Fundamentals Of Power Electronics

Fundamentals of Power ElectronicsSecond editionRobert W. EricksonDragan MaksimovicUniversity of Colorado, BoulderFundamentals of Power Electronics1Chapter 1: Introduction

Chapter 1: Introduction1.1.Introduction to power processing1.2.Some applications of power electronics1.3.Elements of power electronicsSummary of the courseFundamentals of Power Electronics2Chapter 1: Introduction

1.1 Introduction to Power ontrolinputDc-dc conversion:Ac-dc rectification:Dc-ac inversion:Change and control voltage magnitudePossibly control dc voltage, ac currentProduce sinusoid of controllablemagnitude and frequencyAc-ac cycloconversion: Change and control voltage magnitudeand frequencyFundamentals of Power Electronics3Chapter 1: Introduction

Control is invariably damentals of Power Electronics4Chapter 1: Introduction

High efficiency is essential1η PoutPinη0.81 –1Ploss Pin – Pout Pout η0.6High efficiency leads to lowpower loss within converterSmall size and reliable operationis then feasibleEfficiency is a good measure ofconverter performance0.40.200.511.5Ploss / PoutFundamentals of Power Electronics5Chapter 1: Introduction

A high-efficiency converterPinConverterPoutA goal of current converter technology is to construct converters of smallsize and weight, which process substantial power at high efficiencyFundamentals of Power Electronics6Chapter 1: Introduction

–Devices available to the circuit designerDTResistorsCapacitorsFundamentals of Power iconductor devicesChapter 1: Introduction

–Devices available to the circuit eSwitched-modeSemiconductor devicesSignal processing: avoid magneticsFundamentals of Power Electronics8Chapter 1: Introduction

–Devices available to the circuit eSwitched-modeSemiconductor devicesPower processing: avoid lossy elementsFundamentals of Power Electronics9Chapter 1: Introduction

Power loss in an ideal switchSwitch closed:Switch open:v(t) 0 i(t) 0In either event: p(t) v(t) i(t) 0Ideal switch consumes zero powerFundamentals of Power Electronics10i(t)v(t)–Chapter 1: Introduction

A simple dc-dc converter exampleI10A Vg100VDc-dcconverter –R5ΩV50V–Input source: 100VOutput load: 50V, 10A, 500WHow can this converter be realized?Fundamentals of Power Electronics11Chapter 1: Introduction

Dissipative realizationResistive voltage dividerI10A Vg100V – 50V –Ploss 500WR5ΩV50V–Pin 1000WFundamentals of Power ElectronicsPout 500W12Chapter 1: Introduction

Dissipative realizationSeries pass regulator: transistor operates inactive region I10A50V – Vg100V –linear amplifierand base driverPloss 500WPin 1000WFundamentals of Power Electronics– VrefR5ΩV50V–Pout 500W13Chapter 1: Introduction

Use of a SPDT switchI10 A1 Vg100 V 2 –vs(t)R–vs(t)v(t)50 V–VgVs DVgswitchposition:Fundamentals of Power ElectronicsDTs0(1 – D) Tst12114Chapter 1: Introduction

The switch changes the dc voltage levelvs(t)switchposition:VgVs DVgD switch duty cycle0 D 1DTs0(1 – D) TstTs switching period121fs switching frequency 1 / TsDC component of vs(t) average value:Vs 1TsTsvs(t) dt DVg0Fundamentals of Power Electronics15Chapter 1: Introduction

Addition of low pass filterAddition of (ideally lossless) L-C low-pass filter, forremoval of switching harmonics:i(t)1 Vg100 V – L2vs(t)CRv(t)–Pin 500 W–Ploss smallPout 500 W Choose filter cutoff frequency f0 much smaller than switchingfrequency fs This circuit is known as the “buck converter”Fundamentals of Power Electronics16Chapter 1: Introduction

Addition of control systemfor regulation of output voltagePowerinputSwitching converterLoad vg –ivH(s)–Transistorgate driverErrorsignalveδ(t)dTs TsFundamentals of Power Electronics– Pulse-width vc G finputt17Chapter 1: Introduction

The boost converter2 L1Vg ls of Power Electronics18Chapter 1: Introduction

A single-phase invertervs(t)1Vg – 2– v(t)–21load“H-bridge”vs(t)tFundamentals of Power Electronics19Modulate switchduty cycles toobtain sinusoidallow-frequencycomponentChapter 1: Introduction

1.2 Several applications of power electronicsPower levels encountered in high-efficiency converters less than 1 W in battery-operated portable equipment tens, hundreds, or thousands of watts in power supplies forcomputers or office equipment kW to MW in variable-speed motor drives 1000 MW in rectifiers and inverters for utility dc transmissionlinesFundamentals of Power Electronics20Chapter 1: Introduction

A laptop computer power supply erBuckconverterPWMRectifierac line input85–265 VrmsFundamentals of Power essorPowermanagementDiskdriveChapter 1: Introduction

Power system of an earth-orbiting spacecraftDissipativeshunt regulator esFundamentals of Power Electronics22Chapter 1: Introduction

An electric vehicle power and drive systemac machineInverterac machineInvertercontrol busbatteryµPsystemcontroller 3øac lineBatterycharger50/60 HzDC-DCconvertervb–Low-voltagedc busInverterInverterac machineac e-voltage acFundamentals of Power Electronics23Chapter 1: Introduction

1.3 Elements of power electronicsPower electronics incorporates concepts from the fields ofanalog circuitselectronic devicescontrol systemspower systemsmagneticselectric machinesnumerical simulationFundamentals of Power Electronics24Chapter 1: Introduction

