Chaos Analysis and Chaotic EMI Suppression of DC-DC Converters

258 Pages·2014·4.33 MB·English

by  Bo Zhang

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CHAOS ANALYSIS
AND CHAOTIC EMI
SUPPRESSION OF
DC-DC CONVERTERS
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CHAOS ANALYSIS
AND CHAOTIC EMI
SUPPRESSION OF
DC-DC CONVERTERS
Bo Zhang and Xuemei Wang
SouthChinaUniversityofTechnology,P.R.China
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Thiseditionfirstpublished2015
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LibraryofCongressCataloging-in-PublicationData
Zhang,Bo,1962-
ChaosanalysisandchaoticEMIsuppressionofDC-DCconverters/BoZhang,XuemeiWang.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-45100-7(hardback)
1.DC-to-DCconverters.2. Electromagneticinterference–Prevention.3. Chaoticbehaviorin
systems. I.Wang,Xuemei(Electricalengineer)II.Title.
TK7872.C8Z4332014
621.31′32–dc23
2014022263
Typesetin11/13ptTimesLTStdbyLaserwordsPrivateLimited,Chennai,India
1 2015
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Contents
AbouttheAuthors xi
Preface xiii
Acknowledgments xv
1 NonlinearModelsandBehaviorsofDC–DCConverters 1
1.1 Introduction 1
1.2 OverviewofPWMDC–DCConverters 2
1.2.1 PrincipleofPulseWidthModulation 2
1.2.2 BasicTopologiesofDC–DCConverters 3
1.2.3 OperationModesofDC–DCConverters 6
1.2.4 State-SpaceModelofDC–DCConverters 7
1.2.5 DiscreteModelofDC–DCConverters 9
1.3 OverviewoftheNonlinearBehaviorofDC–DCConverters 10
1.4 ReviewofBasicDynamicsConcepts 13
1.4.1 DynamicalSystem 14
1.4.2 LinearandNonlinearDynamicalSystems 16
1.4.3 CharacterizationofNonlinearBehavior 18
1.5 Conclusions 24
References 24
2 SymbolicAnalysisoftheNonlinearBehaviorofDC–DC
Converters 27
2.1 Introduction 27
2.2 OverviewoftheTimeSeriesPrincipleofDiscreteSystems 28
2.2.1 SymbolicDynamicsandSymbolicTimeSeries 28
2.2.2 SymbolizationMethod 30
2.2.3 SymbolicDynamicsofaPeriod-DoublingCascade 32
2.3 BlockEntropy 34
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2.4 SymbolicTimeSeriesAnalysisofDC–DCConverters 38
2.4.1 Period-DoublingBifurcationandChaosofDC–DCConverters 39
2.4.2 BorderCollisionBifurcationandChaosofDC–DCConverters 43
2.5 Conclusions 46
References 46
3 ComplexityoftheNonlinearBehaviorofDC–DCConverters 49
3.1 Introduction 49
3.2 Lempel–ZivComplexityandAnalysisofNonlinearBehaviorof
DC–DCConvertersBasedonL–ZComplexity 51
3.2.1 Lempel–ZivComplexity 51
3.2.2 AnalysisofLempel–ZivComplexityofBuckConverter 52
3.3 SwitchingBlockofDC–DCConverters 53
3.4 WeightLempel–ZivComplexityandAnalysisofNonlinearBehaviorof
DC–DCConvertersBasedonWeightL–ZComplexity 56
3.4.1 WeightLempel–ZivComplexity 57
3.4.2 WeightLempel–ZivComplexityofBuckConverter 57
3.4.3 QualitativeAnalysisofBifurcationPhenomenaBasedon
Complexity 58
3.5 DuplicateSymbolicSequenceandComplexity 61
3.5.1 MainSwitchingBlockandMainSymbolicSequence 61
3.5.2 SecondarySwitchingBlockandSecondarySymbolicSequence 61
3.5.3 DuplicateSymbolicSequence 62
3.5.4 AnalysisofBorderCollisionandBifurcationinDC–DC
ConvertersBasedonDuplicateSymbolicSequence 63
3.6 AppliedExample 65
3.7 Conclusions 72
References 72
4 InvariantProbabilityDistributionofDC–DCConverters 75
4.1 Introduction 75
4.2 InvariantProbabilityDistributionofChaoticMap 76
4.3 CalculatingInvariantProbabilityDistributionoftheChaotic
