Thesis Marco Rivera

Universidad Tecnica Federico Santa MarıaDepartament of Electronics Engineering

Valparaıso, Chile

Doctoral Dissertation

Predictive Control in an Indirect Matrix Converter

Marco Esteban Rivera Abarca

Doctorate Program

Doctorate in Electronic Engineering

Thesis Supervisor

Dr. Jose Rodrıguez Perez - UTFSM

Evaluation Committee

Dr. Cesar Silva Jimenez - UTFSM

Dr. Jose Espinoza Castro - Universidad de Concepcion

November 2011

Dedicado a las personas que mas amo, ustedes le dan sentido a mi vida.

Contents

Contents i

List of Figures v

Nomenclature xiii

Abstract xvi

Resumen xviii

Acknowledgments xx

Agradecimientos xxi

1 Introduction 1

1.1 State of the art review . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Hypothesis and contribution of this thesis . . . . . . . . . . . 5

1.3 Chapter review . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Review of three-phase ac/ac topologies 7

2.1 Classification of ac/ac power converters . . . . . . . . . . . . . 7

2.2 Topologies with dc-link . . . . . . . . . . . . . . . . . . . . . . 9

2.2.1 Back-to-back converter . . . . . . . . . . . . . . . 9

2.3 Topologies without dc-link . . . . . . . . . . . . . . . . . . . . 10

2.3.1 Cycloconverter . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Direct matrix converter . . . . . . . . . . . . . . . 11

ii

Contents iii

2.3.3 Indirect matrix converter . . . . . . . . . . . . . . 13

2.3.4 Three-phase ac/ac buck converters . . . . . . . . . 14

2.3.5 Sparse indirect matrix converters . . . . . . . . . . 15

2.3.6 Indirect three-level matrix converter . . . . . . . . 17

2.4 Hybrid topologies . . . . . . . . . . . . . . . . . . . . . . . . . 18

3 A review of modulation and control methods for

matrix converters 20

3.1 Scalar techniques . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Direct method: Venturini . . . . . . . . . . . . . . 21

3.1.2 Roy’s method . . . . . . . . . . . . . . . . . . . . . 25

3.1.3 Current phase displacement control for Venturini

and Roy methods. . . . . . . . . . . . . . . . . . . 26

3.2 Pulse width modulation methods . . . . . . . . . . . . . . . . 27

3.2.1 Carrier-based modulation method . . . . . . . . . 27

3.2.2 Space vector modulation (SVM) method . . . . . 29

3.3 Direct torque control . . . . . . . . . . . . . . . . . . . . . . . 31

3.4 Predictive control . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4.1 Predictive current control . . . . . . . . . . . . . . 32

3.4.2 Predictive torque control . . . . . . . . . . . . . . 36

3.5 Assessment of the methods . . . . . . . . . . . . . . . . . . . . 42

3.6 Comments and conclusion . . . . . . . . . . . . . . . . . . . . 44

4 The indirect matrix converter 45

4.1 Description of the topology . . . . . . . . . . . . . . . . . . . . 45

4.2 Zero dc-link current commutation . . . . . . . . . . . . . . . . 47

4.3 PWM based control method . . . . . . . . . . . . . . . . . . . 48

4.3.1 Modulation of the rectifier stage . . . . . . . . . . 48

4.3.2 Modulation of the inverter stage . . . . . . . . . . 52

4.3.3 Simulations results . . . . . . . . . . . . . . . . . . 55

5 Model-based predictive control in an IMC 59

Contents iv

6 Predictive current control with reactive power minimization 64

6.1 Control scheme for the IMC . . . . . . . . . . . . . . . . . . . 64

6.2 Input filter and load discrete equations . . . . . . . . . . . . . 65

6.3 Cost function definition . . . . . . . . . . . . . . . . . . . . . . 66

6.4 Discrete time delay error compensation . . . . . . . . . . . . . 67

6.5 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.6 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 72

6.7 The problem in the source current with a weak ac-supply . . . 76

7 Current control for an IMC with input filter resonance mitiga-

tion 77

7.1 Current control scheme for the IMC with active damping ap-

proach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

7.1.1 Active damping approach and implementation . . 78

7.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 79

7.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

8 Imposed sinusoidal source and load currents for an IMC 87

8.1 Fundaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

8.2 The problem on the input side . . . . . . . . . . . . . . . . . . 88

8.3 Predictive current control for the IMC with imposed sinusoidal

source currents . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

8.3.1 Prediction model . . . . . . . . . . . . . . . . . . . 90

8.3.2 Cost function definition . . . . . . . . . . . . . . . 92

8.4 Generation of the source current reference is∗ . . . . . . . . . 92

8.5 Simulation and experimental results . . . . . . . . . . . . . . . 94

8.6 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

9 Conclusions 101

Appendix 103

9.1 Publications in journals . . . . . . . . . . . . . . . . . . . . . . 103

9.2 Publications in conferences . . . . . . . . . . . . . . . . . . . . 104

Contents v

9.3 Projects related with the research . . . . . . . . . . . . . . . . 107

9.4 Experimental setup circuit diagram . . . . . . . . . . . . . . . 108

Bibliography 120

List of Figures

2.1 Classification of ac/ac power converters. . . . . . . . . . . . . . . 8

2.2 Three-phase ac/ac converter topologies with dc-link energy stora-

ge; (a) voltage dc-link back-to-back converter; (b) current dc-link

back-to-back converter. . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Three-phase ac/ac converter topology without dc-link energy sto-

rage: cycloconverter. . . . . . . . . . . . . . . . . . . . . . . . . . 11


rage: direct matrix converter (DMC). . . . . . . . . . . . . . . . 12


rage: indirect matrix converter (IMC). . . . . . . . . . . . . . . . 13


rage: three-phase buck converter. . . . . . . . . . . . . . . . . . . 14

2.7 Three-phase ac/ac converter topologies without dc-link energy

storage; (a) sparse matrix converter (SMC); (b) very sparse ma-

trix converter (VSMC); (c) ultra sparse matrix converter (USMC). 16

2.8 Indirect matrix converter with an additional bridge-leg that al-

lows the mains phase voltages to be switched directly or inverter

into the link. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.9 Circuit topology of the hybrid direct matrix converter and the

implementation of a single switching cell. A cascading of several

H-bridges in each connection of an input and output is also possible. 18

2.10 Circuit topology of the hybrid indirect matrix converter with a

series voltage source in the link. . . . . . . . . . . . . . . . . . . 19

vi

List of Figures vii

3.1 Summary of modulation and control methods for matrix converters. 21

3.2 Direct method: venturini, typical waveforms; a) output voltage

vaN [pu], its reference (bold line) and b) output current ia [pu]. . 24

3.3 Unipolar sinusoidal PWM method and desired output level voltage. 28

3.4 Carrier-based method, typical waveforms; a) line-to-line output

voltage vab [pu]; b) output current ia [pu]. . . . . . . . . . . . . . 29

3.5 Direct torque control scheme. . . . . . . . . . . . . . . . . . . . . 32

3.6 Predictive current control scheme. . . . . . . . . . . . . . . . . . 33

3.7 Predictive current control without power factor correction A =

0; a) output current [A]; (b) reactive power [kVAR]; (c) input

current [A] and input voltage [V/30]. . . . . . . . . . . . . . . . 35

3.8 Predictive current control with power factor correction A = 1; a)

output current [A]; (b) reactive power [kVAR]; (c) input current

[A] and input voltage [V/30]. . . . . . . . . . . . . . . . . . . . . 36

3.9 Predictive torque control scheme. . . . . . . . . . . . . . . . . . . 37

3.10 Predictive control torque without power factor correction λq = 0;

a) speed [rad/s]; b) electrical torque [Nm]; c) output current [A];

d) stator flux [Wb]; e) reactive power [kVAR]; f) input current

[A] and input voltage [V/30]; g) zoom of input current isA and

input voltage vsA. . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.11 Predictive control torque with power factor correction λq = 1; a)

speed [rad/s]; b) electrical torque [Nm]; c) output current [A]; d)

stator flux [Wb]; e) reactive power [kVAR]; f) input current [A]

and input voltage [V/30]; g) zoom of input current isA and input

voltage vsA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.1 Indirect matrix converter topology. . . . . . . . . . . . . . . . . . 46

4.2 (a) Line-to-line input voltages vi and dc-link voltage vdc; (b) valid

current vectors in the α − β plane; (c) first-maximum, second-

maximum and average dc-link voltage vdc. . . . . . . . . . . . . . 49

4.3 Position of the reference current vector in sector II; θi is the angle

respect to α-axis; θsi is the angle in the sector. . . . . . . . . . . 50

List of Figures viii

4.4 Formation of the dc-link voltage vdc and average dc-link voltage

vdc. As it can be observed, the dc-link voltage is given by the

first and second maximun line-to-line input voltages. . . . . . . . 52

4.5 (a) Available vectors on the inverter side; (b) position of the

output reference vector in sector II. . . . . . . . . . . . . . . . . 54

4.6 Formation of the dc-link voltage vdc and dc-link current idc within

a pulse period. Switching state changes of the input stage do

occur at zero dc-link current. . . . . . . . . . . . . . . . . . . . . 55

4.7 Simulation results SVM technique in open-loop control; (a) source

voltage vsA [V/10] and source current isA [A]; (b) output current

ia [A]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.8 Schematic diagram of the current control strategy added to the

modulation technique; the PI controller is in d-q coordinates. . . 56

4.9 Simulation results SVM technique in closed-loop control; (a) source


reference i∗a[A] and measured output current ia [A]. . . . . . . . 57

4.10 Simulation results SVM technique in closed-loop control; (a) source


reference i∗a[A] and measured output current ia [A]. . . . . . . . 58

5.1 FS-MPC generic algorithm. . . . . . . . . . . . . . . . . . . . . . 63

6.1 Predictive current control scheme. . . . . . . . . . . . . . . . . . 65

6.2 Simulation results without instantaneous reactive power mini-

mization; (a) source voltage vsA/10 [V] and current isA [A]; (b)

output current reference i∗a and measured ia [A]; (c) reactive

power qs [VA]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.3 Simulation results; (a) spectrum of source voltage [pu]; (b) spec-

trum of source current [pu]; (c) spectrum of output current [pu]. 70

List of Figures ix

6.4 Simulation results with instantaneous reactive power minimiza-

tion; (a) source voltage vsA/10 [V] and current isA [A]; (b) output

current reference i∗a and measured ia [A]; (c) reactive power qs

[VA]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

6.5 Simulation results; (a) spectrum of source voltage [pu]; (b) spec-

trum of source current [pu]; (c) spectrum of output current [pu]. 71

6.6 Experimental results without instantaneous reactive power mini-

mization; (a) source voltage vsA [50V/div] and current isA [5A/div];

(b) output current reference i∗a and measured ia [5A/div]. . . . . 73

6.7 Experimental results; (a) spectrum of source voltage [pu]; (b)

spectrum of source current [pu]; (c) spectrum of output current

[pu]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

6.8 Experimental results with instantaneous reactive power mini-

mization; (a) source voltage vsA [50V/div] and current isA [5A/div];

(b) output current reference i∗a and measured ia [5A/div]. . . . . 75

6.9 Experimental results; (a) spectrum of source voltage [pu]; (b)

spectrum of source current [pu]; (c) spectrum of output current

[pu]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

7.1 Predictive current control with active damping scheme. . . . . . 80

7.2 Experimental results without active damping approach; (a) source

voltage vsA [50V/div] and current isA [5A/div]; (b) output cur-

rent reference i∗a and measured ia [5A/div]. . . . . . . . . . . . . 81

7.3 Experimental results without active damping approach; (a) spec-

trum of source voltage [pu]; (b) spectrum of source current [pu];

(c) spectrum of output current [pu]. . . . . . . . . . . . . . . . . 81

7.4 Experimental results current control with active damping ap-

proach; a) source voltage vsA [50V/div] and current isA [5A/div];

b) output current ia and reference i∗a [5A/div]. . . . . . . . . . . 83

7.5 Experimental results with active damping approach; (a) spec-

trum of source voltage [pu]; (b) spectrum of source current [pu];

(c) spectrum of output current [pu]. . . . . . . . . . . . . . . . . 83

List of Figures x

7.6 Experimental results current control without and with active

damping approach; a) zoom spectrum of source voltage vsA [pu];

b) zoom spectrum of source current isA [pu]; c) zoom spectrum

of output current ia [pu]. . . . . . . . . . . . . . . . . . . . . . . 84

7.7 Experimental results current control without active damping ap-


b) output current ia and reference i∗a [5A/div] with output fre-

quency reference equal to 100Hz. . . . . . . . . . . . . . . . . . . 85

7.8 Experimental results current control with active damping ap-


b) output current ia and reference i∗a [5A/div] with output fre-

quency reference equal to 100Hz. . . . . . . . . . . . . . . . . . . 86

8.1 Predictive source and output current control scheme with source

current reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

8.2 Simulation results predictive control with imposed sinusoidal source

and load currents; a) source voltage [V/25] and current [A]; b)

output current and reference [A]. . . . . . . . . . . . . . . . . . . 95

8.3 Experimental results predictive control with imposed sinusoidal

source and load currents; a) source voltage [50V/div] and current

[5A/div]; b) output current and reference [5A/div]. . . . . . . . . 95


and load currents; a) source voltage [V/25] and current [A]; b)

output current and reference [A] with an output frequency refer-

ence of 100Hz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97


source and load currents; a) source voltage [50V/div] and cur-

rent [5A/div]; b) output current and reference [5A/div] with an

output frequency reference of 100Hz. . . . . . . . . . . . . . . . . 97


and load currents; a) source voltage [V/25] and current [A] 30o

displacement angle; b) output current and reference [A]. . . . . . 98

List of Figures xi





and load currents; a) source voltage [V/25] and current [A] −30o

displacement angle; b) output current and reference [A]. . . . . . 99




9.1 Experimental setup in the laboratory. . . . . . . . . . . . . . . . 109

9.2 Schematic of the input filter used in the implementation. . . . . 110

9.3 Schematic of the adapter between the dSPACE and FPGA. . . . 111

9.4 Schematic of the FPGA with its different voltage levels. . . . . . 112

9.5 Schematics of voltage regulators included in the FPGA. . . . . . 113

9.6 Schematic of the PROM included in the FPGA card. . . . . . . 114

9.7 Schematic of the led and DIP-switches included in the FPGA card.114

9.8 Schematic of an analog-digital converter CAD included in the

FPGA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

9.9 Schematic of a digital-analog converter CDA included in the FPGA.115

9.10 Schematics of input/output components included in the FPGA. 116

9.11 Schematics of the power circuit in the IMC. . . . . . . . . . . . . 117

9.12 Schematic of the driver implemented in the IMC for the switches. 118

9.13 Schematic of the implementation of voltage measurement in the

IMC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

List of Figures xiii

Nomenclature

Abbreviations

ac Alternating current

dc Direct current

AFE Active front end

CSC Current source converter

DMC Direct matrix converter

FPGA Field-programmable gate array

HDMC Hybrid direct matrix converter

HIMC Hybrid indirect matrix converter

IGBT Insulated gate bipolar transistor

IMC Indirect matrix converter

MPC Model-based predictive control

NPC Neutral point clamped

PCC Predictive current control

PI Proportional/integral controller

PWM Pulse-width modulation

SMC Sparse matrix converter

SVM Space vector modulation

THD Total harmonic distortion

USMC Ultra sparse matrix converter

VSC Voltage source converter

VSMC Very sparse matrix converter

ADC Analog digital controller

DAC Digital analog controller

List of Figures xiv

Variables

A,B,C Input-phase designators

a, b, c Output-phase designators

α, β ℜ (real) and ℑ (imaginary) components

s Laplace variable (not as subscript)

g Cost of quality function

k Discrete time

t Continuous time

Cf Filter capacitor

Lf Filter inductor

Rf Filter resistor

RL Load resistance

LL Load inductance

Ts Sampling time

Superscripts

p Superscript for predicted variables

∗ Superscript for reference variables

Vectors

is Source current [isA isB isC ]T

vs Source voltage [vsA vsB vsC ]T

ii Input current [iA iB iC ]T

vi Input voltage [vA vB vC ]T

io Load current [ia ib ic]T

vo Load voltage [va vb vc]T

i∗s Source current reference [i∗sA i∗sB i∗sC ]T

i∗o Output current reference [i∗a i∗b i

∗c ]T

List of Figures xv

Scalars

vdc Dc-link voltage

idc Dc-link current

qs Input reactive power

q∗s Input reactive power reference

Abstract

The indirect matrix converter has been the subject to investigation for some time.

One of the favorable features of this converter is the absence of a dc-link capacitor,

which allows for the construction of compact converters capable of operating at ad-

verse atmospheric conditions such as extreme temperatures and pressures. These

features have been explored extensively and are the main reasons why the matrix

converters family has been investigated for decades. The indirect matrix converter

features an easy to implement and secure commutation technique, the dc-link zero

current commutation. Moreover, the conventional indirect matrix converter has

bidirectional power flow capabilities and it can be designed to have small sized

reactive elements in its input filter. These characteristics make the matrix con-

verter a suitable technology for high efficiency converters for specific applications

such as military, aerospace, wind turbine generator system, external elevators for

building construction and skin pass mill, where these advantages make up for

the additional cost of an indirect matrix converter compared to conventional con-

verters. This converter uses complex pulse width modulation and space vector

modulation schemes to achieve the goal of unity displacement power factor and

sinusoidal output current. Thanks to technological advances, fast and powerful

microprocessors are used for the control and modulation of power converters.

To deal with the high processing power needed for these microprocessors, some

research has shown the positive potential of model-based predictive control tech-

niques in many power electronics applications. While there are a few challenges to

the predictive control method, it has been demonstrated as an appealing alterna-

tive to power converters control because its concepts are very intuitive and easy

xvi

List of Figures xvii

to understand, and it can be applied to a wide variety of systems. In addition,

it may involve multiple variable systems and non-linear constraints, making it

an easy controller to implement, especially since it is open to modifications and

extensions for specific applications. Predictive current control can be described

as a particular case of model-based predictive control which takes into account

the inherent discrete nature of the switching states of the power converter and

the digital implementation. Most of predictive current control methods applied

in matrix converters take into consideration the output current regulation and

the reactive power minimization on the input side, obtaining input currents in

phase with their respective phase voltages. However, this cannot ensure that they

present a sinusoidal waveform, especially when harmonic distortion in the source

voltage or strong resonances on the input filter are present. To enhance the qual-

ity of the source current, in this document is illustrate how the predictive current

control can be applied to an indirect matrix converter and how both source and

load currents waveforms can be controlled.

Resumen

El convertidor matricial indirecto ha sido objeto de investigacion durante algun

tiempo. Una de las caracterısticas favorables de este convertidor es la ausencia

de un condensador en el enlace dc, permitiendo la construccion de convertidores

compactos y capaces de operar en condiciones atmosfericas adversas, tales como

temperaturas y presiones extremas. Estas caracterısticas han sido estudiadas am-

pliamente y son las razones principales por las que la familia de convertidores

matriciales han sido investigados desde hace decadas. El convertidor matricial in-

directo cuenta con una tecnica de conmutacion facil de implementar y mas segura,

la conmutacion a corriente cero en el enlace dc. Ademas, el convertidor matricial

indirecto convencional tiene capacidad de flujo bidireccional de energıa y puede

ser disenado para tener pequenos elementos reactivos en su filtro de entrada.

Estas caracterısticas hacen que el convertidor matricial sea una tecnologıa ade-

cuada para convertidores de alta eficiencia en aplicaciones especıficas, tales como

aeroespacial, militar, sistemas de generadores eolicos, elevadores externos para

la construccion y el molinos de bolas, donde las ventajas compensan los costes

adicionales de una forma indirecta del convertidor matricial en comparacion a

los convertidores convencionales. Este convertidor usa esquemas de modulacion

por ancho de pulso y vectorial coplejos para asegurar el objetivo de factor de

potencia unitario y corrientes de carga sinusoidales. Gracias a los avances tec-

nologicos, rapidos y poderosos microprocesadores se utilizan para el control y

la modulacion de los convertidores de potencia. Para hacer frente al alto poder

de procesamiento necesarios por estos microprocesadores, algunas investigaciones

han demostrado el potencial positivo de las tecnicas de control predictivo basado

xviii

List of Figures xix

en modelos en muchas aplicaciones de electronica de potencia. Si bien aun existen

algunos desafıos en los metodos de control predictivo, se ha demostrado como una

alternativa atractiva para poder controlar los convertidores de potencia ya que

sus conceptos son muy intuitivos y faciles de entender, pudiendo aplicarse a una

amplia variedad de sistemas. Ademas, esta tecnica puede incluir varios aspectos,

la compensacion de tiempo muerto, y las restricciones no lineales, por lo que es un

controlador de facil aplicacion, sobre todo porque esta abierto a modificaciones y

extensiones para aplicaciones especıficas. El control predictivo de corriente puede

ser descrito como un caso particular de control predictivo basado en modelos, el

cual tiene en cuenta la propia naturaleza discreta de los estados de conmutacion

del convertidor y la implementacion digital. La mayorıa de los metodos de con-

trol predictivo de corriente aplicados en los convertidores matriciales consideran

la regulacion de la corriente de salida y la minimizacion de la potencia reactiva en

el lado de la entrada, obteniendo corrientes de entrada en fase con sus respectivos

voltajes de fase. Sin embargo, esto no puede asegurar que las corrientes de entrada

presentaran formas de onda sinusoidales, especialmente cuando esta presente dis-

torsion armonica en los voltajes de alimentacion y fuertes resonancias en el filtro

de entrada. Para mejorar la calidad de la corriente de entrada, a lo largo de este

documento se ilustrara como el control predictivo de corriente puede ser aplicado

a un convertidor matricial indirecto y como las formas de onda de las corrientes

de entrada y carga pueden ser controladas.

Acknowledgments

I really appreciate the patience, support, understanding, teaching, caring and love

of my family: Marianela, Marco, Consuelo, Caroll, Natalia, Constanza, Sebastian,

Sofıa. You give meaning to my life. Thank you very much.

My sincere thanks to financial support from the National Commission for Scien-

tific and Technological Research (CONICYT) and most especially, to Professor

Jose Rodrıguez of the Universidad Tecnica Federico Santa Marıa, professors Jose

Espinoza and Cesar Silva, without whose valuable assistance and moral support

would not have been possible to complete this work. Finally, I would like to thanks

to: Universidad Tecnica Federico Santa Marıa, Basal Project FB021 and FONDE-

CYT 1100404.

xx

Agradecimientos

Agradezco realmente la paciencia, ayuda, comprension, ensenanzas, carino y amor

de mi familia: Marianela, Marco, Consuelo, Caroll, Natalia, Constanza, Sebastian,

Sofıa. Ustedes le dan el sentido a mi vida. Muchas gracias.

Mi mas sincero agradecimiento al soporte financiero de la Comision Nacional de

Investigacion Cientıfica y Tecnologica (CONICYT) y de manera muy especial,

al profesor Jose Rodrıguez de la Universidad Tecnica Federico Santa Marıa, a

los profesores Jose Espinoza y Cesar Silva, sin cuya valiosa colaboracion y apoyo

moral no habrıa sido posible llevar a termino este trabajo. Finalmente, me gus-

tarıa agradecer a: la Universidad Tecnica Federico Santa Marıa, al Proyecto Basal

FB021 y FONDECYT 1100404.

xxi

Chapter 1

Introduction

The growing industrial development in Chile requires the availability of an ever

increasing amount of electrical energy. As the energy is nowadays limited, a en-

ergy efficiency of industrial processes is a highly relevant topic. Power converters

play an important role in energy efficient processes since they act as an interface

between the mains and the mechanical actuator, and as such are crucial to use

the energy efficiently. Ideal power converters should operate with reduced losses,

inject sinusoidal currents into the network and operate with unitary displacement

factor. The regeneration capability of a matrix converter is also a very important

issue in order to deliver energy back to the mains during braking of mechanical

loads. All these characteristics can be fulfilled by the matrix converters. There are

different kinds of matrix converters. The indirect matrix topology is similar to a

conventional back-to-back inverter but without dc-link capacitor and with bidirec-

tional switches in the front-end. Thanks to this feature, modulation schemes used

for the operation of conventional back-to-back converters can be more or less di-

rectly applied, without the necessity of complex transformations as in conventional

matrix topologies. Moreover, the capacitor-less dc-link permits to reduce the size

of the converter and increase its reliability, as this component has the shortest

lifetime compared to the other components. In addition, new topologies featur-

ing a reduced number of semiconductors have been introduced. These topologies

1

Chapter 1. Introduction 2

can be very competitive in those applications where regeneration is not required.

Despite the apparent simplicity in the topology, it should be considered that this

converter requires a complex switching strategy that avoids the interruption of

the load currents, in order to prevent over-voltages that could destroy the power

semiconductors.

