9780780353831

Nonlinear Phenomena in Power Electronics : Bifurcations, Chaos, Control, and Applications

by ;
  • ISBN13:

    9780780353831

  • ISBN10:

    0780353838

  • Format: Hardcover
  • Copyright: 2001-07-16
  • Publisher: Wiley-IEEE Press
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Summary

Brings the knowledge of 24 experts in this maturing field out from the narrow confines of academic circles, and makes it accessible to graduate students and power electronics professionals alike. * Provides practicing engineers with the knowledge to predict power requirement behavior. * The insights gained from this all-inclusive compilation will ultimately lead to better design methodologies.

Table of Contents

Preface xv
Acknowledgments xix
List of Contributing Authors
xxi
Introduction
1(24)
D. C. Hamill
S. Banerjee
G. C. Verghese
Introduction to Power Electronics
1(4)
Power Switching Devices
2(2)
Sources of Nonlinearity in Power Electronics
4(1)
Power Converters
4(1)
Electrical Machines and Drives
4(1)
Power Systems
5(1)
An Example: The Buck DC/DC Converter
5(10)
Conventional Model of the Buck Converter
6(1)
Continuous Conduction Mode
7(2)
Actual System Behavior
9(1)
Nonlinear Map-Based Model of the Buck Converter
9(4)
Discontinuous Conduction Mode
13(1)
Limitations and Extensions of Average Models
14(1)
Study of Nonlinear Dynamics and Chaos in Power Electronics
15(5)
Conclusions
20(5)
Dynamic Models of Power Converters
25(412)
Introduction to Power Electronic Converters and Models
25(13)
G. C. Verghese
A. M. Stankovic
Introduction
25(1)
Types of Power Electronic Converters
25(1)
High-Frequency PWM DC/DC Converters
25(1)
Other High-Frequency PWM Converters
26(1)
Other Inverters
27(1)
Resonant Converters
27(1)
Phase-Controlled Converters
28(1)
AC/AC Converters
28(1)
Averaged and Sampled-Data Models for Analysis, Simulation, and Control of Converter Dynamics
28(2)
Switched State-Space Model for the Boost Converter
30(2)
Averaged Model for the Boost Converter
32(1)
Averaged Model for Current-Mode Control of the Boost Converter
33(1)
Sampled-Data Models for the Boost Converter
34(2)
Extensions
36(1)
Generalized Averaging
36(1)
Generalized State-Space Models
36(2)
A Closer Look at Sampled-Data Models for Power Converters
38(15)
F. Vasca
M. di Bernardo
G. Olivar
Introduction
38(1)
Poincare Maps for Smooth and Nonsmooth Dynamical Systems
38(2)
Piecewise-Smooth Power Electronic Circuits
40(3)
Power Electronic Systems as Hybrid Systems
43(3)
Stroboscopic Maps
46(2)
Periodic Phase Sequence and Time-Varying Inputs
48(1)
A Stroboscopic Nonswitching Map
48(1)
Closed-Loop Maps
48(1)
Switching Maps
49(1)
S-Switching Maps for DC/DC Converters
49(1)
A-Switching Maps for DC/DC Converters
50(1)
Simplified Maps
51(1)
Conclusions
51(2)
Basics of Bifurcation and Chaos Theory
Introduction to Nonlinear Dynamics and Chaos
53(14)
S. Banerjee
System State, and
53(2)
State-Space Models
Autonomous Systems and Nonautonomous Systems
55(1)
Vector Fields of Linear, Linearized, and Nonlinear Systems
55(2)
Attractors in Nonlinear Systems
57(2)
Chaos
59(2)
Poincare Map
61(1)
Dynamics of Discrete-Time Systems
62(2)
Fractal Geometry
64(2)
Lyapunov Exponent
66(1)
Bifurcation
66(1)
Bifurcations of Smooth Maps
67(6)
J. H. B. Deane
The Pitchfork Bifurcation
68(1)
The Saddle-Node Bifurcation
68(1)
