 

 

-0-6 Vdc -0.4 Vdc —0.2 Vdc 0 0.2 Vdc 0.4 Vdc 0.6 Vdc

Figure 2.7: Nine-phase voltage space-vectors

The 512 resultant space-vectors of figure 2.7 can be divided into four sets,[4-5],[3-6],[2-
7],[1-8], based on the load circuit configuration as discussed the previous section. These four
sets can further be divided based on the number of adjacent ‘on’ inverter switches. For exam-
ple, the eighteen outermost space-vectors of figure 2.7 are the result of switching combinations
of either four or five adjacent ‘on’ switches. Specifically, these space-vectors correspond to
the 18 switching states which form the {4, 5 max} subset. The magnitudes of these vectors are
a result of adjacent phase vectors contributing positively to the resultant voltage space-vector

(see figure 2.8).

a)[0000111111] b)[0001011111]

Figure 2.8: Vector addition of voltage phase space-vectors

Space-vectors corresponding to the four maximum magnitude subsets,{4, 5 max},
{3, 6 max}, {2, 7 max} and {1,8 max} form four l8-sided polygons, shown in figure 2.9.

The polygons enclose all the subsets of the four switching sets.

 

Figure 2.9: The four bounding voltage space-vector subsets of a nine-phase system

In general, the number of polygons is equal to the number of equivalent load circuits.
The next section will show how vectors that form these concentric polygons are used in a

multi-phase Space Vector Pulse Width Modulation algorithm.

16

2.4 Space-Vector PWM implementation

Pulse Width Modulation is a general technique for realizing a voltage reference via an inverter.
The duration of the gating pulses controls the frequency and magnitude of the inverter output
voltage. Space Vector Pulse Width Modulation (SVPWM) is a PWM technique which uses
space-vectors to generate these gating durations.

First, a review of a three-phase SVPWM will be presented, followed by a proposed general
SVPWM algorithm, which extends the present three-phase SVPWM to an n-phase SVPWM.

Finally, several multi-phase SVPWM techniques are presented.

2.4.1 Three-Phase Space-Vector PWM

Three-phase SVPWM [6] increases the DC bus utilization compared to PWM based on Sine-
Triangle comparison [20]. By injecting the third harmonic into the reference voltage signal,
the fundamental of the phase voltage can be increased. SVPWM is implemented by averaging

the time spent in adjacent switching states.

[110]

 

Figure 2.10: Three phase Space Vector PWM

In figure 2.10, the desired voltage v“ is realized by spending t1 time in switching state
[100], t2 time in switching state [110] and to in the zero switching state.

The drawback of this algorithm is the need for trigonometric calculations. This method
can be simplified by adding a voltage offset to the phase voltages [2]. The addition of this

offset centers the three voltage reference signals about the dc axis, implicitly adding the third

17

harmonic and allowing the three signals to be increased. The operation requires only addition
and multiplication operations. This algorithm is extended for n-phase systems in the next

section.

2.4.2 Extension of three-phase SVPWM to n-Phase SVPWM

For an n-phase system, the nth harmonic signal can be injected by adding Vn offset to the

voltage reference. The offset signal is

V1 Vn . V1 Vn
V" o 36 = _olo— — _..I— O
, ff 1 man: [Vdc Vdc] mm lVdc Vdc:l (2 1)

Realizing a voltage space-vector by applying this algorithm to a nine-phase inverter results

in the switching states shown in figure 2.11.

 

11 111 I11 111 11 111
1111 11 11111 11 11
.001 11 1111111 11 ,
TOGO 0|1 11 111 11 I00 00
1000 00 01 111 00 00 99—
000 00 00 0'99 00 00 00—
”000 00 00 H0 00 00 00‘
000 00 I11 111 1|0 00 00"
0,00 [11 11 111,111 ,111 “00.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.11: The Space Vector PWM Realization of the vector 1.0ej30°

Also shown in figure 2.11 are the nine upper gating pulses. The switching states generated
by this algorithm are exclusively from the four subsets described in the previous section. Also
apparent in figure 2.11 is that only one switch changes state at a time. Figure 2.12 shows the

switching state sequence, for half a sampling period, in terms of corresponding space-vectors.

18

 

 

Figure 2.12: Vector sequence for the realization of the voltage space vector 1.0ej3°°

The switching times, [t0 t1 t2 t3 t4 t5 t6 t7], of figure 2.11 can be determined by solving

 

V man: '1
viii—l = Itl(t8 + 1111239)] (2.2)
VTotal
V max 1
V*'—2J——l = Itl(t2 + 21769)] (2.3)
VTotal
V max: “I.
V"l—‘L—1 = nl(t6 +1369» (2.4)
VTotal
V man: '1
V‘L—4’5———| = Kl(t4 +1156] 9 )l (2.5)
VTotal
(2.6)
1
to-l-tl+t8+t2+t7+t3+t6+t4+t5=2f (2.7)
VTotal = (lV1,8 marrl + lI/2,7 marl + “/36 marl + “/45 marl) (28)
1 2
K = §2f3'g'(2 COS(20°) "l" 1)Vdc (2.9)

The reference voltage vector of figure 2.12 can be constructed from vectors which are propor-
tional to the vectors of {V45 mam}, {V35 max}, {V23 max} and {V13 max}.

V' =2fs [lVl,8 maxl(tlej% + tsejo) + IV2,7 maxl(t3ej% + teem)
+ l‘/3,6 maxl(t7ej% + t2ej0) + l1/4,5 maxl(t5€j% + t4€j0):l

(2.10)

In (2.9), f, is the sampling frequency and Vdc is the dc bus voltage. The term 1 / 3 adjusts
for the number of turns per phase. A winding of a nine-phase system has one third the number
of turns per phase than a winding in an equivalent three-phase system. Equivalent systems are
defined as those systems that produce equal air—gap flux for the same voltage. Figures 2.13.a

and b illustrate the placement of windings for a machine designed to operate as either a nine-

phase or three-phase system. This machine will produce the same flux in either configuration.

19

 

 

 

 

Figure 2.13: a) Windings of a 3/9 phase machine in 3-phase operation b) 9-phase operation c)
Windings of a conventional 3-phase machine

Figure 2.13.c shows the winding configuration of a conventional three-phase machine with
the same number of turns. The resultant winding distribution factor for one phase in figure
2.13.a will be less than that of figure 2.13.c. Therefore, the resulting voltage space-vectors
will have lower magnitude. For a conventional three-phase machine, the six possible non-zero
voltage space-vectors have a magnitude of §Vdo while for the three-phase machine of figure
2.13.a the voltage vectors have a magnitude of 2 / 9(2 cos(20°) + 1)Vdc z 2 / 7r.

We define the modulation index as the ratio of the fundamental of the output voltage, V1,

to the dc input voltage.
_ V1

Vdc (2.11)

m

When SVPWM is applied to the conventional three-phase machine of figure 2.13.c, the maxi-

mum possible modulation index is:

7113,), m = Q (2.12)
3
For the equivalent system of figure 2.13.a, the maximum possible modulation is:
3
m3d> max = i (213)

71'

When the same machine is operated in a nine-phase mode, using extended three-phase
SVPWM, the maximum index is
mg¢ max z 0.507 (2.14)

20

 

 

 

 

 

0 0.02 0.04 0.06 0.
seconds

8 0.1

Figure 2.14: Four phase voltages of a 9-phase load generated by a 9-phase SVPWM scheme

As shown in figure 2.14, the ninth order harmonic is present in the phase voltages. This
harmonic injection increases the fundamental content of the waveform and is filtered in a nine-
phase load. However, the increase in fundamental content is not as great as that created by
third order harmonic injection in the three-phase system, 0.507 vs. 0.577.

As the number of phases increases, the magnitude of the voltage offset decreases to zero

and SVPWM converges to Sine-Triangle PWM.

2.4.3 Proposed n-phase SVPWM Techniques

In order to increase the fundamental phase voltage in an n-phase SVPWM system, several
SVPWM techniques are proposed. The first technique allows for lower order harmonic injec-
tion into a system with many phases. The second proposed SVPWM technique uses only those
vectors that form the concentric n-sided polygons described in section 2.4. The third technique
is related to the second one, as it uses the same vectors; however, the zero space-vectors are

not always used.

21

2.4.4 Low Order Harmonic Injection

The proposed technique allows for the J71 order harmonic to be injected into an n-phase
system. The advantage of this technique is the increased fundamental content of the output
voltage due to the lower order harmonic injection. However, fl separate neutrals have to be
used.

In the case of a nine-phase system, the nine-phase symmetrical load is treated as three,
three-phase systems displaced 40°, each producing one third of the total voltage space-vector.
Conventional three-phase SVPWM is applied to each of the three systems to realize the voltage

command.

2.4.5 SVPWM Using Maximum Subsets

Equation 2.10 is based on the use of space-vectors from the {V4,5 max}...{l/1,3 max} sub-
sets. However, the reference voltage space-vector can be realized by using two vectors from
{V4,5 max} and two zero vectors. Figure 2.15 shows how the reference voltage space-vector of

figure 2.12 is realized using four such vectors.

000000000
1000001 1 1
100001 1 1 1

111111111
111111111
100001111

1000001 1 1 20°
000000000 013.6 f

v——

2,4

1,5

Figure 2.15: Voltage space-vector realization using vectors from {V45 max} subset and zero
vectors

The maximum modulation index in this case is
2 0
mgd, max = (;)(COS(10 )) = 0.63 (2.15)

During one sampling period, 18 switches change state. This is the same number of

22

-.LM'I

switches that change state for the extended three-phase SVPWM technique discussed in sec-
tion 2.4.2.

The switching times for this scheme can be determined by reducing (2.10) to (2.5) with
VTotal = V4.5 moor-

The advantage of using only vectors of the subset {V45 max} is that the inverter operates in
the 4-5 equivalent load configuration, which results in a greater modulation index, at the cost of
increased harmonic content (see Table 2.2). The harmonic content can be reduced by including
vectors of subset {V35 max}. However, the maximum modulation index is also reduced. The

switching times are determined by solving (2.4) and (2.5), with VTotal = V45 max + V35 max.

2.4.6 Modified SVPWM With Adjusted Vmo

In previously discussed n-phase SVPWM schemes, the zero space-vectors are used. This is
a necessity for three-phase SVPWM, because at least three switching states are needed to
realize a desired space—vector. The use of zero voltages in the SVPWM scheme of section
2.4.5 result in four switches being simultaneously changed. In order to avoid this and improve
switching efficiency, a non-zero vector is used instead. In general, the closer in proximity the
space-vectors are, the greater the switching efficiency.

The previous SVPWM techniques use eighteen switching sectors, bounded by the vectors
of {V4,5 max}...{V1,8 max}. This technique subdivides each sector into four regions as shown
in figure 2.16. The angle of the desired voltage space-vector determines the sector, while its
magnitude determines the region within that sector. Within each region the voltage space-
vector is realized by the space-vectors of the indices of that region.

For the hatched region of figure 2.16, a desired voltage space—vector can be realized using
the four vectors [100001111], [100000111], [000000111], [110001111]. Figure 2.17 depicts the
corresponding space-vector sequence.

To generate the vector v‘ six switches change state, compared to eighteen switches for
the SVPWM schemes of sections 2.4.2 and 2.4.5. The proposed switching algorithm results

in a maximum of two switches changing between adjacent regions. For example, one switch

23

 

000000
1 0

 
   
    
   
    
   
   
  
  
  

, 100001
. 313‘. 100000
were. 000000

190.00?
oGNNWVWWR
010 Otto
311090011
000 .009\
$t§¢¢§§¢4~
900006400
eeseeeeoe
eeoeeeeee
fihflfiflflflfih
‘90000000\
110101001.
fiflfifififlwfifi
o0 009901

111
111
111
111
110001111
111
111
111

   

 

Q
N 4 Q. ‘
5‘ ”1:155:13?“
{t $9»
.19
11°00
000000M
000000001 111001111 100000011 110000111

 

Figure 2.16: Switching schemes for adjacent sector regions

changes states when the desired voltage vector changes from the region bounded by {V4,5 mam}

and{V3,6 m,,,,.,} to a neighboring region bounded by {V35 max} and{V2,7 max}.

2.4.7 Conclusions

Pole-phase modulation requires the use of a multi-phase system since the phase order is ad-
justed, as well as the number of poles. The necessity of implementing (n > 3)phases via a
n—leg inverter resulted in the proposal of several novel n-phase SVPWM techniques.

The first technique was the extension of conventional three-phase SVPWM to higher order
phase systems. However, this resulted in lower utilization of the dc bus voltage. The second
technique treated the multi-phase system as a sum of lower order phase systems. This tech-
nique resulted in higher dc bus utilization through the injection of the lower order harmonics.

However, it is no longer possible to have one neutral.

24

000000111
1000001 11
1000011 11

110001111
110001111
100001111

1000001 1 1
0000001 11

 

Figure 2.17: The vector sequence for realizing V‘

The third proposed technique utilizes the fact that a multi-phase system has more than one
equivalent load configuration. Along with the zero space-vectors, this technique uses only
space-vectors from a maximum subset (or a combination of maximum subsets) to realized a
desired voltage.

Similar to the third technique, the fourth technique uses only a limited number of switch-

ing states; however, it does not necessarily use the zero space-vectors, improving switching

efficiency.

25

CHAPTER 3

Analysis of the Experimental

Pole-Changing Induction Machine

3.1 Introduction

With the 9-leg inverter supplying the pole-changing induction machine, three possible motor
configurations are possible, the 3-phase/4-pole, the 3—phase/12-pole and the 9-phase/4-pole
motor configurations. Therefore, the two possible combinations for extending speed/torque
capabilities are: 1) 3-phase/4-pole and 3-phase/12-pole or 2) 9-phase/4-pole and 3-phase/12-
pole.

It was shown in [24] that in the 3-phase/4-pole motor configuration the bemfs are unbal-
anced and result in circulating winding currents. Therefore, pole-changing will be between the
3-phase/12-pole and the 9-phase/4-pole motor configurations. However, all three configura-
tions are discussed in detail in terms of coil arrangements, Fourier Series winding distribution,
and MMF. Comparisons are made between the harmonic content of the resulting MMF waves
of the three configurations. The understanding of the winding density and MMF facilitates the
fundamental modeling of the induction motor in chapter 5.

The motor parameters for 9-phase/4-pole configuration were not provided. Therefore, in

the second part of the chapter the machine parameters are analytically and experimentally

26

determined.

3.2 Three Possible Stator Winding Configurations

The experimental machine has seventy two stator slots and eighty seven rotor slots. The
machine has nine windings with eighteen accessible leads. Each of the windings has four coil
groups in series, each consisting of two coils in series occupying adjacent stator slots.

The four coil groups that make up a winding are spatially offset by 90° in the stator. Figure

3.1 shows the nine stator windings and their respective coil groups.

     

I . I I I I I ‘ I'. I“ ‘1p
'32 '63 'M '35 Ice In '38 lea 3phase
I I 4

"A2 in 134 435136 |c1 4c: ico 39h?“

     
 

104 155 in '

+
+
+
+
+
+
+

3, i i i 3, t 3, + «I
+ + + + + + + t +
+ + + + + + + + +
+ + + + + + + + +
L .1 3, ; ; i 41 + a;
+ + + + + + + + +
+ + + + + + + + +

 

Figure 3.1: The coil arrangements and applied voltages for the 3 motor configurations

The machine was originally designed to operate as either a 3-phase/12-pole motor or a
3-phase/4-pole generator. For both configurations, a wye connection is used. The fact that
every other coil in a group is wound in an opposite direction allows for the same neutral in

both configurations. However, it was discovered that for the 3-phase/4-pole configuration

'27

the reverse wound coil had a back emf voltage that is 200° out of phase with respect to the
adjacent same phase coils. This large phase difference results in large circulating currents in
the windings. The issue was solved by changing the phase order of the machine from 3-phase

to 9-phase.