These problems have been recently reported and solved in the literature. However,

there are still some open issues for the operation of this topology:

- The modulation methods that have been presented to date are complex and

need a high computation effort of the controller, making this topology less

attractive in comparison to well known standard solutions.

- Matrix converters operate with high switching frequency; therefore the effi-

ciency of the converter is reduced due to the high losses during each switch-

ing transition. This aspect is critical in high power applications. On the

other hand, the operation at low switching frequency adds the extra issue

of resonances in the input filter.

- Almost all modulation schemes are based on the assumption that the input

voltages are sinusoidal and balanced. This condition is not always met in

the industry, where the voltages can be unbalanced and also distorted.

Despite these issues, after almost three decades of intensive research, the develop-

ment of the matrix converter is reaching industrial application. In effect, at least

one big manufacturer of power converters (Yaskawa) is now offering a complete

line of standard units for up to several megawatts and medium voltage using cas-

cade connection. These units have rated power (and voltages) of 9-114kVA (200V

and 400V) for low voltage MC, and 200-6.000kVA (3.3kV, 6.6kV) for medium

voltage [1].


1.1 State of the art review

Matrix converters are forced-commutated converters which use an array of con-

trolled bidirectional switches to synthesize a variable output voltage with unre-

stricted frequency [2]. This topology has recently attracted a great interest as it

fulfills the most desirable characteristics in a converter: it is compact and allows

the generation of a load voltage with arbitrary amplitude and frequency. More-

over, the operation with sinusoidal input currents and power factor equal to one

is also possible. The capacity of regeneration makes this topology especially at-

tractive to drive loads that need to be braked, increasing the overall efficiency of

a system. The development of matrix converters starts with the works presented

in [3, 4], where the topology was described using bidirectional power switches.

These authors also present a method to generate the output voltages by using a

transfer function applied to the input voltages.

A rather different concept was presented in [5]. Here, the idea of a fictitious dc-link

was introduced and the switching states are arranged in such a way that the in-

put phase with most positive value and the input phase with most negative value

are always selected. This concept is known as indirect transfer function [6], as

an intermediate stage is used for the synthesis of the output voltages. The physi-

cal implementation of this mathematical concept gives rise to the indirect matrix

topology, where a six-switch bidirectional bridge corresponds to the rectifier, fol-

lowed by a capacitor-less dc-link stage connected with a conventional six-switch

unidirectional inverter [7]. This topology has the same performance as the conven-

tional matrix converter in terms of voltage transfer ratio, four quadrant operation,

unity displacement power factor and sinusoidal waveforms. However, due to the

topological similarity between this converter and standard inverters, well known

space vector modulation (SVM) methods can be applied, simplifying the imple-

mentation of control schemes. In addition, it allows the reduction of the number of

switches under certain conditions and the clamp capacitor can be greatly simpli-

fied to one diode and one capacitor [8]. Due to these advantages, indirect matrix

topologies have received considerable attention in the last few years and several


contributions have been made in the form of new modulation methods, with the

control of reactive power in the input currents, the analysis of the operation with

distorted power supply as well as new topologies with reduced number of switches,

also known as sparse matrix converters [9, 10]. In [11, 12] a SVM scheme is pre-

sented that achieves the theoretical maximum output voltage of this topology.

In [13], a modulation method is presented that uses the zero space phasors of the

inverter stage in order to achieve a zero dc-link current commutation of the rec-

tifier, thereby obtaining a soft-switching operation. Thanks to this characteristic,

the switching losses on the side of the rectifier are significantly reduced. In [10],

the efficiency of a sparse matrix converter is improved by employing the lowest

and the second largest phase voltage for the generation of the dc-link voltage. All

these schemes feature a high switching frequency, therefore high semiconductor

losses can be expected on the side of the inverter despite of the aforementioned

improvements. Even though the recent advances in semiconductor technology per-

mit a reduction of the losses by using reverse blocking IGBTs [14], the operation

at a lower frequency is still an interesting issue. In this case, the resonances of the

input filter play an important role that has to be taken into account. It should

be pointed out that most modulation strategies do not consider the filter in the

input side for the generation of sinusoidal currents [9]- [15]. Almost all the existing

modulation schemes assume symmetrical sinusoidal voltages for the operation the

converter. It has been suggested in [16] that the current controllers are unable

to eliminate the distortion in output currents, in this case those strategies that

measure the input voltages generate output voltages of higher quality. In [17] it

has been proposed a hybrid matrix topology to make the converter immune to

a voltage unbalance in the inputs, however, this approach includes the addition

of extra switches and a small dc-link, adding extra complexity to the topology.

The problem has been more or less extensively studied for conventional matrix

topologies, however there are almost no papers reporting the problem in indirect

matrix topologies. The importance of this issue is clear, as it can directly affect

the quality of the process in which the converter is involved.


1.2 Hypothesis and contribution of this thesis

The main contribution of our research is to propose a simple and effective pre-

dictive control scheme for the indirect matrix converter that accomplishes the

standard requirements of other techniques such as unitary power factor and the

operation under abnormal input conditions. This aims to improve the process

quality by reducing the effect in the output process of an abnormal condition in

the mains and also improve the performance of the source currents in despite of

the distorted ac-supply and resonances of the input filter. The hypotheses are:

- It has been reported that predictive control schemes permit a simple way to

control of standard matrix and back-to-back converter topologies featuring

near sinusoidal input currents, unitary displacement power factor and near

sinusoidal output currents; comprising all usual units as modulators and

PI-controllers in only one control block [18]. Therefore it should be easy to

extend this idea to the control of indirect matrix converters.

- It has been reported that an active damping method can be employed to

mitigate the potential resonance of the input filter [19]. This idea can be com-

plemented with predictive control to operate the indirect matrix converter

at a potential resonance frequency in the input filter. The active damping

method does not involve additional measurements or any modification to

the predictive algorithm and thus it is easy to implement.

- The control scheme works under the assumption of a good model of input

filter. Since the proposed scheme always chooses the best option out of the

measured values of input current and voltages, an abnormal supply can be

also considered in the calculation of the optimal switching state.


1.3 Chapter review

This thesis is divided in nine chapters. Chapter 1 is an introduction to the sub-

ject of the research. It contains a comprehensive review of research reported in

the literature to date, establishes the contributions of the thesis and a chapter

preview. Chapter 2 presents a summary of the most popular and important ac/ac

topologies with their relevant characteristics. In Chapter 3, a review of the most

important modulation and control techniques for matrix converters is detailed. In

Chapter 4 a brief description of the indirect matrix converter where its mathemat-

ical model and the most common control and modulation method is described.

An introduction to the model-based predictive control in power electronics is in-

troduced in Chapter 5. In Chapter 6, the first predictive approach is presented:

Predictive current control. The strategy is tested throughout simulation and prac-

tical results. Previously, this strategy was implemented by Dr. Pablo Correa, but

considering a programmable ac-supply. In contrast, we implemented this strategy

using a three -phase variac as the ac-source, which behaves like a weak ac-source

for the system, due to the associated inductance with the autotransformer connec-

tion. The effect of a distorted voltage and filter resonance on the source currents

is analyzed and discussed in order to provide an introduction to the Chapter 7,

where the predictive method was enhanced with an active damping implemen-

tation. In this chapter, the objective was to reduce the harmonic distortion of

the source currents. An improvement on the source current’s performance was

obtained but the ac-source distortion is still a major issue, because the harmonic

distortion of the source voltage is reflected on the source current. This problem

has been mitigated by imposing a sinusoidal source current on the input side,

which improved the performance of the converter, as reported in Chapter 8. Fi-

nally, Chapter 9 includes the conclusions and comments from this research. The

Appendix contains a description of the experimental setup and the list of publi-

cations in ISI Journals and international conferences derived from this research

and international cooperations.

Chapter 2

Review of three-phase ac/ac

topologies

2.1 Classification of ac/ac power converters

A classification of the main ac/ac converters presented in literature to date is

shown in Fig. 2.1. Three subcategories can be identified: converters with dc-link

energy storage, converters without dc-link energy storage, and an intermediate

category of hybrid matrix converters. In the first group are the current and voltage

source topologies, with which it is possible to obtain ac/ac conversion taking

into consideration the presence of a capacitive or inductive dc-link, respectively

[20, 21]. These structures have been widely studied and they are the converters

used in the industry today. In the group of ac/ac circuits without dc-link, different

topologies have been reported in the literature, which are classified into four main

groups: the cycloconverter in a wide power range, the direct matrix converter

(DMC), the indirect matrix converter (IMC) and the three-phase buck converter,

in medium and low power range [1]. The limited voltage control range of the

basic matrix converters is a significant disadvantage compared to converters with

dc-link storage. Therefore, as represented in the third group, combinations of the

basic matrix converter topologies and the voltage source topologies with dc-link

7

Chapter 2. Review of three-phase ac/ac topologies 8

Figure 2.1. Classification of ac/ac power converters.

storage (hybrid matrix converters) were suggested to overcome this limitation.

Table 2.1 indicates a summary with the number of transistors, diodes and power

flux for each ac/ac converter which are described in the next sections.


Table 2.1. Summary of ac/ac topologies.

Converter Transistors Diodes Power Flux

Voltage dc-link 12 12 Bi-directional

Current dc-link 12 12 Bi-directional

Cycloconverter 18∗ 0 Bi-directional

DMC 18 18 Bi-directional

IMC 18 18 Bi-directional

Sparse 15 18 Bi-directional

Very sparse 12 30 Bi-directional

Ultra sparse 9 18 Uni-direccional

HDMC 36 36 Bi-directional

HIMC 22 22 Bi-directional

* thyristor as power switches

2.2 Topologies with dc-link

2.2.1 Back-to-back converter

The back-to-back converter, Fig. 2.2(a), is the coupling of two inverters via a

capacitive dc-link which allows the decoupling of the control tasks of the input

and output side. The input side could be alternatively realized as simple diode

bridge, but the input current would contain significant low-frequency harmonics.

The diode bridge could not feedback braking energy into the mains. Therefore, a

braking resistor in the dc-link would be needed. Alternatively a thyristor bridge at

the input side could feedback braking energy, but would still suffer from significant

low-frequency input current harmonics, especially during the inverter operation.

Instead of defining a voltage in the dc-link, one could also define the current in the

dc-ink via dc-link inductor, Fig. 2.2(b). A disadvantage of such a converter system

is the large physical volume of the dc-link storage element. Furthermore, this

bulky passive component would reduce the system lifetime because its reliability

is relatively low in comparison with the other components in the power circuit.


Figure 2.2. Three-phase ac/ac converter topologies with dc-link energy

storage; (a) voltage dc-link back-to-back converter; (b) current dc-link back-to-back

converter.

2.3 Topologies without dc-link

2.3.1 Cycloconverter

The cycloconverter, Fig. 2.3, is very common in high power applications such as

ball mills in mineral processing and cement kilns. This converter uses thyristors

which are capable of working with high voltage and power over 10 megawatts,

but the main limitation is that the output frequency depends on the natural

commutation of these switches.


U1

V1

W1 U2

V2

W2

ia

ib icva

CBA

Figure 2.3. Three-phase ac/ac converter topology without dc-link energy

storage: cycloconverter.

2.3.2 Direct matrix converter

The direct matrix converter (DMC), Fig. 2.4, consists of an array of bidirectional

switches, which directly connects the power supply to the load without using any

dc-link or large energy storage elements [1]. One of the biggest difficulties in the

operation of this converter was the commutation of the bidirectional switches [22].

This problem has been solved by introducing intelligent and soft commutation

techniques. As mentioned before, after almost three decades of intensive research,

the development of this converter is reaching industrial application. In effect,

at least one big manufacturer of power converters (Yaskawa) is now offering a

complete line of standard units for up to several megawatts and medium voltage

using a cascade connection. These units have rated power (and voltages) of 9-

114kVA (200V and 400V) for low voltage MC, and 200-6.000kVA (3.3kV, 6.6kV)

for medium voltage [1]. Years of continuous effort have been dedicated to the

development of different modulation and control strategies that can be applied to

matrix converters [22,23].


The DMC can be implemented with a half-bridge or with a full-bridge topology.

Aiming for a minimal component count, the half-bridge topology is often em-

phasized in publications. An exception is found in [24], where for the full-bridge

topology of the DMC a control procedure is presented that enables a low stress on

the insulation of the motor windings by minimizing the common mode voltage at

the output with a unity power factor. Consequently, the topology is of particular

interest for high power variable speed drives.

SAa

AC Motor

Bidirectional Switch

vsA

Input Filter

vsB

vsC

isA

isB

isC

vA

vB

vC

iA

iB

iC

fC

fL fR

N SBa

SCa

SAb

SBb

SCb

SAc

SBc

SCc

va vb vc

ia ib ic


storage: direct matrix converter (DMC).


2.3.3 Indirect matrix converter

The indirect matrix converter (IMC) is indicated in Fig. 2.5. One of the favorable

features of an IMC is the absence of a dc-link capacitor, which allows for the

construction of compact converters capable of operating at adverse atmospheric

conditions such as extreme temperatures and pressures [25]. IMC offers the same

performance that the DMC, such as four-quadrant operation, unit power factor,

sinusoidal waveforms with variable frequency and amplitude during motoring and

regeneration operation. But the IMC features an easy to implement and more

secure commutation technique than the former, the dc-link zero current com-

mutation [26]. These characteristics make the IMC suitable technology for high

efficiency converters for specific applications such as military, aerospace, wind tur-

bine generator system, external elevator for building construction and skin pass

mill as reported in [1, 27].


storage: indirect matrix converter (IMC).


2.3.4 Three-phase ac/ac buck converters

In contrast to matrix converters, three-phase ac/ac buck converters (Fig. 2.6)

only enable control of the output voltage, whereas the stationary output fre-

quency equals to the mains frequency at the input. Three-phase buck converters

are traditionally applied as soft-starters for induction motors or for saving energy

by controlling the motor flux. Due to their capacity of instantaneous control of

the output voltage, they also allow for compensation of unbalanced mains volt-

ages and thus can be utilized for power conditioning in power distribution systems.

The topology requires three series switches, providing a bidirectional current path

between the input and output phases (correspond to S1), and three inter-phase

switches (correspond to S2), providing a bidirectional current path between the

output phases. In order to enable a safe commutation, as described in [28] the

series switch and the inter-phase switch that are connected to the input phase

with the smallest voltage are switched on, whereas the other four switches are

modulated at a given duty cycle. A simpler commutation is enabled if the star

point of the input capacitors is connected with the star point of the inter-phase

switches, as suggested in [29].

A

B

C

a

b

c

1S2S


storage: three-phase buck converter.


2.3.5 Sparse indirect matrix converters

As depicted in Fig. 2.5, the input stage of the IMC is implemented with six

four-quadrant switches and could therefore also be operated with a negative link

voltage vdc < 0. On the other hand, for the PWM output stage it is mandatory to

maintain vdc > 0 due to the diodes. Hence, it is possible to consider a reduction in

the number of switches by limiting the operating range of the PWM input stage

to a unipolar link voltage that retains the option of bidirectional current flow.

This circuit variant is referred to as sparse matrix converter (SMC), Fig. 2.7(a).

Compared to the DMC, this topology provides identical functionality, but with a

reduced number of power switches and the option of employing an improved zero

dc-link current commutation scheme, which provides lower control complexity and

higher safety and reliability [30,31]. The very sparse matrix converter (VSMC) is

another fully bidirectional variant of the IMC, Fig. 2.7(b), which shows identical

functionality [30]. Compared to the SMC, there is a smaller number of transistors,

and higher conduction losses due to the increased number of diodes in the con-

duction paths. A more comprehensive simplification of the IMC circuit topology

is possible by limiting the converter to unidirectional power flow. The resulting

topology is the ultra sparse matrix converter (USMC), Fig. 2.7(c). The signifi-

cant limitation of this converter topology is the restriction of its maximal phase

displacement between load-side voltage and input current to ±π/6. Possible ap-

plications would be permanent magnet synchronous machine (PMSM) with no

energy-feedback into the mains.


Figure 2.7. Three-phase ac/ac converter topologies without dc-link en-

ergy storage; (a) sparse matrix converter (SMC); (b) very sparse matrix converter

(VSMC); (c) ultra sparse matrix converter (USMC).


2.3.6 Indirect three-level matrix converter

As mentioned before, the output stage of the IMC is a two-level PWM inverter

(Fig. 2.5). It is thus possible to employ an inverter stage with a three-level charac-

teristic to reduce the switching frequency harmonics of the output voltage. Such

topology was proposed in [30], in which the center point for the output stage is

provided by the star point of the input filter capacitors. The same functionality

with a reduced number of switches was proposed in [32] (Fig. 2.8) and the corre-

sponding space vector modulation was described in [33]. By restricting the system

to unidirectional power flow, a considerable simplification of the indirect three-

level matrix converter circuits is possible. The input stage of this new topology

exhibits the structure of a vienna rectifier [34] and its complexity of the input

stage is comparable to an USMC. It should be emphasized that on the input side,

the transistors are only switched with twice the mains frequency, which results in

very low switching losses.

p

AN

pN

Nn

Nn

pN

n

Figure 2.8. Indirect matrix converter with an additional bridge-leg that

allows the mains phase voltages to be switched directly or inverter into the link.


2.4 Hybrid topologies

The limited voltage control range of the basic matrix converters is a significant

disadvantage compared to converters with dc-link storage. To overcome this lim-

itation, combinations of the basic matrix converter topologies and the converters

with voltage dc-link, so-called hybrid matrix converters, were presented. If the

four-quadrant switches in a DMC are replaced by cascaded H-bridge circuits with

interlink capacitors, then the hybrid DMC topology (HDMC, [35]) results, as

shown in Fig. 2.9. In contrast to all previously discussed topologies, both the in-

put and the output currents for the HDMC are impressed and can be controlled

according to [35] by the use of at least five half-bridges. Transferring the concept

of the HDMC to the hybrid IMC (HIMC) requires in the simplest case only one

H-bridge in the link, as described in [36] (Fig. 2.10).

Figure 2.9. Circuit topology of the hybrid direct matrix converter and the

implementation of a single switching cell. A cascading of several H-bridges in each

connection of an input and output is also possible.


Figure 2.10. Circuit topology of the hybrid indirect matrix converter with

a series voltage source in the link.

Chapter 3

A review of modulation and

control methods for

matrix converters

The most relevant modulation and control methods developed up to now, for the

matrix converter are presented in Fig. 3.1. The first and highly relevant method is

called the direct transfer function approach also known as the Venturini method.

Here, the output voltage is obtained by the product of the input voltage and the

transfer matrix representing the converter. Another strategy is the scalar method

developed by Roy, which consists of using the instantaneous voltage ratio of spe-

cific input phase voltages to generate the active and zero states of the converter’s

switches. A very important solution for the control of matrix converters comes

from the use of pulse width modulation (PWM) techniques previously developed

for voltage source inverters. The simplest approach is to use carrier based PWM

techniques. A very elegant and powerful solution currently in use is to apply space

vector modulation (SVM) in matrix converters. An alternative solution is direct

torque and flux control which has also been proposed for the speed control of

an ac-machine driven by this converter. More modern techniques, such as pre-

dictive control have recently been proposed for the current and torque control of

20

Chapter 3. A review of modulation and control methods for matrix converters 21

Figure 3.1. Summary of modulation and control methods for matrix converters.

ac-machines using matrix converters. In the following pages, a description and a

comparison of these technologies will be presented.

3.1 Scalar techniques

3.1.1 Direct method: Venturini

Modulation is the procedure used to generate the appropriate firing pulses to

each bidirectional switches (Sij). This method was proposed by Venturini in [2,3]

and has been used since, as reported in [22, 37–41]. In this case, the objective of

the modulation is to generate variable frequency and variable amplitude sinusoidal

output voltages (vjN ) from the fixed frequency and fixed amplitude input voltages

(Vi). Here, the instantaneous input voltages are used to synthesize a signal whose

low-frequency component is the desired output voltage. If tij is defined as the time

during which switch Sij is on and Ts as the sampling interval, we can express the

aforementioned synthesis principle as:

vjN =tAjvA+tBjvB+tCjvC

Ts, (3.1)

where vjN is the low-frequency component (mean value calculated over one sam-

pling interval) of the jth output phase and changes in each sampling interval.

With this strategy, a high frequency switched output voltage is generated, but a

fundamental component has the desired waveform.


Obviously, Ts = tAj + tBj + tCj, ∀j, with j = a, b, c and therefore, the following

duty cycles can be defined,

mAj(t) =tAj

Ts, mBj(t) =

tBj

Ts, mBj(t) =

tBj

Ts. (3.2)

Extending eq. (3.1) to each output phase, and using eq. (3.2), the following equa-

tion can be derived,

vo(t) = M(t)vi(t), (3.3)

where vo(t) is the low-frequency output voltage vector, vi(t) is the instantaneous

input voltage vector and M(t) is the low-frequency transfer matrix of the con-

verter, defined as:

M(t) =

mAa(t) mBa(t) mCa(t)

mAb(t) mBb(t) mCb(t)

mAc(t) mBc(t) mCc(t)

. (3.4)

Following an analogous procedure for the input current it can be shown that,

ii(t) = MT (t)io(t), (3.5)

where ii(t) is the low-frequency component input current vector, io(t) the instan-

taneous output current vector and MT (t) the transpose of M(t). Eq. (3.3) and

eq. (3.5) are the basis of the Venturini modulation method, leading to the con-

clusion that the low-frequency components of the output voltages are synthesized

with the instantaneous values of the input voltages and that the low-frequency

components of the input currents are synthesized with the instantaneous values

of the output currents. Suppose that the input voltages vi are given by:

vi(t) =

Vicos(wit)

Vicos(wit− 2π/3)

Vicos(wit+ 2π/3)

, (3.6)

and that due to the low-pass characteristic of the load the output currents io are

sinusoidal and can be expressed as:

io(t) =

Iocos(wot+ φo)

Iocos(wot− 2π/3 + φo)

Iocos(wot+ 2π/3 + φo)

, (3.7)


with wi = 2πfi and wo = 2πfo, where fi and fo correspond to the source and

load frequencies, respectively. Vi corresponds to the input voltage amplitude and

Io the output current amplitude. Furthermore assuming that the desired input

current vector ii is given by:

ii(t) =

Iicos(wit+ φi)

Iicos(wit− 2π/3 + φi)

Iicos(wit+ 2π/3 + φi)

, (3.8)

with Ii as the input current amplitude. Also, assuming that the desired output

voltage vo can be expressed as follows,

vo(t) =

qVicos(wot)

qVicos(wot− 2π/3)

qVicos(wot+ 2π/3)

, (3.9)

and that the following active power balance equation must be satisfied,

Po =3qViIocos(φo)

2=

3ViIicos(φi)

2= Pi, (3.10)

where Po and Pi are the respective output and input active powers, φi is the input

displacement angle and q is the voltage gain of the matrix converter. With the

previous definitions, the modulation problem is reduced to finding a low-frequency

transfer matrix M(t) such that eq. (3.3) and (3.5) are satisfied. The explicit form

of the matrix M(t) can be obtained from [2, 3], and it can be reduced to the

following expression,

mij(t) =1

3

(

1 + 2viN (t)vjN/V2i

)

, (3.11)

where i = A,B,C and j = a, b, c. An important aspect of the solution presented

is that the voltage gain of the converter cannot exceed q = 0.5, due to the working

principle (mean value) and the input voltage waveforms. To increase the gain volt-

age to q =√

3/2 = 0.866, Venturini proposed the injection of the third harmonic,

resulting in the following expression,

mij(t) =1

3

(

1 +2viN (t)vjN

V 2

i

+ 4q

3√

3ζ

)

, (3.12)


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-0.05

0

0.05

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04-1.5

-1

-0.5

0

0.5

1

1.5

Figure 3.2. Direct method: venturini, typical waveforms; a) output voltage

vaN [pu], its reference (bold line) and b) output current ia [pu].

with ζ = sin(wet + βi)sin(3wet) for i = A,B,C, j = a, b, c and βi = 0, 2π3 ,

4π3 .

The same gain voltage q =√

3/2 can be obtained by using the line-to-line volt-

ages in the modulation. Typical waveforms of the output voltage and current are

presented in Fig. 3.2.