Discrete-TimeMapswithEigenvectorMethod 78
4.4 InvariantProbabilityDistributionoftheChaoticMappingoftheBoost
Converter 79
4.5 ApplicationExamplesofInvariantProbabilityDistribution 82
4.5.1 PowerSpectralDensityoftheInputCurrentinaDC–DC
Converters 83
4.5.2 AverageSwitchingFrequency 86
4.5.3 ParameterDesignwithInvariantProbabilityDistribution 88
4.6 Conclusions 90
References 90
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Contents vii
5 EMIandEMCofSwitchingPowerConverters 93
5.1 Introduction 93
5.2 EMIOriginofElectricCircuits 94
5.3 CharacteristicsofSwitchingProcessesofPowerSemiconductors 94
5.4 OverviewofEMIandEMC 98
5.4.1 BasicPrinciplesofEMI 98
5.4.2 EMCRegulations 99
5.5 EMIofPowerElectronicConverters 101
5.5.1 ParasiticParametersofFlybackConverters 102
5.5.2 PrimaryRectifyingCircuit 104
5.5.3 SwitchingLoop 104
5.6 Conclusions 107
References 107
6 DiscreteSubsystemChaoticPointProcessofDC–DCConverters
andEMISuppression 109
6.1 Introduction 109
6.2 DescriptionofChaoticPointProcessofDC–DCConverters 110
6.2.1 ModelofChaoticPointProcessofDC–DCConverters 110
6.2.2 StatisticalCharacteristicsoftheChaoticPointProcessin
Converter 111
6.3 SpectralQuantificationAnalysisofthePWMPulseProcess 113
6.3.1 SpectralQuantificationAnalysisofthePeriodicPWMPulse 113
6.3.2 SpectralQuantificationAnalysisofPWMChaoticSPSP 118
6.4 Conclusions 121
References 121
7 BasisofSpectralAnalysis 123
7.1 Introduction 123
7.2 SomeConcepts 124
7.3 FourierAnalysisandFourierTransform 125
7.4 SpectralDensity 127
7.4.1 EnergySignalsandPowerSignals 128
7.4.2 EnergySpectralDensity 129
7.4.3 PowerSpectralDensity 130
7.5 AutocorrelationFunctionandPowerSpectralDensity 131
7.6 ClassicPowerSpectrumEstimation 133
7.6.1 Periodogram 133
7.6.2 Bartlett 134
7.6.3 Welch 135
7.6.4 BlackmanandTukeyMethod 136
7.6.5 SummaryofClassicPSDEstimators 137
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7.7 ModernSpectralDensityEstimation 138
7.8 Conclusions 139
References 139
8 DynamicChaosSpectrumofChaoticSwitchingConvertersI:
WaveletMethod 141
8.1 Introduction 141
8.1.1 LackofTimeandFrequencyPositioning 141
8.1.2 LimitationfortheTime-VariantSignals 141
8.1.3 LimitationforResolution 142
8.2 BasicPrincipleofWaveletAnalysis 143
8.3 MultiresolutionAnalysisandOrthogonalWaveletsBasis 146
8.4 WaveletTransformandFilterBank 148
8.5 WaveletAnalysisofChaoticPWM 148
8.5.1 BasicPrincipleofChaoticPWMControl 148
8.5.2 WaveletAnalysis 149
8.5.3 WaveletReconstructionofChaoticPWM 151
8.5.4 Time-FrequencyAnalysisoftheChaoticPWM 158
8.5.5 InformationontheTime–FrequencyImageofP(t) 162
8.6 Conclusions 169
References 169
9 DynamicChaosSpectrumofChaoticSwitchingConvertersII:
PronyMethod 173
9.1 Introduction 173
9.2 PronyMethod 174
9.2.1 BasicPrincipleofPronyMethod 175
9.2.2 ClassicalComputingProcessofPronyAnalysis 178
9.3 EstimatingPSDUsingthePronyMethod 179
9.4 ChaoticSpectralEstimationofDC–DCConvertersBased
onthePronyMethod 182
9.5 Conclusions 186
References 186
10 ChaoticPWMSuppressingEMIofPowerElectronicConverters 189
10.1 Introduction 189
10.2 ThePrincipleofChaoticPWMSuppressingEMI 190
10.2.1 BasicTheoryofFrequencyModulation 190
10.2.2 TheFrequencyCharacteristicsofFixedFrequency
PWMWave 194
10.2.3 FrequencyCharacteristicsofSpreadingFrequency
PWMWave 195
10.2.4 ThePrincipleofChaoticPWMSuppressingEMI 196