3.2.1 3-phase lZ-pole Configuration

The 3-phase/12-pole configuration was designed to produce high torque at relatively low
speeds. For this configuration, the nine windings of the machine are arranged in three par-
allel sets. Each set consists of three same-phase windings. This arrangement results in a phase
belt of 10°, as shown in figure 3.2.

a, 3(- phase-belt 10°

sagc'b a'cb'ac'b a'cb' ac'b a'cb'ac‘ba' cb'ac’ba'cb‘ac’ba'c b'

a) [00000000000olecocoa.0000+...ooooooooloooooooococo]...oooooooofloooooooooofl
0° 120° 240° 0° 120° 240° 0° 120° 240° 0° 120° 240° 0° 120° 240° 0° 120° 240°

 

 

 

No
[3) 1'1 ['1 l"L l-l J-l % ['1 J
I LJ l—l l—l I—l r U 9
Stator (radians) 9

Figure 3.2: a) Coil arrangement, b) winding density 70(9) and c) resulting mmf F (6)

As shown in figure 3.2.b the winding density distribution is discontinuous over the stator
with the maximum number of conductor per slots of NC. A Fourier Series approximation of
the winding density and the stator mmf was taken to better understand the stator air-gap flux
distribution.

The Fourier series expansion of density distribution of one of the stator’s winding is:

k=i
70(9) = a0 + 2(a), cos(kO + bk sin(k6)
k=1
a - 1 1r'n(:z:)dr:
o - 27r _,,° °
1 71’
(1;, = —/ n(x)cos(k1:)da:
7r —1r
1 7' ,
bk 2 —/ n(a:)sm(k;1:)d:z:
71' -1r

28

The Fourier series for the density of one winding of the 3-phase/12-pole configuration is:

 

 

N r y 2y 3y 72y
0.0 = ——° /(-1)d6+/ (0)d6+/ (1)d6---/y (—1)d6]
7T L 0 y 2y
N F 3’ 2” 72y(
an = c / (—1)cos(n:r)d1:+/ (0) cos nx)d x---/(— )(cos 1(nx)dx]
71' c 0 y 71y
N ' y 2y 72y(
bn = —° / (—1)sin(n$)d;1:+/ (0) smna:)d:c--(—/1(na:)dx])sin
7T _ 0 y 71y
7r
y 36

where the integrands of the Fourier series are the position of the slots on the stator in radians.

The Fourier series for the other two windings densities are the same as equations (3.1),
but with the integrands shifted by a multiple of the phase belt. For the adjacent winding the
integration terms are shifted 10°. For the third winding the integration terms are shifted by
20°. The Fourier series approximation of k = 100, shown in figure 3.3, is one of the three

winding distributions for the 3-phase/12-pole configuration.

 

1-5 T Y t Y

N (conductor density)

 

 

 

 

 

 

 

radians (stator)

Figure 3.3: The Fourier Series Approx (10 = 100, 1) of Winding Density

The magnetomotive force, F (6) in the air-gap, resulting from one stator winding is shown

29

in figure 3.2.c. The Fourier series expansion of F09) is:

 

 

 

a. = Naif“) f0 y(-1)d6+ / 2y(0)d6+ /2 3”(1)110... f7:2y(—1)d0]
an = Nciu) :/0y(—1) cos(nx)da: + /2y(0)cos(nx)da: - - - £:2y(—1)cos(nx)dx]
bn = Ncfim T/Oy(—1)sin(nx)da: + /2y(0) sin(n:1:)da: - - - 7172°(—1)sin(n:ic)0lar]

 

where 1,,(t) is the current function.
Figure 3.4 shows the single phase stator mmf with [$(t) = 1. The figure show two plots;

one is the fundamental of the mmf (k = 1), and the other is the Fourier series approximation

if the mmf taken out to the 100 term, (I: = 100).

 

 

 

 

 

 

1 2 _ 3 4 5 6 7
radians (stator)

Figure 3.4: The Fourier series Approx (10 = 100, 1) of the air-gap mmf

However, for steady state analysis the applied currents will be sinusoidal and 120° apart:

Ia(t) = sin(27rf(t))
Ib(t) = sin(27rf(t)+-23—7r)

)

47r

[C(t) = sin(27rf(t)+ 3

When these currents are applied to the 3-phase windings of the 3-phase/12-pole configuration,
a sinusoidal stator air-gap mmf is developed. For purposes of analysis, the frequency of the

applied current is 10H 2. Figure 3.5 shows the Fourier series approximation (10 = 100) of the

30

 

 

2-53TIEET: ;:;.:s:«
2.0 1. . ; . ....E.... .4 1.6 ...... . .......... t ........ ......,,.. ..... ..... .... ......... . ......... '1

 

 

 

 

 

 

 

1_5 ........ ””1“ ..... ........... 1,4 .é .......... ......... ......... ......... .1
1.0 > ~ - -- . . ._ . . 12 ........ .......... ....... ........ ......... .
°~5 - _1,o . ...... .......... ........... ......... ......... ......... 3. ......... .
2 -0.5 _ i = z 06
-1.0 ~ _ . . '
3 ‘ E 0.4
.15 .... .3 ....... E ......... It ......................... . _. ; : . ;
-20 . .. .......... .. ......... ......... : ........... ‘_ ............ 0.2 * """" """"" """"" A --------- A ----------
-2.5 4‘ i i 4: i ii 0.0 . : i 1A = : :
o 1 2 3 4 5 6 7 0 10 20 30 4O 50 60 70 80
radians(stator) Hz

Figure 3.5: a)Instantaneous air-gap mmf and b) resulting Fourier Transform

air-gap mmf at one instance of time. In addition, the a Fourier transform 'is applied to the wave
form. From the Fourier transform plot the fundamental is at 6 hz. However, hertz is not in
terms of seconds but stator position. In this case, 6 hz means 6 cycles per one diameter of the
stator. Also notice there are four other frequency components at 30, 42, 66, and 78 hz which
correspond to the 5‘”, 71", 11th and 13‘“ harmonic. In order to measure the amount of harmonic
content in the instantaneous stator air-gap mmf, the total harmonic distortion was calculated
using equation (3.1). For this instant of time. the THD for the air-gap mmf is approximately

21%.

 

F2 — F2
THD = RMS fundametal (31)

f undametal

The previous frequency analysis was performed on the stator air- gap mmf at an instant of
time. Next, an analysis of how the stator air-gap mmf changes with time is conducted. Figure
3.6 shows the resulting amplitude of the Fourier transform of the air- gap mmf over a period of
0.3 seconds. At each time step, (0.005seconds), a fft was taken.

From the figure 3.6 the magnitude of the 5th and 7th harmonics and the fundamental appear

to change over time while the 11th and 13‘“ harmonics do not change over time.

31

 

Figure 3.6: 3-D Fourier transform with respect to time and stator position

3.2.2 3phase-4pole Configuration

As mentioned previously, the 3-phase/4-pole configuration is not practical due to current im-
balances. However, a winding analysis is performed in order to compare the results to the
9-phase/4-pole configuration. The winding configuration is shown in figure 3.7.

a: gphase-belt 30°

iaa'aic'cc‘bb'ba‘aa'cc’c b'bb'aa'ac'cc'bb'ba'aa'cc'cb'b b'
I: .1 I

3)
WWW—W 0 “I121“! fi‘l"1—'1—°1_"I_"l‘2“'1—"I_340 120 1 0 40 240 120WJ

240 1 1 4 240 0 20
N 180° 60° 60° 300° 180° 180° 60“ 300° 300° 180° 60 60° 300° 180° 180° 60° 300° 300°
b) l—I l
l L-l L__l 9

1:'——H_ _,4———-1._
“’Lr" "H___r" “L.__e

Stator (radians)

Figure 3.7: a) Coils arrangement, b) winding density 71(6) and c) resulting mmf F (6)

As shown, the phase belt for this coil arrangement is 30°.

Fourier Series analysis of the winding density and the stator air-gap mmf for the 3-phase/4-

32

pole configuration were conducted.

The results of the winding distribution is shown in figure 3.8.

1.5

 

A

P
a:

 

N (conductor density)
o

 

 

 

 

3 4
radians (stator)

Figure 3.8: The Fourier Series Approx (10 = 1, 100) of the winding density

The Fourier series for the air-gap mmf is shown in figure 3.9

 

Ni (conductor density x i)

 

 

 

 

3 4
radians (stator)

Figure 3.9: The Fourier Series Approx (k = 1, 100) of the air-gap mmf

The same sinusoidal currents applied to the 3-phase/12-pole configuration are applied to
the three phase windings of the 3-phase/4-pole configuration. Likewise, the result is a sinu-

soidal stator air-gap mmf. Figure 3.10 shows the Fourier series approximation (11: = 100) of

33

the air-gap mmf at one instance of time. In addition the a Fourier transform is applied to the

wave form.

 

 

 

 

 

 

 

 

 

 

 

 

 

2 3
radians (stator)

Figure 3.10: a)Instantaneous air-gap mmf and b) resulting Fourier Transform

From the fourier transform plot, figure 3.10, the fundamental is at 2 hz or 2 cy-
cles per one diameter of the stator. There are twelve other frequency components at
[10, 14, 22,26,34,38,46, 50, 58,62,66, 70, 74Hz]. The predominant harmonics are 10, 14,
70 and 74 which correspond to the 5th, 7“, 35th and 37th harmonic. For this instant of time,
the THD for the air-gap mrnf is approximately 15%.

Figure 3.11 is the Fourier transform of the stator air-gap mmf period with respect to stator
position and time. At each time step (0.0053econds) a transform was taken. The applied
current was again f = 10H 2:.

As with the 3-phase/12-pole configuration of the previous section, the magnitude of the
5th and 7th harmonics and the fundamental appear to change over time. In this case ,the 35th

and 37th harmonics do not change over time.

34

IYI

  

          

80

          

70

 

0 1o 20 30 40 50 60

sec
Hz

Figure 3.1 1: 3-D Fourier Transform with respect to time and stator position

3.2.3 9-phase 4-pole Configuration
The 9-phase/4-pole configuration was intended to produce relatively high speeds for power
generation. For this configuration, the nine windings of the machine form a star connection.

This arrangement results in a phase belt of 10°, as shown in figure 3.12.

-), 5- phase-belt 10°
iairbg'ch'di'ea'rb'gc'hd'ie'afbg'ch'di'ea'fb'gc'hd'ie'
I r l

a) I I I
0 40 80 2 1 60 4O 80 20 0° 40° 80° ° 1 60 300° 80° 020°
J 1 40° 1 220g 2602 300°3 340° 20° 60° 1 00° 20140° 1 60 20°40260° 300 340°
I

20" 60° 100

 

 

 

 

Ncl—I n
b) I 1.! u 9
Stator (radians) a

Figure 3.12: a) Coils arrangement, b) winding density 71(0) and c) resulting mmf F(6)

Again, Fourier series analysis of the winding density and the stator air-gap mmf for the

9-phase/4-pole configuration were conducted.

The Fourier series approximation, figure 3.13, shows one of nine winding distributions for

35

the 9-phase/4-pole configuration for k. = 1, 100.

1.5

 

N (conductor density

 

 

 

 

radians (stator)

Figure 3.13: Fourier Series (I: = 1, 100) of the winding density

Next, the Fourier series for the stator air-gap mmf is determined.
Figure 3.14 shows the single phase stator mmf if Ix(t) = 1. The figure show two plots,
one is the fundamental, k = 1, and the other is the Fourier series approximation with k = 100.

1.5 1 r .v t

 

1

0.5~ .

 

 

 

 

3 4
radians (stator)

Figure 3.14: Fourier Series (10 = 100) of the air-gap mmf 9phase-4pole

In the case of the 9-phase/4-pole configuration, nine sinusoidal currents, 40° apart are

36

applied for steady state analysis.

Ia(t) = sin(27rft) Ib(t) = sin(27rft + 291) Ic(t) = sin(27rft + 591)
Id(t) = sin(27r ft) + 63") I,(t) = sin(271 ft) + £31) [)(t) = sin(27r ft) + 131)
Ig(t) = sin(27rft) + NT") Ih(t) = sin(27rft) + 12,—") L-(t) = sin(27rft) + 131)

For analysis purposes, the frequency of the applied current is 10H 2. Figure 3.15 shows
the Fourier series approximation (10 = 100) of the stator air- gap mmf at one instance of time.

In addition, a Fourier transform is applied to the wave form.

 

 

.........................................................

...........................................................

u .
..uc‘...~..-.....-..--.-.-.u...-.-.........---.........q

 

10 50 06°30 ‘50 60 QOA—ao

radians(stator) Hz

 

 

 

 

 

 

 

 

 

Figure 3.15: a)Instantaneous Stator Air-Gap MMF and b) Fourier Transform

From the Fourier transform, figure 3.15, the fundamental is 2 cycles per one diameter of
the stator, a 4-pole motor. There are four other frequency components at 34,38,70,74 Hz,
corresponding to the 17‘”, 19th, 35th and 37“ harmonics. For this instant of time, the THD for
the air-gap mmf is approximately 6.2%.

Figure 3.16 is the Fourier transform of the air—gap mmf period with respect to stator posi-
tion and time. Again, at each time step (0.00556conds) a transform was taken. The applied
current was again f = 10H 2..

In the case of the 9-phase/4-pole configuration there are no 5"“ and 7th harmonics, instead

the 17“ and 19“. Again the 35th and 37th harmonics do not change over time.

37

 

 

 

IYI

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.2
0.1

 

‘\ \
sec 0 ’V0 10 20 30 40 50 60 70 80

Hz

Figure 3.16: 3-D FFT of the 9-phase/4-pole configuration

3.2.4 Comparison Between the 3 configurations

Figure 3.17 is a comparison of the fundamental stator air-gap mmf of all three winding con-
figurations.
The peak values of all three mmf are:

max(MMFK=1 = 1-844Ni)3phase-12pole (3.2)
max(MMFK=1 = 5.48N’i)3pha5e.4p01¢ (3.3)
max(MMFk=I = 5-71Ni)9phase-4pole (3.4)

The highest value for stator air-gap mmf results from the 9-phase/4-pole configuration
due to its low harmonic distortion [10]. The advantages of using nine phases instead of three
phases are 1) balanced bemf, 2) lower harmonic distortion resulting in greater stator mmf. The
3phase-12pole stator mmf is approximately 3.09 times less than the 9phase-4pole configura-

tion.

38

  

 

   

9phase4mle
\ 3phase-4pole

 

 

 

 

3 4
radians (stator)

Figure 3.17: Comparison of the fundamental air-gap mmf
3.3 Steady State Model Development

In this section the motor parameters of the 3-phase/12-pole and 9-phase/4-pole configurations
are determined. First, the parameters are determined experimentally. No-load and locked rotor
tests are performed. Next, the parameters are calculated based on the dimensions of the stator

and the rotor.

3.3.1 Equivalent Rotor Circuit of an Induction Motor

The voltage induced in the rotor bars of an induction motor depends on the relative speed

between the stator and the rotor magnetic field.
“induced = (a X F) ' e (3.5)

The relative velocity between the stator magnetic field and the rotor is 0. The stator magnetic
field is E and f is the length of the rotor bar.