3.1.2 Roy’s method

The scalar method which was proposed in 1987 by G. Roy and G.E. April in [42],

consists of using the instantaneous voltage ratio of specific input phase voltages

to generate the active and zero states of the converter’s switches. The value of

any instantaneous output phase voltage (j = a, b, c) is expressed as follows,

vjN = 1Ts

(

tKvK + tLvL + tMvM

)

, (3.13)

tK + tL + tM = Ts, (3.14)

where the subscript M is assigned to the input voltage which has a different

polarity to the other two inputs. The subscript L is assigned to the smallest of

the other two input voltage magnitudes, subscript K being assigned to the third

input voltage. Equations (3.13) and (3.14) are similar to the ones proposed by

Venturini as mentioned in the previous subsection. In this case, the switching

patterns depend only on the scalar comparison of input phase voltages and the

instantaneous value of the desired output voltage. So, the duty cycles are given

as indicated in eq. (3.15),

mLj =(vjN−vM )vL

1.5V 2

i

mKj =(vjN−vM )vK

1.5V 2

i

mMj = 1 − (mLj +mKj)

, (3.15)

for j = a, b, c, respectively. As with the previously presented basic solution for the

modulation problem, the voltage transfer ratio is limited to q ≤ 0.5, in order to

yield positive values for times tK , tL and tM . By modifying the switching time of

the basic scalar control law, it is possible to add the third harmonic to obtain an

overall voltage transfer ratio of q =√

3/2. So, the modulation duty cycles for the

scalar method can be represented by [42]:

mij =1

3

(

1 +2vivj

V 2

i

+ 23ζ

)

, (3.16)

for i = A,B,C, and j = a, b, c. Eq. (3.12) and eq. (3.16) are equal when the

output voltage is maximum (q =√

3/2).


The difference between the methods is that the term q is used in the Venturini

method and is fixed at its maximum value in the scalar method. The effect on

the output voltage is negligible, except at low switching frequencies, where the

Venturini method is superior.

3.1.3 Current phase displacement control for Venturini and Roy

methods.

According to [39,42], by intentionally shifting or delaying the timing sequence with

respect to the zero crossing of the associated input phase voltage, it is possible

to shift current ii relative to vi (i = A,B,C), therefore altering the input power

displacement factor. Let’s define the following fictitious phase voltages at the input

part of the matrix converter as:

v′A = Visin(wit+ ∆φ),

v′B = Visin(wit+ ∆φ− 2π3 ),

v′C = Visin(wit+ ∆φ+ 2π3 ),

, (3.17)

where, ∆φ is the displacement factor angle between the measured input voltage

vector vi and the input current vector ii.

For the Venturini’s method, the solution of the new m′ij is given by:

m′ij(t) =

1

3

(

1 +2v′

iN(t)vjN

V 2

i

+ 4q

3√

3ζ

)

, (3.18)

for i = A,B,C.

For the Roy’s method, let us now assign M , K and L to A′, B′ and C ′ according

to the rules mentioned before. Then,

m′Lj =

(vjN−v′M

)v′L

1.5V 2

i

m′Kj =

(vjN−v′M )v′K1.5V 2

i

m′Mj = 1 − (m′

Lj +m′Kj)

, (3.19)

for j = a, b, c, respectively. Of course, desired output voltage vjN is still expressed

by eq. (3.9) or eq. (3.13), for Venturini or Roy methods, respectively.


It follows that the input currents ii will be in phase with their respective ficti-

tious voltages. However they will be displaced by an angle ∆φ according to the

real voltage vi. So, the input power displacement factor is totally controllable by

proper adjustment of the timing sequence, regardless of the load characteristic. In

both methods, a reduction of the voltage transfer ratio is observed as the power

displacement factor is reduced as indicated in [42].

3.2 Pulse width modulation methods

3.2.1 Carrier-based modulation method

Many control strategies based on PWM methods which allow for output voltage

regulation while maintaining unity displacement power factor on the input side

have been applied to different kinds of matrix converters, as has been reported in

[43–59]. For simplicity, we will discuss a carrier-based modulation method applied

to a three-phase to single-phase matrix converter, which can be easily extended

to a three-phase to three-phase or multilevel converter. The technique is based on

a sinusoidal pulse width modulation (SPWM), a well know shaping technique in

power electronics where a high frequency triangular carrier signal vtri, is compared

with a sinusoidal reference signal vo as shown in Fig. 3.3, [43,46]. In this method

the switching pulses are generated by using a logical table as a function of the

input voltages and the desired levels on the output side. The different input voltage

states are identified by considering variables xA, xB and xC which are generated

according Table 3.1. If the conditions given in Table 3.1 are not satisfied, the

logic variable take the value 0. The gate pulse pattern generation of the matrix

converter is given according to a switching state selector generated by the following

equation,

N = 16xA + 8xB + 4xC + 2L1 + L0, (3.20)

where L0 and L1 are the output voltage levels (L0 is selected if the level of the

output voltage reference is less than or equal to zero. L1 is selected if the output

voltage level is above zero).


vo*

-1

vtri

+

-L

L1 L0

LoadDMCInput Filtervs

is Rf Lf

vi

ii

vo

io RL LL

n

CfVoltage Source

3 3

3

3

S1 S99

Switching State Selector

Level Selector

Comparator

≥

≥

xA xB xC

Figure 3.3. Unipolar sinusoidal PWM method and desired output level voltage.

Generally, PWM methods can work with variable input power factor, as demon-

strated in [59], where it is possible to synthesize the sinusoidal input currents

with a desired power factor by changing the slope of the carrier and using the off-

set voltages. However, the PWM method presented in this thesis is restricted in

its operation with unity displacement power factor, due to its simplicity. Typical

waveforms of output voltage and current are presented in Fig. 3.4. More details

about this method can be found in [43,46].

Table 3.1. PWM method: input voltage states

Condition Value

vA > vB xA = 1

vB > vC xB = 1

vC > vA xC = 1


0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

-1

0

1

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

-0.2

-0.1

0

0.1

0.2

Figure 3.4. Carrier-based method, typical waveforms; a) line-to-line out-

put voltage vab [pu]; b) output current ia [pu].

3.2.2 Space vector modulation (SVM) method

This method has been proposed in [60–63]. The space-vector approach is based on

the instantaneous space-vector representation of input and output voltages and

currents. Among the 27 possible switching configurations available in three-phase

matrix converters, only 21 are usefull in the SVM algorithm. The first 18 switching

configurations determine an output voltage vector and an input current vector,

having fixed directions. The magnitude of these vectors depends upon the instan-

taneous values of the input voltages and output line currents, respectively. The

last three switching configurations determine zero input current and output volt-

age vectors. The SVM algorithm for matrix converters has the inherent capability

to achieve full control of both the output voltage vector and the instantaneous

input current displacement angle [62–79]. The two-stages SVM method [80] is a

variation of the classic SVM technique which has some important features such

as over modulation, but this method is no longer used. At any given sampling

instant, the output voltage vector and the input current displacement angle are


known as reference quantities. The input line-to-neutral voltage vector is imposed

by the source voltages and is recognized by its measurements. Then, the control

of the input side can be achieved, controlling the phase angle of the input current

vector. Both input current and output voltage vectors are synthesized by consid-

ering the duty cycles. The duty cycles are calculated based on the phase of output

voltage and input current vector references such as is indicated as follows [63],

δ1 = −1Kv+Ki+1 2m√3

cos(φ′o − π2 ) cos(φ′i − π

2 )

cos(∆φ), (3.21)

δ2 = −1Kv+Ki2m√

3

cos(φ′o − π2 ) cos(φ′i +

π6 )

cos(∆φ), (3.22)

δ3 = −1Kv+Ki2m√

3

cos(φ′o + π6 ) cos(φ′i − π

2 )

cos(∆φ), (3.23)

δ4 = −1Kv+Ki+1 2m√3

cos(φ′o + π6 ) cos(φ′i +

π6 )

cos(∆φ), (3.24)

where m is the modulation index; ∆φ is the displacement angle between the

measured input voltage vector vi and the input current reference vector ii∗; and

Kv and Ki are the voltage and current sectors respectively, and where,

φ′o = φo − (Kv − 1)π

6, φ′i = φi − (Ki − 1)

π

6. (3.25)

If the sign of any duty cycle is negative, then the name of the switching state to

apply must have a negative sign. The duty cycle δ0 of the zero vector is such that

the total duty cycle must be equivalent to the unit at a fixed sampling frequency,

i.e.

δ0 = 1 − δ1 − δ2 − δ3 − δ4. (3.26)

Assuming a displacement power factor of 1 on the input side of the DMC, i.e.

∆φ = 0, the maximum modulation index is m =√

3/2. SVM technique for the

IMC will be presented in the next chapter.


3.3 Direct torque control

Today, Direct Torque Control (DTC) is established as a high performance torque

and flux control method for ac-machines fed by voltage source inverters [81, 82].

This method is based on the torque equation of the machine which is expressed as

a function of the angle between the stator and rotor flux vectors in the following

way,

Te = kT (ψrαψsβ − ψrβψsα), (3.27)

with kT = 32p

Lm

LrLs−L2m

, (where Lr, Ls and Lm are the self and mutual inductances,

respectively). The method is also based on the fact that changes in the voltage

delivered by the inverter directly affect the behavior of the machine’s stator flux,

as shown by:

ψs(k + 1) = ψs(k) + Tsvs(k + 1) −RsTsis(k). (3.28)

In [83], the authors proposed that DTC controls an ac-machine by using a matrix

converter. As shown in Fig. 3.5, this method uses a nonlinear hysteresis compara-

tor to control the torque, which delivers the control variable cT . An additional

hysteresis controller is used to create another closed loop to control the flux, which

delivers the variable cψ. A third loop is used to control the power factor of the

input current by controlling the displacement factor ϕ with another nonlinear

controller, which delivers variable cϕ. These variables cT , cψ and cϕ, in conjunc-

tion with the position of the stator flux, reveal which direction to select the gate

drive pulses in the look up table for the matrix converter’s bidirectional switches.

Although look up tables for DTC using a voltage source inverter are well known

and published in several papers and textbooks, the application of this method in

a matrix converter has additional complexity. In effect, the selection of a single

switching state for the matrix converter is not based exclusively on the informa-

tion of torque error and flux error. Rather, the designer must know a priori what

additional effect this switching state will have on the behavior of the input power

factor. To obtain this information is complex [84]. The results of this method

generally show very good performance dynamics in the control of the machine.

However, the input filter of the matrix converter presents higher resonances.


T

Figure 3.5. Direct torque control scheme.

To improve the general drive performance, use of DTC in matrix converters is

a subject of intensive study today. Some works are focused on improving the

behavior of the input filter [84–88].

3.4 Predictive control

3.4.1 Predictive current control

Thanks to advances in processors, predictive control schemes have recently emerged

as feasible approaches [18]. Predictive current control (PCC) scheme is illustrated

in Fig. 3.6. It shows converter’s switching state selection that leads the controlled

variables closest to their respective references at the end of the sampling period.

This strategy uses the converter and load models to predict the future behavior of

load currents and reactive power. A simple but functional time-continuous model

of a passive load side can be expressed as:

diodt

=1

LLvo − RL

LLio. (3.29)


LoadDMCInput Filtervs

is Rf Lf

vi

ii

vo

io RL LL

n

CfVoltage Source

3 3

3

3

27

iok+1qs

k+1

io*

Load Current

Reference

S1 S99

Cost

Function

Optimization

Reactive

Power

Prediction

isvs

3 3 3

Output

Current

Prediction

iovi

3 3

vi

27

Figure 3.6. Predictive current control scheme.

The state variable model of the ac-input side is given by eq. (3.30) and eq. (3.31)

from Fig. 2.5 as follows,

disdt

=1

Lf(vs − vi −Rf is), (3.30)

dvi

dt=

1

Cf(is − ii). (3.31)

Given the first order nature of the load model, a first order discrete approximation

allows the future load current to be predicted as:

io(k + 1) =Tsvo(k + 1) + LLio(k)

LL +RLTs, (3.32)

where Ts corresponds to the sampling time. On the input side, the equations

represent a second order model. As such, an exact discrete state model is best

used to obtain the supply current in the sampling instant k + 1, in order to

predict the future reactive power. So, the general expression to predict the line

input current is:

is(k + 1) = c1vs(k) + c2vi(k) + c3is(k) + c4ii(k), (3.33)

where ci (i = 1, 2, 3, 4) values are calculated such that the discrete model provides

the exact values of the continuous system.


Two main conditions must be fulfilled for the converter to operate properly: first,

the line side of the converter must minimize the instantaneous reactive power and

secondly, the load current must follow the reference with good accuracy. Both

requirements can be merged into a single quality function g as follows,

g = io(k + 1) +Aqs(k + 1), (3.34)

where,

io(k + 1) = |i∗α − iα(k + 1)| + |i∗β − iβ(k + 1)|, (3.35)

qs(k + 1) = |vsα(k + 1)isβ(k + 1) − vsβ(k + 1)isα(k + 1)|. (3.36)

The first term considers the comparison between the reference load currents and

the predicted ones. The second term corresponds to the predicted input reactive

power. Both are expressed in α-β components. The control method operates as

follows: at each sampling time, all possible switching states are used to calculate

the predicted values of the load and input current, allowing the evaluation of

function g in eq. (3.34). After that, the valid switching state that produces the

minimum value of g is selected for the next modulation period. Fig. 3.7 shows the

behavior of the matrix converter when the quality function has a value of A = 0,

for the weighting factor. The load current ia is almost sinusoidal and the reactive

power has high values. In this case the input current presents very high distortion

which is originated by a strong resonance of the input filter. Fig. 3.8 shows the

behavior of the matrix converter when a control of the input power factor is being

considered. This is achieved by increasing the value of the weighting factor to

A = 1. It can be observed that the load current ia is almost sinusoidal and that

the input reactive power is near to zero. This new control strategy practically

eliminates the resonance of the input filter. The improvement in the quality of the

input current is remarkable. Different techniques for matrix converters have been

proposed under the name of predictive current control, as reported in [89–100].

In [91], a predictive current control for an induction machine fed by a matrix

converter is developed by considering a classic stage that handles speed, flux

and torque control. It does this by means of field-oriented control (FOC), which

generates the reference currents for the predictive stage.


0.02 0.03 0.04 0.05 0.06 0.07 0.08-20

0

20

0.02 0.03 0.04 0.05 0.06 0.07 0.08-20

0

20

0.02 0.03 0.04 0.05 0.06 0.07 0.08

-20

0

20

Figure 3.7. Predictive current control without power factor correction

A = 0; a) output current [A]; (b) reactive power [kVAR]; (c) input current [A]

and input voltage [V/30].

A similar idea is presented in [94] to control a permanent magnet synchronous

machine (PMSM). Using this scheme it is also feasible to control other variables

within an electrical system; for example, minimizing common-mode voltage, re-

ported in [92], or increasing efficiency and reducing switching losses, as presented

in [93]. Recently, this idea has been extended to indirect matrix converters, as

reported in [26] and [98].


0.02 0.03 0.04 0.05 0.06 0.07 0.08-20

0

20

0.02 0.03 0.04 0.05 0.06 0.07 0.08-20

0

20

0.02 0.03 0.04 0.05 0.06 0.07 0.08

-20

0

20

Figure 3.8. Predictive current control with power factor correction A = 1;

a) output current [A]; (b) reactive power [kVAR]; (c) input current [A] and input

voltage [V/30].

3.4.2 Predictive torque control

A diagram of the predictive torque control (PTC) strategy is shown in Fig. 3.9.

This control method has been introduced in [23, 101–107]. Similar to the pre-

viously explained method, predictive torque control (PTC) consists of choosing,

at fixed sampling intervals, one of the 27 feasible switching states of the DMC. The

selection of the switching state for the following time interval is performed using

a quality function minimization technique. This quality function g represents the

evaluation criteria in order to select the best switching state for the next sampling

interval. For the computation of g, the input current vector is, the electric torque

Te, and the stator flux ψs in the next sampling interval are predicted, assuming the

application of each valid switching state, by means of a mathematical model of the

input filter and the induction machine (IM). A PI controller is used to generate

the reference torque T ∗e to the predictive algorithm. A mathematical discrete-time

model is derived to predict the behavior of the system under a given switching

state, based on well known dynamic equations for an IM [23,101–103].


Figure 3.9. Predictive torque control scheme.

The stator and rotor voltage equations in fixed stator coordinates for a squirrel-

cage induction machine can be presented as:

vo = Rsio +dψs

dt, (3.37)

vr = Rrir +dψr

dt− jpωψr = 0, (3.38)

where Rs and Rr are the stator and rotor resistances, ψs and ψr are the stator

and rotor fluxes, ω is the mechanical rotor speed and p is the number of pole pairs

of the IM. The stator and rotor fluxes are related to the stator and rotor currents

by:

ψs = Lsio + Lmir, (3.39)

ψr = Lmio + Lrir, (3.40)

where Ls, Lr and Lm are the self and mutual inductances respectively.

Finally, the electric torque produced by the machine can be obtained by:

Te =3

2pξImψrψs =

3

2pξ(ψrαψsβ − ψrβψsα), (3.41)


where ξ = Lm

LrLs−L2m

and ψr is the complex conjugate of vector ψr and the sub-

scripts α and β represent real and imaginary components of the associated vector.

Eq. (3.37) and eq. (3.38) can be rewritten, solving the stator and rotor currents

in terms of the stator and rotor fluxes from eq. (3.39) and eq. (3.40), as:

dψs

dt=

−RsLrLrLs − L2

m

ψs +RsLm

LrLs − L2m

ψr + vo, (3.42)

dψr

dt=

RrLmLrLs − L2

m

ψs −RrLs

LrLs − L2m

ψr − jpωψr. (3.43)

The next step is to define a discrete-time model based on these continuous-time

equations. Using a forward Euler approximation [23], the following discrete equa-

tions are computed from (3.42) and (3.43),

ψs(k + 1) = (1 − χLr)ψs(k) + χLmψr(k) + vo(k), (3.44)

ψr(k + 1) = λLmψs(k) + (1 − λLs)ψr(k) − jpω(k)ψr(k), (3.45)

where χ = TsRs

LrLs−L2m

, λ = TsRr

LrLs−L2m

, and Ts is the sampling period.

If a certain voltage vector vo(k) is applied from the matrix converter, then equa-

tions (3.41), (3.44) and (3.45) are used by the proposed method to predict the

stator flux and the electric torque produced by the IM during the next sampling

interval. The quality function represents the evaluation criteria to decide which

switching state is the best to apply. The function is composed of the absolute error

of the predicted torque, the absolute error of the predicted stator flux magnitude

and the absolute error of the predicted reactive input power, resulting in:

g = Te(k + 1) + λψψs(k + 1) + λqqs(k + 1), (3.46)

where λQ and λψ are weighting factors that handle the relation between reactive

input power, torque and flux conditions. This quality function must be calculated

for each of the 27 feasible switching states. The state that generates the optimum

value, in this case a minimum, will be chosen and applied during the next sampling

period. In that sense, the technique assigns costs to the objectives reflected in g,

weighted by λT , λψ and λq, and then chooses the switching state that presents the


lowest cost. Typical simulation waveforms without and with input factor correc-

tion are presented in Fig. 3.10 and Fig. 3.11, respectively. Both cases present good

behavior on the output side. Input currents, on the other hand, present significant

differences. Implementing the method with λq = 0, the input current shows high

distortion and phase shift with its phase voltage. Using the added term to control

the input factor and considering λq > 0, the input current is close to sinusoidal,

as shown in Fig. 3.11. Such as reported in [107] the same idea has been extended

for an indirect matrix converter.


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-100

0

100

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-50

0

50

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-20

0

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-20

0

20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-20

0

20

0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44-20

-10

0

10

20

Figure 3.10. Predictive control torque without power factor correction

λq = 0; a) speed [rad/s]; b) electrical torque [Nm]; c) output current [A]; d) stator

flux [Wb]; e) reactive power [kVAR]; f) input current [A] and input voltage [V/30];

g) zoom of input current isA and input voltage vsA.


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-100

0

100

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-50

0

50

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-20

0

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-20

0

20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-20

0

20

0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44-20

-10

0

10

20

Figure 3.11. Predictive control torque with power factor correction λq =

1; a) speed [rad/s]; b) electrical torque [Nm]; c) output current [A]; d) stator flux

[Wb]; e) reactive power [kVAR]; f) input current [A] and input voltage [V/30]; g)

zoom of input current isA and input voltage vsA.


3.5 Assessment of the methods

The performance of all methods can be compared considering the following figures

of merit:

i) theoretical complexity,

ii) quality of load current,

iii) dynamic response,

iv) sampling frequency,

v) switching frequency,

vi) resonance of input filter.

Table 3.2 presents a comparison of these methods. In terms of complexity, al-

though carrier based methods involve many equations, with respect to the other

techniques they are very simple to implement for generating gate drive pulses for

bidirectional power switches [53]. Predictive technique [18, 89] is very simple in

comparison to SVM [60, 63] and direct torque control methods, which are com-

plex. In DTC, the engineer must know the effect of any switching state on the

behavior of torque, flux and the input power factor of the matrix converter, which

is a complex task [83, 84]. All the methods deliver a high quality current to the

load. The main difference is that some methods work with fixed switching fre-

quency and other strategies, such as DTC and PTC, work with variable switching

frequency. It can also be observed that some methods operate with low sampling

and switching frequency while others require higher frequencies. All methods have

good dynamic behavior, which is acceptable for all main practical applications.

The resonance of the input filter is a key issue in the operation of matrix convert-

ers. An important observation, usually overlooked is that a control or modulation

method has a very significant influence on the behavior of the input filter [108]. In

effect, methods working with fixed switching frequency, like Venturini, Roy and

SVM have a reduced resonance in the input filter.

Chap

ter3.

Areview

ofm

odulation

and

control

meth

ods

form

atrixcon

verters43

Table 3.2. Comparison between control and modulation methods for matrix converters

Venturini Scalar Carrier

Based

PWM

Space

Vector -

Modulation

Direct

Torque

Control

Predictive

Current

Control

Predictive

Torque

Control

Complexity low low very low very high high low low

Sampling

frequency

very low very low low low very

high

high high

Switching

frequency

very low very low low low high high high

Dynamic

response

good good good good fast very fast very fast

Resonance

input fil-

ter

low low medium low very

high

from very

high to

low

from very

high to

low


Carrier based methods that do not take care of the quality of the input current

originate strong resonances in the input filter. This behavior can be drastically

improved taking into consideration the input current. DTC has very strong res-

onances in the input filter, while predictive techniques have mixed results. The

introduction of the control of the reactive power in the quality function introduces

an important reduction of the resonance in predictive methods [26,89,91,98,100,

102,106]. Other techniques that have been applied to matrix converters are fuzzy

control [109,110], neural networks [111,112], genetic algorithms [113,114], etc.

3.6 Comments and conclusion

The area of matrix converters has shown continuous development in recent years

in terms of new topologies, new control methods and applications. This chapter

has presented a number of control methods highly investigated today which, in

principle, exhibit good performance [39,51,80]. These methods have different the-

oretic principles and different degrees of complexity. With the results reported in

this chapter, predictive control appears as the most promising alternative due to

its simplicity and flexibility to include additional aspects in the control. However,

with the results reported to date in the literature it is not possible to establish

which method is the best. A deeper research must be done in the future to clarify

the advantages of each method or to select the best alternative. This comparison

must include more advanced aspects such as detailed evaluation of losses, system

integration, electromagnetic compatibility, etc.

Chapter 4

The indirect matrix converter

4.1 Description of the topology

The most important characteristics of matrix converters are [3]:

• A simple and compact power circuit;

• Generation of load voltage with arbitrary amplitude and frequency;

• Sinusoidal input and output currents;

• Operation with unity displacement power factor;

• Regeneration capability.

These highly attractive characteristics are the reason for the tremendous interest

in this topology. The indirect matrix converter (IMC) topology is shown in Fig.

4.1 and it consists of a rectifier connected to the inverter through a dc-link without

energy storage element. The converter synthesizes a positive voltage in the dc-link

by selecting a switching state in the rectifier that connects one phase to point p

and the other phase to point n. On the rectifier side, dc-link voltage vdc is obtained

as a function of the rectifier switches and the input voltages vi as follows,

vdc =[

Sr1 − Sr4 Sr3 − Sr6 Sr5 − Sr2

]

vi. (4.1)

45

Chapter 4. The indirect matrix converter 46

r1S r3S r5S

r4S r6S r2S

i1S i3S i5S

i4S i6S i2S

o

Figure 4.1. Indirect matrix converter topology.

Input currents ii are defined as a function of the rectifier switches and the dc-link

current idc as:

ii =

Sr1 − Sr4

Sr3 − Sr6

Sr5 − Sr2

idc. (4.2)

On the inverter side, dc-link current idc is determined as a function of the inverter

switches and the output currents io as:

idc =[

Si1 Si3 Si5

]

io, (4.3)

and finally, output voltages are synthesized as a function of the inverter switches

and the dc-link voltage vdc as:

vo =

Si1 − Si4

Si3 − Si6

Si5 − Si2

vdc. (4.4)

These equations correspond to the nine and eight valid switching states for the

rectifier and the inverter stage, respectively. Following the restrictions of no short

circuits in the input and no open lines in the output, the whole converter presents

72 possible switches combinations. But, another operational condition for the IMC

is that the dc-link voltage must always be positive vdc > 0. As indicated in eq.