The Period-Doubling Bifurcation
69(1)
The Neimark Bifurcation
70(3)
Bifurcations in Piecewise-Smooth Maps
73(16)
S. Banerjee
C. Grebogi
The Normal Form
77(2)
Bifurcations in the One-Dimensional Normal Form
79(1)
Border Collision Pair Bifurcation
80(1)
Border-Crossing Bifurcations
81(1)
Bifurcations in the Two-Dimensional Normal Form
82(2)
Classification of Border Collision Bifurcations
84(1)
Border Collision Pair Bifurcation
84(1)
Border-Crossing Bifurcations
85(4)
Nonstandard Bifurcations in Discontinuous Maps
89(5)
I. Dobson
S. Banerjee
The Method of Schwarzian Derivatives
94(7)
C. K. Tse
Background
94(1)
Problem Description
94(1)
Mechanism of Period Doubling
95(1)
Schwarzian Derivative and Period-Doublings ad infinitum
96(1)
Application to Power Electronics
97(1)
Illustrative Example: The Boost Converter
98(2)
Interpretation and Application of the Result
100(1)
Remarks and Summary
100(1)
Coexisting Attractors, Basins of Attraction, and Crises
101(10)
E. Fossas
G. Olivar
Characteristic (Floquet) Multipliers
101(1)
Invariant Sets and Invariant Manifolds
102(1)
Homoclinic and Heteroclinic Orbits
103(1)
Coexisting Attractors
104(1)
The Role of Invariant Manifolds and Basins of Attraction
105(1)
Crises
106(1)
Interior Crises
107(1)
Boundary Crises
108(1)
Two-Dimensional Maps
109(2)
Experimental and Computational Techniques for Investigation of Nonlinear Phenomena
Techniques of Experimental Investigation
111(12)
C. K. Tse
Introduction
111(1)
Overview of Simulation Study and Verification
111(1)
Experimental Investigation
112(1)
Displaying Time-Domain Waveforms, Attractors, and Spectra
112(2)
Displaying Poincare Sections
114(1)
Principle of Poincare Section Measurement
115(2)
Example: Free-Running Cuk Converter
117(1)
Poincare Sections for Nonautonomous Circuits
118(1)
Displaying Bifurcation Diagrams
118(1)
Basic Operational Requirements
119(1)
Digital Implementation and Related Issues
120(1)
Other Methods, Problems, and Practical Issues
121(1)
Example: Boost Converter Under Current-Mode Control
121(2)
Techniques of Numerical Investigation
123(6)
S. Banerjee
D. C. Hamill
Simulation of Power Electronic Circuits
123(1)
Problems Arising from Varying Topology
124(1)
Problems Arising from Incompatible Boundary Conditions
125(1)
Obtaining Bifurcation Diagrams
125(1)
Plotting Basins of Attraction in Systems with Multiple Attractors
126(1)
Computing the Maximal Lyapunov Exponent
127(2)
Computation of Averages Under Chaos
129(20)
J. L. Rodriguez Marrero
G. C. Verghese
R. Santos Bueno
S. H. Isabelle
Introduction
129(1)
Chaotic Operation of DC/DC Converters Under Current-Mode Control
130(1)
Describing Chaotic Behavior Via Densities
130(4)
Calculation of the Time-Average of the Inductor Current
134(1)
Analysis of DC/DC Converters
135(7)
Average Switching Frequency and Average Duty Ratio
142(1)
Experimental Results
143(2)
Conclusions
145(4)
Calculation of Spectral Peaks in a Chaotic DC/DC Converter
149(16)
J. H. B. Deane
Characterization of Spectral Properties
149(2)
Motivation and Outline
151(1)
The Simplified Mapping
152(2)
Approximation of the Mean State Variables
154(1)
The Power Density Spectrum of the Inductor Current
155(3)
The Invariant Density Algorithm
158(2)
Practical Results
160(1)
Experimental Results
160(3)
Discussion
163(2)
Computer Methods to Analyze Stability and Bifurcation Phenomena