The induced rotor voltage results in current, I R, flowing in the rotor bars. Due to the
reactance of the rotor, the current lags the peak induced voltage, as seen in figure 3.18.

From figure 3.18, the induced rotor current produces the rotor magnetic field E. The sum

of the rotor and stator magnetic field in the air-gap is the net magnetic field Bad. The resulting

39

\ IS max (out of paper)
\ .

paper)

 

 

Figure 3.18: Stator and Rotor Magnetic Fields
torque is from the interaction between the stator and rotor magnetic fields.
Tinduced = (kB—R X E) (3-6)

The greater the relative velocity, 6, the greater the induced voltage and current, and rotor
magnetic field. The relative velocity is at maximum when the rotor is not turning and is at
minimum when the rotor is spinning at the same velocity as the stator magnetic field. The
difference between rotor speed, um, and synchronous speed, wsync, is called the slip speed.
Slip, s, is defined as:

s = w x 100 (3.7)

wsync
The locked-rotor voltage, E RO, is the maximum possible induced voltage for a given applied

stator voltage. When the slip is not one, the induced rotor voltage is determined as follows:
E3 = SE30 (3.8)

The frequency of the rotor voltage and current, f,, is proportional to the stator voltage fre-

quency, f,, by slip.
fr = st (3.9)

40

Therefore, at unity slip the rotor frequency is the same as the stator electrical frequency. At
locked-rotor condition the reactance, X R0, will be a function of stator frequency. For any

other slip, the rotor reactance can be expressed in terms of X R0 by the slip:
X, = err = 27r(f,.Lr) = 27rs(f3Lr) = 5X30 (3.10)

With a rotor resistance of R, the rotor current is defined as:

ER SE30 _ E30

1 =__,_=__.___________
R Rr+JXr Rr+JSXRO %+JXRO

(3.11)

3.3.2 Equivalent Circuit of an Induction Motor

In order to complete the per-phase equivalent circuit, the rotor impedances and current stator
equivalent terms must be determined. Similar to a transformer’s turn ratio, the effective turns
ratio is used to reflect the rotor parameters to the stator equivalent circuit. Let an be the
effective turns ratio between the stator and rotor. Therefore the reflected rotor voltage, current,

resistance and reactance are as follows:

1, = 2. (3.12)
Off

E1 = ajfERo (3.13)

R2 = (13,123 (3.14)

X2 = Grit-X30 (3-15)

Figure 3.19 shows the per-phase equivalent circuit of an induction motor with rotor parameters
referred to the stator side.

From figure 3.19 the magnetization current ,Im, is the current required to produce the air-
gap flux. The Rc terms represent core resistance from both stator and rotor. However, stator
core losses are far greater than rotor losses. This is because the induction machine is operated
close to synchronous speed, resulting in low relative motions between magnetic fields.

The magnetization reactance along with the other motor parameters can be estimated by

performing several tests. These tests are the DC Test, the No-load Test and the Locked-Rotor

41

 

 

go
“""'“"_r.""“""“’

 

Figure 3.19: Per Phase Equivalent Model

Test. The DC Test measures the resistance of the stator winding. With applied DC voltage
there is no induced voltage in the rotor and all reactances are zero. The only voltage drop is
the copper resistance, R1, of the stator winding.

The magnetizing reactance, X m, is estimated from the the No-Load Test. The induction
motor is operated very close to zero slip for the No-Load Test. For the actual experiment,
a dynamometer was used to turn the motor at synchronous speed. Therefore, losses from
windage and friction could be neglected. At zero slip R2/s becomes infinitely large, resulting
in the load current being zero. The input power is consumed in the core losses, RC, and in

maintaining the air-gap flux. The resulting equivalent circuit is shown in figure 3.20.

Wm '24
¢ r

R1 1X1 lxz

 

:Vphase R2

 

Figure 3.20: No-Load Equivalent Model

The magnetization current is very high in an induction machine compared to a transformer,
due to the high reluctance of the air gap. Only a small amount of the total current passes

through the RC branch. Therefore [m z I 1 and input impedance is

use V 088
IZNLI = L”; z —’”I" = X1+ X... (3.16)
I m

42

For the locked-Rotor test the motor is energized (full-load current) with the rotor locked
in place,s=l. Recall unity slip means that the relative motion between the stator magnetic
field and rotor conductors is at maximum. Therefore, for a given stator voltage the maximum
amount of voltage and current is induced in the rotor. Since there is no conversion from
electric to mechanical power Rg/s reduces to R2, rotor resistive losses. The rotor impedance,
jX2 + R2, is very small compared to the magnetization reactance and core losses. Therefore,
most of the input current passes through ng + R2 and the equivalent circuit of figure 3.19

reduces to the circuit of figure 3.21.

 

%
to—
VP

2°
2

 

(-----< -'-"“'-"
U
3
I)
8

 

Figure 3.21: Locked—Rotor Equivalent Model

From figure 3.21, the total impedance of lock-rotor circuit is

 

V 0.86 .
lZLRl = p}: = (R1 + R2) + ](X1 + X2) (3.17)

By measuring the phase voltage, the phase current and the power factor, cos(gb) the equivalent

impedance can be determined. The resistance of the circuit is
IZLRICOSW) = (R1 + R2) (3.18)
The stator resistance R1 is determined from the DC Test. Therefore
Rz = IZLRICOSW) — R1 (319)
The combined stator and rotor reactance is
IZLRlsm(¢) = (X1 + X2) (3-20)

Distinguishing between the rotor and stator reactance is not straightforward. Typically, the

values assigned to the rotor and stator reactance are based on design.

43

3.3.3 Equivalent Circuit Per-Phase Parameters

The DC, No-load and Lock-Rotor tests were conducted for both configurations; 4-pole/9-

phase and 12-pole/3-phase.

359qu _ _

‘_—

 

(b)

Figure 3.22: The phase voltage and current: (a) 12pole-3phase (b) 4pole-9phase

Figure 3.22 shows the phase voltage and current for both configurations. From the DC
Test, stator resistances for the 4-pole/9-phase configuration is 0.206752. For the 12-pole/3-
phase configuration the per-phase stator resistance is 0.0699.

The dynamometer drove the motor to synchronous speed. The stator voltage was adjusted
and recorded as was the phase current. Figure 3.23 is the resulting magnetization curve for the
4-pole/9-phase configuration.

Saturation appears to begin at 40 Vprms with a phase current of 2.6 amps. Due to the
dynamometer driving the motor there should be no friction, windage or rotor losses. The
only resistive lost will be from the stator windings, which is less than 1.5 watts and can be

considered negligible. Thus, the impedance is mostly reactive.

40Wms ~ ‘fphase

IZeql = m ~ [m = X1 + Xm =15.4Q (3.21)

 

Also plotted in figure 3.23 is the per-phase input power. These measurements were taken
with the motor decoupled from the dynamometer in order to get an idea of mechanical losses.
The real power at the knee of the magnetization curve is approximately 40 watts. This is due

to friction, windage and rotor losses.

 

 

 

 

 

so 140
50» 120
(I)
3::
(U
‘0 40 1003
E as
a a
2 30 so a
o. 0
> 8
: .C
20- 50 a
10-- 40
0o ‘2 it 6 i0 20
lphase rrns

Figure 3.23: The Magnetization Curve for the 4pole-9phase Motor

Next the motor was reconfigured for 12-pole/3-phase operation and the No-Load Test was

performed. Figure 3.24 shows the magnetization curve.

 

45 Y ¥ Y Y 1

40 ' ' I .' I
35

m 30

E

8’. 25

(U

E.

> 20
15
10

 

 

 

 

0o ‘2 :4 ‘6 a io i2 i4 16
lphaserrns

Figure 3.24: The Magnetization Curve for the 12pole-3phase Motor

Saturation appears to begin at 26.8 Vprm, which corresponds to a phase current of 7.8
amps. The phase magnetization current for the 12-pole/3-phase configuration is approxi-
mately three times the magnetization current of the 4-pole/9-phase motor. Again, there should
be no friction, windage or rotor losses due to the dynamometer. The only resistive lost will be

from the stator windings which is less than 4.2 watts and can be considered negligible. The

45

Phase Power W 100 120 140 160 180 200

 

V,,,.,,.. 12.40 13.45 14.22 14.80 15.27 15.80
1pm,, 13.40 15.20 17.00 18.70 20.10 22.00
IZLRI 0.92 0.88 0.84 0.79 0.76 0.72

PF 0.60 0.59 0.58 0.58 0.59 0.57

R1 + R2 0.56 0.52 0.48 0.46 0.44 0.41

(X1 + X2)(60/15Hz) 3.01 2.96 2.86 2.73 2.58 2.46

(L1 + L2)mH(60Hz) 7.8 7.6 7.2 6.9 6.5 6.2
5,0,... 166.16 204.44 241.74 276.76 306.93 347.60
51,01,8er 1495 1840 2176 2491 2762 3128

Table 3.1: Locked-Rotor Test 4—pole/9-phase

total reactive impedance is:

26-8M‘m3 ~ V'phase
7.8A,,,,, ~ 1,,

 

lzeq| = = XI + X... = 3.49 (3.22)

The total reactance of the 12-pole/3-phase is 4.5 times less the total impedance of the 4pole-
9phase configuration.

Next, the Locked—Rotor Test is performed on both motor configurations. For the Lock-
Rotor Test the applied stator voltage frequency was 15H 2. At unity slip, the rotor electrical
frequency is the same as the stator electrical frequency. However at the normal operating
point rotor speed is near synchronous speed, thus, the the rotor electrical frequency is very
low compared the the stator electrical frequency. As a compromise, the applied stator voltage
frequency is set to 25% of the normal operating frequency. For the 4-pole/9-phase motor

configuration the following data was measured and calculated:

Since the stator copper resistance was determined from the DC Test, the load resistance
R2 can be calculated. To determined the stator and rotor reactance some assumptions have
to be made. The motor was originally designed for high starting torques in order to start a
conventional internal combustion engine. Also, the motor has relatively many rotor bars, 78.
These characteristics are similar to the NEMA design class D induction motor. The rule of
thumb for design class D motors is the leakage reactance is evenly split between the rotor and

stator.

46

The last thing to determine is the Full-load current. For the Locked-Rotor test several

full-load currents were used. The following data was measured and calculated.

 

 

Phase Power W 80 100 120 140 160 180
V,,,,,,. 7.18 7.70 8.67 9.37 9.90 10.40
1pm. 16.00 17.20 19.20 20.50 21.00 22.00
|ZLRI 0.45 0.45 0.45 0.46 0.47 0.47

PF 0.70 0.75 0.72 0.73 0.77 0.79
R1 + R2 0.31 0.34 0.32 0.33 0.36 0.37

X1+ X2(60/15Hz) 1.29 1.17 1.25 1.25 1.20 1.17
(L1 + L2)mH(@60Hz) 3.4 3.1 3.3 3.3 3.2 3.1
swam 344.64 397.32 499.39 576.25 623.70 686.40
spawflg 1034 1 192 1498 1729 1871 2059

 

Table 3.2: Locked-Rotor Test 12-pole/3—phase

Figure 3.25 shows the measured total power and real power from the Lock-Rotor test on

the 12-pole/3-phase motor.

 

   
  

 

 

 

1000 Y T T: 1 1 : 1 1 1
900. ........ ......... .......... ....... ......... ........ ........ 10.9
800 - ' ‘ ' ' ' 0.8
700 - 0.7
600- 0.6
é’
to 500.- 0.5 Pf
3 2 i . 2 i ; i 2
p ........ ...... ; ......... - .......... .........;.. .....', ........ ' ....... g ........ .J
400 g g Total Power . 3 g g 0'4
300. ........ ......... ......... ....... ...... g ......... g ......... ........ . 0.3
. g : g 5 Real Power .
200.... ...... 1.. .......... ......... 1....._ ......... ....... .. 02
100 ...... ......... ......... - ......... ........ .. 0_1
0 1 1 1 1 1 1 1 1 8
25 30 35 40 45 50 55 60 65 7
lp amps rms

Figure 3.25: Total, Real Power and pf from Locked-Rotor 12pole-3phase

The Lock-Rotor parameters were chosen at approximately 1.2kW input power. The
measured motor parameters for both the 4pole-9phase and 12pole-9phase configurations are

tabulated below:

47

Parameters R1 R2 X m X1 X 2

 

 

4pole—9phase 207m!) 380m!) 15.09 375mQ 375m!)
12pole—3phase 69m§2 44mQ 3.40 l95mQ 195mQ

Table 3.3: Measured Parameters

3.3.4 Calculated Parameters

In the previous section, the per-phase parameters were determined eXperimentally. Those
values will be compared to the analytically derived parameter values in this section. The
following values were determined; R,, R,“ L,., L, and Lm.

For the induction motor, the following leakage reactances are analytically derived: rotor
and stator slot reactance, stator end-tum reactance, rotor ring reactance, zig-zag reactance and
belt reactance. (The rotor bars of the induction motor are unskewed.) Figure 3.26 shows the

slot, rotor ring and end-tum flux leakage of the induction motor.

 

 

 

 

 

 

 

l:—:\
[I \\
It} )1

1 / ~‘.,~_-;/ 1 i
I l
: +. . :
1Faoe Leakage . 1 Y : I
: . L, :
I .- .
I .r::\ x g

' @n

m
v
”

I

 

. f .E.)' .
Rotor Ring Rotor Slot
b) Leakage Leakage

Figure 3.26: Slot and End-turn Flux Leakage

Stator slot flux leakage is that flux that does not link with the rotor. This flux only links

48

with conductors that produced it. Figure 3.27 show the dimensions a induction motor stator
and rotor slots. The stator slot has a trapezoidal shape; however, to simplify integration we

will assume that the stator slot is rectangular. Let C be the total number of conductors in the

I4;/

stator slot.

 

0.,
of.
\

\

de

ldsdsm / 1’ “‘1
I I
[I] ‘ Wr ’
I

Figure 3.27: Slot Geometry a) stator slot b) rotor slot

 

 

00
00

 

 

90
\
4—JP—>
a.
x

 

 

0
O
0
\
\
\
\

 

O
G
\
\

From figure 3.27, the magnetic field intensity across the stator slot is:
ff! 0 dl = Hwb, = Ci (3.23)

The magnetic density in the cross section of dzr - l is

 

B = 00H = 11, Cl (3.24)
wbs
The differential flux is
Ci
d4) = B(l)(d:c) = uoH(l)(d:1:) = [roQb—(lsmckde) (3.25)

This differential flux is generated by C (a: / ds) number of conductors. The same conductors

are linked by the differential flux. The differential inductance is

 

 

dL = W (3.26)
The inductance is
‘13 :1: dz
Lstatorslot =A ,uiolstack(CZ)2 wa =Mo lzstackC (3:13) (3-27)

49

Including the mouth of the slot the stator slot inductance is

d3 + dsm
Bwbs wsm

 

 

Lstatorslot = #0’3tackC2( ) (328)

The total stator slot inductance is determined by the total number of slots, Nstam, multi-
plied by the slot inductance of equation 3.28. Since the phase coils are in series for both the
lZ-pole/3-phase and 4-pole/9-phase configurations of the induction motor the per-phase in—
ductance can be found by multiplying equation 3.28 by Nstam / m, where m is the number of

phases.
N stator d3 dsm
+

3wbs wsm

 

 

 

”01%ka ) (3.29)

Lper—phase—stator—slot =

The rotor slot inductance was similarly derived, with C = 1 and Nmtm. being the number of

rotor slots.