(4.1), the dc-link voltage is synthesized by the rectifier stage switches and the


input voltages vi. At any instant, only three of the nine valid switching states

that can be applied to the rectifier stage to produce a positive dc-link. For this

reason, at every sampling time, only three of the nine valid switching states are

considered [26].

Finally, the number of valid switching states is reduced to 24. It should be noted

that the IMC topology includes an extra freedom degree that alleviates the com-

plexity of the commutation sequence, the zero dc-link current commutation [7,31].

In addition, the rectifier includes an LfCf filter on the input side which is needed

to prevent over-voltages and to provide filtering of the high frequency components

of the input currents produced by the commutations and the inductive nature of

the load. As indicated previously, the filter consists of a second order system

described by:disdt

=1

Lf(vs − vi) −

RfLf

is, (4.5)

dvi

dt=

1

Cf(is − ii). (4.6)

The load model is obtained similarly. Assuming an inductive-resistive load as

shown in Fig. 4.1, the following equation describes the behavior of the load,

diodt

=1

LLvo − RL

LLio. (4.7)

4.2 Zero dc-link current commutation

One approach to current commutation in indirect matrix converters is given in [30]

by combining a multistep commutation strategy of the input stage and the dead-

time commutation of a conventional dc-link inverter for the output stage, in such

a way as to avoid the possibility that more than one bidirectional switch is on at

the same time at each half bridge, so as to avoid short circuit of the input lines.

IMC provides a degree of control freedom that is not available for the conventional

direct matrix converter. This can be uses to simplify the complex commutation

problem. A simplified approach to solve the current commutation problem in

an IMC was presented in [7, 30], where a zero dc-link current commutation is


Table 4.1. Valid switching state on the rectifier side.

State Sr1 Sr2 Sr3 Sr4 Sr5 Sr6 iA iB iC vdc

1 1 1 0 0 0 0 idc 0 −idc vAC

2 0 1 1 0 0 0 0 idc −idc vBC

3 0 0 1 1 0 0 −idc idc 0 −vAB4 0 0 0 1 1 0 −idc 0 idc −vAC5 0 0 0 0 1 1 0 −idc idc −vBC6 1 0 0 0 0 1 idc −idc 0 vAB

7 1 0 0 1 0 0 0 0 0 0

8 0 0 1 0 0 1 0 0 0 0

9 0 1 0 0 1 0 0 0 0 0

proposed. If the three-phase to two-phase matrix converter commutates when the

inverter stage is in freewheeling operation (either all the upper devices or all the

lower devices in the inverter circuit are gated), it is only important to make sure

that short circuit of the input lines is avoided. The open circuit of the load in this

case would not cause any problem as the dc-link current would be zero. The zero

dc-link current commutation therefore would allow a dead-time commutation of

two bidirectional switches on the input side during the period of time while the

inverter stage is in a freewheel state. At first sight the main advantage of this

commutation technique is the reduction in the switching losses of the input stage

which ideally would be negligible as it can be arranged to commutate at zero

current every time.

4.3 PWM based control method

4.3.1 Modulation of the rectifier stage

This technique is applicable to conventional IMC, SMC, VSMC and USMC, al-

lowing the switching of the rectifier stage at zero dc-link current. Valid switching

states on the rectifier side are given as indicated in Table 4.1. In this case, zero


0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.040

200

400

600

0.022 0.024 0.026 0.028 0.03 0.032 0.034 0.036 0.038 0.04200

400

600 st

nd

st

nd

Figure 4.2. (a) Line-to-line input voltages vi and dc-link voltage vdc; (b)

valid current vectors in the α−β plane; (c) first-maximum, second-maximum and

average dc-link voltage vdc.

states are not considered in order to obtain consistently positive dc-link voltage.

For instance, if state 1 is applied, that is, if Sr1 and Sr2 are on, phase A of the

input voltage will be connected to the positive rail of the dc-link and phase C

of the input voltage to the negative rail. Therefore, the line-to-line voltage vAC

will be reflected in the dc-link. At the same time, idc current will flow throughout


si

i

Figure 4.3. Position of the reference current vector in sector II; θi is the

angle respect to α-axis; θsi is the angle in the sector.

phase A, and throughout phase C will flow −idc. With this, each current vector

can be represented in α − β axis, as indicated in Fig. 4.2(b). In this figure, it is

possible to identify six sectors of π/3.

As shown in Fig. 4.2(c), in this method the dc-link voltage is defined by segments

of the input line-to-line voltages, according to the rectifier state. Therefore, the

voltage employed by the inverter for output voltage formation shows two different

levels. For example, in sector II, the dc-link voltage is given by the line-to-line

voltages vAC and vBC . In addition, it is possible to appreciate that in the first π/6

of sector II, the maximum voltage corresponds to vAC and the second maximum

to vBC . But in the next π/6 of sector II, the maximum voltage corresponds to vBC

and the second maximum to vAC . If a unity displacement power factor operation

is desired, a current vector in phase with its respective input voltage must be

defined, which will be given by eq. (4.8) as follows,

i∗A

i∗B

i∗C

=

Iicos(wit)

Iicos(wit− 2π/3)

Iicos(wit+ 2π/3)

, (4.8)

with wi = 2πfi where fi is the input frequency and Ii corresponds to the input

current amplitude given by the load current throughout eq. (4.2) and eq. (4.3).

As this current vector is in phase with the input voltage vector, the position of


the current vector in α−β axis is determined considering the measurement of the

input voltages vi, given by:

θi = arctan(vβs /vαs ), (4.9)

where vαs and vβs are the α − β components of vi. Comparing θi with the angles

that limit each sector, it is possible to know in which of the six sectors the current

reference vector is located. To know the position inside of the sector, the angle θi

is compared with the inferior angle of the previously identified sector ∠inf−sectorr ,

θsi = θi − ∠inf−sectorr . (4.10)

With all this information it is possible to determine the working cycles for the

rectifier side as follows,

δ1 = sin(π/3 − θsi), δ2 = sin(θsi). (4.11)

Finally, the time that is connected to the dc-link the voltage which generates the

first and second maximum are given by:

δr1 = δ1/(δ1 + δ2), δr2 = δ2/(δ1 + δ2). (4.12)

Thus, the average dc-link voltage vdc, which is considered for the inverter modu-

lation, is defined as:

vdc = δr1vfmax + δr2vsmax, (4.13)

where vfmax corresponds to the first maximum and vsmax, the second one. Fig. 4.4

shows the dc-link voltage vdc and average dc-link voltage vdc, where it is possible

to appreciate that the dc-link voltage is given by the first and second maximum

line-to-line input voltages.


0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.060

200

400

600

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.060

200

400

600

Figure 4.4. Formation of the dc-link voltage vdc and average dc-link volt-

age vdc. As it can be observed, the dc-link voltage is given by the first and second

maximun line-to-line input voltages.

4.3.2 Modulation of the inverter stage

Similar to the rectifier stage, on the load side, the valid inverter switching states

(Tabla 4.2) are considered to obtain the voltage vector which can be applied

to the converter, such as indicated in Fig. 4.5(a). In comparison to the rectifier

modulation, in this case there are three working cycles. The third is related to the

zero vector, which is needed to ensure zero dc-link current and allow proper and

safe commutation on the rectifier stage. Such as in classic voltage source inverters,

the idea in the SVM technique is to synthesize a voltage vector considering the

two adjacent vectors and the zero vector, Fig. 4.5(b). In this case, the position of

the reference vector is determined as:

θo = arctan(vβo /vαo ), (4.14)

θso = θo − ∠inf−sectori . (4.15)


Table 4.2. Valid switching state on the inverter side.

State Si1 Si2 Si3 Si4 Si5 Si6 vuv vvw vwu idc

1 1 1 0 0 0 1 vdc 0 −vdc iou

2 1 1 1 0 0 0 0 vdc −vdc iou + iov

3 0 1 1 1 0 0 −vdc vdc 0 iov

4 0 0 1 1 1 0 −vdc 0 vdc iov + iow

5 0 0 0 1 1 1 0 −vdc vdc iow

6 1 0 0 0 1 1 vdc −vdc 0 iou + iow

7 1 0 1 0 1 0 0 0 0 0

8 0 1 0 1 0 1 0 0 0 0

Working cycles of adjacent vectors are obtained as follows,

γ1 = mvsin(π/3 − θso),

γ2 = mvsin(θso),(4.16)

where mv, is a variable that relates rectifier and inverter stages as:

mv = m(δ1 + δ2),

0 < m < 1.(4.17)

But in this case, a link between rectifier and inverter stages must be established,

which is given by:

γi1 = γ1/(γ1 + γ2),

γi2 = γ2/(γ1 + γ2),

γi0 = 1 − γi1 − γi2,

(4.18)

τp1 = γi1δr1 τs1 = γi1δr2



. (4.19)

Finaly, the times for each vector application on the rectifier and inverter side are

defined by eq. (4.20) and (4.21) as follows,

tr1 = δr1Ts,

tr2 = δr2Ts,(4.20)


o

so

Figure 4.5. (a) Available vectors on the inverter side; (b) position of the

output reference vector in sector II.

tp1 = τp1Ts ts1 = τs1Ts



. (4.21)

With this, and as indicated in Fig. 4.6, it is possible to obtain an average dc-link

voltage vdc, which is used to modulate the inverter side. As mentioned before, the

rectifier commutation is made at zero dc-link current, minimizing switching losses

on the rectifier side in a safe manner.


r1 r

s

p1

p2

p0

s1

s2

s0

s1

p1

p2

p0

s2

s0

r1

Figure 4.6. Formation of the dc-link voltage vdc and dc-link current idc

within a pulse period. Switching state changes of the input stage do occur at zero

dc-link current.

4.3.3 Simulations results

The method has been tested in open-loop control, considering a modulation index

equal to m = 0.866. As indicated in Fig. 4.7, a source current in phase with its

voltage can be achieved. A PI current controller was adjusted to regulate the

load current acting on the output voltage reference. The schematic diagram of

the current control strategy is presented in Fig. 4.8. By means of this method,

it is possible to set a specific load current reference. The controller will act on

the system setting the appropriate value of the output voltage reference to the

SVM algorithm in order to track the reference signal. As indicated in Fig. 4.9, by

considering a closed-loop control, and when the displacement is equal to φ = 0,

an improved source current can be obtained. In Fig. 4.10. The reference output

current delivered to the PI controller was set sinusoidal with an amplitude of

i∗a=21A and f∗s=60Hz and i∗a=14.7A and f∗s=100Hz after t = 0.12s. The resulting

load current is easily tracked with respect to its reference. The input current is

almost sinusoidal with a small distortion.


0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13-40

-20

0

20

40

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13

-20

-10

0

10

20

Figure 4.7. Simulation results SVM technique in open-loop control; (a)

source voltage vsA [V/10] and source current isA [A]; (b) output current ia [A].

f f

fL

L

Figure 4.8. Schematic diagram of the current control strategy added to

the modulation technique; the PI controller is in d-q coordinates.


0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13-40

-20

0

20

40

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13

-20

-10

0

10

20

Figure 4.9. Simulation results SVM technique in closed-loop control; (a)

source voltage vsA [V/10] and source current isA [A]; (b) output current reference

i∗a[A] and measured output current ia [A].


0.06 0.08 0.1 0.12 0.14 0.16 0.18-40

-20

0

20

40

0.06 0.08 0.1 0.12 0.14 0.16 0.18

-20

-10

0

10

20

Figure 4.10. Simulation results SVM technique in closed-loop control; (a)

source voltage vsA [V/10] and source current isA [A]; (b) output current reference

i∗a[A] and measured output current ia [A].

Chapter 5

Model-based predictive control in

an IMC

Predictive control is a very wide class of controllers that have found rather recent

application in static power converters. As described in [18,115], different predictive

methods have been proposed in the literature such as deadbeat, hysteresis-based,

trajectory-based and model-based predictive control (MPC). The main character-

istic of predictive control is the use of the model of the system for the prediction

of the future behavior of the controlled variables. This information is used by the

controller in order to obtain the optimal actuation, according to a predefined op-

timization criterion. The optimization criterion in the hysteresis-based predictive

control is to keep the controlled variable within the boundaries of a hysteresis area,

while in the trajectory-based predictive control method, the variables are forced

to follow a predefined trajectory. In deadbeat control, the optimal actuation is

the one that makes the error equal to zero in the next sampling instant. A more

flexible criterion is used in MPC, expressed as a cost function to be minimized.

The difference between these groups of controllers is that deadbeat-based control

and MPC with continuous control set need a modulator, in order to generate the

required voltage. This will result in having a fixed switching frequency. The other

controllers directly generate the switching signals for the converter, do not need

59

Chapter 5. Model-based predictive control in an IMC 60

a modulator, and present a variable switching frequency. Some of the advantages

of this approach are,

• A simple and intuitive concept.

• Easy inclusion of non-linearities in the model.

• Straightforward treatment of constrains.

• The multiple-input multiple-output case is considered in the formulation.

• The versatility of the method allows its application on a wide variety of

systems.

However, this control approach has some disadvantages, as follows,

• The processing cost is directly related to the number of valid switching

states and hence in the case of the indirect matrix converter will require

a fast processor that uses only a few microseconds to evaluate all possible

predictions.

• It also has a strong dependency on the model used to predict the behavior

of the system.

• Stability can be difficult to probe because of the constraints and non-linearities

included in the model.

Model-based predictive control (MPC) is a control theory composed of a series of

non-linear regulation algorithms that determine the actuation from an optimiza-

tion process, based on predictions from a model of the system [116]. Predictive

control approach considers the benefit of the discrete nature of power converters,

which have a finite number of valid commutation states because they are based

on discrete valves, which have only two states: ON and OFF. Thus, it predicts

the system behavior on real-time for each possible commutation state and selects

the one that minimizes a cost function as future control action. Fundamentally,

and based on [117], the design of the controller consists of the following aspects:


1. Converter model, where are identified all possible switching states and their

relation to input-output voltage/current. The total number of switching

states is equal to the number of different combinations of each switch, how-

ever, not all combinations are possible, since each converter has its operating

restrictions and therefore invalid commutation states are not considered.

2. Discrete-time model of the system, to predict the future behavior of the

variables to be controlled. Here it is important to define the variables that

are measurable and those that are not, because occasionally, the variables

that are required for the predictive model are not accessible and therefore

must be estimated.

3. Cost function, which represents the desired behavior of the system, This can

be expressed as the measurement error between a reference and the predicted

variable. One of the advantages of this method is that different kinds of

variables and restrictions control can be included in this cost function.

Once the controller is implemented, the behavior of the controlled variables for

all possible switching states must be predicted and the cost function must be

evaluated for each prediction, selecting the switching state that minimizes this

function and this optimal switching state is applied in the next sampling time.

This approach is known also as a Finite Set MPC (FS-MPC), since the possible

control actions (switching states) are finite. A simplified algorithm for the real-

time implementation of FS-MPC is shown in Fig. 5.1. Multiple variables, system

constraints, disturbances, saturations, and basically, every characteristic that can

be mathematically modeled and measured can be included in the predictive model

and cost function. This is the basis of the great flexibility and control potential

that can be achieved with FS-MPC. Moreover, the fact that power converters

have a reduced and limited number of switching states makes this method feasible

to implement with present-day available microprocessing resources. Since only a

discrete mode of the system is necessary, rather than approximated linear models

together with control system design theory and modulation algorithms, a simpler

and more direct design and implementation of the controller can be achieved.


As reported in [18, 115], this family of non-linear control techniques has been

implemented on a wide variety of converters with different applications such as,

1. Current control on a wide variety of converters such as active front end

(AFE) rectifiers, voltage source inverters, neutral point clamped (NPC) mul-

tilevel converters, matrix converters, and others.

2. Torque and flux control, considering an induction motor as a load.

3. Direct control of the active and reactive powers for a three-phase PWM

rectifier.

4. Control of a NPC converter, where it is possible to control the load currents

while balancing the capacitor voltages and reducing the average switching

frequency.

5. Control of a direct matrix converter, where different control strategies have

been developed for the output current control, torque and flux control with

the instantaneous reactive power minimization and the reduction of switch-

ing losses and common mode voltage.

In summary, with its great potential and flexibility, predictive control emerges as

a promising tool for electric power conversion. In the particular case of matrix

converters, a problem observed in predictive control implementations has been

the input current distortion due to the filter resonance, which is altered by the

harmonics of the network and by the converter itself. As mentioned above, FS-

MPC technique does not present a fixed switching frequency, and this may be

situated close to the resonant frequency of the filter, affecting the input currents.

In the following chapters some solutions to avoid this problem will be presented.


optg

1...for j n

optk

1k

jg

j n

Figure 5.1. FS-MPC generic algorithm.

Chapter 6

Predictive current control with

reactive power minimization

This chapter presents a current control scheme with instantaneous reactive power

minimization for an indirect matrix converter. The strategy uses the commutation

state of the converter in the subsequent sampling time according to an optimiza-

tion algorithm given by a simple cost functional and the discrete system model.

Simulation and experimental results with a laboratory prototype are provided in

order to validate the control scheme. The effect of a distorted source voltage and

filter resonance is analyzed.

6.1 Control scheme for the IMC

The control scheme for the IMC is represented in Fig. 6.1. The approach pursues

the selection of the switching state of the converter that leads the output currents

closest to their respective references at the end of the sampling period. In addition,

the reactive power on the line side must be minimized and finally the dc-link

voltage must be always positive [98]. First, the control objectives are obtained

and the necessary variables to obtain the prediction model are measured and

calculated, respectively.

64

Chapter 6. Predictive current control with reactive power minimization 65

Figure 6.1. Predictive current control scheme.

The model of the system and measurements are used to predict the behavior

of the variables to be controlled in the subsequent sampling time for each of

the valid switching states and as a final point, the predicted values are used

to evaluate a cost function which deals with the control objectives. After that,

the valid switching state that produces the minimum value of the cost function

is selected for the next sampling period. In order to discretize the differential

equations shown in eq. (4.1)-(4.7), in the following section it will be presented the

model used as the derivative approximation to estimate the value of each function

one sample time in the future (the variables predicted value).

6.2 Input filter and load discrete equations

The predicted values of the input side are:[

vi(k + 1)

is(k + 1)

]

= Φ

[

vi(k)

is(k)

]

+ Γ

[

vs(k)

ii(k)

]

, (6.1)

where,

Φ ∼= eATs , (6.2)

Γ ∼= A−1(Φ − I2x2)B, (6.3)


with,

A =

[

0 1/Cf

−1/Lf Rf

]

, B =

[

0 −1/Cf

1/Lf 0

]

(6.4)

The load current prediction can be obtained using a forward Euler approximation

in eq. (4.7) as:

io(k + 1) = d1vo(k) + d2io(k), (6.5)

where, d1 = Ts/LL and d2 = (1−RLTs/LL) are constants dependent on load para-

meters and the sampling time, Ts [89]. Note that the current is(k+1) and io(k+1)

depends upon the switches state through eq. (4.2) and eq. (4.4), respectively.

6.3 Cost function definition

With the system discretized model, including the load, the input filter and the

IMC, the predictive algorithm is very straight forward to implement. The goal of

this method is to apply the ideal switching state, which is the voltage space vector

vo that produces the least amount of error between the desired load current io∗

and the predicted load current response io in a given sampling time. Hence, if

the dynamic model is accurate the control algorithm will always give the best

performance. A quality function is then defined in order to be able to measure

the error between the reference and the predicted load current response. This

quality function is then computed every sample period for each commutation

state possible on the converter to select the one with the smallest error in order

to apply it at the beginning of the next sample period. The quality function can

be as simple as:

io = (i∗oα − ioα)2 + (i∗oβ − ioβ)2, (6.6)

where ioα and ioβ denotes the load current in α− β coordinates for k + 1 sample

time, and i∗oα and i∗oβ their respective references. An extra term can be added

to this quality function to minimize other parameters which should be subject

to control such as the instantaneous reactive power consumed by the IMC input

along with the filter, the common mode voltage, the commutation losses, the


positive voltage in the dc-link, and so forth. The cost function used to validate

the control scheme in this case is:

g = io + λqqs, (6.7)

which allows the control of the load current and the minimization of the instan-

taneous reactive power on the input side. In eq. (6.7), λq is a weighting factor

and qs denotes the predicted value of the instantaneous reactive power in k+ 1

sampling time, which can be expressed as follows,

qs = (vsαisβ − vsβisα)2, (6.8)

with vsα, vsβ, isα and isβ the source voltages and currents in α − β coordinates,

respectively. The instantaneous reactive power calculation leads to a minimiza-

tion of qs in order to have a unity displacement power factor on the input side.

Noting that g = 0 (for an arbitrary λq) gives perfect tracking of the load current

and unity displacement power factor at the source side, then by minimizing g, the

optimum value for commutation state is guaranteed. In practice, by the appro-

priate selection of the weighting factor λq, a given THD of the input and output

currents is obtained. The principal method for selection of the weighting factors

has been presented in [118].

6.4 Discrete time delay error compensation

Several measured and calculated variables are needed, as well as the knowledge of

the nine rectifier-side and the eight inverter-side valid switching states, to compute

the control scheme algorithm. With these IMC rectifier and inverter side valid

states there are 72 possible switching combinations which must be calculated to

select the one resulting in the less error in the quality function. If the three valid

rectifier-side switching states giving positive dc-link voltage are calculated before

the quality function calculation routine, then only 24 switching combinations must

be computed, resulting in saved computation time, but still a numerical burden

for the microelectronic controller causing an unwanted delay.


The variables measured are vs(k), is(k), vi(k), and io(k), leaving the IMC input

current ii(k) and the IMC output voltage vo(k) as functions of the kth selected

switching state to be calculated. In order to counter the delay error due to the

discrete time computation an effective and simple method is implemented: the

quality function calculation for k + 2. First the variables in k + 1 are predicted

using the already applied switching state S(k), then the variables to be controlled

are predicted for k + 2. The sample time should be sufficient for data acquisition

at time t(k), then compute the variables for k + 1 using S(k) and then calculate

the g(k + 2) to select the optimum S(k + 1), all in the same interval. vs(k + 1) is

considered equal to vs(k) due to its very small change in one sample time [26].

6.5 Simulation results

Two different simulations were carried out to probe the control method feasibility.

Simulations with and without instantaneous reactive power minimization were

done in order to evaluate the effect of introducing the instantaneous reactive power

minimization in the control scheme. The simulation parameters are established

according to the experimental setup available in the laboratory. They are indicated

in Table 6.1 and the sampling period of the control algorithm was set at Ts = 20µs.

The outputs of the controller are used to deliver the gate driver signals for the

IGBTs. These outputs are set directly by the control algorithm and no modulator

is needed. First, the control scheme is simulated without including the term that

minimize the instantaneous reactive power on the input side of the system, so λq =

0 in eq. (6.7). Results in Fig. 6.2(a) show the chaotic behavior of the input current

with a high harmonic distortion such as represented in the spectrum indicated in

Fig. 6.3(b), where it is shown that the resonance of the input filter is situated

in fres = 650Hz, according to the filter parameters. With this it is possible to

observe 1.1%, 87.2% and 91.3% of 3th, 5th and 7th harmonic, respectively. On

the other hand, the output currents follow the reference accurately as indicated

in Fig. 6.2(b). Fig. 6.3(c) shows the spectrum of the load current ia. Fig. 6.2(c)

shows the instantaneous reactive power on the input side.


Table 6.1. Experimental setup parameters

Variables Description Value

Ts Sampling time 20µs

Vs Supply phase voltage 105V

fs Supply frequency 50Hz

Lf Input filter inductance 5.9mH

Cf Input filter capacitance 10µF

Rf Input filter resistance 0.5Ω

RL Load resistance 10Ω

LL Load inductance 15mH

fo Output frequency 50Hz

λq Weighting factor 0; 0.003

Due to the chaotic behavior of the source current, a high reactive power is pre-

sented on the input side, which is not desired. In this case, the ac-supply vsA is

clean with a sinusoidal waveform and not harmonic distortion (Fig. 6.3(a)).

In the second case, Fig. 6.4, the control strategy is evaluated considering λq =

0.003 in eq. (6.7). Fig. 6.4(a) shows an improved input behavior, with almost

sinusoidal current in correct phase with the input phase voltage, fulfilling the con-

dition of unitary displacement power factor, with a reduced harmonic distortion

such as indicated in Fig. 6.5(b). In this case it is possible to observe 0.3%, 2.7%

and 1.2% of 3th, 5th and 7th harmonic, respectively. On the output side, the load

current presents good tracking with respect to its reference, Fig. 6.4(b). Fig. 6.4(c)

shows the improvement in the instantaneous reactive input power minimization,

thus the goal of proposed predictive current control is clearly verified. It must

be acknowledged that the main advantage of the proposed control method is the

simplicity of implementation, since the controller does not need a complex mod-

ulation unit. This can reduce the overall cost of the complete system.


