Chen / Zhang Equivalent-Small-Parameter Analysis of DC/DC Switched-Mode Converter

1. Auflage 2018
ISBN: 978-981-13-2574-8
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 248 Seiten

Reihe: CPSS Power Electronics Series

This book focuses on the applications of Equivalent-Small-Parameter Method (ESPM) in solving the steady-state periodic solutions, as well as stability analysis, of kinds of open-loop or closed-loop operated DC/DC converters, such as PWM, quasi-resonant and resonant ones. The analytical expressions of DC components and harmonics of state variables (inductor current and capacitor voltage) with DC/DC converters can be obtained by ESPM, which can be helpful to understand the nonlinear operating mechanism of switched-mode converters. It can also be useful for stability analysis and design for practical converters. Modeling and analysis on all kinds of DC/DC converters are introduced in detail in this book, along with a large amount of simulation or experimental waveforms to verify the correctness of the theoretical analysis based on ESPM.

Dr.Yanfeng Chen received the M.E. degree in power electronics technology from Wuhan University, China(1995), and the Ph.D degree in circuits and systems from South China University of Technology, China(2000). From November 2005 to December 2006, she was a Research Associate with the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong. She is currently a Professor at the School of Electric Power, South China University of Technology, Guangzhou, China. Her main research interests are modeling and analysis of nonlinear systems and power electronics. Dr. Bo Zhang was born in Shanghai, China, in 1962. He received the B.S. degree in electrical engineering from Zhejiang University, Hangzhou, China, in 1982, the M.S. degree in power electronics from Southwest Jiaotong University, Chengdu, China, in 1988, and the Ph.D. degree in power electronics from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1994. He is currently a Professor and the Vice Dean at the school of Electric Power, South China University of Technology, Guangzhou, China. He has authored or coauthored more than 350 papers and has 17 patents. His current research interests include nonlinear analysis and control of power electronics and AC drives.

Autoren/Hrsg.