Nro or dr
t ”allstack _ (3.30)

1'

 

Lper—phase — rotor — slot =

Since the induction motor is cordially wound the the end-turn reactance has several com-

ponents. From figure 3.26 the total end-tum reactance of the stator is:
XET = Xtop + 2Xface (3.31)

The top flux leakage, Xtop, is generated by the opposite side of the conductors in the stator
slots. Most of the flux path is through air as shown in figure 3.28. (However, not shown in
figure 3.28 is the stator housing which is made of aluminum.) Unlike the conductors in the
slots, the outer-stator conductors are contained in a defined space. Instead of taking the form
of the stator slot, these unconstrained conductors form a half cylindrical bundle. The total
flux leakage from these conductors can be divided into two components, leakage inside the

conductor bundle and leakage outside the bundle

(Prep = (pinsidebundle + ‘I’outsidebundre (332)

From Ampere’s law the magnetic field inside the conductor bundle is:

2
if H 1 d1: Hvrr = N1 = (C(:—2))2' (3.33)

50

 

 

Figure 3.28: Stator Top Flux Leakage a) Single Conductor b) Conductor Bundle model c)
Dimension of actual conductor bundle
The total number of conductors across the top is C and C (7‘2 / 25") is the proportional number

of conductors below dr. The differential flux is

poiCr

dq’ = B (”(017") = FUadeT) (3.34)

This differential flux is generated by C (1"2 / t2) number of conductors. The same conductors

are linked by the differential flux. The differential inductance is

2 2
dL = w (3.35)
t ls a. 002 3 ls OC'2
Linside—bundle = / flfTLdT = 'M— (3°36)
0 wt 477
The inductance outside the conductor bundle is

l, 002 x

Lautside—bundle = y-f—— 11K?) (337)

The term a: is chosen to be the outer limit of the magnetic field. In this case, the x is the

distance to the edge of the housing. The total stator top leakage inductance is

51

_ 1.11002 lsmfloCz 2: _ lstackMoC'z 2:

The face leakage can be derived similar to the top leakage. Again assume the conductors form
a half cylindrical bundle. The length of the bundle simply is the distance from the bottom of
the stator to the outer edge of the stator. The bundle will have an outer and inner flux. The

total inductances for both face leakages is:

lyoke#o CZ

47r +

2 2
L ,m = 2 {yr—.516; 1n(.:i) = lfli’c%g[0.25 +1n(§)] (3.39)

The final end-tum leakage is the rotor ring leakage. Figure 3.29 show the outer conductor
ring of the squirrel cage. The flux leakage path is orthogonal to the mutual flux of the stator
and rotor. The leakage flux will link the iron of the stator and create eddy currents in the stator
stacks. The result is radial force on the motor. This force can become significant at low slip

when the rotor current is high.

 
  

Figure 3.29: Rotor Ring a) Leakage Flux b) Dimension

For the derivation of the flux leakage, only the flux outside the ring will be considered.
In order to simplify the calculations, the rectangular rotor ring is modeled as a cylindrical

conductor. The magnetic field through the air is:

fH 0 dl = H27r — 2wrrCi (3.40)

52

The total flux, around the entire rotor, is:

Phrizf BdA=/ B(27rRoD)dr=/ WW (3.41)

wrr vrr wrr WT _ 2w1‘1‘
The total rotor ring inductance is:

N<I> — 2 ...
L = T = 2,3,«ROD 1n i—w— (3.42)

wrr
Air-gap Inductance

The air gap inductance of the induction motor is calculated assuming finite permeability in the
stator and rotor. This is accomplished by dividing the the air gap inductance by the equivalent

air gap length and a saturation factor term.

8 C'2 A
m = ( pole) 9 (343)
7r139.0917)
The saturation factor
SF: MMFair—gap‘i'MMEron (344)

 

MMF..._,..,
The total M M Firm, is the summation of the ampere-tums in the: stator yoke, stator teeth,
rotor core, rotor teeth and air-gap. These five terms in series form the the magnetic circuit of
the induction motor.

The first step in calculating saturation factor, SF, is to determine the flux density in all five
components. The flux is calculated from the impressed phase voltages used in the previous
section. The ampere-turns per length needed to induce the flux density in iron components is
estimated from a-c magnetization curves provide by the steel industry. The estimated values
of ampere-tums per meter are multiplied by the length of the iron components. The ampere-
tums of each iron component is added together with the effective air-gap ampere-turns to get
the total ampere-tums of the induction motor.

The effective air-gap is determined by multiplying the air-gap by an empirical approxima-
tion of the Carter coefficient.

A(Sg + 2010)

= 3.45
/\(59 + 11)“) — 10%)) ( )

 

53

Parameters Measured Calculated

 

 

Lm 39mH 23mH
L, + L, ZmH 1.2mH

 

Table 3.4: Measured versus Calculated Inductances for 4-pole/9-phase configuration

Parameters Measured Calculated

 

 

Lm 8.5mH 4.5mH
L3 + L, 1mI-I 1.2mH

 

Table 3.5: Measured versus Calculated Inductances for 12-pole/3-phase configuration

The resulting air-gap inductance for the 3-phase/12-pole configuration is 4.5mH compared
to the measured value of 8.5mH. For the 9-phase/4-pole configuration the calculated air-gap

inductance is 23mH, compared to the measured value of 39mH.

54

CHAPTER 4

Coordinate Transformation

4.1 Introduction

In chapter 7 a novel scheme of controlling the pole-changing induction motor drive is intro-
duced. This scheme is based on Rotor Flux Field Orientation Control (R-FOC). For conven-
tional R-FOC, machine variables, i.e. current and voltages, are mapped between the sym-
metrical 3-phase coordinate system and the orthogonal rotor flux coordinate system using
Park-Clark Transformation [13]. For electrically balanced systems the transforation between
the symmetrical 3-phase and Z-phase system is unique. This transformation can be used when
operating the induction machine as a 3-phase/12-pole motor. The objective of this chapter
is to develop a coordinate transformation in order to implement R-FOC for 9-phase/4-pole
operation.

Unlike, symmetrical 3-phase operation, there are an infinite number of coordinate trans-
formations between an orthogonal system and a 9-phase symmetrical system. Therefore, a
coordinate transformation is derived based on two requirements. The first requirement is that
the commanded current realization in the nine stator windings, result in an equal distribution
of phase current in all nine windings. This is to avoid saturation, minimize winding loses and
equally distribute the thermal load.

The second requirement makes possible the pole-changing control scheme of chapter 7.

The coordinate transformation has to decouple, from the nine stator windings, the measured

55

torque and flux producing currents,(2'd12,iq12,z'd4 and M), of both the 3-phase/12-pole and
9—phase/4-pole motor when operated simultaneously. It will be shown that this can be accom-
plished measuring only four of the nine phase currents. This reduces the number of current
sensors needed.

A brief review of the Park-Clark Coordinate transformation will be given. This is followed
by a detailed development of the coordinate transformation between the 9-phase symmetrical
system and the orthogonal system. Next the reduced coordinate transformation is introduced.
Simulation results are presented which show the reduce coordinate transformation does deter-

mine the feedback currents ( 72,112, 1,112, 2',“ and z'q4) from only four measured phase currents.

4.2 3-Phase 12-Pole: Park-Clark Coordinate Transforma-
tion

The rotor flux reference frame currents i312 and i312 commands are realized in the stator sta-

tionary reference frame using classic Park-Clark transformation [19],[1].

i312 = X12,31275:14312 (4-1)
where
Q12 033:2 033:2
X12 = 033:2 012 03x2 (42)
031:2 031:2 Q12
and
C03(912) 5111(912)
012 = 008(612 + :—33 sin(012 + 2311) (4.3)
cos(612 + 2371) sin(012 + :33-
and
' 1 0 t
0 1
1 O . . .
[312 = O 1 2«mm = [ zdr12 zqr12 ] (4-4)
1 0
. 0 1 _

 

 

56

The rotor flux angle 612 is estimated from the measured quadrature and direct currents
{2,112, 1,112}. These currents are estimated from the phase currents by the inverse Park-Clark

coordinate transformation.

4.3 9-Phase 4-Pole: Coordinate Transformation

Unlike the 3-phase coordinate transform in the previous section, there is no unique transforma-
tion for realizing the commanded rotor flux reference frame currents it}, and 2'34 in the 9-phase
winding reference frame. R-FOC requires the coordinate transformation to be invertible in
order to map variables between the stationary and rotor flux reference frames. The rest of
this section is dedicated to developing an invertible coordinate transformation. Several of the
desired results of such a transformation are the minimization of winding loses and the equal-
ization of current density over the stator. Ensuring that no winding carries more current than
any other is important for several reasons. Greater current in one winding will result in greater
localized thermal loading. Unbalanced thermal distribution will result in unbalanced winding
resistance, R-FOC is sensitive to winding resistance. Another reason for equalized current
distribution is the avoidance of flux saturation.

The development of the 9-phase coordinate transformation begins with the commanded
torque and flux currents currents 3'34 and 2'34, which are in the rotor flux-linkage reference
frame. An optional intermediate step before being mapped into the 9-phase symmetrical ref-
erence frame, is the mapping of the commanded currents into the imaginary-real reference
of the stator. However, since the transformation between to orthogonal coordinate systems is
unique this step can be skipped. The coordinate transformation developed here will directly
map the commanded currents in the rotor reference frame directly into the 9-phase symmetri-

cal reference frame.

57

f09=1 e[417/9

fd9=1e’6"’9 .
ld4
fb9=1d2rfl9
feg=1ei8m9
‘\ 2n/9
\
fig: 14’0"”
fl9=1ej16nl9
fgg= 1 9i 1211/9 fh9=1ei14m9

Figure 4.1: 9-phase symmetrical components
4.4 Development of Coordinate Transformation

Figure 4.1 shows the nine axes symmetrical reference frame and the orthogonal rotor reference
frame with the commanded currents 7534 and 2'34. The nine axes symmetrical reference frame
can be thought of as the sum of three symmetrical three-axes reference frames oriented 40
degrees with respect to each other. The commanded currents, can be divided into components

and realized in the three reference frames. The components of the commanded currents are:
i(t)ds4 = i(t)ds4adg + i(t)ds4beh + i(t)ds4cfi (4-5)

i(t)qs4 : z.(t)qs4adg + 2.'(t)qs4beh + i(t)qs4cfi (46)

Figure 4.2 shows the six current components in the respective reference frame. Each of these

commanded current components are then realized by the following transformations:

id id d £32 id beh

. 340. g . s4

134 = Q40 . 135 = 041; . (4-7)
. zqs4adg . zqs4beh

7'37 7'38

58

   

    

lqs(4adg) fa9 fQQ

 

Figure 4.2: Three 3-phase axes reference frames with stationary currents

z39 .
- z i c
2,6 = Q4, [ #34 f ] (4.8)
- zqs4ifc
253
where
cos(04) sin(64)
Q40 = cos(94 + $321) sin(04 + 2T") (4.9)
cos(94 + 3%) sin<94 + :31)
cos(J—G ‘92”) sin(94 — 2?"
Q43 = cos(94 + ‘72" — 23") sin(94 — 251 — 3g!) (4.10)

L cos(94 + 2?" - 2—975) sin(94 + 27" - 2?"
cos(04 + 2575) sin(64 + 297.?)

cos(04+-—§3+ 255) sin(94— 2373+2975) (4.11)

_ cos(04 + 2—:i" + 391) sin(04 + 335 + 395)

04c

 

 

The overall transformation from the two commanded stationary, orthogonal currents

{234, z'q4} into the nine axes reference frame is:

2.34 = X4'idq4component (4-12)

59

where

q

z.ds4adg
Q4a 032:2 031:2 :qs‘iadg

X = 03:52 Q41; 032:2 idq3, = .d84beh (4-13)
0312 03322 04c 1384th
zds4ifc
- z.qs4ifc .1

 

 

In equations (4.5) and (4.6) the currents {id,4, 2,134} were divided into components that
were not necessarily equal. However a equal stator current distribution can be achieved if the

components are divided equally.

. 1 . 1 . 1 .
1.1.94 = Elds4adg = Ezdsrlbeh = gzdszicfi (4-14)
, 1 . 1 , 1 _
zqs4 = gzqs4adg = §2q34beh = gzqszicfi (4-15)

Thus, {idq34} can be realized using only {id34adg, iqs4adg}. The nine phase realization of equa-

tion (4.12) becomes

7:34 = X4fl4 [ids4adgiq34adg], (416)
Where A, is
. 1 0 .
0 1
1 1 0
54 - g 0 1 (4-17)
1 0
. 0 1 .

 

 

Equal current distribution of the commanded currents results in least amount of stator winding

loses.

4.5 Pole-Changing 'h'ansition 4-pole and 12-pole Operation

While operating in either 12-pole or 4-pole configuration, only the respective quadrature and
direct currents are needed for R-FOC. However, during the pole-changing transition, both sets

of currents, {idqs4} and {idqslg}, must be realized and extracted from the stator windings.

60

4.5.1 Simultaneous Realization of iqu4 and idqslg

The commanded currents of the both the 12-pole and 4-pole motors are simultaneously real-

ized by summing (4.1) and (4.16)
is 2 i312 + is4 : X12fil2iziqs12 + X4184 [ids4adgiqs4adg], (418)

where is are the nine stator winding currents.

4.5.2 Simultaneous Extraction of idqs4 and idqslg

The extraction of {3,1434} and {idqslg} from the measured stator windings is not as straightfor-

ward as the stator realization of those currents. Expanding the left side of equation (4.18):

2.51 = isl2a + 7:340 7:54 = £3120 + is4d i5? = 23120 + 7:349
7332 = ism + i545 iss = ism + is4e iss = 23121: + 7534}. (4-19)
7:83 = isl2a + 2..‘34c 2.36 = z.312c + 7is!” 7:59 = z..sl2c + is4i

the nine stator windings are dependent on twelve motor currents. These results in equation
(4.18) being non-invertible. However, {@134} and {idqslg} can still be obtained from the stator
currents by rearranging equation (4.18).

From equation (4.19) define i, as

7:5 = [C] [icombined] (420)

where 2'00”,de is the realized stator currents of both the 4pole-9phase and 12pole-3phase
motors

zcombined = [{is4aa i34b) "-34i}: {1.312(1) 2.sl2ba ileCH’ (421)
and with [I] being the identity matrix

I3x3
C = 19129 I33:3 (4.22)
1323

Therefore the stationary nine axes realization of commanded stator currents for both ma-

chines operating simultaneously is:
. . . . . I
zS : Xcombz'ned/Bcombined [zd347’0347’d3127’4312] (423)

61

where
Q46 031-2 032:2 032:2

0312 Q46 033:2 031:2
0312 033:2 Q4c 033:2

032:2 0322 032:2 012

X combined =

and

0 I.
flcombined :. I: B4 6 2 -|

02.132 123:2

T = XcornbirredIBcombined

The combined machine transformation matrix T is a 9x4 matrix.