0.4 0.42 0.44 0.46 0.48 0.5-10

0

10

0.4 0.42 0.44 0.46 0.48 0.5-5

0

5

0.4 0.42 0.44 0.46 0.48 0.50

500

1000

Figure 6.2. Simulation results without instantaneous reactive power min-

imization; (a) source voltage vsA/10 [V] and current isA [A]; (b) output current

reference i∗a and measured ia [A]; (c) reactive power qs [VA].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

th th

res

Figure 6.3. Simulation results; (a) spectrum of source voltage [pu]; (b)

spectrum of source current [pu]; (c) spectrum of output current [pu].


0.4 0.42 0.44 0.46 0.48 0.5-10

0

10

0.4 0.42 0.44 0.46 0.48 0.5-5

0

5

0.4 0.42 0.44 0.46 0.48 0.50

500

1000

Figure 6.4. Simulation results with instantaneous reactive power mini-

mization; (a) source voltage vsA/10 [V] and current isA [A]; (b) output current

reference i∗a and measured ia [A]; (c) reactive power qs [VA].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

th th res

Figure 6.5. Simulation results; (a) spectrum of source voltage [pu]; (b)



6.6 Experimental results

A laboratory IMC prototype designed and built by Universidad Tecnica Federico

Santa Marıa, thanks to the support of the Power Electronics Systems Laboratory

of ETH in Zurich, was used for the experimental evaluation. The converter fea-

tures IGBTs of type IXRH40N120 for the bidirectional switch, standard IGBTs

with anti-parallel diodes IRG4PC30UD for the inverter stage. The control scheme

was implemented in a dSPACE 1103 which is connected to additional boards that

include the FPGA for the commutation sequence generation and the signal con-

ditioning for the measurement of voltages and currents. A brief description of the

experimental setup will be presented in the Appendix.

Similarly to the previous section, first, the control strategy is evaluated considering

λq = 0 in eq. (6.7). Fig. 6.6(a) shows the chaotic behavior of the input current with

a high harmonic distortion such as indicated in the spectrum of Fig. 6.7(b). Here

it is observed that the input filter resonance is situated in fres = 650Hz, approxi-

mately, according to the filter parameters. As mentioned before, it is necessary to

add an input filter to assist the commutation of switching devices and to mitigate

against line-current harmonics. However, the filter configuration, which is shown

in Fig. 4.1, presents a resonance frequency and it can be excited by the utility due

to the potential 5th and 7th harmonics in the ac-source and also by the converter

itself. Due to the available ac-source in the laboratory, the input filter resonance

is reflected in the source voltage as seen in Fig. 6.6(a) and the spectrum of Fig.

6.7(a). A summary of the total harmonic distortion (THD) is presented in Table

6.2.

Table 6.2. Experimental THD results with λq = 0

Harmonic vsA isA ia

THD 36.48% 66.07% 8.80%

3th 2.22% 12.25% 0.20%

5th 3.11% 6.40% 0.23%

7th 2.82% 8.55% 0.31%


Figure 6.6. Experimental results without instantaneous reactive power

minimization; (a) source voltage vsA [50V/div] and current isA [5A/div]; (b) out-

put current reference i∗a and measured ia [5A/div].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

th thres

th

th thres

th

Figure 6.7. Experimental results; (a) spectrum of source voltage [pu]; (b)



As was reported in [98]- [119], when a distortion is present in the source volt-

age, the source current is not sinusoidal. For all the aforementioned reasons, it is

necessary to include a term which can help to overcome this problem.

It is known that most industrial application requires unity displacement power

factor in the grid side. For this reason, through the instantaneous reactive power

minimization, the system is forced to work with a unity displacement power factor

on the input side. The results are indicated in Fig 6.8. The measured source current

and voltage of phase A is shown in Fig. 6.8(a) and the reference and measured

output current of phase a in Fig 6.8(b). As expected, the source current fulfils the

condition of unitary power factor showing an almost sinusoidal waveform and, as

a consequence, the instantaneous reactive power is minimized. This is achieved

by increasing the value of the weighting factor from λq = 0 to λq = 0.003 which

has been empirically adjusted as explained in [118], where first it is established

in a value equal to zero in order to prioritize the control of the output current

and later it is increased slowly aiming to obtain unity displacement power factor

in the input currents while maintaining consistent and ideal behaviour on the

output side. In Fig. 6.8(b) it is possible to observe a very good tracking of the

load current ia respect to its reference i∗a. The improvement in the quality of the

source current is remarkable because an important reduction of distortion due to

the mitigation of the input filter resonance is realized. The same effect is observed

in the source voltage spectrum, Fig. 6.9(a). As can be observed in Fig. 6.8(a),

the source currents show a ripple corresponding to the resonance frequency of

the input filter and the harmonic distortion of the ac-supply such as it can be

observed in the spectrum of Fig. 6.9(a). The THD of source voltage and current

and the output current are indicated in Table 6.3.


Figure 6.8. Experimental results with instantaneous reactive power min-

imization; (a) source voltage vsA [50V/div] and current isA [5A/div]; (b) output

current reference i∗a and measured ia [5A/div].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

th th resth

th th resth

Figure 6.9. Experimental results; (a) spectrum of source voltage [pu]; (b)



Table 6.3. Experimental THD results with λq = 0.003

Harmonic vsA isA ia

THD 14.82% 21.03% 8.54%

3th 1.57% 10.68% 0.97%

5th 4.90% 2.25% 1.41%

7th 2.21% 5.21% 1.15%

6.7 The problem in the source current with a weak

ac-supply

In Fig. 6.7(a) is shown the spectrum of the source voltage vsA when the term

that minimizes the instantaneous reactive power is not included in the cost func-

tion, λq = 0. In this case, the ac-source was altered, as it was highly distorted

due to the high distortion of the input current and the low-order harmonics. Of

course, the differences between simulation and experimental results are given by

the ac-source. This phenomenon is due to the utilization of a three-phase variac

as the ac-supply, which behaves like a weak ac-source for the system, due to the

associated inductance of the autotransformer connection. On the other hand, Fig.

6.9(a) shows the spectrum of the source voltage vsA when λq = 0.003. Thanks to

the minimization of the instantaneous reactive power, the harmonic distortion of

the source voltage is decreased from a THD of 36.48% to 14.82%. In Fig. 6.6(b),

a distorted source current with a THD of 66.07% was observed, but when the in-

stantaneous reactive power is minimized, a THD of 21.03% is obtained as depicted

in Fig. 6.8(b). The load current THD was 8.80% in the first case, Fig. 6.6(c), but

when the weighting factor λq is considered as λq = 0.003, an output current with

a THD of 8.54% was observed, Fig. 6.8(c).

As well the improvement of the input current is remarkable, the experimental

results do not present a desirable performance yet. For this reason, in the following

chapters, the predictive method is modified in order to improve the behavior of

the input current under a polluted ac-supply.

Chapter 7

Current control for an IMC with

input filter resonance mitigation

In the previous chapter, a predictive control scheme for the indirect matrix con-

verter with instantaneous reactive power minimization was presented. In that case,

the source currents were highly distorted. This effect was observed because the

predictive method does not have any direct control over the source current and

because of distortions in the ac-supply and filter resonance. In this chapter, the

predictive method is improved by including a method to mitigate the resonance ef-

fect of the input filter. The active damping method is based on a virtual harmonic

resistor which damps the filter resonance. Experimental results are presented to

demonstrate that the proposed control method can generate good tracking of the

output current references, achieve unity displacement power factor and reduce the

input current distortion caused by the input filter resonance.

7.1 Current control scheme for the IMC with active

damping approach

As mentioned before, an input filter is necessary to assist the commutation of

switching devices and to mitigate against line-current harmonics. However, the

77

Chapter 7. Current control for an IMC with input filter resonance mitigation 78

filter configuration shown in Fig. 4.1 presents a resonance frequency and it can be

excited by the utility due to potential harmonics in the ac-source and also by the

converter itself.

To suppress the resonances, different propositions have been reported. For exam-

ple, it is feasible to choose a proper filter resonant frequency, which may limit

performance since the LfCf resonant frequency is a function of the power system

impedance, which usually varies with the power system operating conditions. Also,

it is possible to use a high commutation frequency or connect a physical resistor

damper with the filter circuit. The first solution results in output currents featur-

ing low THD, but the converter power losses are increased significantly, wasting

energy unnecessarily and decreasing the converter efficiency. This cannot be tol-

erated in static converters where the energy efficiency is an important issue. The

second one is the classical solution; where a damping resistor physically connected

in parallel to the inductor is used to mitigate a fixed series resonance. There is an-

other strategy with which it is possible to mitigate different resonances, between

the series and parallel resonances, as reported in [19], by using active damping

control.

7.1.1 Active damping approach and implementation

Active damping is a control technique which achieves the attenuation of system

resonance without affecting the efficiency of the converter. The method considers

a virtual harmonic resistive damper Rd, which is immune to system parameter

variations, in parallel with the input filter capacitor Cf as shown in Fig. 7.1,

without affecting the fundamental component [120–126]. The converter draws a

damping current proportional to the capacitor voltage which is extracted by the

converter itself, emulating the damping resistance Rd as indicated by,

id =vi

Rd. (7.1)

As only the harmonics are mitigated and not the fundamental component, the

damping current is calculated using the harmonic capacitor voltage vih. To do

this, the input voltage vi is considered in d− q axes, passing this voltage through


a dc-blocker digital filter, deleting the fundamental element and considering only

the harmonic components. The converter is required to draw the current that

produces the input filter resonance in the matrix converter. The transformation in

d−q axes was done by the implementation of a synchronous reference frame-phase

looked loop (SRF-PLL) [127]. Once the voltage harmonics have been obtained,

the current damping harmonics are calculated as indicated in eq. (8.11) where

vihdq corresponds to all harmonic components present in vi.

idhdq =

vihdq

Rd. (7.2)

Then, the active damping in the IMC topology is implemented by passing the

harmonic component effect present on the input side to the output side, adding

this effect to the load current reference [126]. This is possible because in the IMC

topology the input current ii is related to the output current by eq. (4.2) and eq.

(4.3). Thus, the new load current reference can be expressed as:

[

i∗do

i∗qo

]

=

[

I∗do

I∗qo

]

+

[

iddh

iqdh

]

, (7.3)

where, io∗dq =

[

i∗do i∗qo

]T

, Io∗dq =

[

I∗do I∗qo

]T

=[

I∗o 0]T

is the required

load current and the damping reference current is given by eq. (8.11) as idhdq =

[

iddh iqdh

]T

. An essential aspect of the active damping control is that it does

not require any extra measurements and, furthermore, does not incorporate any

modification of the algorithm where only the output current reference has been

modified, such as seen in Fig. 7.1.

7.2 Experimental results

Results without and with the active damping implementation are presented in

this section. In the IMC a ratio transfer equal to 0.866 can be achieved, but in

this case, a different operation point is considered because the only objective of

this experimental validation is to demonstrate the effect of the active damping

implementation.


Figure 7.1. Predictive current control with active damping scheme.

The parameters used in the experimental tests have been given in Table 6.1 and

the sampling time is defined as Ts = 20µs. Fig. 7.2(a) shows the measured source

current and voltage of phase A and Fig 7.2(b) shows the reference and measured

output current of phase a. As expected, the source current fulfils the condition of

unitary displacement power factor because it is in phase with respect to its voltage,

so as a consequence, the instantaneous reactive power is minimized. However, the

source current and voltage show a ripple corresponding to the resonance frequency

of the input filter and the harmonic distortion of the ac-supply such as it is

observed in Fig. 7.3. Fig. 7.2(a) shows that the voltage source is altered when the

system is in resonance. As explained in the previous chapter, this phenomenon

is due to the utilization of a three-phase variac as the ac-source, which behaves

like a weak ac-supply for the system, due to the inductance associated with the

autotransformer connection.


Figure 7.2. Experimental results without active damping approach; (a)

source voltage vsA [50V/div] and current isA [5A/div]; (b) output current reference

i∗a and measured ia [5A/div].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

th th resth

th th resth

Figure 7.3. Experimental results without active damping approach; (a)

spectrum of source voltage [pu]; (b) spectrum of source current [pu]; (c) spectrum

of output current [pu].


Table 7.1. Experimental THD results without active damping

Harmonic vsA isA ia

THD 14.82% 21.03% 8.54%

3th 1.57% 10.68% 0.97%

5th 4.90% 2.25% 1.41%

7th 2.21% 5.21% 1.15%

On the other hand, very good tracking of the load current to its reference is

observed in Fig. 7.2(b). The THD of source voltage and current and the output

current are indicated in Table 7.1.

For the second case, the improvement in the quality of the source current and

voltage is noticeable due to an important reduction of distortion by filter reso-

nance mitigation, as shown in Fig. 7.4(a). As well, an almost sinusoidal source

current is obtained, a distortion harmonic due to the unclean ac-supply is still ob-

served which cannot be mitigated by the active damping method. Similarly to the

aforementioned case, the output current follows its reference accurately despite

the distortion added to the reference by the active damping method. In Fig. 7.2

a distorted input current with a THD of 21.03% is observed, but when the reso-

nance mitigation is applied using active damping, a 20.84% of THD is obtained.

This is a relatively small value considering the polluted source with 13.05% of

THD under normal operation. The output current THD is 8.54% without active

damping action, and 6.53% with active damping operation. It is expected that

with a clean ac-source the input and output currents THD can be decreased.

By including the active damping approach, the input and output currents distor-

tion are attenuated considerably. In the IMC topology it is possible to observe the

series resonance, which is produced by the ac-supply and the parallel resonance,

which is generated by the converter itself and the control method.


Figure 7.4. Experimental results current control with active damping ap-

proach; a) source voltage vsA [50V/div] and current isA [5A/div]; b) output current

ia and reference i∗a [5A/div].

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

0 200 400 600 800 10000

0.5

1

Figure 7.5. Experimental results with active damping approach; (a) spec-

trum of source voltage [pu]; (b) spectrum of source current [pu]; (c) spectrum of

output current [pu].


Table 7.2. Experimental THD results with active damping

Harmonic vsA isA ia

THD 13.05% 20.84% 6.53%

3th 1.36% 10.59% 1.18%

5th 3.96% 4.75% 2.11%

7th 1.17% 4.55% 1.08%

400 600 8000

0.05

0.1

400 600 8000

0.005

0.01

400 600 8000

0.05

400 600 8000

0.05

0.1

400 600 8000

0.005

0.01

400 600 8000

0.05

Figure 7.6. Experimental results current control without and with active

damping approach; a) zoom spectrum of source voltage vsA [pu]; b) zoom spectrum

of source current isA [pu]; c) zoom spectrum of output current ia [pu].

According to the filter parameters and as observed in Fig. 7.3 and Fig. 7.5, the

resonance frequency is located around 650Hz which is amplified by the converter

and the distorted ac-supply. From Fig. 7.6 it is verified that the filter resonance is

mitigated by considering the active damping method. This is reflected in a more

sinusoidal ac-source.


Figure 7.7. Experimental results current control without active damping

approach; a) source voltage vsA [50V/div] and current isA [5A/div]; b) output cur-

rent ia and reference i∗a [5A/div] with output frequency reference equal to 100Hz.

Because the 3th, 5th and 7th harmonics are from the ac-source itself, the active

damping method is not able to mitigate these harmonics because the ac-source

and network models are not included in the control strategy, but the operation

of the converter in an industrial application must be independent of the grid

parameters, to which it is connected. For this reason, an active damping technique

is incorporated in the control, where the only parameter to be adjusted is the

virtual resistor regardless of the grid model. As mentioned before, the resonance

and distortion effect is reflected in the load current as it can be observed in Fig.

7.6(f). As shown in Fig. 7.7 and Fig. 7.8, a different output frequency is considered,

which is established in 100Hz. As can be observed, the active damping approach

mitigates the resonance of the input filter. But, similar to the previous case and

due to a weak ac-supply in our laboratory, the source currents are distorted as

well.


Figure 7.8. Experimental results current control with active damping ap-

proach; a) source voltage vsA [50V/div] and current isA [5A/div]; b) output current

ia and reference i∗a [5A/div] with output frequency reference equal to 100Hz.

7.3 Comments

In summary, the resonance of the input filter is still a major concern that directly

affects the selection of the design parameters and the modulation method. The

reduction of resonances in the input filter, as described in this chapter, is an

important improvement in the converter’s performance. This approach reduces

power losses as compared to the use of real resistive damping. Experimental results

indicate that the presented strategy allows good tracking of the output current to

its reference and minimizes the instantaneous reactive power on the input side at

the same time. Active damping improves the quality of the input currents even

in the presence of a weakly damped input filter. The ac-supply has an important

influence in the behavior of the source current and better results can be expected

by optimizing the input filter and also with a clean ac-supply. In order to improve

the behavior of the source currents and force them to have a sinusoidal waveform

in spite of the filter resonances and distortions of the ac-supply, a new idea is

proposed for the IMC in the following chapter.

Chapter 8

Imposed sinusoidal source and

load currents for an IMC

A new strategy for indirect matrix converters which allows an optimal control

of source and load currents is presented in this chapter. This method uses the

commutation state of the converter in the subsequent sampling time according

to an optimization algorithm given by a simple cost functional and the discrete

system model. The control goals are regulation of output current according to an

arbitrary reference and also good tracking of the source current to its reference

which is imposed to have a sinusoidal waveform. Simulation and experimental

results support the theoretical development.

8.1 Fundaments

Most of PCC methods applied in matrix converters take into consideration the

output current regulation and the reactive power minimization on the input side,

obtaining input currents in phase with their respective phase voltages. However, as

reported in the previous chapters, this cannot ensure that they present a sinusoidal

waveform, especially when harmonic distortion is present in the source voltage. To

overcome this issue and enhance the quality of the source current, the following

87

Chapter 8. Imposed sinusoidal source and load currents for an IMC 88

pages this chapter illustrate how the PCC can be applied to an IMC and how

both source and load currents waveforms can be directly controlled. First, it is

necessary to define the impedance model of the input filter as:

Zc =1

jwsCf, (8.1)

Zl = Rf + jwsLf , (8.2)

where ws = 2πfs, with fs the source frequency. The load impedance is represented

by:

Zo = RL + jwoLL, (8.3)

where wo = 2πfo, with fo the load frequency. Finally, the filter model in terms of

impedance is given as:

vs = vi + isZl,

is = ii + vi/Zc.(8.4)

8.2 The problem on the input side

SVM and PWM techniques generate a desired output voltage with unity displace-

ment power factor [16,25,80,128,129], but there is a displacement angle between

the source line current is and input current ii due to the filter parameters and con-

sequently a displacement angle between the source voltage and current, requiring

additional controllers to handle this angle [130]. From eq. (8.1), eq. (8.2) and eq.

(8.4), this displacement angle is given as follows,

δ = arctan(

wsCf (Vs −Rf Is))/(Is(1 − w2sLfCf )

)

, (8.5)

where Vs and Is are the source voltage and current fundamental amplitudes re-

spectively. In [130] it has been proposed that two power factor compensation

methods can be used, each one considering direct SVM in order to compensate

the displacement angle δ between source voltage and current with the goal to

obtain a unity displacement power factor from a voltage transfer ratio greater

than or equal to 0.35, but the compensated displacement angle decreases while

the voltage transfer ratio increases and additionally, and the source current does


not present a sinusoidal waveform. In [131] the authors proposed a modified direct

SVM method to control matrix converters with transfer ratio less than 0.5, allow-

ing compensation to a maximum displacement angle of π/6 (30o) but the source

currents are not considered in this work, presenting a distorted waveform as well.

Predictive techniques that have been proposed in the last years have focused on

the minimization of the reactive power on the input side but there are no reports

of additional works based on a source current control [18,23,26,89,115].

In summary, today, most of the work on matrix converters has focused on the

control of the output side while maintaining unity displacement power factor

on the input side but there are no reports of a control of the source current

with imposed waveform like the model proposed in this chapter. In comparison to

classical controllers, by using a predictive algorithm, the controller and modulator

merges in only one block, making it easier to implement than SVM and PWM

methods. The proposed predictive strategy presented in the following sections

suggests that a control of the source current with imposed waveform should be

performed rather than a reactive power minimization and also the active damping

implementation. The predictive algorithm evaluates at every sampling time Ts all

of the 24 possible states and chooses the one that returns the minimal value for

the cost functional g to be applied in the next sampling instant. The minimization

of g guarantees two goals: that the output currents follow their references with

accuracy and that the converter draws sinusoidal input currents with a desired

input displacement power factor according to their references as well.

8.3 Predictive current control for the IMC with imposed

sinusoidal source currents

In order to minimize the computational cost, the α−β linear transform is applied

to all three-phase current and voltage vectors, defined as:

[

uα

uβ

]

=

[

2/3 −1/3 −1/3

0√

3/3 −√

3/3

]

ua

ub

uc

, (8.6)


where the vector [ua ub uc]T is the three-phase current or voltage vector, and

[uα uβ]T is the α− β vector. In [26] a predictive control strategy for an IMC has

been presented, where the approach pursues the selection of the switching state

of the converter that leads the output currents close to their respective references

at the end of the sampling period, while minimizing the instantaneous reactive

power on the input side. As mentioned before, the strategy proposed in [26] cannot

ensure sinusoidal waveform of source current, especially when harmonic distortion

is present in the source voltage or resonances in the input filter. The proposed

MPC scheme is represented in Fig. 8.1, where in comparison to the before men-

tioned strategy, the term which minimizes the reactive power on the input side

is replaced by a direct control of the source current waveforms in order to force

them to follow a sinusoidal reference independently of the distortion present on

the input side.

8.3.1 Prediction model

Since the predictive controller is formulated in discrete time, it is necessary to de-

rive a discrete time model for the load-converter system. As indicated in previous

sections, the input side can be represented by a state space model [89], with the

states variables is and vi obtained from eq. (4.5) and eq. (4.6) as follows,

[

vi

is

]

= A

[

vi

is

]

+ B

[

vs

ii

]

, (8.7)

where,

A =

[

0 1/Cf

−1/Lf −Rf/Lf

]

,

B =

[

0 −1/Cf

1/Lf 0

]

.

(8.8)


Figure 8.1. Predictive source and output current control scheme with

source current reference.

Such as indicated in previous chapters, the discrete-time state space model is

determined as:

[

vi(k + 1)

is(k + 1)

]

= Φ

[

vi(k)

is(k)

]

+ Γ

[

vs(k)

ii(k)

]

, (8.9)

with,

Φ = eATs , Γ = A−1(Φ − I2x2)B. (8.10)

The output current prediction can be obtained using a forward Euler approxima-

tion in eq. (4.7) as:

io(k + 1) = d1vo(k) + d2io(k), (8.11)

where, d1 = Ts/LL and d2 = 1 − RLTs/LL, are constants dependent on load


parameters and the sampling time Ts [89]. Note that the current is(k + 1) and

io(k + 1) depend upon Si(k) through eq. (4.2) and eq. (4.3).

8.3.2 Cost function definition

The error between the predicted load currents and its references can be expressed

as follows,

io(k + 1) = (i∗oα − ioα)2 + (i∗oβ − ioβ)2, (8.12)

where ioα and ioβ denotes the load current in α− β coordinates for k + 1 sample

time, and i∗oα and i∗oβ their respective references. Furthermore, the error between

the reference and predicted value of the source current can be expressed as:

is(k + 1) = (i∗sα − isα)2 + (i∗sβ − isβ)2, (8.13)

where, i∗sα and i∗sβ correspond to the source current references and isα and isβ

are the source current predictions in sample k + 1. Expressions of eq. (8.12) and

eq. (8.13) are merged in a single cost function as indicated in eq. (8.14) which is

evaluated for every switching state, and is applied to the converter the switching

state that minimizes this quality function, as has been explained before. Finally,

eq. (8.12) and eq. (8.13) are combined into a single so-called quality function as

follows,

g = io(k + 1) + γiis(k + 1), (8.14)

where γi is a weighting factor. As indicated in the previous chapters, noting that

g = 0 (for an arbitrary value of γi) gives perfect tracking of the load and source

currents, then by minimizing g, the optimum value for commutation state is guar-

anteed. In practice, by the appropriate selection of the weighting factor γi, a given

total harmonic distortion (THD) of the input and output currents is obtained.

