Power electronic systems : walsh analysis with MATLAB®

Power Electronic Systems: Walsh Analysis with MATLAB® builds a case for Walsh analysis as a powerful tool in the study of power electronic systems. It considers the application of Walsh functions in analyzing power electronic systems, and the advantages offered by Walsh domain analysis of power electronic systems.

Solves Power Electronic Systems in an Unconventional Way

This book successfully integrates power electronics as well as systems and control. Incorporating a complete orthonormal function set very much unlike the sine-cosine functions, it introduces a blending between piecewise constant orthogonal functions and power electronic systems. It explores the background and evolution of power electronics, and discusses Walsh and related orthogonal basis functions. It develops the mathematical foundation of Walsh analysis, and first- and second-order system analyses by Walsh technique. It also describes the Walsh domain operational method and how it is applied to linear system analysis.

Introduces Theories Step by Step

While presenting the underlying principles of Walsh analysis, the authors incorporate many illustrative examples, and include a basic introduction to linear algebra and MATLAB® programs. They also examine different orthogonal piecewise constant basis functions like Haar, Walsh, slant, block pulse functions, and other related orthogonal functions along with their time scale evolution.

* Analyzes pulse-fed single input single output (SISO) first- and second-order systems

* Considers stepwise and continuously pulse width modulated chopper systems

* Describes a detailed analysis of controlled rectifier circuits

* Addresses inverter circuits

Power Electronic Systems: Walsh Analysis with MATLAB® is written for postgraduate students, researchers, and academicians in the area of power electronics as well as systems and control.

Author Notes

Anish Deb obtained his BTech in 1974 (recipient of Calcutta University silver medal), MTech in 1976 (recipient of Calcutta University gold medal and P. N. Ghosh memorial gold medal), and PhD (Tech) in 1990 from the Department of Applied Physics, University of Calcutta, India. In 1978, he joined the Department of Applied Physics, University of Calcutta, as Lecturer in 1983. In 1990, he became Reader (associate professor) in the same department. He has been holding the post of Professor since 1998. His research interest includes automatic control in general and application of "alternative" orthogonal functions in power electronics and systems and control. He has authored one book entitled "Triangular orthogonal functions for the analysis of continuous time systems" and published more than 65 research papers in different national and international journals and conferences.

Suchismita Ghosh obtained her BTech (2008) from the Calcutta Institute of Engineering and Management, West Bengal University of Technology, India, and MTech (2010) from the Department of Applied Physics, University of Calcutta, India. She is currently an assistant professor in the Department of Electrical Engineering, MCKV Institute of Engineering, West Bengal University of Technology, India. She has taught courses on power electronics, basic electrical engineering, control systems, and electrical machines. Her research area includes automatic control in general and application of "alternative" orthogonal functions in systems and control. She is presently involved in research with Anish Deb and has published five research papers in international journals and national conferences.