1.000 0 1.000 0 1
0.7660 —0.6428 —0.50 —O.8660
—0.9397 0.3420 —0.50 0.8660

—0.50 —0.8660 1.0 0
T: —0.9397 —0.3420 —0.50. —0.866

0.1736 —0.9848 —0.50 0.8660

—0.50 0.8660 1.0 0

0.1736 0.9848 —0.50 —0.8660
0.7660 0.6428 —0.50 —0.8660J

 

 

b

(4.24)

(4.25)

(4.26)

(4.27)

The transformation matrix T has a rank of 4. This means that only four measured stator

currents are needed to extract {idqs4} and {idqslg}. Equation (4.28) shows the possible trans-

formations, each transformation consisting of four rows of [T]

-1 —1

id“ T(1,2) 7:51 T(1,2) i31
iqs4 T(4, I) i34 _ T(7, 2) 1:37
111312 _ T(2, 3) 2'52 - T(2, I) 2'32
iqsl2 T(5,1) iss T(8, I) isg

T(9, :) '1 r39

_ T(3, 2) 7:33

— T(2, 2) 1:32

T(5, Z) i35

From 4.28 three new coordinate transformations can be defined as:

T(1,:) ‘1 T(1,:) ’1 T(9,:) ‘1
__ T(4,:) _ T(7,:) _ T(3,')
Tl— T(2,:) T2“ T(2,:) T3“ T(2,~)
T(5,:) T(8,:) T(5, )

62

(4.28)

(4.29)

4.5.3 Example of Extraction of 33,134 and idqslg from Four Stator Wind-

ings

 

 

 

 

 

 

 

O 0.01 0.02 0.03 0.04 0.05
seconds

Figure 4.3: Example of decoupling idq3 and idq9 from 4 stator windings

The stator current contribution from the 4pole motor is shown in plot (a) of figure 4.3.
These four currents are {3,40, i844, i345, i348} from equation (4.19). The stator current con-
tribution from the 12-pole motor is shown in plot (b) of figure 4.3. The three currents are
{03120,0312b,i312c} from equation (4.19). The currents of the 12-pole configuration have a fre-
quency three times that of the currents of the 4-pole currents and twice the amplitude. Plot (0)
shows the actual stator winding currents {231, 3'34, 3'52, 3'55} from (4. 19), the current sum of the
two independent motors. Using the transformation matrix of (4.28), the actual stator currents

are decoupled into {idq34},and {idqslg} as shown in plot ((1).

4.6 Conclusions

In this chapter, a coordinate transformation for the pole-changing scheme of chapter 7 was de-

veloped. Based on the requirements of minimizing core losses and saturation avoidance, the

63

transformation mapped currents between the 9-phase symmetrical system, set up by the 9 sta-
tor windings, and orthogonal rotor flux reference frame. It was shown that this transformation

can be reduced to a 4x4 transformation thus eliminating the need for four current sensors.

CHAPTER 5

Modeling and Simulations

5.1 Introduction

With the goal of controlling the experimental induction machine during pole-changing, a novel
induction motor model was developed to analyze the current, flux and torque transient behav-
iors during pole-changing. The model is different from conventional induction motor mod-
els because the inductances are calculated from the actual stator windings, which are non-
sinusoidally distributed.

Using this model, several different pole-changing scenarios are studied. For each case,
no controller is employed. The first scenario is an instantaneous change in motor pole/phase
configuration during steady state operation. The current and torque transients are evaluated.

Next, the change in configuration occurs during motor acceleration. The 3-phase/12-pole
is accelerating from start, before asynchronous speed is reached the applied voltages are in-
stantaneously changed to 9-phase/4-pole motor operation. The results are compared with the
first scenario, transient result.

Finally, the produced electromagnetic torque and resulting phase currents are studied when
input voltages consist of a combination of 3-phase/12-pole and 9-phase/4-pole motor steady
state voltages. The air-gap flux distribution resulting from the different voltage combination

ratios are shown using a finite element model of the machine.

65

5.2 Novel Induction Motor Model

Classical AC machine theory, i.e. generalized reference frame theory [13],[25], is not readily
applicable to modeling this experimental machine for continuous operation pole-changing. In
order to produce torque and current responses to pole-changing, the machine is modeled using
fundamental magnetic theory.

Starting with the Fourier series expansion of the winding distribution, from chapter 3, the
resulting air-gap flux density is derived. Integrating the flux density over the stator results in

the flux-linkage. Both the mutual and self inductances of the machine are calculated.

5.2.1 Classical AC Theory: Generalized Reference Frame

In conventional models of asynchronous and synchronous machines the pole number, P, is
an explicit factor in the electromagnetic torque equation. Equation (5.1) gives the the electro-
magnetic torque equation of a 3-phase, conventionally wound induction machine in the stator

reference frame.

T. = (g) (rm)T (3‘;— [L,.]) tab... (5.1)

Therefore, the pole number of the machine can only be changed by changing P. The
challenge in modeling the experimental induction machine is simulating its pole-changing.
The motor model for the proposed drive system ,the pole number should be a function of the
applied voltages, not an explicit factor. This can be accomplished by deriving the self and
mutual inductances, L3, of (5.1), from the actual stator winding distribution.

In the actual machine the winding distribution allows for the formation of two different coil
groupings, depending upon the applied voltages. As shown in chapter 3, one coil grouping

arrangement results in four poles and the other results in the machine having twelve poles.

66

5.2.2 Inductance Calculation

Conventionally, when calculating inductances it is assumed that the stator windings are wound
sinusoidally. Figure 5.1 shows the stator winding as for both an ideally wound 4-pole and 12-

pole machine. The terms N34 and N312 are slot conductor densities. The winding function,

conductors

as axis

  

 

Figure 5.1: Stator “Finding Conductor Density for a 4-pole and 12-pole Induction Motor.

n“, for the ideally wound 4-pole machine is

nag = N,4SII1(¢M) 0 S (baa S 3' 71’ S (baa S 2377‘

5.2
Tia, = _ s4SiI1((}5a3) g3 (baa S 71' 2T” S ¢as S 27" ( )

It has been shown [13] that a 2P-pole machine can be modeled as an equivalent 2-pole machine

with a winding function of

”as N52 Sin(¢as) 0 S ¢as S 71'
”08 = _ 52 Sin<¢as) 7‘- S ¢as < 27!-

(5.3)

A 4-pole machine produces double the amount of torque and half the amount mechanical speed
relative to electrical speed of a 2-pole machine for the same turns and current. This conven-
tional model works for modeling the experimental induction machine in either the 4~pole or
12-pole configuration, but does not adequately model the motor in the transition between the
two configurations. In order to understand the stator currents and the torque during the pole-
changing transition, a model was developed that accounted for the non-ideal stator winding
distributions. Figure 5.2 shows how one of the nine stator windings is distributed.

Each stator winding has 4 coil groups that are spaced 90 degrees around the stator, figure

5.3. Each of the coils spans 10 degrees. This conductor distribution allows the coils from

67

Stator

    

Figure 5.2: Location of one of the nine stator windings

adjacent windings to form larger phase belts; thus, making it possible to have different number

of poles.
a 3 axis

conductors

       

 

 

._> ‘Ps

Figure 5.3: Conductor Density of one of the nine stator windings.

The Fourier series approximation of this winding distribution of figure 5.3 is given as

nu, = Np geos(4§)sin(¢a,)+]%cos(1%r)sin(3¢a,) (5.4)

+% 004%) sin(5¢a,)...

where Np is the maximum conductor density.
Figure 5.4 shows the conductor distribution using the first three terms of the Fourier series.

Using the distribution function of 5 .4 and applying Ampere's Law, the mmf of winding as

68

as axis

conductors

 

 

~—> cps

Figure 5.4: Conductor density waveform resulting from the first four terms of the Fourier
series.

is

1' 4 4 1 12
MMFa, .—_ pro, / — cos(l) sin(¢..) + - cos(—7:) sin(3¢,,) (5.5)
0 7T 9 3 9
1 2
+gcos(—g£)sin(5¢as) d.”

where 2'“, is the applied current. From the mmf, the flux density in the air-gap can be

determined from

MMF..(¢.)
g

(5.6)

 

Br(¢s) = #0

where g is twice the air-gap length in the radial direction and no is the permeability of air. The

flux linkage of a single turn is:

¢s+1r
<I>((j>,)= A B.(¢.)rld¢. (5.7)
tbs-Hr
@025.) = i‘j- A MMF..(¢.)(¢.)rzd¢. (5.8)

_ (4sz'- [‘3 3: - 1 12: .
@(dbs) — g /S 0 7rcos( 9 )sm(¢as)+ 3cos( 9 )srn(3¢a,) (5.9)

1

+3 cos(mT”) 5mm...) . . . d¢srld¢s

69

The total flux linkage is

)‘as = Llsias '1'

1
5
1

+- cos(———) sin(5¢>as).

5

20
+— cos(——7r) sin(5¢')as)...

9
207r
9

2 .
#oszas

 

fl:

'— COS

47r ,
(—9-) SIH(¢as) +

3

1
— cos

Dividing by the current 2'“, the the self inductance of winding a is

N
Lasas = Lls + ( 8

2

 

2

) muorlal

127r ,
(7) Sln(3¢08)

(5.10)

¢s+1r 1r
] L [0 $c03(£97‘r) Sin(¢as) + %C08(%Zr-) sin(3¢as)

..d¢srldq53

(5.11)

From these calculations, the mutual inductance between stator winding a and rotor wind-

ing a is

Lasar = -0.133 [cos(0r)]5 + 0.072 [(:os(6r)]3 + 0.117 cos(0r) + 0.120 [(:os(6r)]7

The mutual inductance between stator winding b and rotor winding a is

Lb... = --042 S111(6r) + 0.127cos(6.) — 0.032 [cos(a.)]3

The entire 9x9 matrix of the mutual inductance between rotor and stator windings is

 

h

+0.147 [cos(Br)]5 — 0.092 [cos(l9,.)]7 + 0.021 sin(6r) [cos(6,.)]4

—0.027 sin(6r) [cos(6,.)]2 — 0.077 sin(0r) [008(9r)]6

Lasar
Lbsar
Lcsar

Ldsar
Lesar

L f sar
Lgsar

thar
Lisar

Lasbr
Lbsbr
Lcsbr
Ldsbr
Lesbr
Lfsbr
Lgsbr
thbr
Lisbr

Lascr
Lbscr
Lcscr

Ldscr
Lescr

Lfscr
Lgscr

thcr
Liscr

Lasdr
Lbsdr
Lcsdr
L dsdr
Lesdr
L f 3dr
Lgsdr

thdr
Lisdr

Laser
L bser
Loser

L dser
Leser

L f ser
L gser

ther
Liser

Las fr
Lbs fr
Lcs fr
Lds fr
Les fr
L f3 fr
Lgs fr
th fr
Lis fr

Lasgr
Lbsgr
Lcsgr
Ldsgr
Lesgr
Lfsgr
Lgsgr

thgr
Lisgr

5.2.3 Machine Model in Stator Reference Frame

The machine modeled in the stator reference frame is:

 

Vabcdefghis
Vabcdefghir

H

rs + pLs
P(Lsr)T

70

12L...r
r, + er

Iabcdefghis
Iabcdefghil'

Lashr
Lbshr
Lcshr

Ldshr
Leshr
Lfshr
Lgshr

thhr
Lishr

Lasir
Lbsir
Lcsir
Ldsir
Lesir
L f sir
L gsir
thir

Lisir
d

l

 

(5.12)

(5.13)

(5.14)

(5.15)

. <5 .
Te : (labcdefghis)T (Eb—“([Lsr1) labcdefghir (516)

where L8,, Lr, Ls are the 9x9 inductance matrices described in the previous section. As
mentioned previously, the inductance matrices are derived from only half of the windings
because of rotor symmetry. The result is either a 2 or 6-pole motor instead of a 4 or 12-pole
motor.

Rearranging equation 5.15 and setting Vabcdefghi, = 0

dLsr _ dLsr
Cs [vabcdefghis — rslabcdefghis + dt L7- l—dt Iabcdefghir] =

dlabcde f ghis

dt (5.17)

cm; _ de. _ d1. .
Cr [-——L3 1‘labcdefghis — rslabcdefghir + —L., Irrlabcdefghis] = M (5.18)

 

 

 

 

 

dt dt dt
1 do),
Te _ oa — = 1
l T: .1 ( J) dt (5 9)
d6,
w, — dt (5.20)
where J is the rotor inertia and:
dL dL ‘1
s = Ls — "Id—1 31' .21
C I: dt ' dt ] (5 )
dLT 1dL.,. ‘1
r = r _ ——8: _ - 2
c [L ...] (52)

The term dLsr/dt is the derivative of the mutual inductance.

5.3 Simulation Results

Equations (5.17) and (5.20) were implemented into a Matlab s-function for simulation. Three
types of simulations were conducted. The first set of simulations validated the novel machine
model, in addition, to producing current and torque transients resulting from pole-changing

during steady state operation.

71

5.3.1 Simulation Simulink Model

Figure 5.5 shows the Simulink model of the experimental induction machine. (Again, the 12-

pole and 4-pole motors are modeled as a 6-pole motor and a 2-pole motor.) Two different sets

1 2-pole
Configuration

    

4-pole
Configuration

  
 
 
 
 

9 phase IM
4 term Fouirer Series
Winding F(X)

 
 
 

theta

 
 
  

Te

 
 

Tload

  
 

-1
Load Torque

 

Figure 5.5: Experimental Induction Motor Model: Two Sets of Applied Voltages

of applied voltages were applied to the model. The set of nine voltages that result in a 6-pole

motor are:
va(t) = sin (27rt) vb(t) = sin (27rt + 3375) vc(t)
va(t) = sin (27rt) vb(t) = sin (21rt + 2?") vc(t)
va(t) = sin (27rt) vb(t) = sin (27rt + 2—55) vc(t)

sin (27rt + 5575)
sin (27rt + 531) (5.23)
sin (2m + 47")

The nine currents that result in a 2-pole motor are:

sin (27rt + 3431')

sin (27rt + l—g")

sin (27rt + 167")
(5.24)

va(t) = sin (27rt) vb(t) = sin (27rt + 391) vc(t)
vd(t) sin (27rt + £91) ve(t) = sin (21rt + 83") Uf(t)
vg(t) sin (27rtuT") vh(t) = sin (27rt + 1:37") v,(t)

5.3.2 Model Validation of Pole-changing Machine

Applying the voltage sets of (5.23) or (5.24) to the motor model results in the motor acceler-

ating freely. Figures 5.6.a and 5.6.b show the resulting speed and developed electromagnetic

72

 

 

      

 

 

 

 

 

400 20
350
15 . ......................................
300 , 6-pole motor
I"! torque
1o . . ..... ...................
o 250 ,7 I S 2-pole motor torque
3 200 E ' '
U z 5 ..................................................
E
150
100 f 0 ---------------
50 I
' _5 .........................................................
0 I
so ' 1 -10
1O 15 O 5 1O 15
seconds seconds
(a) Speed of the 6-pole and 2-pole motor (b) Electromagnetic Torque of the 6-pole and 2-pole
motor

Figure 5.6: Comparison of Speed and Torque During Free Acceleration

torque from both the 2-pole configured motor and the 6-pole motor. A static load of 1N m was
applied.

The maximum speed obtained for the 2-pole machine is 372rad/s and 123rad/s for the 6-
pole motor. The resulting speed and produced torque shows that the pole-number is changed
when the voltages are changed, validating the concept of modeling inductances based the

actual physical winding distribution in order to determine a motor pole number.

1 2-pole

motor

4—pole model

 

0 200 400 600 800 1000 1200 1400 1600 1800
rpm

Figure 5.7: Open-loop, Speed-torque characteristics: Comparison of Experimental and Simu-

lation Results.