8.4 Generation of the source current reference is∗

Assuming a sinusoidal source waveform, the amplitude of is∗, in terms of the

amplitude of io∗, vs and the system parameters, can be obtained using a power


balance equation between the input and output side of the IMC, i.e.

poη = pi, (8.15)

where po is the output active power, pi is the input active power and η is the

efficiency of the IMC. The active power po can be expressed as,

po =3

2I∗o

2RL, (8.16)

where I∗o is the amplitude of the output current reference. The input power pi is

defined as:

pi =3

2Revi · ii∗, (8.17)

where vi = Viejθvi , ii = Iie

jθii , Vi and Ii are the amplitudes of the input voltage

and current, respectively. Using the equations of the input filter and expressing

the filter parameters as impedances at a fixed source frequency of ωs = 2πfs, the

input voltage and current amplitudes can be expressed as follows,

vi =vs − is(jωsLf +Rf ), (8.18)

ii = is −vi

jωsCf, (8.19)

where vs = Vsejθvs , is = Ise

jθis , Vs and Is are the amplitudes of the source

voltage and current, respectively, and θvi≈ θvs . Replacing (8.18) and (8.19) in

(8.17), replacing (8.17) and (8.16) in (8.15), and solving the quadratic equation

for Is, the obtained solution for the source current amplitude I∗s , using a unitary

displacement power factor in the mains (θis = θvs) is:

I∗s =Vsk1 −

√

V 2s k2 + I∗o

2k3

k4, (8.20)

where,

k1 = 8π2f2sLfCf − 1, k2 = k2

1 ,

k3 = 4ηRLRfk1, k4 = 2Rfk1. (8.21)

In addition, it is necessary to implement a Phase-Locked-Loop (PLL) to obtain

the phase of the fundamental source voltage in order to generate the sinusoidal


reference. Finally, the resulting source current reference is defined as:

i∗sA = I∗s sin(wst+ θ)

i∗sB = I∗s sin(wst− 2π/3 + θ)

i∗sC = I∗s sin(wst+ 2π/3 + θ)

, (8.22)

where θ is the parameter that allows a variable power factor and it is considered

equal to zero in order to obtain unity displacement power factor.

8.5 Simulation and experimental results

Both simulation and experimental results are presented in this section, by consid-

ering the same parameters employed in the previous chapters, which are indicated

in Table 6.1. The control operates with a sample time of Ts = 20µs. The control

strategy is evaluated considering the cost function indicated in eq. (8.14) and

with a weighting factor λi equal to λi = 20. This variable has been empirically

adjusted as explained in [118], where first it is established in a value equal to zero

in order to prioritize the control of the output current and later it is increased

slowly aiming to obtain minimal THD of source and load currents.

Simulation results are presented in Fig. 8.2(a) which show the source current isA

and its respective reference i∗sA and source voltage vsA, where the condition of

unitary power factor is fulfilled. This condition is imposed by the source current

reference i∗sA = I∗s sin(wst+ θ), because the phase of this current reference is the

same of the source voltage. In this method, the source current is forced to have

a sinusoidal waveform with an amplitude of Is = 2.11A. On the output side, the

load current ia presents good behavior with an almost sinusoidal waveform and

4.5A of amplitude, according to its reference (Fig. 8.2(b)). In order to validate

the simulations, Fig. 8.3 shows the experimental results by considering the same

parameters and references.

In Fig. 8.3(a) is shown the source current isA and its respective source voltage

vsA, where the condition of unitary power factor is fulfilled, which is imposed by

the source current reference i∗sA, being both source voltage and current in phase.


0.4 0.41 0.42 0.43 0.44 0.45-5

0

5

0.4 0.41 0.42 0.43 0.44 0.45-5

0

5

Figure 8.2. Simulation results predictive control with imposed sinusoidal

source and load currents; a) source voltage [V/25] and current [A]; b) output

current and reference [A].

Figure 8.3. Experimental results predictive control with imposed sinu-

soidal source and load currents; a) source voltage [50V/div] and current [5A/div];

b) output current and reference [5A/div].

Again, the source current is forced to have a sinusoidal waveform independently

of the distortion present in the source voltage or the resonance of the input filter,

with an amplitude of Is = 2.11A. For this reason, the source current isA is almost


Table 8.1. Experimental THD results with θ = 0

vsA isA ia

THD 15.67% 29.24% 7.79%

3th 1.25% 9.88% 1.03%

5th 3.74% 4.00% 2.67%

7th 1.04% 3.89% 1.84%

sinusoidal and the harmonic distortion and filter resonance are almost mitigated.

As it can be shown in Fig. 8.3(a), the source voltage is not completely clean

because of the utilization of a three-phase variac as the ac-source, which behaves

like a weak ac-supply for the system, due to the inductance associated with the

autotransformer connection. On the output side, the load current ia presents good

behavior with a near sinusoidal waveform and an amplitude of 4.5A according to

its reference Fig. 8.3(b). This method does not involve greater calculations and

the considered sampling time Ts is equal to the Ts used in [26]. With this idea

almost sinusoidal source and output currents can be obtained, realizing desirable

tracking to their respective references. The proposed strategy is immune to source

voltage distortion and/or input filter resonances. A summary of the experimental

THD is presented in Table 8.1. A different output frequency is considered in order

to demonstrate the strategy in a different operation point, such as indicated in

simulation results in Fig. 8.4 and experimental results in Fig. 8.5, where an output

frequency of 100Hz has been imposed on the load. To demonstrate the effectiveness

of the proposed method, two tests have been done such as shown in Fig. 8.6 to

Fig. 8.9. Simulation results with a displacement of θ = 30o and θ = −30o between

source voltage and current, while maintaining the output current control, are

presented in Fig. 8.6 and Fig. 8.8, respectively. Similar experimental results are

indicated in Fig. 8.7 to Fig. 8.9. Again, the source voltage presents an harmonic

distortion due to the ac-supply utilized and the filter resonance.


0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5-5

0

5

0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5-5

0

5


source and load currents; a) source voltage [V/25] and current [A]; b) output

current and reference [A] with an output frequency reference of 100Hz.



b) output current and reference [5A/div] with an output frequency reference of

100Hz.


0.4 0.41 0.42 0.43 0.44 0.45-5

0

5

0.4 0.41 0.42 0.43 0.44 0.45-5

0

5


source and load currents; a) source voltage [V/25] and current [A] 30o displace-

ment angle; b) output current and reference [A].





0.4 0.41 0.42 0.43 0.44 0.45-5

0

5

0.4 0.41 0.42 0.43 0.44 0.45-5

0

5


source and load currents; a) source voltage [V/25] and current [A] −30o displace-

ment angle; b) output current and reference [A].





Table 8.2. Experimental THD results with θ = +30

vsA isA ia

THD 16.81% 19.21% 7.45%

3th 0.80% 5.23% 2.44%

5th 3.45% 1.59% 1.96%

7th 0.63% 1.66% 1.59%

Table 8.3. Experimental THD results with θ = −30

vsA isA ia

THD 16.09% 19.65% 7.84%

3th 0.74% 5.41% 3.02%

5th 3.64% 2.77% 1.66%

7th 0.77% 2.84% 0.77%

Simulation and experimental results verified that it is possible to control both

source and output currents at the same time, while keeping near sinusoidal wave-

forms on both sides in spite of distortions or perturbations in the source voltage.

A summary of the experimental THD are presented in Table 8.2 and Table 8.3

for both cases. It is expected that with a clean ac-source the input and output

currents THD can be decreased.

8.6 Comments

Simulation and experimental results indicate that the presented strategy provides

good tracking of the source and output current to their references, making it

possible to control both source and output currents at the same time, while keeping

almost sinusoidal waveforms on both sides in spite of distortions or perturbations

in the source voltage. Better results can be obtained by considering using a clean

ac-supply.

Chapter 9

Conclusions

The main objective of our research has been to propose, develop and implement

a simple predictive control scheme for the indirect matrix converter that accom-

plishes the standard requirements of other techniques such as unitary power factor

and the improvement of the input current in an operation under abnormal input

conditions.

This document contains a review of the most important ac/ac topologies and the

well established modulation and control techniques for matrix converters. A brief

description of the indirect matrix converter topology and the main space vec-

tor modulation technique throughout simulation results have also been presented.

A predictive current control strategy was proposed which has been extended to

minimize the instantaneous reactive input power. Together with the theoretical

background, the study includes simulation results as well as experimental valida-

tion of the hypothesis and proposed control algorithms. Predictive current control

applied to passive load, effectively controlling the output current from the IMC

to the load and allowing maintenance of the input currents in phase with its in-

put voltage, although they are highly distorted. This distortion was due to the

utilization of a three-phase variac as the ac-supply, which behaves like a weak ac-

source for the system, due to the associated inductance with the autotransformer

connection.

101

Chapter 9. Conclusions 102

An active damping implementation was tested to mitigate the resonance of the

input filter. Active damping as found to improve the quality of the input cur-

rents even in the presence of a weakly damped input filter, but the distortion

from the ac-supply cannot be mitigated with this technique. This issue is still a

major concern that directly affects the selection of the design parameters and the

modulation method. The reduction of resonances in the input filter, as observed

in this thesis, is an important improvement in the converter’s performance.

The ac-supply has an important influence in the behavior of the source current and

better results can be expected by optimizing the input filter in combination with

a clean ac-supply. In order to improve the behavior of the source current with

the available ac-supply, a predictive control method for a conventional indirect

matrix converter has been proposed and the results presented in this thesis. The

algorithm allows simultaneous control of source and output currents with almost

sinusoidal waveforms, according their references. Simulation and experimental re-

sults indicate that the presented strategy provides good tracking of the source

and output current to their references, making it possible to control both source

and output currents at the same time, while keeping near sinusoidal waveforms

on both sides in spite of distortions or perturbations in the source voltage.

In summary, our findings indicate that this predictive control scheme is a simple

and effective alternative to conventional methods for the indirect matrix converter.

The predictive methods presented in this document can be easily implemented,

taking advantage of the present technologies available in digital signal processors.

Finally, with predictive control it is possible to obtain near sinusoidal input and

output currents in presence of resonances on the input filter and a distorted ac-

supply, which presents interesting possibilities in terms of a conceptually different

approach to optimization in the control of power converters.

Appendix

9.1 Publications in journals

1. P. Correa, J. Rodriguez, M. Rivera, J. Espinoza, J. Kolar, Predictive con-

trol of an indirect matrix converter, IEEE Transactions on Industrial

Electronics, Vol. 56 No 6, pp. 1847-1853; June 2009. (Published)

2. J. Rodriguez, P. Wheeler, B. Wu, J. Espinoza, M. Rivera, C. Rojas, Predic-

tive current control with resonance mitigation in a direct matrix

converter, IEEE Transactions on Power Electronics, 2011. (Published)

3. J. Rodriguez, P. Wheeler, M. Rivera, C. Rojas, A. Wilson, Control of a

matrix converter with imposed sinusoidal input currents, SS on Ma-

trix Converters, IEEE Transactions on Industrial Electronics, 2011. (Under

review)

4. J. Rodriguez, P. Wheeler, J. Kolar, M. Rivera, A review of control and

modulation methods for matrix converters, SS on Matrix Converters,

IEEE Transactions on Industrial Electronics, 2011. (Under review)

5. J. Rodriguez, M. Rivera, C. Rojas, Current control for an indirect ma-

trix converter with filter resonance mitigation, SS on Matrix Con-

verters, IEEE Transactions on Industrial Electronics, 2011. (Under review)

6. M. Rivera, J. Rodriguez, J. Espinoza, C. Rojas, A. Wilson, Imposed sinu-

soidal source and load currents for an indirect matrix converter, SS

103

Appendix 104

on Matrix Converters, IEEE Transactions on Industrial Electronics, 2011.

(Under review)

7. A. Wilson, J. Rodriguez, P. Wheeler, L. Empringham, C. Rojas, M. Rivera,

An assessment of model predictive current control and space vec-

tor modulation in a direct matrix converter, SS on Matrix Converters,

IEEE Transactions on Industrial Electronics, 2011. (Under review)

8. J. Espinoza, F. Villarroel, C. Rojas, J. Rodriguez, M. Rivera, Finites states

model predictive control with fuzzy decision making applied to a

direct matrix converter, SS on Matrix Converters, IEEE Transactions

on Industrial Electronics, 2011. (Under review)

9.2 Publications in conferences

1. M. Rivera, J. Espinoza, R. Vargas, J. Rodriguez, Behavior of the pre-

dictive DTC based matrix converter under unbalanced ac supply,

Industrial Applications Society, Annual General Meeting, IAS 2007, New

Orleans, USA. (Published)

2. M. Rivera, R. Vargas, J. Espinoza, J. Rodriguez, C. Silva, Current con-

trol in matrix converters connected to polluted ac voltage supplies,

Power Electronics Specialists Conference, PESC 2008, Rhodes, Greece. (Pub-

lished)

3. R. Vargas, M. Rivera, J. Rodriguez, J. Espinoza, P. Wheeler, Predictive

torque control with input PF correction applied to an induction

machine fed by a matrix converter, Power Electronics Specialists Con-

ference, PESC 2008, Rhodes, Greece. (Published)

4. M. Rivera, P. Correa, J. Rodriguez, I. Lizama, J. Espinoza, Predictive

control of the indirect matrix converter with active damping, 6th

International Power Electronics and Motion Control Conference, IPEMC

2009, Wuhan, China. (Published)

Appendix 105

5. I. Lizama, J. Rodriguez, B. Wu, P. Correa, M. Rivera, M. Perez, Predic-

tive control for current source rectifiers operating at low switching

frequency, 6th International Power Electronics and Motion Control Con-

ference, IPEMC 2009, Wuhan, China. (Published)

6. M. Rivera, P. Correa, J. Rodriguez, I. Lizama, J. Espinoza, C. Rojas, Pre-

dictive control of the indirect matrix converter with active damp-

ing, Energy Conversion Congress and Expo, ECCE 2009, California,

USA. (Published)

7. J. Rodriguez, J. Espinoza, M. Rivera, F. Villarroel, C. Rojas, Predictive

control of source and load currents in a direct matrix converter,

IEEE International Conference on Industrial Technology, ICIT 2010, Val-

paraıso, Chile. (Published)

8. J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, C. Rojas, Predictive cur-

rent control with reactive power minimization in an indirect ma-

trix converter, IEEE International Conference on Industrial Technology,

ICIT 2010, Valparaıso, Chile. (Published)

9. J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, C. Rojas, Predictive torque

and flux control of an induction machine fed by an indirect matrix

converter, IEEE International Conference on Industrial Technology, ICIT

2010, Valparaıso, Chile. (Published)

10. J. Rodriguez, B. Wu, M. Rivera, A. Wilson, V. Yaramasu and C. Rojas,

Model predictive control of three-phase four-leg neutral-point-

clamped inverters, IEEE International Power Electronics Conference, IPEC

2010, Sapporo, Japan. (Published)

11. M. Rivera, J. Rodrıguez, Predictive control of an indirect matrix con-

verter, IEEE International Conference on Networking, Sensing and Control,

ICNSC 2010, Chicago, USA. (Published)

12. J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, C. Rojas, Predictive con-

trol of a direct matrix converter operating under an unbalanced

Appendix 106

ac source, IEEE International Symposium on Industrial Electronics, ISIE

2010, Bari, Italy. (Published)

13. J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, C. Rojas, Predictive torque

and flux control of an induction machine fed by an indirect matrix

converter, IEEE International Symposium on Industrial Electronics, ISIE

2010, Bari, Italy. (Published)

14. V. Yaramasu, J. Rodriguez, B. Wu, M. Rivera, A. Wilson, C. Rojas, A

simple and effective solution for superior performance in two-level

four-leg voltage source inverters: predictive voltage control, IEEE

International Symposium on Industrial Electronics, ISIE 2010, bari, Italy.

(Published)

15. J. Rodriguez, B. Wu, M. Rivera, C. Rojas, V. Yaramasu, A. Wilson, Predic-

tive current control of three-phase two-level four-leg inverters, In-

ternational Power Electronics and Motion Control Conference, EPE-PEMC

2010, Ohrid, Macedonia. (Published)

16. M. Rivera, J.L. Elizondo, M. E. Macias, O.M. Probst, O.M. Micheloud,

J. Rodriguez, C. Rojas and A. Wilson, Model predictive control of a

double fed induction generator DFIG with and indirect matrix

converter, IECON 2010, Phoenix, USA. (Published)

17. J.L. Elizondo, M. Rivera, M. E. Macias, O.M. Probst, M. Oliver, O.M Mich-

eloud, J. Rodriguez, Model predictive control of a double fed induc-

tion generator with and indirect matrix converter, 41 Principal

Congreso de Investigacion y Desarrollo del Tecnologico de Monterrey, Jan.

2011, Mexico. (Published)

18. M. Rivera, I. Contreras, J. Rodriguez, R. Pena, A simple current con-

trol method for four-leg indirect matrix converters, IEEE European

Conference on Power Electronics and Applications, EPE 2011, Birmingham,

England. (To be published)

Appendix 107

9.3 Projects related with the research

1. FONDECYT 108 0059, Control of Indirect Matrix Converters, J. Ro-

driguez.

2. Basal Project FB021, Predictive Control in a Four-Leg Indirect Ma-

trix Converter, May 2010 - June 2011, M. Rivera.

3. Basal Project FB021, Optimizacion de la operacion de un convertidor

matricial indirecto ante una red distorsionada, May 2011 - June 2012,

M. Rivera.

4. FONDECYT 110 0404, High Performance Control of Electrical Ma-

chines, J. Rodriguez.

Appendix 108

9.4 Experimental setup circuit diagram

In Fig. 9.1 depicts a view of the experimental setup implemented in the laboratory,

which consists of a IMC prototype designed and built by Universidad Tecnica Fe-

derico Santa Marıa, thanks to the support of the Power Electronics Systems Lab-

oratory of ETH in Zurich. This converter features IGBTs of type IXRH40N120 for

the bidirectional switch, standard IGBTs with anti-parallel diodes IRG4PC30UD

for the inverter stage. The control scheme was implemented in a dSPACE 1103

which is connected to additional boards that include the FPGA for the commu-

tation sequence generation and the signal conditioning for the measurement of

voltages and currents.

Fig. 9.2 to Fig. 9.13 present schematic diagrams of the different components con-

sidered in the setup. Fig. 9.2 shows the schematic scheme of the input filter which

consists of an RLC filter with the options to connect an additional inductor in

parallel to the resistor and a resistor in series to the capacitor. As shown in the

schematic, this input filter is connected to the IMC throughout a harting connec-

tor. As mentioned before, this converter is controller with a dSPACE which sends

the switch signals to the FPGA, for this reason it is necessary to add an adapter

between the dSPACE and FPGA. The schematic of this adapter is indicated in

Fig. 9.3. A special card for the FPGA was built with different components as

shown in Fig. 9.4 to Fig. 9.10. This card works with different voltage levels so,

it is necessary include voltage regulators to allow operate with 3.3 V, 2.5 V, and

1.2 V as shown in Fig. 9.4 and Fig. 9.5. A PROM memory is necessary in or-

der to store the code for the commutation and other necessary information in

the FPGA. The schematics of this memory are given in Fig. 9.6. DIP-switches

and some leds have been included and their schematics are indicated in Fig. 9.7.

The schematic of analog-digital converters and digital-analog converters needed

for the implementation are included in Fig. 9.8 and Fig. 9.9, respectively. The

schematics of the input/output connections in the FPGA are shown in Fig. 9.10.

The schematics of the main card which include the power circuit of the IMC and

voltage measurements are indicated in Fig. 9.11 to Fig. 9.13.

Appendix 109

The schematic of the IMC with its rectifier and inverter stages is shown in Fig.

9.12. Finally, the voltage measurements on the input side, are included in the

main card and these signals are directly connected to the dSPACE throughout

SMB connectors as shown in the schematic of Fig. 9.13.

Figure 9.1. Experimental setup in the laboratory.

Appendix 110

100pF

Cfa

10mH

Lfc

100pF

Cfb

100pF

Cfc

10mH

Lfb

10mH

Lfa

12

34

56

78

910

1112

1314

15

Con1

Conector Harting

100pF

Cfc2

100pF

Cfb2

100pF

Cfa2

10mHLfc2

1KRfc

10mHLfb2

10mHLfa2

1K Rfb

1KRfa

1KRfc2

1KRfb2

1KRfa2

Figure 9.2. Schematic of the input filter used in the implementation.

Appen

dix

111

1

1

2

2

3

3

4

4

D D

C C

B B

A A

Title

Number RevisionSize

A4

Date: 19-05-2011 Sheet ofFile: M:\1 - Diseño y armado del IMC\..\Dspace.SchDocDrawn By:

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

Con3

DB-50

1

20

2

21

3

22

4

23

5

24

6

25

7

8

9

10

11

12

13

14

15

16

17

18

19

27

26

Con1

D Connector 25

1B1

1A2

1Y3

2A6

G4

VCC16

3Y11

2Y5

2B7

GND8

4B15

4A14

4Y13

G12

3A10

3B9

U3

SN75173D

4A19

1A1

1Y2

4Y18

NC3

NC17

1Z4

4Z16

EN5

EN15

2Z6

3Z14

NC7

NC13

2Y8

3Y12

2A9

3A11

VCC20

GND10

U1

MC75172BDW

4A19

1A1

1Y2

4Y18

NC3

NC17

1Z4

4Z16

EN5

EN15

2Z6

3Z14

NC7

NC13

2Y8

3Y12

2A9

3A11

VCC20

GND10

U2

MC75172BDW

RU11

CU1

DB15 20DB15 8

DB15 21DB15 9

DB15 22DB15 10DB15 23DB15 11DB15 24DB15 12DB15 25

DB15 19DB15 7

DB15 18DB15 6

DB15 15DB15 3

DB15 16DB15 4

DB15 17DB15 5

DB15 14DB15 2

DB15 1

GND DB50 2

DB50 3

DB50 4

DB50 5

DB50 6

DB50 7

DB50 8

DB50 9

DB50 11

DB50 12

DB50 13

DB50 14

DB50 15

DB50 16

DB50 17

DB50 21

DB50 22

DB50 23

DB50 24

DB50 25

DB50 26

DB50 27

DB50 28

DB50 29

DB50 31

DB50 32

DB50 33

DB50 18

DB50 19

DB50 20

DB50 10

DB50 30

DB50 34

DB50 35

DB50 36

DB50 37

DB50 38

DB50 39

DB50 40

DB50 41

DB50 42

DB50 43

DB50 44

DB50 45

DB50 46

DB50 47

DB50 48

DB50 49

1234

Tx1

Conector Fibra

1234

Tx2

Conector Fibra

1234

Rx

Conector Fibra

RU12

RU13

RU14

RU21

RU22

RU23

RU24

CU2CU3

RU31

RU32

RU33

RU34

5GND

Rrx

5

GNDGND

Rtx12

Rtx115

Qtx1QNPN

GND

GND

Rtx22

Rtx215

Qtx2QNPN

GND

GND

5

5

GND

5

5

5GND

GND

GND

5 5 5

GND GND GND

DB15 12DB15 25

DB15 25DB15 12

DB15 11DB15 24

DB15 24DB15 11

DB15 10DB15 23

DB15 10 DB15 23

DB15 9DB15 22

DB15 22DB15 9

DB15 8DB15 21

DB15 21DB15 8

DB15 20DB15 7

DB15 7 DB15 20

DB15 19DB15 6

DB15 6 DB15 19

DB15 18DB15 5

DB15 5 DB15 18

DB15 4DB15 17

DB15 4 DB15 17

DB15 3DB15 16

DB15 16DB15 3

DB15 15DB15 2

DB15 2 DB15 15

DB15 14DB15 1

DB15 14DB15 1

DB

50 3

4

DB

50 3

5

DB

50 3

6

DB

50 3

7

DB

50 3

8

DB

50 3

9

DB

50 4

0

DB

50 4

1

DB

50 4

2

DB

50 4

3

DB

50 4

4

DB

50 4

5

GND

DB

50 1

7

DB50 1

DB50 18

DB50 2

DB50 19

DB50 3

DB50 20

DB50 4

DB50 21

DB50 46

DB50 6

DB50 22

DB50 5

DB50 1

DB50 47

DB50 9

DB50 26

5

5

D1LED1

1KR

5

GND

Fig

ure

9.3

.Sch

ematic

ofth

eadapter

between

the

dSPA

CE

and

FPG

A.