Part I. Converters in equilibriumInductor waveformsvL(t)Averaged equivalent circuitRLt–V1iL(t)20 Vg – VLVg –R– iLPredicted efficiency100%–VLDTsVI1iL(DTs)IiL(0)D' : 1D'TsDTsswitchposition:D' RD –Vg – VD' VDD Ron0.00290%0.01Ts80%t0.0270%0.0560%η50%RL/R 0.140%Discontinuous conduction mode30%20%Transformer entals of Power Electronics25Chapter 1: Introduction

Switch realization: semiconductor devicesThe IGBTcollectorSwitching area–Qrn–Vgminority carrierinjectiontrppA(t) vA iAarea QrVgCollectorarea iLVgtrt0Fundamentals of Power Electronics26t1 t2tChapter 1: Introduction

Part I. Converters in equilibrium2. Principles of steady state converter analysis3. Steady-state equivalent circuit modeling, losses, and efficiency4. Switch realization5. The discontinuous conduction mode6. Converter circuitsFundamentals of Power Electronics27Chapter 1: Introduction

Part II. Converter dynamics and controlClosed-loop converter systemPowerinputAveraging the waveformsSwitching converterLoadgatedrive vg(t) -width vc G (s)cmodulatorδ(t)vaveraged waveform v(t) Tswith ripple neglectedvoltagereference vrefvc(t)dTs Tsactual waveform v(t)including ripple– transistorgate t circuit –1:DVg – V d(t)D' : 1 vg(t)Fundamentals of Power Electronics –I d(t)I d(t)Cv(t)R–28Chapter 1: Introduction

Part II. Converter dynamics and control7.Ac modeling8.Converter transfer functions9.Controller design10.Input filter design11.Ac and dc equivalent circuit modeling of the discontinuousconduction mode12.Current-programmed controlFundamentals of Power Electronics29Chapter 1: Introduction

Part III. Magneticsn1 : kdcurrentdensityJ: nki4226Pot core x (T)transformersize 0kHz400kHz500kHz1000kHzSwitching frequencyFundamentals of Power Electronics30Chapter 1: Introduction

Part III. Magnetics13.Basic magnetics theory14.Inductor design15.Transformer designFundamentals of Power Electronics31Chapter 1: Introduction

Part IV. Modern rectifiers,and power system harmonicsPollution of power system byrectifier current harmonicsA low-harmonic rectifier systemboost converteri(t)ig(t) iac(t)vac(t)Lvg(t)Q1–vcontrol(t)vg(t)multiplierX D1Cv(t)R–ig(t)RsPWMva(t)v (t) – errGc(s)vref(t) kx vg(t) vcontrol(t)compensatorcontrollerHarmonic amplitude,percent of fundamental100%100%91%80%THD 136%Distortion factor 59%73%60%iac(t) 52%40%32%19% 15% 15%13% 9%20%0%1357Ideal rectifier (LFR)91113151719Model ofthe idealrectifiervac(t)2p(t) vac / ReRe(vcontrol) v(t)––acinputHarmonic numberi(t)dcoutputvcontrolFundamentals of Power Electronics32Chapter 1: Introduction

Part IV. Modern rectifiers,and power system harmonics16.Power and harmonics in nonsinusoidal systems17.Line-commutated rectifiers18.Pulse-width modulated rectifiersFundamentals of Power Electronics33Chapter 1: Introduction

Part V. Resonant convertersThe series resonant converterQ1LQ3D1C1:nD3 Vg –RQ2–Q4D2VZero voltageswitchingD41vds1(t)Q 0.2Vg0.9Q 0.20.80.35M V / .350.60.7511.523.5510Q 2001.5conductingdevices:Q1Q4turn offQ 1, Q 4X D2D3tcommutationinterval23.5510Q 200.20.40.60.811.21.41.61.82F fs / f0Fundamentals of Power Electronics34Chapter 1: Introduction

Part V. Resonant converters19.20.Resonant conversionSoft switchingFundamentals of Power Electronics35Chapter 1: Introduction

AppendicesRMS values of commonly-observed converter waveformsSimulation of convertersMiddlebrook’s extra element theoremL12Magnetics design tables50 µH2 CCM-DCM1 –528 V20 dB Gvg 1VgOpen loop, d(t) constant–20 dB–60 dB–80 dB5 Hz8R 25 ΩClosed loopvx50 Hz500 Hz5 kHz85 kΩR3C3120 kΩ6vz–vyLM3241.1 nF 12 V5vref –value {LIMIT(0.25 vx, 0.1, 0.9)}fC22.7 nFEpwm50 kHzv–7VM 4 VRR2L 50 µΗfs 100 kΗz–40 dBR111 kΩ4XswitchR 3Ω C340 dBiLOAD3500 µF –A.B.C.D.R447 kΩ5V.nodeset v(3) 15 v(5) 5 v(6) 4.144 v(8) 0.536Fundamentals of Power Electronics36Chapter 1: Introduction

Fundamentals of Power Electronics Chapter 1: Introduction30 Part III. Magnetics Φ i –i 3i –2i 2i 2Φ current density J layer d 1 layer 2 layer 3 0 0.02 0.04 0.06 0.08 0.1 Switching frequency B max (T) 25kHz 50kHz 100kHz 200kHz 250kHz 400kHz 500kHz 1000kHz Pot core size 4226 3622 2616 2213 1811 1811 2213 2616 n 1: n 2: n k R 1 R 2 R k i 1 .