73

The model response was also compared to actual machine response. In figure 5.7, the
speed torque curves from actual operation of the 12-pole and 4-pole motors are compared
with the model results. For this case, the resulting speed and torque of the 6-pole and 2-pole
motor models were scaled by three in order to be compared with the actual motor results. (In

chapter 6 the setup used to obtain the experimental results is described in detail.)

5.3.3 Instantaneous Pole-changing During Steady State Operation

Having developed a way to model pole-changing, the next step is to observe the effects of
instantaneously changing the pole configuration. Figures 5.8.3 and 5.8.b show the change
in speed and torque when the applied voltages are instantaneously rearranged from one pole
configuration to another. In this case the voltages are switched from the 6-pole configuration
to the 2-pole configuration 3 seconds after the 6-pole motor reached steady state.

Figure 5.8.0 shows the nine phase currents of the machine before and after the pole change.
The resulting current transient lasts approximately 100ms and has a peak current twice that of
the steady state current. These currents result in a large torque transient. The peak torque of
this transient is larger in negative direction, approximately four times the starting torque of the
2-pole motor in figure 5.6.b. The effect of this adverse torque is a dip in speed immediately
after the pole-change. The magnitude of the speed dip increases with increasing load until the

2-pole motor is unable to produce enough torque.

5.3.4 Instantaneous Pole-changing During Acceleration

In the second simulation scenario, the poles are changed while the 6-pole motor is accelerat-
ing. Figure 5.9.a compares the speed response of the conventional 2-pole motor to the speed
response of the pole-changing motor, which switches from a 6-pole motor to a 2-pole motor
when speed reaches 118rad/s.

For the pole-changing motor, steady state is reached approximate 4 seconds sooner than
the 2-pole motor. This shows that the continuously operated, 6/2 pole-changing induction

machine has better response and range, than either the 2-pole or 4-pole motor.

74

      

4
seconds seconds

(a) Speed (b) Electromagnetic Torque

amps

 

seconds

(C) Phase [Arms

Figure 5.8: Pole-Changing from 6-pole to 2-pole at t=3seconds

75

reds/sec

 

seconds seconds

(a) Speed (b) Electromagnetic Torque

 

_. 1111 11111111111,1111111111111101111»

1,
11111111111111111111111111III 1111111111111111II1l12111
111 1111111111111111111111111111

11111111111111111111|‘II'111111111IIII1II1
111111” ‘11 11111111111111111'11111111111111111111111111
11 '1

J (1111111111111111,1II1I1111IIIIIII1III

 

 

 

 

 

l I l 1
1.4 1.45 1.5 1.55 1.6

(c) Phase Currents

Figure 5.9: Pole-Changing from 6-pole to 2-pole when speed reaches 118 radians per second

76

Figure 5.9.b shows the torque produced in both cases. The torque transient at the instant
of pole—changing is less severe than that of the torque transient in figure 5.8.b. The peak
current during the pole-changing transient is approximately half the peak current in figure
59.0 when the poles are switched after the 6-pole motor reaches steady state. In the case of
the pole-change during steady state the total flux level is at a minimum. When the 9-phase
voltages are applied, the maximum flux is not instantaneously achieved. Its rate of increases
is a function of motor parameters. Since the motor is loaded and the air-gap flux has not
reached maximum, not enough torque is initially produced to prevent deceleration. In the case
of motor changing poles prior to reaching steady state, the flux has not decreased to steady
state level. When the 9-phase voltages are applied, there is enough flux to produce torque
preventing the speed to dip. These results suggest that the key to smooth pole-changing is
adjusting the flux prior to pole-changing. In chapter 7 this idea is expanded to simultaneously
and independently controlling the air-gap flux of both pole configurations prior to, during, and

after pole-changing.

5.3.5 Gradual Pole-changing

In the previous two sections, the instantaneous change in voltage results in large dV/dT cur-
rents in the windings. This suggests a gradual change in voltage to bring about a change in
poles. In order to obtain an understanding of the effects of a gradual transition from one pole-
configuration to the other, simulations were performed, where both the 9-phase voltage set,
(5.24), and 3-phase voltage set (5.23) are simultaneously applied to the motor model. Three
separate voltage combinations are applied to the motor model: 1)80% of the voltages from the
3-phase set plus 20% of the 9-phase voltage set. 2) 20% 9—phase and 80% 3-phase voltages
and 3)50% 3-phase voltages and 50% 9-phase voltages. Again no speed or torque control is
implement.

Figures 5.10.a shows the speed response of motor for each of the three combinations of
applied voltages. When the combination of 20% of 9-phase voltage and 80% 3-phase voltage

are applied, the motor operates as a 6-pole but produces less torque than the motor with 100%

77

 

 

      
 
 
 
 
 
 

 

 

  

 

 

 

 

 

 

 

 

 

 

350 ....................................... i ....... :20%2-pole _ . : ; g ;
23:2.po:e / 80%6-pole‘ ...... _. ................. -
- a . . .
300 ..................................... 2 p0 // ...... .50% 2 pole...i ...... ...... 3,...800'6 2-pole_
: 7 ...: 50% 6-pole E E 5 29% 6-pole
0250 ...... l ........................ I ............ 5...).l': ..... l...--1 . . z . .....
3 5’ : . . . .
6200 ........................................ ).’.: ................. . .....................................................
g 20% 2- -pole ’,/ -
150 ...... 80% 6~p0|€ ....... 1;)”, ....................... .....4
u T- :7
100*“ 2,! -------------------------------- ' .............................................................
50.... .,_ ............................................... . ...............................................................
. 5 :50% 2-pole ' . 5 5
o ..... ‘5 ...... I ....... :5 0%6.po:le....s ...... ...... :t ..... EH”:
2 i 1 1 L 4 I i ' ' '
024581012141618 02468101214161820
seconds seconds
(a) Speed (b) Electromagnetic Torque
25 r t r
20 ............ ............ ............ ............ ........... q
. : 50% 2Lpole
U) 15 . 2 .......... I . ..50% 6:p°|e ...... .1
g .
<
10 a
80% 6-pole
5 ................................. 20% 64,019 ......
0 i i i i
0 5 10 15 20 25
seconds

(C) Phase [Arms

Figure 5.10: Comparison of Speed, Torque and Current for different voltage combinations

78

applied 3-phase voltage set. Likewise, for the combination of 50%9-phase and 50% 3-phase
applied voltages, the motor responds as sluggish 6-pole motor. However, when the combina-
tion of 80% 9-phase and 20% 3-phase applied voltages, motor reaches 2-pole asynchronous
speed, but much slower that if the applied voltages were 100% as in figure 5.6.b. Figure 5.10.b
shows the corresponding produced torque. Figure 5.10.c shows the corresponding phase a rrns
current. In the two cases were the motor only reached a steady state speed of 122rad/s the the
rrns phase current was greater than the phase current of the motor with 100% 3-phase voltages.
Therefore, the motor efficiency is reduced.

In order to better understand the air-gap flux distribution in this case, FEA was performed
on the machine, using a commercial package, Flux2D. Figure 5.11 shows the magnetizing flux
for the 3phase-12pole configuration.

This model was build using Flux-2D. The purpose of this model was to analyze the air-gap
flux distribution during the pole-changing transition.

As shown in figure 5.11.c, when the applied voltages are a combination of 80% 9-phase
and 20% 3-phase voltages, twelve pole are established, 4 dominant poles and 8 minor poles.
The 4 dominant poles result in the motor responding as a 4-pole motor and reaching the steady
state speed of 372rad/s, but less efficient than a 4-pole motor. As the percentage of 9-phase
voltage decreases and the percentage of 3-phase voltage increases, the 4 dominant poles’ flux
path becomes smaller and smaller to a point were the twelve poles dominant and the motor
responds 12-pole motor. This transitions occurs at approximately at the combination of 75%
9-phase and 25% 3-phase voltages. Experimental results confirmed this.

The significance of figure 5.11.c is that two fields can be established in the air-gap and

torque can be produced.

5.4 Conclusions

Deriving the self and mutual inductances from the actual physical stator winding distribution
enables the simulation the pole-changing capability of the actual machine. The number of

poles is implicitly incorporated in the induction machine electrical equations through the in-

79

    
   
    

  

‘vlri‘ii

will!

 

(a) Flux paths: 4—pole motor with 9—phase (b) Flux paths: 12—pole motor with 3-phase
voltages applied voltages applied

 

(c) Magnetizing flux pattern for 80% 9-phase volt-
age and 20% 3-phase voltage.

Figure 5.11: Flux Distribution: Flux 2D

80

ductances. However, approximating the winding distribution using Fourier series results in
a more complex and computational intensive model, compared to the conventional modeling
techniques where the winding distribution is sine function.

Instantaneous pole—changing results in large torque transients and undesired speed de-
creases. It was noticed that the current and torque transients were less severe if the pole-
changing occurred prior to reaching steady states operation. This suggest that the key to
obtaining a smooth pole-changing is adjusting the air-gap flux levels prior to pole changing.

In addition it is shown that two air-gap fluxes can simultaneously exist.

81

CHAPTER 6

Experimental Setup: Hardware and

Software

6.1 Introduction

 

Emerson
Dynanometer

 

 

 

. L . 48Vdc
. :38“?! Bank C

 

Figure 6.1: Overall Experimental Setup

The laboratory setup consisted of standard equipment and specially developed hardware

for this effort.

82

 

Figure 6.2: Overall Experimental Setup

6.2 Hardware Setup

Figures 6.1 and 6.2 show the major components of the experimental setup. The four-quadrant
Emerson Industrial 20HP Dynamometer was used to load the machine. To interface with and
control the dynamometer, a Visual C++ GUI was developed. Between the dynamometer and
the induction motor is the in-line SHI MCRT model 9-02T torque meter. This meter is rated
at 22 Nm and has an of accuracy +/- 0.02 Nm. Mounted on the other end of the dynamometer

motor shaft is the BEI incremental encoder with 2048 pules per revolution.

6.2.1 Inverter

The 9-leg inverter used can supply a maximum of 25 Arms per phase at 60 Vdc. It consists of

three 3-leg Powerex IGBT Modules and 9 current sensors.

6.2.2 FPGA/ADC Interface

Figure 6.4 is a functionality block diagram of the FPGA/ADC Interface. It was designed on
a Xilinx x4008 FPGA using the Xilinx Foundation Series 2.1i. The design uses 192 Config—
urable Logic Blocks (CLB) with 98% utilization of gates. A 15MHz crystal oscillator supplies

83

 

Figure 6.3: 9-leg Inverter

the clock signal. The FPGA/ADC Interface has several functions, which are:

n—l

. Generating 18 PWM pulses based on Symmetrical SVPWM, with dead-time;

N

. Calculating the position, speed and direction of the motor from the encoder’s quadrature

signals;

U)

. Controlling three l4-bit ADCs, which sample and convert the nine phase currents (or

eight currents and one torque signal);

:5

Controlling the EPP parallel port communications with the PC; and

(It

. Generating external interrupt signal for the control program located on the PC.

Using the 9-phase SVPWM algorithm developed in chapter 2, the FPGA/ADC Interface
produces 12-bit resolution PWM signals. In addition, a preset dead-time is implemented in
the signals. Located off the FPGA, but powered and controlled by it, the ADC board is used
for measuring the nine winding currents. Three Maxim high-speed, multichannel, 14-bit data-
acquisition ICs, measure the nine Hall effect current probes. The three ADCs convert three
samples simultaneously in 3115; the total conversion time of all nine samples is under 11,us.

The ADC board interfaces with the FPGA via a 12—bit data bus (only 12 bits of resolution are

84

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

to Fe r ”51ch" “1 V 12b't
- - State Machine '
Gown 1 tion
Wax, 9-phase
. . SVPWM MO
Generator m
r— . 18 out
Dual-Port —I—
RAM

 

 

 

 

 

 

 

 

 

 

1 r ‘Doodtlme I
[ ADC Quaduature Inputs J

 

 

 

 

 

Communication Speed I Position
Controller Calculator

 

 

 

 

 

 

 

 

 

 

 

[Islam a

 

toBCurontHTomuounson

Figure 6.4: FPGA/ADC PWM Functionality Block Diagram

used, due to I/O constraint of the FPGA) and a 4-bit control bus. The currents are sampled and
converted at the PWM switching frequency.

The switching frequency is updated every interrupt from the PC. For this work the switch-
ing frequency was a constant 6.5KHz. (This was reduced from IOKHz due to the length of
the control program, and the required number of sample conversions.) The FPGA/ADC Inter-
face initiates the control interrupt. (This task was originally assigned to the PC; however, the
RTLinux thread could not produce a consistent interval.) The FPGA/ADC Interface sends an
interrupt signal to the PC parallel port (IRQ 7) to initiate the control program. The PC used
for this work is the 2500MHz Intel Pentium 4 Processor.

85

6.3 Software

For this work, data was acquired and analyzed, using Matlab, on the control processor. As
previously mentioned, the operating system of the PC is a RTLinux patched kernel [3]. It
is a ”deterministic,” real-time Operating system [4]. A major advantage of using RTLinux is
that the control code can be ported easily to another PC. Another advantage of using RTLinux
is the use of a multi-functional complex processor, which greatly aids in the development
process. Data acquisition is more convenient, because data does not have to be moved to
another platform for analysis.

The actual control program is written in C++ and implemented as an RTLinux thread.
Figure 6.5 shows the overall organization of the control program thread and its interactions.
The thread is set to the highest priority, an advantage of RTLinux.

Two separate threads are developed: the control routine and the sensor calibration routine.
The sensor calibration routine is initiated upon startup. The gain and offsets of current sensors
are normalized and nulled. Upon completion, the control thread is enabled and enters a wait
state until an external IRQ interrupt. While in the wait state, lower priority applications, i.e.
user threads such as data acquisition and the GUI, can operate.

Data is be passed from the real-time thread to the user thread via FIFOs (first-in-first-
out). Much of the experimental data for this work was collected using this technique. In
addition, data can be passed from user applications to the real-time thread, i.e. speed or torque
commands from the GUI.

The interrupt cycle begins with the FPGA/ADC Interface initiating the ADC sample-hold
and the conversion of the phase currents. Once the conversion is complete, the interrupt signal
is sent to the control thread. However, due to the high latency of IRQ interrupt, the interrupt
signal is sent after the second AD conversion. The control thread then requests the transfer of
current data (12 ll-bit words) from the FPGA/ADC Interface. The FPGA/ADC Interface ne-
gotiates the communications with the PC, using Microsoft’s Enhanced Parallel Port Protocol,
EPP mode.

Once the current, speed and position data are uploaded to the PC the current measurements

86

 

RTLin x h in xK rnal
RTLin x ntrol Thread

Anti-Allasing Filter |
..., r —+
__ EPP Panallel Port (PCI Bus) To FPGAIADC
Generator

Rate Loop

 

 

 

Current Transformations
Current Loops
VoltageTransformations

Voltage Checking/Scaling
Data Acquistion r

    

 

 

   

 

 

I
i
g
l
l
l
L

   

 

 

 

Figure 6.5: Software Organization

are passed through anti-aliasing filters.

After current and speed data are transferred, the control program begins. A PI compen-
sator, with anti-windup, is used for the speed loop. The resulting torque command is passed
to the R—FOC routine. This routine is discussed in the next chapter. The commanded voltages

are scaled and checked against the DC bus, (6.1).

Vdc
(Vqtotal)2 + (thotal)2 S 7:?“ (6.1)
The commanded voltages are transferred to the FPGA/ADC Interface for PWM calculation
and output.
6.4 Power

The power flow of the experimental setup is shown in figure 6.6. The dynamometer is fed with
3-phase 460V1rns voltage from an isolation transformer, which is connected to the building’s

high voltage transformer. Power for the 9—leg inverter is supplied by a 48 Vdc battery pack.