Appendix 112

VCCINT70

VCCINT88

VCCINT174

VCCINT192

VCCAUX17

VCCAUX38

VCCAUX69

VCCAUX89

VCCAUX121

VCCAUX142

VCCAUX173

VCCAUX193

VCCO_76

VCCO_723

VCCO_632

VCCO_649

VCCO_560

VCCO_573

VCCO_484

VCCO_498

VCCO_3110

VCCO_3127

VCCO_2136

VCCO_2153

VCCO_1164

VCCO_1177

VCCO_0188

VCCO_0201

U7J

XC3S200-4PQ208C

4.7K R30

4.7K R28

330 R3

3.3

3.3

GND

47nF

C23

470nF

C24

4.7uF

C25

3.3

GND3.3

GND3.3

GND3.3

GND3.3

GND3.3

GND

1.2

GND

1nF

C50

47nF

C51

470nF

C52

4.7uF

C53

2.5

GND

1nF

C38

47nF

C39

470nF

C40

4.7uF

C41

3.3

GND

DriveDone=yes

1nF

C22

2.5

1nF

C49

1nF

C37

OE-INIT

CF-PROG

DONE-CE

47nF

C30

470nF

C31

4.7uF

C32

1nF

C29

47nF

C34

470nF

C35

4.7uF

C36

1nF

C33

47nF

C46

470nF

C47

4.7uF

C48

1nF

C45

47nF

C55

470nF

C56

4.7uF

C57

1nF

C54

47nF

C59

470nF

C60

4.7uF

C61

1nF

C58

47nF

C63

470nF

C64

4.7uF

C65

1nF

C62

47nF

C67

470nF

C68

4.7uF

C69

1nF

C66

GND

51

23

J20

PWR2.5

GND

Figure 9.4. Schematic of the FPGA with its different voltage levels.

Appen

dix

113

1

1

2

2

3

3

4

4

D D

C C

B B

A A

Title

Number RevisionSize

A4

Date: 19-05-2011 Sheet ofFile: M:\1 - Diseño y armado del IMC\..\FPGA reguladores.SchDocDrawn By:

4.7uF

C72

D8LED3

68pF

C74

GND

17KR721K

R44

2.2uF

C78

4.7uF

C77

4.7uF

C81

2.2uF

C95

2.2uF

C83

68pF

C80

10K

R75

GND GND

3.3

GNDGND

5

.4KR73

10K

R74

GND GND

1.2

GNDGND

5

10K

R67

GND GND

2.5

GNDGND

5

10KR76

.56KR77

10KR78

5

10KR79

5

10KR80

5

Vin2

SD1

Vout4

SENSE5

GN

D3

LP3966_ADJ

GN

D6

REG1

LP3966

Vin2

SD1

Vout4

SENSE5

GN

D3

LP3966_ADJG

ND

6REG2

LP3966

Vin2

SD1

Vout4

SENSE5

GN

D3

LP3966_ADJ

GN

D6

REG3

LP3966

0.1uF

C27

0.1uF

C28GND

5

GND

-Vin1

+Vin2

3

Com4

-Vo5 6

+Vo7

8

9

10

DC/DC

DC/DC Converter D

0.1uF

C42 15

-15

Reguladores de Voltaje de la tarjeta FPGA

11

22

33

Z2REF30XX

2.048AD10K

Rz5

GND

2.048AD

GND

100nF

Cz2

2.048AD

GND

1nF

Cz1

C5VCap Pol3

GND

5

Fig

ure

9.5

.Sch

ematics

ofvo

ltage

regula

tors

inclu

ded

inth

eFPG

A.

Appendix 114

M154

M055

M256

DONE103

CCLK104

TDO158

TCK159

TMS160

HSWAP_EN206

PROG_B207

TDI208

U7I

XC3S200-4PQ208C

D01

DNC2

CLK3

TDI4

TMS5

TCK6

CF7

OE/RESET8

DNC9

CE10

GND11

DNC12

CEO13

DNC14

DNC15

DNC16

TDO17

VCCINT18

VCCO19

VCCJ20

U6

XCF02SVO20CGND

GNDMaster -serial mode

Turn on pullof resistors of user IO during configuration

3.3

R23

100

R25 100GND

R27 100

3.3 Master serial configuration

DONE-CE

OE-INITCF-PROG

TCK_MTMS_M

TDI_MTCK_MTMS_M

TDO_M

Data_serial

R22 100

R24100

R26 100

TDI_M_in

TCK_M_inTMS_M_in

TDO_M_out

Figure 9.6. Schematic of the PROM included in the FPGA card.

202U7K

3.3

GNDGND

GCK0GCK1

BA

NK

4

IO/VREF_4102

IO_L01N_4/VRP_4101

IO_L01P_4/VRN_4100

IO97

IO/VREF_496

IO_L25N_495

IO_L25P_494

IO93

IO_L27N_4/DIN/D092

IO_L27P_4/D190

IO_L30N_4/D287

IO_L30P_4/D386

IO/VREF_485

IO_L31N_4/INIT_B83

IO_L31P_4/DOUT/BUSY81

IO_L32N_4/GCLK180

IO_L32P_4/GCLK079

U7E

XC3S200-4PQ208C

220 R29220 R31220 R32220 R33

4.7

kR

35

4.7

kR

36

4.7

kR

37

4.7

kR

38

1234 5

678

S1

SW-DIP4FPGA_90FPGA_87FPGA_86FPGA_85

FPGA_81

Data_serial

OE-INIT

Figure 9.7. Schematic of the led and DIP-switches included in the FPGA card.

Appendix 115

DOutA1

VDrive2

DVcc3

Range14

Range05

ADDR6

AGnd7

AVcc8

DCapA9

Vss10

Va111

Va212

Vb213

Vb114

Vdd15

DCapB16

AGnd17

RefSel18

CSNeg19

SClk20

CnvStNeg21

Busy22

DOutB23

DGnd24

CAD4

Conversor AD

5

10uF

C88

0.1uF

C89

0.1uF

C905

GND GND

GND 10uF

C91

0.1uF

C92

GND GND

680nF

C93

GND

680nF

C94

GND

10uFC102

0.1uFC103

GND GND

GNDGND

GND10uFC104

0.1uFC105

GND GND

5CAD4 DOutA

CAD4 ADDR

CAD4 DOutBCAD4 Busy

CAD4 CnvStNegCAD4 Sclk

CAD4 CSNeg

GND

CAD4 Va1 CAD4 Vb115-15

Sock1 2 Sock1 45

CAD4 R0

Figure 9.8. Schematic of an analog-digital converter CAD included in the

FPGA.

Din1

Clk2

CS3

OutA4

AGnd5

Ref6

OutB7

Vdd8

CDA1

Conversor Digital Análogo

5

220 R68

220 R70 100pFC96

100pFC98

GND

GND

CDA1 DinCDA1 ClkCDA1 CS

GND2.048AD

1

2

Cx1

1

2

Cx2GND

GND GND

Cz3

Figure 9.9. Schematic of a digital-analog converter CDA included in the

FPGA.

Appen

dix

116

1

1

2

2

3

3

4

4

D D

C C

B B

A A

Title

Number RevisionSize

A4

Date: 19-05-2011 Sheet ofFile: M:\1 - Diseño y armado del IMC\..\FPGA I-O.SchDocDrawn By:

8

1

4

3

2

AO1ATL082CD

84

75

6

AO1BTL082CD

8

1

4

3

2

AO2ATL082CD

84

75

6

AO2BTL082CD

8

1

4

3

2

AO3ATL082CD

84

75

6

AO3BTL082CD

8

1

4

3

2

AO4ATL082CD

84

75

6

AO4BTL082CD

15

15

15

15

15

15

15

15

-15

-15

-15

-15

-15

-15

-15

-15

R AO1R AO2

R AO3

R AO4

R AO5

GND

R AO6R AO7

R AO8

R AO9

R AO10

GND

R AO11R AO12

R AO13

R AO14

R AO15

GND

R AO16R AO17

R AO18

R AO19

R AO20

GND

C AO1

15GND

C AO2GND -15

C AO3

15GND

C AO4GND -15

R AO21R AO22

R AO23

R AO24

R AO25

GND

R AO26R AO27

R AO28

R AO29

R AO30

GND

C AO5

15GND

C AO6GND -15

R AO31R AO32

R AO33

R AO34

R AO35

GND

R AO36R AO37

R AO38

R AO39

R AO40

GND

C AO7

15GND

C AO8GND -15

CAD1 Vb1

CAD1 Va1

CAD2 Va1

CAD2 Vb1

CAD3 Vb1

CAD3 Va1

CAD4 Va1

CAD4 Vb1

Sock3 1

Sock3 18

Sock3 2

Sock3 17

Sock3 6

Sock3 13

Sock3 7

Sock3 12

Sock3 16

Sock3 3

Sock3 8

Sock3 11

Sock3 4

Sock3 15

Sock3 10

Sock3 9

Sock3 1

Sock3 16Sock3 2

Sock3 15

Sock3 9

Sock3 12Sock3 6

Sock3 11

Sock3 17Sock3 3

Sock3 7

Sock3 10

Sock3 4

Sock3 13

Sock3 18

Sock3 8

Sock1 46Sock1 45Sock1 44Sock1 43

Sock1 1Sock1 2Sock1 3Sock1 4Sock1 5Sock1 6

Sock1 8Sock1 9Sock1 10Sock1 11Sock1 12Sock1 13Sock1 14Sock1 15Sock1 16Sock1 17Sock1 18Sock1 19Sock1 20Sock1 21Sock1 22Sock1 23 Sock1 24

Sock1 25Sock1 26

Sock1 42Sock1 41

Sock1 39Sock1 38Sock1 37Sock1 36Sock1 35Sock1 34Sock1 33Sock1 32Sock1 31Sock1 30Sock1 29Sock1 28Sock1 27

Sock2 1Sock2 2

Sock2 5Sock2 6

Sock2 8Sock2 9Sock2 10Sock2 11Sock2 12Sock2 13Sock2 14Sock2 15Sock2 16Sock2 17Sock2 18Sock2 19Sock2 20Sock2 21Sock2 22Sock2 23 Sock2 24

Sock2 25Sock2 26

Sock2 46Sock2 45

Sock2 42Sock2 41

Sock2 39Sock2 38Sock2 37Sock2 36Sock2 35Sock2 34Sock2 33Sock2 32Sock2 31Sock2 30Sock2 29Sock2 28Sock2 27

Componentes de entrada y salida de la tarjeta FPGA

123456789

1011121314151617181920212223 24

25262728293031323334353637383940414243444546

Sock1

Vertical Socket 23x2

123456789

1011121314151617181920212223 24

25262728293031323334353637383940414243444546

Sock2

Vertical Socket 23x2

1234

Rx2

Conector Fibra

1234

Rx1

Conector Fibra

5GND

Rrx1

3.3

Fibra Rx1

Rrx2

Fibra Rx2

12345678910

1112131415161718

Sock3

Vertical Socket 9x2

GNDGND

5GND

3.3

GND GND GNDGND

53.3

53.3

1234

Tx

Conector Fibra

R01A C01A

GND

R01B C01B

GND

R02A C02A

GND

R02B C02B

GND

R03A C03A

GND

R03B C03B

GND

R04A C04A

GND

R04B C04B

GND

GND

GND

Rtx2

Rtx15

Fibra TxQtxQNPN

Fig

ure

9.1

0.Sch

ematics

ofin

put/

outp

ut

com

ponen

tsin

cluded

inth

eFPG

A.

Appen

dix

117

1

1

2

2

3

3

4

4

D D

C C

B B

A A

Title

Number RevisionSize

A4

Date: 19-05-2011 Sheet ofFile: M:\1 - Diseño y armado del IMC\..\Circuito de Potencia.SchDocDrawn By:

QApIGBT-N

Input Phase u Input Phase v Input Phase w

Output Phase u 1

Output Phase v 1

Output Phase w 1

p

n

Supa Gate Svpa Gate Swpa Gate

Supb Gate Svpb Gate Swpb Gate

Suna Gate Svna Gate Swna Gate

Sunb Gate Svnb Gate Swnb Gate

Sup Gate

Sun Gate

Svn Gate

Svp Gate

Swp Gate

Swn Gate

Supa Emitter Svpa Emitter Swpa Emitter

Suna Emitter Svna Emitter Swna Emitter

Supb Emitter Svpb Emitter Swpb Emitter

Sunb Emitter Svnb Emitter Swnb Emitter

Sun Emitter

Svn Emitter

Swn Emitter

Swp Emitter

Svp Emitter

Sup Emitter

Circuito de Potencia de Convertidor

1

23

QapaIGBT IXRH

1

23 Qapb

IGBT IXRH

1

23

QbpaIGBT IXRH

1

23 Qbpb

IGBT IXRH

1

23

QcpaIGBT IXRH

1

23 Qcpb

IGBT IXRH

1

23

QanaIGBT IXRH

1

23 Qanb

IGBT IXRH

1

23

QbnaIGBT IXRH

1

23 Qbnb

IGBT IXRH

1

23

QcnaIGBT IXRH

1

23 Qcnb

IGBT IXRH

QAnIGBT-N

QBpIGBT-N

QBnIGBT-N

QCpIGBT-N

QCnIGBT-N

Fig

ure

9.1

1.Sch

ematics

ofth

epo

wer

circuit

inth

eIM

C.

Appendix 118

Swpa Emitter

Swnb Emitter

Swpa Gate

Swpb Gate100nF

Ccpa

10ohm

Rcpa

100nF

Ccpb

10ohm

Rcpb

1k

RcpaL

Dcpa

1k

RcpbL

Dcpb

Swpa Emitter

Swpb Emitter

100nF

Cc

5Vgnd

5V100nF

Cc2

3 4

UnB

SN74LS06D

11 10

UnE

SN74LS06D

270ohmRcpaD

5V

5Vgnd

270ohm

RcpbD5V

5Vgnd

Nwpab

Nwpab

1

2

3

4 5

6

7

8

DC/DCc

DC/DC Converter

N/C1

Anode2

Cathode3

N/C4

VEE5

Vo6

Vo7

VCC8

DRVcpa

Driver Single

N/C1

Anode2

Cathode3

N/C4

VEE5

Vo6

Vo7

VCC8

DRVcpb

Driver Single

5V

gnd

Figure 9.12. Schematic of the driver implemented in the IMC for the switches.

Appendix 119

8

1

4

3

2

AO2ATL082CD

84

75

6

AO2BTL082CD

15

15

-15

-15

R AO12

R AO13

R AO14

R AO15

R AO17

R AO18

R AO19

R AO20

C AO3

15

C AO4-15

5Vgnd

5Vgnd

5Vgnd

5Vgnd

5V

gn

d5

Vg

nd

Cx4SMB

Cx3

SMB

R02A C02A

R02B C02B

5V

gn

d5

Vg

nd

R AOA

R AOB

Muvs

Mvus

Mvws

Mwvs

So

ck3

18

So

ck3

17

Figure 9.13. Schematic of the implementation of voltage measurement in

the IMC.

Bibliography

[1] E. Yamamoto, T. Kume, H. Hara, T. Uchino, J. Kang, and H. Krug, “De-

velopment of matrix converter ans its applications in industry,” 35th Annual

Conference of the IEEE Industrial Electronics Society IECON 2009, Porto,

Portugal, 2009.

[2] P. Wheeler, J. Rodriguez, J. Clare, L. Empringham, and A. Weinstein, “Ma-

trix converters: a technology review,” Industrial Electronics, IEEE Trans-

actions on, vol. 49, no. 2, pp. 276 –288, 2002.

[3] M. Venturini, “A new sine wave in sine wave out, conversion technique which

eliminates reactive elements,” in Proc. POWERCON 7, 1980.

[4] M. Venturini and A. Alesina, “The generalized transformer: A new bidirec-

tional sinusoidal waveform frequency converter with continuously adjustable

input power factor,” in Proc. IEEE PESC’80.

[5] J. Rodriguez, “A new control technique for ac-ac converters,” in Proc.

IFAC Control in Power Electronics and Electrical Drives Conf., Lausanne,

Switzerland, 1983.

[6] J. Oyama, T. Higuchi, E. Yamada, T. Koga, and T. Lipo, “New control

strategy for matrix converter,” Power Electronics Specialists Conference,

1989. PESC ’89 Record., 20th Annual IEEE, pp. 360 –367 vol.1, Jun. 1989.

120

Bibliography 121

[7] L. Wei and T. Lipo, “A novel matrix converter topology with simple commu-

tation,” Industry Applications Conference, 2001. Thirty-Sixth IAS Annual

Meeting. Conference Record of the 2001 IEEE, 2001.

[8] M. Hamouda, F. Fnaiech, and K. Al-Haddad, “Space vector modulation

scheme for dual-bridge matrix converters using safe-commutation strategy,”

Industrial Electronics Society, 2005. IECON 2005. 31st Annual Conference

of IEEE, p. 6 pp., 2005.

[9] L. Wei, T. Lipo, and H. Chan, “Matrix converter topologies with reduced

number of switches,” Power Electronics Specialists Conference, 2002. pesc

02. 2002 IEEE 33rd Annual, 2002.

[10] J. Kolar and F. Schafmeister, “Novel modulation schemes minimizing the

switching losses of sparse matrix converters,” Industrial Electronics Society,

2003. IECON ’03. The 29th Annual Conference of the IEEE, vol. 3, pp.

2085 – 2090 Vol.3, 2003.

[11] J. Igney and M. Braun, “A new matrix converter modulation strategy max-

imizing the control range,” Power Electronics Specialists Conference, 2004.

PESC 04. 2004 IEEE 35th Annual, 2004.

[12] ——, “Space vector modulation strategy for conventional and indirect ma-

trix converters,” Power Electronics and Applications, 2005 European Con-

ference on, 0 2005.

[13] S. Kim, S.-K. Sul, and T. Lipo, “Ac/ac power conversion based on ma-

trix converter topology with unidirectional switches,” Industry Applications,

IEEE Transactions on, vol. 36, no. 1, pp. 139 –145, 2000.

[14] J. Itoh, I. Sato, A. Odaka, H. Ohguchi, H. Kodachi, and N. Eguchi, “A novel

approach to practical matrix converter motor drive system with reverse

blocking igbt,” Power Electronics, IEEE Transactions on, vol. 20, no. 6,

pp. 1356 – 1363, 2005.

Bibliography 122

[15] F. Schafmeister and J. Kolar, “Novel modulation schemes for conventional

and sparse matrix converters facilitating reactive power transfer indepen-

dent of active power flow,” Power Electronics Specialists Conference, 2004.

PESC 04. 2004 IEEE 35th Annual, 2004.

[16] M. Jussila and H. Tuusa, “Comparison of simple control strategies of space-

vector modulated indirect matrix converter under distorted supply voltage,”

Power Electronics, IEEE Transactions on, vol. 22, no. 1, pp. 139 –148, 2007.

[17] C. Klumpner, “A hybrid indirect matrix converter immune to unbalanced

voltage supply, with reduced switching losses and improved voltage transfer

ratio,” Applied Power Electronics Conference and Exposition, 2006. APEC

’06. Twenty-First Annual IEEE, p. 7 pp., 2006.

[18] S. Kouro, P. Cortes, R. Vargas, U. Ammann, and J. Rodriguez, “Model pre-

dictive control: A simple and powerful method to control power converters,”

Industrial Electronics, IEEE Transactions on, vol. 56, no. 6, pp. 1826 –1838,

2009.

[19] B. Wu, High-Power Converters and AC Drives, 2006.

[20] I. Takahashi and Y. Itoh, “Electrolytic capacitor-less pwm inverter,” Proc.

International Power Electronics Conference IPEC 90, pp. 131 – 138, Apr.

1990.

[21] M. Baumann and J. Kolar, “Comparative evaluation of modulation methods

for a three-phase/switch buck power factor corrector concerning the input

capacitor voltage ripple,” Power Electronics Specialists Conference, 2001.

PESC. 2001 IEEE 32nd Annual, 2001.

[22] L. Zhang, C. Watthanasarn, and W. Shepherd, “Control of ac-ac matrix con-

verters for unbalanced and/or distorted supply voltage,” Power Electronics

Specialists Conference, 2001. PESC. 2001 IEEE 32nd Annual, vol. 2, pp.

1108 –1113 vol.2, 2001.

Bibliography 123

[23] M. Rivera, R. Vargas, J. Espinoza, and J. Rodriguez, “Behavior of the

predictive dtc based matrix converter under unbalanced ac-supply,” Power

Electronics Specialists Conference, 2008. PESC 2008. IEEE, pp. 202 –207,

Sep. 2007.

[24] K. Mohapatra and N. Mohan, “Open-end winding induction motor driven

with matrix converter for common-mode elimination,” Power Electronics,

Drives and Energy Systems, 2006. PEDES ’06. International Conference

on, pp. 1 –6, 2006.

[25] J. Kolar, T. Friedli, F. Krismer, and S. Round, “The essence of three-phase

ac/ac converter systems,” Power Electronics and Motion Control Confer-

ence, 2008. EPE-PEMC 2008. 13th, pp. 27 –42, 2008.

[26] P. Correa, J. Rodriguez, M. Rivera, J. Espinoza, and J. Kolar, “Predic-

tive control of an indirect matrix converter,” Industrial Electronics, IEEE

Transactions on, vol. 56, no. 6, pp. 1847 –1853, 2009.

[27] P. Zanchetta, P. Wheeler, J. Clare, M. Bland, L. Empringham, and D. Kat-

sis, “Control design of a three-phase matrix-converter-based ac/ac mobile

utility power supply,” Industrial Electronics, IEEE Transactions on, vol. 55,

no. 1, pp. 209 –217, 2008.

[28] B.-H. Kwon, B.-D. Min, and J.-H. Kim, “Novel topologies of ac choppers,”

Electric Power Applications, IEE Proceedings -, vol. 143, no. 4, pp. 323 –330,

Jul. 1996.

[29] P. Ziogas, D. Vincenti, and G. Joos, “A practical pwm ac controller topol-

ogy,” Industry Applications Society Annual Meeting, 1992., Conference

Record of the 1992 IEEE, pp. 880 –887 vol.1, Oct. 1992.

[30] J. Kolar, M. Baumann, F. Schafmeister, and H. Ertl, “Novel three-phase ac-

dc-ac sparse matrix converter,” Applied Power Electronics Conference and

Exposition, 2002. APEC 2002. Seventeenth Annual IEEE, 2002.

Bibliography 124

[31] J. Kolar, F. Schafmeister, S. Round, and H. Ertl, “Novel three-phase

ac/ac sparse matrix converters,” Power Electronics, IEEE Transactions on,

vol. 22, no. 5, pp. 1649 –1661, 2007.

[32] C. Klumpner, M. Lee, and P. Wheeler, “A new three-level sparse indirect

matrix converter,” IEEE Industrial Electronics, IECON 2006 - 32nd Annual

Conference on, pp. 1902 –1907, 2006.

[33] M. Y. Lee, P. Wheeler, and C. Klumpner, “A new modulation method for the

three-level-output-stage matrix converter,” Power Conversion Conference -

Nagoya, 2007. PCC ’07, pp. 776 –783, 2007.

[34] J. Kolar, H. Ertl, and F. Zach, “Design and experimental investigation of

a three-phase high power density high efficiency unity power factor pwm

(vienna) rectifier employing a novel integrated power semiconductor mod-

ule,” Applied Power Electronics Conference and Exposition, 1996. APEC

’96. Conference Proceedings 1996., Eleventh Annual, vol. 2, pp. 514 –523

vol.2, Mar. 1996.

[35] R. Erickson and O. Al-Naseem, “A new family of matrix converters,” Indus-

trial Electronics Society, 2001. IECON ’01. The 27th Annual Conference of

the IEEE, 2001.

[36] C. Klumpner, “Hybrid direct power converters with increased/higher than

unity voltage transfer ratio and improved robustness against voltage supply

disturbances,” Power Electronics Specialists Conference, 2005. PESC ’05.

IEEE 36th, pp. 2383 –2389, 2005.

[37] J. Rodriguez, E. Silva, F. Blaabjerg, P. Wheeler, J. Clare, and J. Pontt, “Ma-

trix converter controlled with the direct transfer function approach: analy-

sis, modelling and simulation,” Taylor and Francis-International Journal of

Electronics, vol. 92, no. 2, pp. 63 –85, Feb. 2005.

[38] S. Bernet, S. Ponnaluri, and R. Teichmann, “Design and loss comparison

of matrix converters, and voltage-source converters for modern ac drives,”

Bibliography 125

Industrial Electronics, IEEE Transactions on, vol. 49, no. 2, pp. 304 –314,

Apr. 2002.

[39] J. Rzasa, “Capacitor clamped multilevel matrix converter controlled with

venturini method,” Power Electronics and Motion Control Conference,

2008. EPE-PEMC 2008. 13th, pp. 357 –364, Sep. 2008.

[40] Y. Mei and L. Huang, “Improved switching function modulation strategy

for three-phase to single-phase matrix converter,” Power Electronics and

Motion Control Conference, 2009. IPEMC ’09. IEEE 6th International, pp.

1734 –1737, May. 2009.

[41] S. Lopez Arevalo, P. Zanchetta, P. Wheeler, A. Trentin, and L. Empringham,

“Control and implementation of a matrix-converter-based ac-ground power-

supply unit for aircraft servicing,” Industrial Electronics, IEEE Transac-

tions on, vol. 57, no. 6, pp. 2076 –2084, Jun. 2010.