165(12)
Y. Kuroe
Introduction
165(1)
Nonlinear Systems and Stability of Periodic Solutions
165(2)
Computer Methods to Analyze Stability
167(2)
Computation of the Jacobian Matrix
169(2)
Analysis Method Based on Transient Simulator
171(3)
Computer Method to Analyze Bifurcation Phenomena
174(1)
Classification of Bifurcations
174(1)
Method to Determine Bifurcation Values
175(2)
Computation of Operating-Mode Boundaries
177(15)
Y. Kuroe
T. Kato
G. C. Verghese
Introduction
177(1)
What Is Operating-Mode Analysis?
178(1)
Computation of Operating-Mode Boundary by Curve Tracing
179(1)
Conditions that Define Operating-Mode Boundaries
179(2)
Numerical Tracing of Boundary Curves
181(1)
Computation of Steady-State Sensitivities
182(1)
Numerical Examples
183(4)
Computation of Operating-Mode Boundaries by a Binary-Box Method
187(1)
Basic Approach
187(1)
Binary-Box Method
188(1)
Application to More Complicated Converters
188(4)
Nonlinear Phenomena in DC/DC Converters
Border Collision Bifurcations in the Current-Mode-Controlled Boost Converter
192(7)
S. Banerjee
P. Ranjan
Modeling and Analysis
192(3)
Analysis of Bifurcations
195(4)
Bifurcation and Chaos in the Voltage-Controlled Buck Converter with Latch
199(9)
S. Banerjee
D. Kastha
S. Das
Overview of Circuit Operation
199(1)
Experimental Results
200(2)
Coexisting Attractors and Crises
202(6)
Routes to Chaos in the Voltage-Controlled Buck Converter without Latch
208(21)
M. di Bernardo
G. Olivar
F. Vasca
Buck Converter Modeling Under Voltage-Mode Control
208(1)
Differential equations
209(1)
Discrete-Time Map and Periodic Orbits
210(2)
Different Types of Periodic Orbits
212(1)
Analytical Study of Periodic Orbits: Existence and Stability
212(5)
One-Dimensional Bifurcation Diagrams
217(1)
The Main Bifurcation Diagram
217(2)
Secondary Bifurcations
219(1)
Chaotic Attractors in the Buck Converter
220(1)
3T-Periodic Orbits and the Three-Piece Chaotic Attractor
220(1)
Invariant Manifolds and Basins of Attraction
220(3)
6T-Periodic Orbits
223(1)
12T-Periodic Orbits
224(1)
5T-Periodic Orbits and the Jump to Larger Chaos
225(4)
Saddle-Node and Neimark Bifurcations in PWM DC/DC Converters
229(11)
C. C. Fang
E. H. Abed
Introduction
229(1)
General Sampled-Data Model for Closed-Loop PWM Converters
229(3)
Periodic Solution Before and After Local Bifurcation
232(1)
Saddle-Node Bifurcation in Buck Converter Under Discrete-Time Control
232(2)
Neimark Bifurcation in Buck Converter Under Voltage-Mode Control
234(2)
Neimark Bifurcation in Buck Converter with Input Filter Under Voltage-Mode Control
236(2)
Neimark Bifurcation in Buck Converter with Input Filter Under Current-Mode Control
238(2)
Nonlinear Analysis of Operation in Discontinuous-Conduction Mode
240(8)
C. K. Tse
Review of Operating Modes
240(1)
Derivation of Discrete-Time Maps
241(2)
Period-Doubling Bifurcation
243(2)
Computer Simulations and Experiments
245(1)
Remarks and Summary
246(2)
Nonlinear Phenomena in the Cuk Converter
248(14)
C. K. Tse
Review of the Cuk Converter and its Operation
248(1)
Discrete-Time Modeling for Fixed Frequency Operation
249(2)
Free-Running Current-Mode-Controlled Cuk Converter
251(1)
Autonomous System Modeling
251(2)
Dimensionless Equations
253(1)
Stability of Equilibrium Point and Hopf Bifurcation
254(2)
Local Trajectories from Describing Equation