87

Tmachine 460 Vrms

l 60Arms

  

 

 
   

48 Vdc 20hp

.9439 Dc motor Dynanometer 1:1.
Inverter Isolation

Figure 6.6: Experimental Setup Power Diagram

88

CHAPTER 7

Control of the Pole-Changing Motor

7 .1 Introduction

In this chapter a novel control scheme for a pole-changing induction machine is introduced.
During the pole-changin g transition the machine is controlled as two separate motors, a 4-pole
and a 12-pole. During the transition, the total produced torque and flux are a sum of the torque
and flux produced by the 4-pole and l2-pole motors. A dual rotor flux oriented control (R-
FOC) scheme is introduced [11]. Using the coordinate transformation developed in chapter 4,
both sets of commanded currents are realized on the nine stator windings.

First, R-FOC is reviewed. Using conventional R-FOC for each configuration, speed-torque
curves, speed response, and torque response are presented. Using the coordinate transforma-
tion of chapter 4, a dual R-FOC scheme is developed and presented. Results showing that the
two motors can operate simultaneously and produce torque are presented.

As was revealed in chapter 5, the key to a smooth pole transition is adjusting the flux.
For the novel pole-changing scheme both motor flux and torque levels are adjusted during
the transition. Results showing the flux and torque of both motors during pole-changing are
presented.

Finally, an overall torque management strategy is proposed, along with simulated results.

89

7 .2 Review of Rotor Flux Oriented Control (R-FOC) of In-
duction Motors

The induction machine equations from chapter 5 are presented here for convenience.

 

 

Vabcde f ghis = rs + pLs pLsr Iabcdefghis (7 1)
Vabcdefghir p(Lsr)T 1' r + PLr Iabcdefghir .
. T d .
Te = (labcdefghis) (EGLSJ) labcdefghil' (72)

As shown in [14] and [25], transforming the induction machine equations into the rotor flux-
linkage, \II", reference frame, fast torque control can be achievable. The three relevant refer-
ence frames, stationary (or stator), rotor and rotor flux-linkage, are shown in figure 7.1,[25].

The rotor flux-linkage space vector is the sum of the transformed stator and rotor currents

 

 

i __________________ ’8 mm
5 ,r’ :\ ‘l’rr
I, l \
I” I \ W" _1'-
’I/ I . lmr’l’mrl (Dr
/’ I [Sq
0* '
o‘orfi l
I
Roto : p
U 6 I
I
Stator : .
’a

Figure 7.1: Stator, Rotor and Flux currents

iii-Tr = Lrgrr + ngsr (73)

where L, is the rotor self inductance and Lm is the magnetizing inductance. From the rotor

flux-linkage space vector, the magnetizing current space vector is defined as:

6|

',,,,= "T 7.4
2 Ln. ( )

 

90

From figure 7.1 the magnetizing current is collinear with the quadrature component of the sta-
tor current space vector in the rotor flux reference frame. The relationship between these two
vectors is found from performing a coordinate transformation on the rotor voltage equation of

(7.1) into the rotor flux reference frame.

dill—r. . _
dt + 3(a)... —w,)\11,, (7.5)

 

u—r : Rrirr +

With the rotor voltage set to zero, the transformed equation is split into orthogonal parts. The

imaginary part is:
dgmr '7 .
Tr—di— + imr : 7'sq (7-6)
with
T. = L./R. (7.7)

From the real part of the transformed rotor voltage equation

isd
mr : r + —-—-——_ g 7.8
w w Trlz'mu ( )

From equation (7.6), the magnetizing current can be controlled by the stator current. The
desire to control magnetizing current is due to the following

3P L2 ., .
Te :: (?) fihmrlzsd (7.9)

From equation (7.9) the electromagnetic torque is determined by the magnetizing current and
the direct component of the stator current in the rotor flux reference frame. Similar to control-
ling a DC machine, one of the variables is held constant, field flux, and the other is adjusted,
the armature current, to control the torque. In the case of an induction machine, the magnetiz-
ing current is held constant because of its relatively slow time constant, T, and id is adjusted

to achieve the desired torque.

7 .2.1 Current Loops

Equations (7.6) and (7.8) result from coordinate transformation on the rotor voltage equation

into the rotor flux reference frame. Performing the same transformation on the stator voltages

91

results in:

- - d '2...
0T3_ +2.31: = — _ jwerTsisr — (1 — 0)T8 (jwmrlimrl + —|:F'l') (7-10)

where the stator time constant is T, = L,/R, and the total leakage factor is a = l —
ern/ (LrLs). The two components of the stator current space vector in the rotor flux refer-
ence frame are id and iq:

is, : id +jz'q = ise‘jp (7.11)
Replacing the stator current space vector in (7.11) with id and iq, and separating the equation

into real and imaginary parts yields:

 

did , _ ud . dlimrl
0T, dt + 2,; — R, + wmraTszq (1 0)T, dt (7.12)
0T dig +z' - uq w aTi (1 0)T li lw (7 l3)
3 dt q — Rs mr s d 3 mr mr -

Ignoring the coupling terms on the right side of the stator voltages of (7.12) and (7.13), the

relationships between the current and the voltage become:

did . __ ud
0T3? + 2d — E: (7.14)
di , u

A current loop model is shown in figure 7.2. Pole-zero cancelation between the first-order

lq* + Kp we I 0W u 1
' s Ls+R

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pl Controller System 00 Bus Motor I
Delay 1/Fs ‘1
b1 s+b2
‘_
8+8
Anti - aliasing Lowpass
Filter

Figure 7.2: Simple Current Control Loop.

models of the motor and the PI controller was used to determine the gains of the controller.
The goal was unity gain for the current control loops for both of the motor configurations. The

bandwidth chosen for both current loops was 150Hz and the switching frequency was 5.6kHz.

92

As shown by Kazmierkowski, [17], the terms containing the magnetizing current of (7.11)
can be neglected because of the relatively large time constant and high switching frequency of
the inverter. Due to fast switching, the inverter acts as current source, impressing AC currents
onto the motor stator windings [14]. The two coupling voltage speed terms from equation
(7.11) are:

usdx = wmroTsz'q

(7.16)

usqx = "wmrUTsid
These can be treated as feed-forward terms and added to the output of the PI controller. Figure

7.3 shows the two current controllers and the decoupling network. As shown in figure 7.3, an

 

 
    
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ud E; :
'd Ud Co d
Command lq Limit de mman
. Filter ‘ C23
x Iq Feedback
x
wmr ’9
W
Uq
I 2
Command lq Limit Uq Command
Filter t E
lq Feedback

Figure 7.3: Iq Current Control Loop with Anti-windup.

anti-windup term was added to the PI controller. Figure 7.4 shows the flux model.

For the 4-pole motor, the SVPWM scheme introduced in chapter 2 is used. The motor
parameters from Table 3.5 were used for tuning the current control loops and the slip estimator.
Using the setup described in chapter 6, experiments were conducted. In the following section

the results are presented.

93

 

 

 

 

   

 

 

»i:' ~

4 -2 Coordinate id
Transformation ib—b 4- 1
I" x "s *— 1

 

 

 

 

 

 

 

 

 

 

 

Figure 7.4: Magnetizing current imr and Rotor Flux angle p Model

7 .2.2 Performance Results of the 12-pole and 4-pole Motor

In this section, the experimental motor was operated in both the 4-pole and 12-pole motor
configurations. The dynamometer was operated in speed regulation mode with a set point of
500 rpm. Figures 7.5.a and b show the response of the 12-pole motor to an id command. This
command was a dc biased square wave. In figure 7.5.a the commanded and resulting currents
are plotted. The current 2}, is commanded at 5 A.

The plot of 2}, shows the the effect of some current coupling. This was due to saturation.
Figure 7.5.b compares id feedback with the measured torque. Similar to 12-pole testing, the 4-
pole motor was loaded by the dynamometer operating at 500 rpm in speed regulation. Figures
7 .5 .c and d show the resulting id and z'q and measured shaft torque. The flux producing current
command for the 4-pole motor, iq, was 3.5 A. From figure 7.5.c, no coupling effects were
noticed. Figure 7.6 shows the results of testing the bandwidth of the current controller for the
4-pole configuration. A swept sine input was applied to the id current loop. The loop was
designed for a bandwidth of 150Hz. However, only 75Hz bandwidth was obtained. This can
be explained by the large inertia load of the dynamometer motor. The speed controller used
for both motor configurations was a PI controller with anti-windup. Figures 7.7.a and b show
the speed response of both motors to a step command. Figures 7.7.c and (1 show the speed
torque curves for each configuration. The curves were obtained by operating the motors in
velocity mode and the dynamometer in torque mode.

The results of the experiments show:

94

 

 

 

 

 

 

 

 

 

 

l l l l l l l L

 

 

 

15

amps

L ii""' .
234567891011122345678910111

 

 

4
2
0
seconds seconds 2

(a) iq12,id12 Feedback (b) id 12 Commanded (solid),id12 Feedback (dashed),
Measured Torque)

 

- e o
- ......................... I ...................... -

 

15 y I v I I r v f
. . . . . . . .
. . . . . . . .
z I I l I I o e

  
 

‘ !- E L 10 _. ..... . ......................................... 10
' : E 5 Id . . : . : .
'd s s s s 3 I ld Id ;

... ....... ./ Torque ... ..... .. 5

 

Nm

feedback3 i E 5

\lq;

 

 

 

.. commanded i

 

 

345678910111232557

 

 

. H; ------- .... ---- -‘ 0* ........................... ; ....... ',.......;.....; ..... .0
L r r r 1 A J 1 - i i '1 4' i ; i

 

8
seconds seconds

(c) iq4,id4 Feedback (d) iq4 Commanded (solid),iq4 Feedback (dashed),
Measured Torque)

Figure 7.5: 12-pole and 4-pole id Control

95

 

amps

 

 

 

 

 

: i r i i i i i i
2.86 2.865 2.87 2.875 2.88 2.885 2.89 2.895 2.9
seconds

Figure 7.6: Id frequency response (between 60-7OHz

1. The experimental pole-changing motor can operate either as a 4-po‘le motor or a 12-pole

motor;
2. The produced speed-torque characteristics of both motors; and
3. Both motors can be controlled with field oriented control.

The third result is the most important, as it leads to the simultaneous control of both motors

with all four current components, id4,iq4,id12 and 2,12, separately controlled.

7 .2.3 Experimental Results of 4-2 Coordinate Transformation

In order to proceed to the objective of independently connolling both motors simultaneously,
the coordinate transformation proposed in chapter 4 is verified. One of the results of coordinate
transformation (4.27) is that only four of the nine phase currents are needed to calculate 2.8034
and immg from which idlg, iqlg, 2',“ and iq4 are estimated. Using different combinations of
four phase currents, the three coordinate transformations of (4.29), T 1, T2 and T3, each result
in the same estimated current sets, rim/34 and immg. The following experiments show that
averaging the resulting currents from each transformation results in more accurate estimations.

Figure 7.8.a shows the estimated currents 71,14 and iq4 from the T 1 transformation. Figure

96

    

seconds seconds
(a) 12-pole Speed Response (b) 4-pole Speed Response

 

o 100 200 300 400 500 0 200 400 600 300 1000
rpms rpms
(c) 12-pole Speed-Torque Curve (d) 4-pole Speed-Torque Curve

Figure 7.7: Motor performance: Speed Response

97

 

I.)
(3
B
C

         
     

Id : I
Id feedback id feedback
., 15—~commanded--~'~~ - - -- ‘ ....3...“ --------

 

15 'commanded

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. l
tn
Q
E .
a 5 1'1 W] .M
I i‘ .'
till 1113‘ I1. M
l 1 . .
o, l ......................................................
'q 'q c [q 5 feedgack é
Commanded - - feedback K i ommanded ‘ :6 i i
“ 0.8 1 1.2 1,4 1,6 1.8 2 2.2 '” 0.8 1 12 1.4 1.8 2 2.2
seconds seconds6
(a) T1: 4 of the 9 phase currents (b) (T2 + T3) / 2: 6 of the 9 phase currents
” T; Id , 3
feedback Id
5 5 Id ........ feedback 1 l
commanded
1. l
| I
I 1 i i '
Iq . .
. : . _.. commanded' ....... 3‘ Id [.1
I q : : 3 Efeedback
E Commanded-- E gfeedback , E 3
_: 1 1' r i i i i 5 J_ r I
" ca 1 1.2 1,4 1.6 1.8 2 2.2 08 1 1.2 1.4 1.6 1.8 2 2.2
seconds seconds

 

 

 

(c) (T 1 + T3) / 2: 6 of the 9 phase currents (d) (T1 + T2 + T3) /3 8 of the 9 phase currents

Figure 7.8: 4-2 Coordinate Transformation

7.8.b shows the estimated currents 2'44 and iq4 resulting from the averaging of the calculated
currents imgn and isafiT3 from T2 and T3 respectively. Figure 7.8.c shows the estimated
currents resulting from the averaging of the calculated currents imgfl and 2'“,ng from T1
and T3 respectively. Finally, figure 7.8.d shows the estimated currents i,“ and iq4 resulting
from the averaging of the calculated currents imam. 2',an and immg from T1, T2 and T3
respectively.

The noise is a result of measured phase current offsets. Averaging the outputs of the
transformations filters the noise. The following figures show the calculated imr and 1'54 currents
for the T1,(T1+ T2)/2 and (T1 + T2 + T3)/2.

Figure 7.9.a shows the stator currents 1,, for: T 1, the average of T 1 and T2 and the average

98

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figures b (and c)

l L l

 

 

 

_20 i 1 .2c 1 i i i ; i i 1
4.8 5 5.2 5.4 5.6 5.6 6 0.2 5.96 5.96 6 6.02 6.04 6.06 6.08 6.16.12
seconds seconds
(a) isa for during id step command (b) Closer view of isa
2° 3 r 1. 7 :
"B i M i

   

15--

 

"Tl:T2:T3_"

  

oooooooooooooooooooooooooooooooooooooooooooooooooo

1O

 

 

 

' L i L i T
5.96 5.96 6 6.02 6.04 6.06 6.08 6.1 6.12
seconds

(c) Closer view of £33

Figure 7.9: Reduced Coordinate Transformation: Orthogonal Stator Current Component 1:33
and im

of T 1, T2 and T3, during the torque step command of the previous figures. Figures 7.9.b and
0 show a close up view of the currents during the torque transient. All three stator current
components are in phase, showing that all three coordinate transformations of 4.29 calculate

the same i304 and i354 currents.

7 .3 Simultaneous Operation of 12/4-pole Motor

The results of chapter 5 revealed large torque and current spikes resulting from the instanta-
neous switching between pole configurations. There, it also was shown that the motor can

operate with a combination of 12-pole and 4—pole applied voltages. Therefore, it should be

99

in.
b
.9.
(0
...-I
U)

    

 
 
       
 

 

 
 

 

 

 

I

I

l

l (9812 ‘~~ ls12 00r
lS12 I

l """""""" . (0r plZTStator 0t-

: ' R ' ‘1’

' A, rr12

(a) 4-pole Stator Flux and 12-pole Stator Flux(b) 4-pole and 12-pole Rotor Flux Reference Frame
moving independently

Figure 7.10: Dual 12-pole and 4-pole Reference Frames

possible to have a gradual change in pole configuration, avoiding these large current transients
while still operating. A scheme was devised, [8], to simultaneously operate the experimental

motor torque as the superposition of torques from the 4-pole and the 12-pole motor.