List of Principal Symbols	p. xi
Preface	p. xiii
Authors	p. xv
1 Introduction	p. 1
1.1 Evolution of Power Electronics	p. 1
1.2 Analysis of Power Electronic Circuits	p. 2
1.2.1 Fourier Series Technique	p. 4
1.2.2 Laplace Transform Method	p. 4
1.2.3 Existence Function Technique	p. 5
1.2.4 State Variable Method	p. 5
1.2.5 Averaging Technique	p. 6
1.2.6 z-Transform Analysis	p. 6
1.2.7 Other Methods of Analysis	p. 6
1.3 Search for a New Method of Analysis	p. 7
References	p. 8
2 An Alternative Class of Orthogonal Functions	p. 11
2.1 Orthogonal Functions and Their Properties	p. 11
2.2 Haar Functions	p. 13
2.3 Rademacher and Walsh Functions	p. 15
2.3.1 Representation of a Function Using Walsh Functions	p. 21
2.4 Block Pulse Functions and Their Applications	p. 22
2.4.1 Representation of a Function as a Linear Combination of BPFs	p. 25
2.5 Slant Functions	p. 27
2.6 Delayed Unit Step Functions	p. 28
2.7 General Hybrid Orthogonal Functions	p. 30
2.8 Sample-and-Hold Functions	p. 30
2.9 Triangular Functions	p. 32
2.10 Hybrid Function: A Combination of SHF and TF	p. 34
2.11 Applications of Walsh Functions	p. 36
References	p. 40
3 Walsh Domain Operational Method of System Analysis	p. 47
3.1 Introduction to Operational Matrices	p. 47
3.1.1 Operational Matrix for Integration	p. 48
3.1.1.1 Representation of Integration of a Function Using Operational Matrix for Integration	p. 55
3.1.2 Operational Matrix for Differentiation	p. 58
3.1.2.1 Representation of Differentiation of a Function Using Operational Matrix for Differentiation	p. 59
3.2 Time Scaling of Operational Matrices	p. 62
3.2.1 Time-Scaled Operational Matrix for Integration	p. 63
3.2.2 Time-Scaled Operational Matrix for Differentiation	p. 65
3.3 Philosophy of the Proposed Walsh Domain Operational Technique	p. 65
3.4 Analysis of a First-Order System with Step Input	p. 69
3.5 Analysis of a Second-Order System with Step Input	p. 72
3.6 Oscillatory Phenomenon in Walsh Domain System Analysis	p. 73
3.6.1 Oscillatory Phenomenon in a First-Order System	p. 74
3.6.2 Analytical Study of the Oscillatory Phenomenon	p. 75
3.7 Conclusion	p. 86
References	p. 86
4 Analysis of Pulse-Fed Single-Input Single-Output Systems	p. 89
4.1 Analysis of a First-Order System	p. 90
4.1.1 Single-Pulse Input	p. 90
4.1.2 Pulse-Pair Input	p. 92
4.1.3 Alternating Double-Pulse Input	p. 92
4.2 Analysis of a Second-Order System	p. 94
4.2.1 Single-Pulse Input	p. 94
4.2.2 Pulse-Pair Input	p. 95
4.2.3 Alternating Double-Pulse Input	p. 95
4.3 Pulse-Width Modulated Chopper System	p. 97
4.3.1 Case I: Stepwise PWM	p. 97
4.3.1.1 Walsh Function Representation of Significant Current Variables	p. 97
4.3.1.2 Determination of Normalized Average and rms Currents through Load and Semiconductor Components	p. 100
4.3.1.3 Determination of Exact Normalized Average and rms Current Equations Considering Switching Transients	p. 103
4.3.2 Case II: Continuous PWM	p. 107
4.3.2.1 Mathematical Operations	p. 111
4.3.2.2 Simulation of an Ideal Continuously Pulse-Width Modulated DC Chopper System	p. 112
4.3.2.3 Determination of Normalized Average and rms Currents through Load and Semiconductor Components	p. 113
4.3.2.4 Simulation of an Ideal Chopper-Fed DC Series Motor	p. 120
4.4 Conclusion	p. 127
References	p. 128
5 Analysis of Controlled Rectifier Circuits	p. 131
5.1 Representation of a Sine Wave by Walsh Functions	p. 132
5.2 Conventional Analysis of Half-Wave Controlled Rectifier	p. 134
5.3 Walsh Domain Analysis of Half-Wave Controlled Rectifier	p. 137
5.3.1 Computational Algorithm	p. 140
5.4 Walsh Domain Analysis of Full-Wave Controlled Rectifier	p. 145
5.4.1 Single-Phase Full-Wave Controlled Rectifier	p. 146
5.4.2 Representation of the Load Voltage by Walsh Functions	p. 147
5.4.3 Determination of Normalized Average and rms Currents	p. 151
5.4.3.1 Exact Equations for Phase-Controlled Rectifier	p. 152
5.4.4 Computational Algorithm	p. 160
5.5 Conclusion	p. 162
References	p. 163
6 Analysis of Inverter Circuits	p. 165
6.1 Voltage Control of a Single-Phase Inverter	p. 166
6.1.1 Single-Pulse Modulation	p. 168
6.1.1.1 Walsh Function Representation of Single-Pulse Modulation	p. 169
6.1.1.2 Computation of Normalized Average and rms Load Currents for Single-Pulse Modulation	p. 172
6.2 Analysis of an RL Load Fed from a Typical Three-Phase Inverter Line-to-Neutral Voltage	p. 175
6.3 Conclusion	p. 179
References	p. 179
Appendix A Introduction to Linear Algebra	p. 181
Appendix B Selected MATLAB® Programs	p. 191
Index	p. 275

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