256(2)
Computer Simulation Study
258(4)
Nonlinear Dynamics in Thyristor and Diode Circuits
I. Dobson
Introduction
262(1)
Ideal Diode and Thyristor Switching Rules
263(1)
Static VAR System Example
263(2)
Poincare Map
265(2)
Jacobian of Poincare Map
267(7)
Thyristor Current Function and Transversality
268(1)
Relations Between On and Off Systems
269(1)
Derivation of Jacobian Formula
270(1)
Interval Containing a Switch-On
270(1)
Interval Containing a Switch-Off
271(1)
Assembling the Jacobian
272(1)
Discussion of Jacobian Formula
273(1)
Switching Damping
274(4)
Simple Example
274(1)
Switching Damping in the SVC Example
275(1)
Variational Equation
276(2)
Switching Time Bifurcations
278(8)
Switching Time Bifurcations and Instability
278(2)
Switching Time Bifurcations for Transients
280(1)
Misfire Onset as a Transcritical Bifurcation
281(2)
Noninvertibility and Discontinuity of the Poincare Map
283(1)
Multiple Attractors and Their Basin Boundaries
284(2)
Diode Circuits
286(3)
Transversality and Poincare Map Jacobian Formula
286(1)
Poincare Map Jacobian for the DC/DC Buck-Boost Converter in Discontinuous Mode
286(2)
Poincare Map Continuity and Switching Time Bifurcations
288(1)
Firing Angle Control
289(3)
Nonlinear Phenomena in Other Power Electronic Systems
Modeling a Nonlinear Inductor Circuit
292(6)
J. H. B. Deane
Introduction
292(1)
The Circuit
292(1)
Saturating and Hysteretic Inductor Modeling
293(1)
Differential Equation for the Circuit
294(1)
Results
295(1)
Bifurcation Diagram Comparison
296(1)
Poincare Section Comparison
297(1)
Conclusions
298(1)
Inverters Under Tolerance Band Control
298(15)
A. Magauer
Introduction
298(1)
Functioning Principle
299(1)
System Model and Equation
300(2)
Poincare Map
302(1)
Circuit Realization
303(1)
Mode of Oscillations, Bifurcations, and Crises
303(1)
Chaotic Mode
304(1)
Symmetry-Breaking Bifurcation
305(2)
Merging Crisis
307(1)
Interior Crisis
308(1)
Saddle-Node Bifurcation and Square-Wave Mode
308(3)
Boundary Crisis
311(1)
Period-Doubling Bifurcations
312(1)
Conclusions
312(1)
Nonlinear Noise Effects in Power Converters
313(15)
P. T. Krein
P. Midya
Introduction
313(1)
Discussion of Switching Noise
314(1)
External Noise Effects in Open-Loop Converters
315(1)
External Noise Action
315(1)
Background of Analysis
316(2)
Summary of Assumptions
318(1)
Probability Density Function of Switch Timing
318(1)
Implications of the Non-Gaussian Duty Ratio Distribution with Latch
319(2)
External Noise Effects in Closed-Loop DC/DC Converters
321(1)
The Nature of Closed-Loop Noise Effects
321(1)
The Closed-Loop Process and System Model
321(1)
Time Domain Noise Analysis
322(1)
Confirmation
323(1)
Frequency Domain Analysis
324(3)
Summary
327(1)
Nonlinear Phenomena in the Current Control of Induction Motors
328(10)
I. Nagy
Z. Suto
System Model
329(1)
Voltage Source Converter (VSC)
329(1)
AC Side
330(1)
Hysteresis Current Control (HCC)
331(1)
Poincare Map
332(1)
Nonlinear Phenomena
333(1)
Sensitive Dependence on Initial Condition
333(1)
Period Doubling Bifurcation
333(2)
Intermittency
335(1)
Coexisting Attractors
336(1)
Numerical Values
336(1)
Conclusions
337(1)
Analysis of Stability and Bifurcation in Power Electronic Induction Motor Drive Systems
338(15)
Y. Kuroe
Introduction
338(1)
Model of Power Electronic Induction Motor Drive Systems
338(1)