[42] G. Roy and G.-E. April, “Cycloconverter operation under a new scalar con-

trol algorithm,” Power Electronics Specialists Conference, 1989. PESC ’89

Record., 20th Annual IEEE, pp. 368 –375 vol.1, Jun. 1989.

[43] J. Rodriguez, “High performance dc motor drive using a pwm rectifier with

power transistors,” Electric Power Applications, IEE Proceedings B, vol.

134, no. 1, p. 9, Jan. 1987.

[44] J. Itoh, I. Sato, A. Odaka, H. Ohguchi, H. Kodatchi, and N. Eguchi, “A novel

approach to practical matrix converter motor drive system with reverse

blocking igbt,” Power Electronics Specialists Conference, 2004. PESC 04.

2004 IEEE 35th Annual, vol. 3, pp. 2380 – 2385 Vol.3, Jun. 2004.

[45] K. Mohapatra, P. Jose, A. Drolia, G. Aggarwal, and S. Thuta, “A novel

carrier-based pwm scheme for matrix converters that is easy to implement,”

Power Electronics Specialists Conference, 2005. PESC ’05. IEEE 36th, pp.

2410 –2414, Jun. 2005.

Bibliography 126

[46] Z. Idris, M. Hamzah, and A. Omar, “Implementation of single-phase matrix

converter as a direct ac-ac converter synthesized using sinusoidal pulse width

modulation with passive load condition,” Power Electronics and Drives Sys-

tems, 2005. PEDS 2005. International Conference on, vol. 2, pp. 1536 –

1541, Nov. 2005.

[47] Y.-D. Yoon and S.-K. Sul, “Carrier-based modulation technique for matrix

converter,” Power Electronics, IEEE Transactions on, vol. 21, no. 6, pp.

1691 –1703, Nov. 2006.

[48] T. Satish, K. Mohapatra, and N. Mohan, “Steady state over-modulation of

matrix converter using simplified carrier based control,” Industrial Electron-

ics Society, 2007. IECON 2007. 33rd Annual Conference of the IEEE, pp.

1817 –1822, Nov. 2007.

[49] P. Loh, R. Rong, F. Blaabjerg, L. Shan, and P. Wang, “Carrier-based modu-

lation schemes for various three-level matrix converters,” Power Electronics

Specialists Conference, 2008. PESC 2008. IEEE, pp. 1720 –1726, Jun. 2008.

[50] S. Thuta, K. Mohapatra, and N. Mohan, “Matrix converter over-modulation

using carrier-based control: Maximizing the voltage transfer ratio,” Power

Electronics Specialists Conference, 2008. PESC 2008. IEEE, pp. 1727 –1733,

Jun. 2008.

[51] Y. Miura, S. Horie, S. Kokubo, T. Amano, T. Ise, T. Momose, and Y. Sato,

“Application of three-phase to single-phase matrix converter to gas engine

cogeneration system,” Energy Conversion Congress and Exposition, 2009.

ECCE 2009. IEEE, pp. 3290 –3297, Sep. 2009.

[52] P. C. Loh, R. Rong, F. Blaabjerg, and P. Wang, “Digital carrier modula-

tion and sampling issues of matrix converters,” Power Electronics, IEEE

Transactions on, vol. 24, no. 7, pp. 1690 –1700, Jul. 2009.

[53] T. Sanada, S. Ogasawara, and M. Takemoto, “Experimental evaluation of

a new pwm control scheme for matrix converters,” Power Electronics Con-

ference (IPEC), 2010 International, pp. 2366 –2371, Jun. 2010.

Bibliography 127

[54] P. Kiatsookkanatorn and S. Sangwongwanich, “A unified pwm strategy for

matrix converters and its dipolar pwm realization,” Power Electronics Con-

ference (IPEC), 2010 International, pp. 3072 –3079, Jun. 2010.

[55] T. Yamashita and T. Takeshita, “Pwm strategy of single-phase to three-

phase matrix converters for reducing a number of commutations,” Power

Electronics Conference (IPEC), 2010 International, pp. 3057 –3064, Jun.

2010.

[56] J. Itoh and K. Maki, “Single-pulse operation for a matrix converter synchro-

nized with the output frequency,” Power Electronics Conference (IPEC),

2010 International, pp. 2781 –2788, Jun. 2010.

[57] S. Ishii, H. Hara, T. Higuchi, T. Kawachi, K. Yamanaka, N. Koga, T. Kume,

and J. Kang, “Bidirectional dc-ac conversion topology using matrix con-

verter technique,” Power Electronics Conference (IPEC), 2010 Interna-

tional, pp. 2768 –2773, Jun. 2010.

[58] P. Potamianos, E. Mitronikas, and A. Safacas, “A modified carrier-based

modulation method for three-phase matrix converters,” Power Electronics

and Applications, 2009. EPE ’09. 13th European Conference on, pp. 1 –9,

Sep. 2009.

[59] Y.-D. Yoon and S.-K. Sul, “Carrier-based modulation method for matrix

converter with input power factor control and under unbalanced input

voltage conditions,” Applied Power Electronics Conference, APEC 2007 -

Twenty Second Annual IEEE, pp. 310 –314, Mar. 2007.

[60] L. Huber and D. Borojevic, “Space vector modulated three-phase to three-

phase matrix converter with input power factor correction,” Industry Ap-

plications, IEEE Transactions on, vol. 31, no. 6, pp. 1234 –1246, Nov. 1995.

[61] F. Blaabjerg, D. Casadei, C. Klumpner, and M. Matteini, “Comparison of

two current modulation strategies for matrix converters under unbalanced

input voltage conditions,” Industrial Electronics, IEEE Transactions on,

vol. 49, no. 2, pp. 289 –296, Apr. 2002.

Bibliography 128

[62] O. Simon, J. Mahlein, M. Muenzer, and M. Bruckmarm, “Modern solutions

for industrial matrix-converter applications,” Industrial Electronics, IEEE

Transactions on, vol. 49, no. 2, pp. 401 –406, Apr. 2002.

[63] D. Casadei, G. Serra, A. Tani, and L. Zarri, “Matrix converter modulation

strategies: a new general approach based on space-vector representation of

the switch state,” Industrial Electronics, IEEE Transactions on, vol. 49,

no. 2, pp. 370 –381, Apr. 2002.

[64] L. Helle, K. Larsen, A. Jorgensen, S. Munk-Nielsen, and F. Blaabjerg, “Eval-

uation of modulation schemes for three-phase to three-phase matrix convert-

ers,” Industrial Electronics, IEEE Transactions on, vol. 51, no. 1, pp. 158 –

171, Feb. 2004.

[65] D. Casadei, G. Serra, A. Tani, and L. Zarri, “A novel modulation strategy

for matrix converters with reduced switching frequency based on output

current sensing,” Power Electronics Specialists Conference, 2004. PESC 04.

2004 IEEE 35th Annual, vol. 3, pp. 2373 – 2379 Vol.3, Jun. 2004.

[66] S. Pinto and J. Silva, “Direct control method for matrix converters with

input power factor regulation,” Power Electronics Specialists Conference,

2004. PESC 04. 2004 IEEE 35th Annual, vol. 3, pp. 2366 – 2372 Vol.3, Jun.

2004.

[67] M. Jussila, M. Salo, and H. Tuusa, “Induction motor drive fed by a vector

modulated indirect matrix converter,” Power Electronics Specialists Con-

ference, 2004. PESC 04. 2004 IEEE 35th Annual, vol. 4, pp. 2862 – 2868

Vol.4, 2004.

[68] L. Wang, D. Zhou, K. Sun, and L. Huang, “A novel method to enhance

the voltage transfer ratio of matrix converter,” TENCON 2004. 2004 IEEE

Region 10 Conference, vol. D, pp. 81 – 84 Vol. 4, Nov. 2004.

[69] K.-B. Lee and F. Blaabjerg, “Reduced-order extended luenberger observer

based sensorless vector control driven by matrix converter with nonlinearity

Bibliography 129

compensation,” Industrial Electronics, IEEE Transactions on, vol. 53, no. 1,

pp. 66 – 75, Feb. 2005.

[70] M. Jussila and H. Tuusa, “Space-vector modulated indirect matrix converter

under distorted supply voltage - effect on load current,” Power Electronics

Specialists Conference, 2005. PESC ’05. IEEE 36th, pp. 2396 –2402, Jun.

2005.

[71] F. Gao and M. Iravani, “Dynamic model of a space vector modulated matrix

converter,” Power Delivery, IEEE Transactions on, vol. 22, no. 3, pp. 1696

–1705, Jul. 2007.

[72] S. Kwak, T. Kim, and O. Vodyakho, “Space vector control methods for

two-leg and three-leg based ac to ac converters for two-phase drive sys-

tems,” Industrial Electronics, 2008. IECON 2008. 34th Annual Conference

of IEEE, pp. 959 –964, Nov. 2008.

[73] H.-H. Lee, H. Nguyen, and T.-W. Chun, “New direct-svm method for matrix

converter with main input power factor compensation,” Industrial Electron-

ics, 2008. IECON 2008. 34th Annual Conference of IEEE, pp. 1281 –1286,

Nov. 2008.

[74] D. Casadei, G. Serra, A. Tani, and L. Zarri, “Optimal use of zero vectors for

minimizing the output current distortion in matrix converters,” Industrial

Electronics, IEEE Transactions on, vol. 56, no. 2, pp. 326 –336, Feb. 2009.

[75] H. She, H. Lin, X. Wang, and S. Xiong, “Space vector modulated matrix

converter under abnormal input voltage conditions,” Power Electronics and

Motion Control Conference, 2009. IPEMC ’09. IEEE 6th International, pp.

1723 –1727, May. 2009.

[76] F. Bradaschia, E. Ibarra, J. Andreu, I. Kortabarria, E. Ormaetxea, and

M. Cavalcanti, “Matrix converter: Improvement of the space vector modula-

tion via a new double-sided generalized scalar pwm,” Industrial Electronics,

2009. IECON ’09. 35th Annual Conference of IEEE, pp. 4511 –4516, Nov.

2009.

Bibliography 130

[77] E. Ibarra, J. Andreu, I. Kortabarria, E. Ormaetxea, and E. Robles, “A fault

tolerant space vector modulation strategy for matrix converters,” Industrial

Electronics, 2009. IECON ’09. 35th Annual Conference of IEEE, pp. 4463

–4468, Nov. 2009.

[78] M. Y. Lee, P. Wheeler, and C. Klumpner, “Space-vector modulated mul-

tilevel matrix converter,” Industrial Electronics, IEEE Transactions on,

vol. 57, no. 10, pp. 3385 –3394, Oct. 2010.

[79] E. Ormaetxea, J. Andreu, I. Kortabarria, U. Bidarte, I. Martinez de Alegria,

E. Ibarra, and E. Olaguenaga, “Matrix converter protection and computa-

tional capabilities based on a system on chip design with an fpga,” Power

Electronics, IEEE Transactions on, vol. PP, no. 99, pp. 1 –1, 2010.

[80] R. Cardenas-Dobson, R. Pena, P. Wheeler, and J. Clare, “Experimental

validation of a space vector modulation algorithm for four-leg matrix con-

verters,” Industrial Electronics, IEEE Transactions on, vol. PP, no. 99, pp.

1 –1, 2010.

[81] I. Takahashi and T. Noguchi, “A new quick response and high efficency con-

trol strategy for an induction motor,” Industrial Electronics, IEEE Trans-

actions on, vol. 22, no. 5, pp. 820 –827, Sep. 1986.

[82] M. Kazmierkowski, R. Krishnan, and F. Blaabjerg, “Control in power elec-

tronics,” Academic Press, 2002.

[83] D. Casadei, G. Serra, and A. Tani, “The use of matrix converters in direct

torque control of induction machines,” Industrial Electronics, IEEE Trans-

actions on, vol. 48, no. 6, pp. 1057 –1064, Dec. 2001.

[84] C. Ortega, A. Arias, C. Caruana, J. Balcells, and G. Asher, “Improved

waveform quality in the direct torque control of matrix-converter-fed pmsm

drives,” Industrial Electronics, IEEE Transactions on, vol. 57, no. 6, pp.

2101 –2110, Jun. 2010.

Bibliography 131

[85] D. Xiao and F. Rahman, “A modified dtc for matrix converter drives using

two switching configurations,” Power Electronics and Applications, 2009.

EPE ’09. 13th European Conference on, pp. 1 –10, Sep. 2009.

[86] K.-B. Lee and F. Blaabjerg, “Sensorless dtc-svm for induction motor driven

by a matrix converter using a parameter estimation strategy,” Industrial

Electronics, IEEE Transactions on, vol. 55, no. 2, pp. 512 –521, Feb. 2008.

[87] J.-X. Wang and J. guo Jiang, “Variable-structure direct torque control for

induction motor driven by a matrix converter with overmodulation strat-

egy,” Power Electronics and Motion Control Conference, 2009. IPEMC ’09.

IEEE 6th International, pp. 580 –584, May. 2009.

[88] D. Xiao and F. Rahman, “An improved dtc for matrix converter drives

using multi-mode isvm and unity input power factor correction,” Power

Electronics and Applications, 2009. EPE ’09. 13th European Conference

on, pp. 1 –10, Sep. 2009.

[89] S. Muller, U. Ammann, and S. Rees, “New time-discrete modulation

scheme for matrix converters,” Industrial Electronics, IEEE Transactions

on, vol. 52, no. 6, pp. 1607 – 1615, Dec. 2005.

[90] M. Rivera, R. Vargas, J. Espinoza, J. Rodriguez, P. Wheeler, and C. Silva,

“Current control in matrix converters connected to polluted ac voltage sup-

plies,” Power Electronics Specialists Conference, 2008. PESC 2008. IEEE,

pp. 412 –417, Jun. 2008.

[91] R. Vargas, J. Rodriguez, U. Ammann, and P. Wheeler, “Predictive cur-

rent control of an induction machine fed by a matrix converter with reac-

tive power control,” Industrial Electronics, IEEE Transactions on, vol. 55,

no. 12, pp. 4362 –4371, Dec. 2008.

[92] R. Vargas, U. Ammann, J. Rodriguez, and J. Pontt, “Predictive strategy to

control common-mode voltage in loads fed by matrix converters,” Industrial

Electronics, IEEE Transactions on, vol. 55, no. 12, pp. 4372 –4380, Dec.

2008.

Bibliography 132

[93] R. Vargas, U. Ammann, and J. Rodriguez, “Predictive approach to increase

efficiency and reduce switching losses on matrix converters,” Power Elec-

tronics, IEEE Transactions on, vol. 24, no. 4, pp. 894 –902, Apr. 2009.

[94] F. Morel, J.-M. Retif, X. Lin-Shi, B. Allard, and P. Bevilacqua, “A predictive

control for a matrix converter-fed permanent magnet synchronous machine,”

Power Electronics Specialists Conference, 2008. PESC 2008. IEEE, pp. 15

–21, Jun. 2008.

[95] P. Gamboa, J. Silva, S. Pinto, and E. Margato, “Predictive optimal matrix

converter control for a dynamic voltage restorer with flywheel energy stor-

age,” Industrial Electronics, 2009. IECON ’09. 35th Annual Conference of

IEEE, pp. 759 –764, Nov. 2009.

[96] F. Barrero, M. Arahal, R. Gregor, S. Toral, and M. Duran, “One-step mod-

ulation predictive current control method for the asymmetrical dual three-

phase induction machine,” Industrial Electronics, IEEE Transactions on,

vol. 56, no. 6, pp. 1974 –1983, Jun. 2009.

[97] Y. Li, N.-S. Choi, H. Cha, and F. Peng, “Carrier-based predictive current

controlled pulse width modulation for matrix converters,” Power Electronics

and Motion Control Conference, 2009. IPEMC ’09. IEEE 6th International,

pp. 1009 –1014, May. 2009.

[98] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas, “Predictive

current control with reactive power minimization in an indirect matrix con-

verter,” Industrial Technology (ICIT), 2010 IEEE International Conference

on, pp. 1839 –1844, Mar. 2010.

[99] R. Vargas, J. Rodriguez, C. Rojas, and P. Wheeler, “Predictive current

control applied to a matrix converter: An assessment with the direct transfer

function approach,” Industrial Technology (ICIT), 2010 IEEE International

Conference on, pp. 1832 –1838, Mar. 2010.

[100] J. Rodriguez, J. Espinoza, M. Rivera, F. Villarroel, and C. Rojas, “Pre-

dictive control of source and load currents in a direct matrix converter,”

Bibliography 133

Industrial Technology (ICIT), 2010 IEEE International Conference on, pp.

1826 –1831, Mar. 2010.

[101] J. Rodriguez, J. Pontt, R. Vargas, P. Lezana, U. Ammann, P. Wheeler, and

F. Garcia, “Predictive direct torque control of an induction motor fed by

a matrix converter,” Power Electronics and Applications, 2007 European

Conference on, pp. 1 –10, Sep. 2007.

[102] R. Vargas, M. Rivera, J. Rodriguez, J. Espinoza, and P. Wheeler, “Predictive

torque control with input pf correction applied to an induction machine

fed by a matrix converter,” Power Electronics Specialists Conference, 2008.

PESC 2008. IEEE, pp. 9 –14, Jun. 2008.

[103] C. Ortega, A. Arias, and J. Espina, “Predictive vector selector for direct

torque control of matrix converter fed induction motors,” Industrial Elec-

tronics, 2009. IECON ’09. 35th Annual Conference of IEEE, pp. 1240 –1245,

Nov. 2009.

[104] T. Geyer, G. Papafotiou, and M. Morari, “Model predictive direct torque

control; part i concept, algorithm, and analysis,” Industrial Electronics,

IEEE Transactions on, vol. 56, no. 6, pp. 1894 –1905, Jun. 2009.

[105] G. Papafotiou, J. Kley, K. Papadopoulos, P. Bohren, and M. Morari, “Model

predictive direct torque control; part ii implementation and experimental

evaluation,” Industrial Electronics, IEEE Transactions on, vol. 56, no. 6,

pp. 1906 –1915, Jun. 2009.

[106] R. Vargas, U. Ammann, B. Hudoffsky, J. Rodriguez, and P. Wheeler, “Pre-

dictive torque control of an induction machine fed by a matrix converter

with reactive input power control,” Power Electronics, IEEE Transactions

on, vol. 25, no. 6, pp. 1426 –1438, Jun. 2010.

[107] J. Rodriguez, J. Kolar, J. Espinoza, M. Rivera, and C. Rojas, “Predictive

torque and flux control of an induction machine fed by an indirect matrix

converter,” Industrial Technology (ICIT), 2010 IEEE International Confer-

ence on, pp. 1857 –1863, Mar. 2010.

Bibliography 134

[108] J. Itoh, K. Koiwa, and K. Kato, “Input current stabilization control of a ma-

trix converter with boost-up functionality,” Power Electronics Conference

(IPEC), 2010 International, pp. 2708 –2714, Jun. 2010.

[109] H. Karaca, R. Akkaya, and H. Dogan, “A novel compensation method based

on fuzzy logic control for matrix converter under distorted input voltage

conditions,” Electrical Machines, 2008. 18th International Conference on,

pp. 1 –5, Sept. 2008.

[110] K. Park, E.-S. Lee, and K.-B. Lee, “A z-source sparse matrix converter with

a fuzzy logic controller based compensation method under abnormal input

voltage conditions,” Industrial Electronics (ISIE), 2010 IEEE International

Symposium on, pp. 614 –619, Jul. 2010.

[111] P. Q. Dzung and L. M. Phuong, “A new artificial neural network - direct

torque control for matrix converter fed three-phase induction motor,” Power

Electronics and Drives Systems, 2005. PEDS 2005. International Confer-

ence on, vol. 1, pp. 78 –83, 2005.

[112] H. H. Lee, P. Q. Dzung, L. M. Phuong, and L. D. Khoa, “A new artifi-

cial neural network controller for direct control method for matrix convert-

ers,” Power Electronics and Drive Systems, 2009. PEDS 2009. International

Conference on, pp. 434 –439, Nov. 2009.

[113] P. Zanchetta, M. Sumner, J. Clare, and P. Wheeler, “Control of matrix

converters for ac power supplies using genetic algorithms,” Industrial Elec-

tronics, 2004 IEEE International Symposium on, vol. 2, pp. 1429 – 1433

vol. 2, May 2004.

[114] P. Zanchetta, J. Clare, P. Wheeler, M. Bland, L. Empringham, and D. Kat-

sis, “Control design of a three-phase matrix converter mobile ac power

supply using genetic algorithms,” Power Electronics Specialists Conference,

2005. PESC ’05. IEEE 36th, pp. 2370 –2375, Jun. 2005.

Bibliography 135

[115] P. Cortes, M. Kazmierkowski, R. Kennel, D. Quevedo, and J. Rodriguez,

“Predictive control in power electronics and drives,” Industrial Electronics,

IEEE Transactions on, vol. 55, no. 12, pp. 4312 –4324, dec. 2008.

[116] E. Camacho and C. Bordons, “Model predictive control,” Springer, 1999.

[117] J. Rodriguez, J. Pontt, C. Silva, P. Correa, P. Lezana, C. P., and U. Am-

mann, “Predictive current control of a voltage source inverter,” Industrial

Electronics, IEEE Transactions on, vol. 54, no. 1, pp. 495 –503, 2007.

[118] P. Cortes, S. Kouro, B. La Rocca, R. Vargas, J. Rodriguez, J. Leon,

S. Vazquez, and L. Franquelo, “Guidelines for weighting factors design in

model predictive control of power converters and drives,” Industrial Tech-

nology, 2009. ICIT 2009. IEEE International Conference on, pp. 1 –7, feb.

2009.

[119] A. Timbus, P. Rodriguez, R. Teodorescu, M. Liserre, and F. Blaabjerg,

“Control strategies for distributed power generation systems operating on

faulty grid,” Industrial Electronics, 2006 IEEE International Symposium

on, vol. 2, pp. 1601 –1607, jul. 2006.

[120] D. Casadei, J. Clare, L. Empringham, G. Serra, A. Tani, A. Trentin,

P. Wheeler, and L. Zarri, “Large-signal model for the stability analysis of

matrix converters,” Industrial Electronics, IEEE Transactions on, vol. 54,

no. 2, pp. 939 –950, 2007.

[121] J. Wiseman and B. Wu, “Active damping control of a high-power pwm

current-source rectifier for line-current thd reduction,” Industrial Electron-

ics, IEEE Transactions on, vol. 52, no. 3, pp. 758 – 764, 2005.

[122] A. Qiu, Y. W. Li, B. Wu, N. Zargari, and Y. Liu, “High performance current

source inverter fed induction motor drive with minimal harmonic distor-

tion,” Power Electronics Specialists Conference, 2007. PESC 2007. IEEE,

pp. 79 –85, 2007.

Bibliography 136

[123] Y. W. Li, B. Wu, N. Zargari, J. Wiseman, and D. Xu, “Damping of pwm

current-source rectifier using a hybrid combination approach,” Power Elec-

tronics, IEEE Transactions on, vol. 22, no. 4, pp. 1383 –1393, 2007.

[124] Y. W. Li, “Control and resonance damping of voltage-source and current-

source converters with lc filters,” Industrial Electronics, IEEE Transactions

on, vol. 56, no. 5, pp. 1511 –1521, May 2009.

[125] S. Mariethoz and M. Morari, “Explicit model-predictive control of a pwm

inverter with an lcl filter,” Industrial Electronics, IEEE Transactions on,

vol. 56, no. 2, pp. 389 –399, 2009.

[126] M. Rivera, P. Correa, J. Rodriguez, I. Lizama, and J. Espinoza, “Predic-

tive control of the indirect matrix converter with active damping,” Power

Electronics and Motion Control Conference, 2009. IPEMC ’09. IEEE 6th

International, pp. 1738 –1744, May 2009.

[127]

[128] R. Pena, R. Cardenas, E. Reyes, J. Clare, and P. Wheeler, “A topology for

multiple generation system with doubly fed induction machines and indirect

matrix converter,” Industrial Electronics, IEEE Transactions on, vol. 56,

no. 10, pp. 4181 –4193, 2009.

[129] T. Friedli and J. Kolar, “Comprehensive comparison of three-phase ac-

ac matrix converter and voltage dc-link back-to-back converter systems,”

Power Electronics Conference (IPEC), 2010 International, pp. 2789 –2798,

2010.

[130] M. Nguyen, H. Lee, and T. Chun, “Input power factor compensation al-

gorithms using a new direct-svm method for matrix converter,” Industrial

Electronics, IEEE Transactions on, vol. PP, no. 99, pp. 1 –1, 2010.

[131] H. Nguyen, H.-H. Lee, and T.-W. Chun, “An investigation on direct space

vector modulation methods for matrix converter,” Industrial Electronics,

Bibliography 137

2009. IECON ’09. 35th Annual Conference of IEEE, pp. 4493 –4498, nov.

2009.

Thesis Marco Rivera

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