Equivalent-Small-Parameter Analysis of DC/DC Switched-Mode Converter (eBook)

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.

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