Model of Induction Motor and its Mechanical Load
338(2)
Model of Inverter and Rectifier
340(3)
Poincare Map and Periodicity of Steady States
343(1)
Case I
343(1)
Case II
344(1)
Case III
345(1)
Stability Analysis
345(3)
Analysis of Bifurcations
348(5)
Nonlinear Control and Control of Chaos
Conventional Nonlinear Controls in Power Electronics
353(4)
P. T. Krein
Introduction
353(1)
Hysteresis Controllers
354(1)
Nonlinear Modulation
354(2)
Multipliers in the Loop
356(1)
Sliding Mode and Switching Surface Control
357(14)
P. T. Krein
Introduction
357(1)
Hysteresis Control
358(2)
Switching Surface Control Analysis
360(1)
Trajectories and Equilibria
360(1)
Switching Surface-Based Control Laws
361(1)
Necessary Conditions for Switching Surface Controls
362(1)
Sample Outputs and Hysteresis Design Approaches
363(2)
Global Stability Considerations
365(1)
Successor Points
365(1)
Behavior Near a Switching Surface
366(1)
Choosing a Switching Surface
367(2)
Higher Dimensions
369(1)
Summary
369(2)
Energy-Based Control in Power Electronics
371(15)
A. M. Stankovic
G. Escobar
R. Ortega
S. R. Sanders
Introduction
371(1)
Circuit-Theoretic Approaches
372(1)
Basic Control
372(2)
Adaptation
374(1)
Estimation and Output Feedback
375(1)
Passivity-Based Control
376(1)
Basic Controller
376(2)
Adaptation
378(1)
Hamiltonian Control
379(1)
Connections with Sliding-Mode Control
380(1)
Sliding-Mode Controller Revisited
381(1)
Passivity-Based Sliding-Mode Controller
382(1)
Combining SMC with Prediction
383(1)
Conclusions
384(2)
Ripple Correlation Control
386(7)
P. T. Krein
Background
386(1)
Ripple-Based Control
386(1)
Ripple Correlation
387(2)
Some Application Examples
389(1)
Adaptive Dead Time
389(1)
Solar Power Processing
390(1)
Motor Power Minimization in Drives
391(1)
Summary
392(1)
Control of Chaos
393(13)
M. di Bernardo
G. Olivar
C. Batlle
Introduction
393(1)
A Combination of OGY and Pyragas Methods
394(1)
Application to the Current-Mode-Controlled Boost Converter
395(3)
Controlling Border-Collision Bifurcations
398(1)
Local Feedback Strategy
399(1)
An Example: A Two-Dimensional Map
400(1)
Time-Delay Control of Chaos
401(1)
An Example: TDAS for the Current-Mode Boost Converter
402(2)
Conclusions
404(2)
Closed-Loop Regulation of Chaotic Operation
406(12)
J. L. Rodriguez Marrero
R. Santos Bueno
G. C. Verghese
Introduction
406(1)
Dynamics and Control
406(2)
Experimental Results
408(1)
The OGY Method
409(2)
Review of the OGY Method
411(1)
Controlling DC/DC Converters
412(3)
Integral Control
415(2)
Conclusions
417(1)
Control of Bifurcation
418(10)
C. K. Tse
Y.-M. Lai
Background
418(1)
Controlling Bifurcation in Discontinuous-Mode Converters
419(1)
Controlling Bifurcation in Current-Mode-Controlled DC/DC Converters
420(1)
Use of Compensating Ramp for Controlling Bifurcation
420(4)
Effects on Dynamical Response
424(1)
Experimental Measurements
425(1)
Variable Ramp Compensation
426(2)
Synchronization of Chaos
428(9)
C. K. Tse
Background
428(1)
The Drive-Response Concept
429(1)
Synchronization in Chaotic Free-Running Cuk Converters
430(1)
Derivation of the Conditional Lyapunov Exponents
431(1)
Numerical Calculation of the Conditional Lyapunov Exponents
432(1)
Computer Simulations
433(1)
Remarks on Practical Synchronization
433(4)
Index 437(4)
About the Editors 441

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