Chen, Yanfeng

Zhang, Bo

Inhaltsverzeichnis

1;Preface;6
1.1;General Nonlinear Modeling;7
1.2;Steady-State and Transient Analysis of Open-Loop  Converter Systems;7
1.3;Analysis of Steady-State of Closed-Loop Converter Systems;7
1.4;Stability Analysis;8
1.5;Extension of ESP Method in Fractional-Order DC/DC Converter;8
2;Acknowledgements;10
3;Contents;11
4;About the Authors;16
5;1 Introduction;17
5.1;1.1 Introduction;17
5.2;1.2 Small-Signal Linearized Averaging Methods;19
5.3;1.3 Large-Signal Analysis Methods;21
5.3.1;1.3.1 State-Space Averaging Method Based Large-Signal Averaging Method;22
5.3.1.1;1.3.1.1 Analytic Method and Phase Plane Method [28–30];22
5.3.1.2;1.3.1.2 Large-Signal Equivalent Circuit Method [31];24
5.3.1.3;1.3.1.3 Switching Signal Flow Diagram Method [33–35];25
5.3.2;1.3.2 Ripple-Analysis Based Large-Signal Averaging Method;26
5.3.2.1;1.3.2.1 Extended Ripple Analysis Method [37];27
5.3.2.2;1.3.2.2 Three Port Model of n-Order Harmonic [38];29
5.3.2.3;1.3.2.3 Development of Averaging Method—Asymptotic Method, Improved Averaging Method and General Averaging Method [21–26];31
5.3.2.4;1.3.2.4 Symbolic Analysis Method—Equivalent Small Parameter Method [40–52];34
5.4;1.4 Summary;35
5.5;References;36
6;2 A General Nonlinear Mathematical Model of DC/DC Converter;39
6.1;2.1 Basic Topology and Constraints of DC/DC Converters;39
6.2;2.2 Operating Modes of DC/DC Converters;42
6.3;2.3 General Nonlinear Modeling of DC/DC Converters;43
6.4;2.4 Summary;47
6.5;References;47
7;3 Equivalent-Small-Parameters Method (ESPM);49
7.1;3.1 Fundamental Principles of ESPM;49
7.2;3.2 A Simplified Edition;53
7.3;3.3 Error Estimation for the Approximate Periodic Solutions;54
7.4;3.4 General Solutions for Strong Nonlinear High-Order Systems Described by Matrix Equations;56
7.5;3.5 Summary;59
7.6;References;59
8;4 Analysis of Open-Loop PWM DC/DC Converters Based on ESPM;60
8.1;4.1 Introduction;60
8.2;4.2 General Method for Analysis of PWM Switching Power Converter by ESPM;61
8.3;4.3 Analysis of the Open-Loop Boost Converter Under CCM Operation;63
8.3.1;4.3.1 Modeling of the CCM-Boost Converter;63
8.3.2;4.3.2 The Equivalent Mathematical Model Based on ESPM;65
8.3.3;4.3.3 The Steady-State Periodic Solution of the Boost Converter Based on ESPM;68
8.3.3.1;4.3.3.1 Solution of the Main Term;68
8.3.3.2;4.3.3.2 Solution of the First Correction Term;69
8.3.3.3;4.3.3.3 Solution of the Second Correction Term;69
8.3.4;4.3.4 Simulations;72
8.4;4.4 Analysis of the Open-Loop Buck Converter Under CCM Operation;74
8.4.1;4.4.1 Modeling of the CCM-Buck Converter;74
8.4.2;4.4.2 The Equivalent Mathematical Model Based on ESPM;75
8.4.3;4.4.3 The Steady-State Periodic Solution of the Buck Converter Based on ESPM;76
8.4.4;4.4.4 Simulations;78
8.5;4.5 Analysis of the Open-Loop Cuk Converter Under CCM Operation;79
8.5.1;4.5.1 Modeling of the CCM-Cuk Converter;79
8.5.2;4.5.2 The Steady-State Periodic Solution of the Cuk Converter Based on ESPM;81
8.5.3;4.5.3 Simulations;83
8.6;4.6 Transient Analysis of the Open-Loop PWM Converter by ESPM;84
8.6.1;4.6.1 The Solution Procedure;84
8.6.2;4.6.2 Initial Value Determination;88
8.6.3;4.6.3 Transient Analysis of Open-Loop PWM Boost Converter;89
8.6.4;4.6.4 Simplified Calculation;93
8.7;4.7 Summary;94
8.8;References;94
9;5 Analysis of Voltage-Mode Controlled CCM-PWM DC/DC Converters Based on ESPM;96
9.1;5.1 Introduction;96
9.2;5.2 Modeling the Closed-Loop VMC-PWM Converter with CCM Operation;97
9.2.1;5.2.1 Mathematical Description of the Closed-Loop System;97
9.2.2;5.2.2 Expression of the Duty Cycle d;98
9.2.2.1;5.2.2.1 Expression of d with Proportional Feedback Control;98
9.2.2.2;5.2.2.2 Expression of d with Proportional-Integral Feedback Control;99
9.2.3;5.2.3 Series Expansion of Switching Function ?(t) for Closed-Loop Systems;102
9.3;5.3 Solution of the Time-Varying Closed-Loop System with CCM Operation;104
9.3.1;5.3.1 Solution of Main Component;105
9.3.2;5.3.2 Solution of the First-Order Correction;106
9.3.3;5.3.3 Solution of the Second-Order Correction;107
9.4;5.4 Examples;108
9.4.1;5.4.1 Boost Regulator with Proportional Control;108
9.4.1.1;5.4.1.1 Find the Main Term of the Steady State Solution;109
9.4.1.2;5.4.1.2 Find the First-Order Correction;110
9.4.1.3;5.4.1.3 Find the Second-Order Correction;110
9.4.2;5.4.2 Boost Regulator with Proportional-Integral Control;112
9.5;5.5 Improvement of the Algorithm;114
9.5.1;5.5.1 Improved Algorithm for Duty Cycle Correction;114
9.5.2;5.5.2 Correction Algorithm for Series Expansion of the Switching Function ?(t);115
9.5.3;5.5.3 Double Iterative Symbol Algorithm;116
9.5.4;5.5.4 Analysis Example;118