7.3.1 Dual F 0C

In order to independently control each motor, the two sets of torque and field producing cur-
rents, z'dqlg, for the 12-pole motor and idq4, for the 4-pole motor, have to be independent. For
conventional rotor flux orientation the orthogonality of the stator current components in and
ig is preserved when these currents are transferred into the rotor flux reference frame. It was
shown in chapter 4 that the coordinate transformations (4.29) produce two independent sets of
orthogonal currents from a 9-phase symmetrical system. These two orthogonal currents can
be mapped into their respective rotor flux reference frames.

Figure 7.10 show the two space vector currents 3,4 and 5,12 rotating over the same stator
windings. These two independent resultant current space vectors can be produced by the 9-leg

inverter. The total stator current of the motor is
gStator'Total = Z94 + T312 (7-17)

Applying the coordinate transformation (4.28) results in two orthogOnal currents sets imm

100

and imam rotating with respect to each other at a rate of c1234 — c2812. Figure 7.lO.b shows
the two current sets @034 and 2,0312 mapped into their respective rotor flux-linkage reference
frames, ‘11,,12 and ‘11,”, and rotating with respect to each other at wmr4 — wmr”. The two
independent stator currents of (7.17) establish two independent rotor fluxes, shown in (7.18)

in their respective reference frames.

‘I’rrn = Lr12irr12 + Lm12isr12

 

 

_ __ _. 7.18
er4 = Lr4zrr4 + Lm4zsr4 ( )
Following equations (7.4)-(7.8):
- 1irrl2
zmrl2 '- Lm12 (719)
- W174
mr = 7.
l 4 Lm4 ( 20)
dgmr -. .
Tr12_dt_12 + Zmr12 = llsq12 (721)
dgmr -: .
Tr4—Z-[t-i + Zmr4 = z.sq4 (722)
with
Ta. = Lag/RM (7.23)
Trl2 = Lr12/Rr12 (7-24)
isd12
wmr 2 = wr 2 + —-.———' (7-25)
1 1 Tr12lzmrl2|
isd4
m, = ,. + _ 7.26
w 4 w 4 Tr4limr4‘ ( )

From equation (7.9) the torque for a conventional motor is the product of two components,
imr = ( \Ilrrhr) and id in the same reference frame, the rotor flux reference frame. The torque is
invariant to the change in reference frames,i.e. the torque calculated in the rotor flux reference
is the same torque in the stationary reference frame and the rotor reference frame. In the case

of controlling two motors there are two reference frames, where torque is produced, defined

10]

by Wfllg and WW” respectively. The torques, T812 and T64, can be calculated in each of their

respective reference frames and summed.

L2 .2 - L2 —
Trotaz = ngiimr-Hlidm + 3_l4liimr4id4| (7-27)
Lr12 Lr4

In the following section are the results of several experiments where the total shaft torque is
shown to be the sum of both motor torques. In order to conduct these experiments, the control

scheme of figure 7.11 was used.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Pl
Controller
human
Pl — 12-pole
Controller [ ii _
4t09 a .:
Trunformatloni §
Pl - .
lqudw'tflfl
. Hy j Pl ‘ +0010 ‘—
"“ Controller 9 .
Decou lin la. IB to lq ld' Flux
. p 0 L “9°" l —E 4to2(|aa12)
l—mptolqui 12 _
role ~ 20111134)
1— 12-POIO Flux

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 7.11: Dual machine control scheme.

7.3.2 Experimental Results: Controlling idq4 and idqlg

This sections shows the results of controlling the 12—pole and 4-pole motors simultaneously
and independently. Operating in speed mode at 600 rpm, the dynamometer acted as the motor
load. The shaft torque was measured between the dynamometer and motor. As shown in figure
7.11, the current commands for the 12-pole motor are idlg and iqlg, and for the 4-pole motor
the commands are For the first experiment the flux producing currents of both motors, 2'9”
and 294,, were held constant as was 23,112. A DC biased square wave was the 1144 command. As
shown in figure 7.12, the dual motor control scheme effectively decouples i,“ and idqlg. The
resulting torque is the sum of the constant torque from the 12-pole motor and varying torque

of the 4-pole motor. 2',“ and iq4.

102

 

-----------------

........

  

Commanded/feedack . q

 

6.... ...... commanded/feedaCku'g. ........

. IWW

 

 

 

2 ........................ m4 ...................... .
............ ,Commandedlfeedack
0_.J ......... i ........ i ......... ; ........ bum“; ......... i ........ i ..... .
4 5 6 7 8 9 10 11
seconds

Figure 7.12: Torque, 2,14, step command

For the next experiment, the torque commanded for both motors was a DC biased square
wave. The square waves were 180 degrees out of phase and scaled appropriately in order to
produce a total constant torque. Both flux levels were held constant, as shown in figures 7.13.a
and b. Figure 7.13.b shows iq4 and iq12 feedback. The resulting shaft torque stayed relatively
constant.

For the final experiment, all four currents, idq4 and idqu, were varied7.13.c.From the start
to to, only the 12-pole motor is commanded to produce torque. Between to and t1, the 4-
pole motor commands, 2.14 with iq4 still set to zero. As expected there is no change in torque.
Likewise, when the 4-pole commands iq4 with 2'44 commanded back to zero, no additional
torque is produced. However, when both m and iq4 are nonzero as well as 73,112 and im the
torque increases during t2 to 133.

As shown in the previous experiments, both 12-pole motor torque and 4-pole motor torque
can be commanded simultaneously with the resultant torque being the summation. Therefore,
during pole-changing, both motors can produce torque at the same time, making a gradual

pole-changing transition possible.

103

14

 

 

- 1&4 ' ;
--eemandeém i

-.-—— —-;
I

_ l
ld12 .
IIIoiommandedm;

    

 

 

amps
Oi

...; ........ t........, ........ ;. ....... 1. . ............. 4

 

 

 

 

    

 

 

 

:‘fi

 

 

 

 

2“: j g ShaflTorquej ; ; f j 2 z .- i' . . : P' ' : :
, - a 3 .3 g ‘ r ‘ ' lq4 lq4 E lq12 lq12

4 4.5 9 9.5 6 9.5 '7 is a 9.5 9 9.5 ‘4 73 ‘5 5"5 ‘5 6.5 ‘7 7‘5 ‘8 9.5 ‘9 95
SGCOHdS seconds

 

 

 

 

 

 

(a) 4 and 12-pole torque commands and (b) The estimated and commanded flux
measured shaft torque of both motors

|d12=7 |d12=7

amps

amps

Nm

 

seconds
(c) qu12 vs qu4

Figure 7.13: 4-pole and 12-pole alternating torque commands

104

Pole-changing

_*

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

+Transition .. Iu4
A £112
0
124
A
/ i212
0
Tdomandod
\\ \
\
Nrn \ \ , ’\
T84 , ’ I \ T612
0 t0 t1 t2 t3
time

Figure 7.14: Pole-changing control scheme
7 .4 Pole-Changing Transition: Flux Control

It previously has been shown that pole-changing during motoring operation results in large
current and torque transients. For propulsion applications, large torque transients result in
speed oscillations, while current transients result in saturation and excess thermal loading. In
order to avoid such transients a novel control scheme for an induction machine drive system
was developed [8]. The induction machine’s flux and torque levels are controlled and adjusted
in a manner to guarantee smooth torque production during pole-changing. In order to control
the flux and torque level during pole-changing, the control scheme of simultaneous operation
of the 12-pole and 4-pole motors is used.

While in the current pole configuration, the flux of the desired pole configuration is es-
tablished. Next, the produced torque of the current pole configuration is decreased while the
torque of the desired pole configuration is increased. The sum of both torques meets the de-

manded torque. Once the demanded torque is met solely by the new pole configuration, the

105

old pole configuration flux is decreased. Figure 7.14 demonstrates the transitioning from a
lZ-pole configuration to a 4-pole motor configuration.

First, the 4-pole flux is established. During this period, to-tl, the 4-pole motor does not
produce torque, while the lZ-pole motor continues to meet the demanded torque. Once the
4-pole rotor flux has been established, after 7'4 seconds, 2'44 is increased and 2,112 is decreased.
During this period, t1-t2, both motors are producing torque to meet the demand. Once the
4-pole motor is the sole torque producer, the 12-pole flux can be decreased.

The rate at which the fluxes are adjusted depends on several things, the rotor flux time
constants of both machines 7'4 and 112 and the total saturation level. During simultaneous
torque production, the risk of saturation increases due to the presence of two flux fields. Both
fluxes have to be adjusted to prevent saturation and to maintain useable torque.

An example of the pole-changing scheme is shown in figure 7.15. The figure shows the

transition period of approximately 1.9.

 

 

..|d4 .......... Measured ........

Torque

 

 

 

0 .5 1.0 1.5
seconds

Figure 7.15: Gradually adjusting 73014 and im

106

7 .5 Possible Implementation Strategy for Novel Pole-
changing Control in a Vehicle

The experimental induction motor drive system has four operating states, the 12-pole high
torque state and the 4-pole high speed state and two additional states resulting from field

weakening. The four operating states are shown in terms of torque and speed capability in

 

figure 7.16.
Torque
1 11 111 IV
\\\\\\\\ 5
S 12 pole\\:c12'pflet
C t - ons an
\ ons an§£ Power 4-pole

\t orque
W: Constant

P
._ ; ,. WW ,iililifiZ...

Speed

 

 

 

 

 

 

 

Figure 7.16: Constant torque and power regions

Determining which operational state depends on the torque and speed demands. For a ve—
hicle, the first state of operation is the lZ-pole motor for high starting torque. This is followed
by the 12-pole constant power state, to continue acceleration. For cruising, the next state is
the 4-pole constant torque state. For higher speeds, the next state is the 4-pole constant power
state.

This control strategy can be viewed as a state machine. The transition diagram shown in
figure 7.17.

Both speed and torque are required to determine which configuration meets the applica-
tion’s demands.

For the following simulation, the transition diagram without field weakening was used.

Figure 7.18 compares the response of three closed-loop, speed control schemes. In the first

107

 
 
   
 
   
   
   
 

   
 
 

1 2-pole
Configuration
Constant Power

    
  
 
 
 
  
 
 
 

    
   

4-pole
Configuration
4-pole

Constant Torque
‘ Configuration

Constant Power

1 2-pole
Configuration
Constant Torque

  

Figure 7.17: Control States with field weakening

case, the pole-changing induction drive is operated entirely in the 9-phase/4-pole configura-
tion. Given a speed command of 100rad/ s the machine took approximately 6 seconds to reach
95% of the desired speed. In the second case, when the speed reached 70rad/s the torque
command 73.112 was instantaneously switched to zero while i,“ was commanded to 100%. In
this case, it took 4.5 seconds for the machine to reach 95% of desired speed. In addition, at
70rad/s the speed did not increase for 0.5 seconds. In the third simulation, the pole-changing
scheme is used. In this case, the machine took approximately 3 seconds to reach 95% of
desired speed.

Figure 7.19 shows the torque response for all three simulation cases. Comparing the torque
responses of figure 7.1% and 7.19c, the torque produced was less erratic when the pole-

changing scheme was employed.

108

 

120

 

 

1 00 WW

 

 

 

80 "
/ xi ,R\controlled pole change

\ I; 1 2-pole to 4-pole
I i

 

radians per seconds
0')
O

 

 

 

 

 

 

 

.'\ 1
,r" instantaneous pole change
’/ 12-pole to 4-pole
40 r'
I; 4-pole operation
20 ,3
.l
0
O 5 1 0 1 5

seconds

Figure 7.18: Speed comparison (simulation): 4pole operation, instantaneous pole change,
controlled pole change.

 

 

 

 

 

 

20- .................... ' ..................... 3 ..................... t .................... r .................... -
1o. .......................................................................................................... -
0 CT ............................................ '.' .' ....... 2'". 7'77, ............... 'TT‘T ..,.: ..................
-10 _L 1 l 1
0 ()5 1.5 2 255
a) 4-pole Te
................ pole change.......f ......................................... _
5 E \

   

 

 

 

 

 

 

 

 

 

 

 

 

seconds
0) 12-pole to 4-pole control change

Figure 7.19: Torque Comparison (simulation): a) 4pole operation b) instantaneous pole
change 12 to 4 c) controlled pole change

109

CHAPTER 8

Conclusions

The presented work is an extension of previous work on the integral starter/alternator. The
toroidally wound, induction machine was designed as the starter/alternator for 42 Volt vehi-
cles. As part of the starter/alternator effort, the induction machine and 9-leg inverter were
designed and constructed. In addition, previous analysis included: calculation of steady state
parameters for both the 3-phase/12-pole and 3-phase/4-pole configurations, development of
vector control of both configurations and thermal analysis of the machine.

Discontinuous operation, zero torque production, is a consequence of pole-changing be-
tween starter and alternator operations. As part of the work presented, a control scheme was
developed which results in continuous operation and smooth torque production during the
pole-changing transition. Therefore, a novel induction drive system with speed/torque capa-
bilities greater than equivalent sized conventional systems was presented, with the intention

of being utilized in applications such as hybrid vehicle propulsion.

8.1 Accomplishments

As a consequence of the development of the pole-changing control scheme, the following

items were accomplished in this work:

1. A PWM scheme for 9-phase operation was developed and implemented. As a result, of

this work a generalized scheme for n-phase SVPWM was developed [12]. In addition,

110

a novel implementation method of that scheme was patented [7]. Several other 9-phase

switching schemes, resulting in lower switching losses, also were developed.

2. Detailed analysis of the stator windings and the resulting magnetomotive force for 9-
phase and 3—phase operation was conducted. Based on this analysis the motor param-
eters were derived. As a result of this work, a method was developed and patented for

improvement in torque ”smoothness” from a conventional induction machine [10].

3. A unique coordinate transformation from a 9-phase symmetrical system to an orthogo-

 

nal system was developed. The inverse transformation also was developed based on the

constraints which minimized core and winding losses [8].

4. A model of the pole-changing motor was developed directly from fundamental electro-
magnetics. This model was used to simulate the machine during pole-changing and to

validate the control scheme.

5. An experimental setup was prepared. Hardware and software specifically developed for

this work included:

(a) RTLinux real-time motor control development system;
(b) FPGA/AD 9—phase Motor Controller Interface card; and

(c) Dynamometer Graphical User Interface.

6. A novel pole-changing control scheme, based on independently controlling two motors

sharing the same stator windings, was developed [11].

7. A proposed method for implementing the novel pole-changing control scheme in a drive

system for vehicle propulsion was presented.

8.2 Future Work

The work presented can be continued in several possible ways:

11]

 

1. Implementation of the pole-changing drive:

(a) The pole-changing drive can be implemented in a vehicle in order to evaluate re-

sponsiveness.
(b) The drive can be evaluated for efficiency improvements, in applications currently

using a conventional motor with field weakening.

2. Evaluating the possibility of different pole ratios should be undertaken. Additional work

has shown it may be possible to construct a machine with three pole configurations.

3. Using FEA, a more efficient machine can be designed. Due to space constraints the
starter/alternator was wound toroidally. Machine efficiency may be improved with dif-

ferent winding patterns.

112

BIBLIOGRAPHY

[1] R. Bojoi, M. Lazzari, F. Profumo, and A. Tenconi. Digital Field-Oriented Control for
Dual Three-Phase Induction Motor Drives. IEEE Transactions on Industry Applications,
39(3):752—760, May-June 2003.

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