Power Electronic Systems: Walsh Analysis with MATLAB®

300 Pages·2014·6.89 MB·English

by  Anish Deb, Suchismita Ghosh

Power electronic SyStemS
Walsh analysis With MatlaB®

Power electronic SyStemS

Walsh analysis With MatlaB®
Anish Deb
Suchismita Ghosh
Boca Raton London New York
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of a particular pedagogical approach or particular use of the MATLAB® software.

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Contents
List of Principal Symbols ......................................................................................xi
Preface ...................................................................................................................xiii
Authors ...................................................................................................................xv
1 Introduction .....................................................................................................1
1.1 Evolution of Power Electronics ...........................................................1
1.2 Analysis of Power Electronic Circuits ................................................2

1.2.1 Fourier Series Technique ........................................................4
1.2.2 Laplace Transform Method ....................................................4
1.2.3 Existence Function Technique ...............................................5
1.2.4 State Variable Method .............................................................5
1.2.5 Averaging Technique ..............................................................6
1.2.6 z-Transform Analysis ..............................................................6
1.2.7 Other Methods of Analysis ....................................................6
1.3 Search for a New Method of Analysis ...............................................7
References .........................................................................................................8
2 An Alternative Class of Orthogonal Functions .....................................11
2.1 Orthogonal Functions and Their Properties ...................................11
2.2 Haar Functions ....................................................................................13
2.3 Rademacher and Walsh Functions ...................................................15
2.3.1 Representation of a Function Using Walsh Functions .....21
2.4 Block Pulse Functions and Their Applications ..............................22
2.4.1 Representation of a Function as a Linear
Combination of BPFs .............................................................25
2.5 Slant Functions ....................................................................................27
2.6 Delayed Unit Step Functions .............................................................28
2.7 General Hybrid Orthogonal Functions............................................30
2.8 Sample-and-Hold Functions ..............................................................30
2.9 Triangular Functions ..........................................................................32
2.10 Hybrid Function: A Combination of SHF and TF ..........................34
2.11 Applications of Walsh Functions ......................................................36
References .......................................................................................................40
3 Walsh Domain Operational Method of System Analysis ....................47
3.1 Introduction to Operational Matrices ..............................................47
3.1.1 Operational Matrix for Integration .....................................48
3.1.1.1 Representation of Integration
of a Function Using Operational Matrix
for Integration .........................................................55
vii
viii Contents
3.1.2 Operational Matrix for Differentiation ...............................58
3.1.2.1 Representation of Differentiation of a
Function Using Operational Matrix for
Differentiation ........................................................59
3.2 Time Scaling of Operational Matrices .............................................62
3.2.1 Time-Scaled Operational Matrix for Integration ..............63
3.2.2 Time-Scaled Operational Matrix for Differentiation ........65
3.3 Philosophy of the Proposed Walsh Domain Operational
Technique .............................................................................................65
3.4 Analysis of a First-Order System with Step Input .........................69
3.5 Analysis of a Second-Order System with Step Input .....................72
3.6 Oscillatory Phenomenon in Walsh Domain System Analysis .....73

3.6.1 Oscillatory Phenomenon in a First-Order System ............74
3.6.2 Analytical Study of the Oscillatory Phenomenon ............75
3.7 Conclusion ............................................................................................86
References .......................................................................................................86
4 Analysis of Pulse-Fed Single-Input Single-Output Systems ..............89
4.1 Analysis of a First-Order System ......................................................90
4.1.1 Single-Pulse Input ..................................................................90
4.1.2 Pulse-Pair Input .....................................................................92
4.1.3 Alternating Double-Pulse Input ..........................................92
4.2 Analysis of a Second-Order System .................................................94
4.2.1 Single-Pulse Input ..................................................................94
4.2.2 Pulse-Pair Input .....................................................................95
4.2.3 Alternating Double-Pulse Input ..........................................95
4.3 Pulse-Width Modulated Chopper System .......................................97
4.3.1 Case I: Stepwise PWM ..........................................................97
4.3.1.1 Walsh Function Representation of
Significant Current Variables ................................97
4.3.1.2 Determination of Normalized Average
and rms Currents through Load and
Semiconductor Components ...............................100
4.3.1.3 Determination of Exact Normalized
Average and rms Current Equations
Considering Switching Transients .....................103
4.3.2 Case II: Continuous PWM ..................................................107
4.3.2.1 Mathematical Operations ....................................111
4.3.2.2 Simulation of an Ideal Continuously
Pulse-Width Modulated DC Chopper
System ................................................................112
Contents ix
4.3.2.3 Determination of Normalized Average
and rms Currents through Load and
Semiconductor Components ...............................113
4.3.2.4 Simulation of an Ideal Chopper-Fed DC
Series Motor ..........................................................120
4.4 Conclusion ..........................................................................................127
References .....................................................................................................128
5 Analysis of Controlled Rectifier Circuits ..............................................131
5.1 Representation of a Sine Wave by Walsh Functions ....................132
5.2 Conventional Analysis of Half-Wave Controlled Rectifier .........134
5.3 Walsh Domain Analysis of Half-Wave Controlled Rectifier ......137

5.3.1 Computational Algorithm ..................................................140
5.4 Walsh Domain Analysis of Full-Wave Controlled Rectifier .......145
5.4.1 Single-Phase Full-Wave Controlled Rectifier ...................146
5.4.2 Representation of the Load Voltage by Walsh
Functions ...............................................................................147
5.4.3 Determination of Normalized Average and rms
Currents .................................................................................151
5.4.3.1 Exact Equations for Phase-Controlled
Rectifier ..................................................................152
5.4.4 Computational Algorithm ..................................................160
5.5 Conclusion ..........................................................................................162
References .....................................................................................................163
6 Analysis of Inverter Circuits ....................................................................165
6.1 Voltage Control of a Single-Phase Inverter ....................................166
6.1.1 Single-Pulse Modulation ....................................................168
6.1.1.1 Walsh Function Representation of
Single- Pulse Modulation .....................................169
6.1.1.2 Computation of Normalized Average
and rms Load Currents for Single–Pulse
Modulation ............................................................172
6.2 Analysis of an RL Load Fed from a Typical Three-Phase
Inverter Line-to-Neutral Voltage ....................................................175
6.3 Conclusion ..........................................................................................179
References .....................................................................................................179
Appendix A: Introduction to Linear Algebra ..............................................181
Appendix B: Selected MATLAB® Programs ................................................191
Index .....................................................................................................................275