9.6;5.6 Experiments and Verification;120
9.6.1;5.6.1 Diagram of the Experimental Circuit;120
9.6.2;5.6.2 Comparison of Experiment, ESPM and Simulation for Open-Loop System;123
9.6.3;5.6.3 Comparison of Experiment, ESPM and Simulation for Closed-Loop System;126
9.7;5.7 Summary;128
9.8;References;129
10;6 Analysis of Voltage-Mode Controlled DCM-PWM DC/DC Converters Based on ESPM;130
10.1;6.1 Introduction;130
10.2;6.2 Time-Varying Equation for Closed-Loop DCM-Operated Converter System;131
10.3;6.3 Determination of Switching Function and Duty Cycle;132
10.3.1;6.3.1 The Waveform-Based Determination Method for d3;133
10.3.2;6.3.2 Traditional Determination Method for d3;135
10.4;6.4 Solution of Time-Varying Equation for Closed-Loop DCM-Operated System;135
10.4.1;6.4.1 Solution of the Main Component;135
10.4.2;6.4.2 Solution of First-Order Correction;136
10.4.3;6.4.3 Solution of Second-Order Correction;138
10.5;6.5 Analysis Example;140
10.6;6.6 Summary;143
10.7;References;143
11;7 Analysis of Current-Mode Controlled PWM DC/DC Converters Based on ESPM;145
11.1;7.1 Introduction;145
11.2;7.2 The Basic Principle of Constant Frequency Current-Mode Control;146
11.3;7.3 Symbolic Analysis of Closed-Loop Current-Mode Controlled Converter System;148
11.3.1;7.3.1 Expression of the Duty Cycle for Closed-Loop CMC System;149
11.3.1.1;7.3.1.1 Accurate Solution of Duty Cycle;149
11.3.1.2;7.3.1.2 Simplified Solution of Duty Cycle;150
11.3.2;7.3.2 Solution of the Closed-Loop Equation of the CMC Converter;152
11.4;7.4 Examples;153
11.4.1;7.4.1 Double-Loop Current-Mode Controlled Boost Converter;153
11.4.1.1;7.4.1.1 Symbolic Analysis with Simplified Solution of Duty Cycle;154
11.4.1.2;7.4.1.2 Symbolic Analysis with Accurate Solution of Duty Cycle;157
11.4.2;7.4.2 Single-Loop Current-Mode Controlled Buck Converter;159
11.5;7.5 Steady-State Analysis of CMC-Boost in DCM Operation;162
11.5.1;7.5.1 Description of the CMC Converter in DCM;163
11.5.2;7.5.2 Steady-State Solution of the CMC Converter with DCM Operation;167
11.6;7.6 Summary;171
11.7;References;172
12;8 Analysis of PFM Quasi-resonant DC/DC Converters Based on ESPM;173
12.1;8.1 Introduction;173
12.2;8.2 Classification of Quasi-resonant Converters;176
12.2.1;8.2.1 Zero-Current Switch;176
12.2.2;8.2.2 Zero-Voltage-Switch;176
12.2.3;8.2.3 Duality Between ZVS and ZCS;177
12.3;8.3 Modulation Principle of the Quasi-resonant Converter;177
12.4;8.4 Symbolic Analysis of ZCS PFM Quasi-resonant Buck Converter System;179
12.4.1;8.4.1 Circuit Operating Principle of the Converter;179
12.4.2;8.4.2 Nonlinear Model of Quasi-resonant Converter and Its Solution by ESPM;183
12.4.2.1;8.4.2.1 The Order-Reduced Model of QRC Main Circuit;183
12.4.2.2;8.4.2.2 The Full-Order Model of QRC Main Circuit;187
12.5;8.5 Summary;194
12.6;References;195
13;9 Stability Analysis of PWM Power Switching Converters Based on ESPM;196
13.1;9.1 Stability Analysis of Equilibrium Points;196
13.1.1;9.1.1 Mathematical Model of PWM Close-Loop System;197
13.1.2;9.1.2 Stability Analysis Method of Equilibrium Points: Characteristic Equation Analysis Method;198
13.1.3;9.1.3 Example;199
13.2;9.2 Large-Signal Stability Analysis Methods of Buck Regulator;201
13.2.1;9.2.1 Steady-State Analysis Method-1 Based on ESPM;204
13.2.2;9.2.2 Steady-State Analysis Method-2 Based on ESPM;206
13.2.3;9.2.3 Analysis Method Considering the Saturation of Duty-Ratio;207
13.2.4;9.2.4 Stability Analysis by Numerical Simulation;210
13.2.4.1;9.2.4.1 LFO Under Different Switching Frequency;210
13.2.4.2;9.2.4.2 Simulations Under Different Feedback Capacitor;210
13.3;9.3 Summary;211
13.4;References;212
14;10 Extension of ESPM to Fractional-Order DC/DC Converters;213
14.1;10.1 Induction;213
14.2;10.2 Mathematical Model of Fractional-Order Boost Converter Operating in CCM;214
14.2.1;10.2.1 An Equivalent Model Based on the ESPM;216
14.2.2;10.2.2 Periodic Steady-State Solutions of Fractional-Order Boost Converter in CCM;219
14.2.3;10.2.3 Discussion of the Order-Related Phenomena;223
14.2.4;10.2.4 Numerical Simulations and Comparisons;224
14.2.5;10.2.5 Equivalent Circuit Implementation of Fractional-Order Devices;227
14.2.6;10.2.6 PSIM Simulations Based Equivalent Realization Circuits of Fractional Elements;231
14.2.7;10.2.7 Experimental Results;233
14.3;10.3 Mathematical Model of Fractional-Order Boost Converter Operating in DCM;235
14.3.1;10.3.1 Equivalent System of DCM Non-integer Order Differential Equations;235
14.3.2;10.3.2 Periodic Steady-State Solutions of Fractional-Order Boost Converter in DCM;239
14.3.3;10.3.3 Comparisons and Verification;242
14.4;10.4 Summary;246
14.5;References;246