Fundamentals of Power Electronics...Fundamentals of Power Electronics Chapter 1: Introduction20 1.2...

Fundamentals of Power Electronics Chapter 1: Introduction1

Fundamentals of Power ElectronicsSecond edition

Robert W. EricksonDragan Maksimovic

University of Colorado, Boulder


Chapter 1: Introduction

1.1. Introduction to power processing1.2. Some applications of power electronics1.3. Elements of power electronics

Summary of the course


1.1 Introduction to Power Processing

Dc-dc conversion: Change and control voltage magnitudeAc-dc rectification: Possibly control dc voltage, ac currentDc-ac inversion: Produce sinusoid of controllable

magnitude and frequencyAc-ac cycloconversion: Change and control voltage magnitude

and frequency

Switchingconverter

Powerinput

Poweroutput

Controlinput


Control is invariably required

Switchingconverter

Powerinput

Poweroutput

Controlinput

Controller

reference

feedbackfeedforward


High efficiency is essential

High efficiency leads to lowpower loss within converter

Small size and reliable operationis then feasible

Efficiency is a good measure ofconverter performance

0 0.5 1 1.5

0.2

0.4

0.6

0.8

1

Ploss / Pout

ηη =Pout

Pin

Ploss = Pin – Pout = Pout1η – 1


A high-efficiency converter

A goal of current converter technology is to construct converters of smallsize and weight, which process substantial power at high efficiency

ConverterPin Pout


Devices available to the circuit designer

DTs Ts

Resistors Capacitors Magnetics Semiconductor devices

Linear-mode

+ –

Switched-mode



Signal processing: avoid magnetics

DTs Ts


Linear-mode

+ –

Switched-mode



Power processing: avoid lossy elements

DTs Ts


Linear-mode

+ –

Switched-mode


Power loss in an ideal switch

Switch closed: v(t) = 0

Switch open: i(t) = 0

In either event: p(t) = v(t) i(t) = 0

Ideal switch consumes zero power

+

v(t)

–

i(t)


A simple dc-dc converter example

Input source: 100VOutput load: 50V, 10A, 500WHow can this converter be realized?

+– R

5Ω

+

V50V

–

Vg

100V

I10A

Dc-dcconverter


Dissipative realization

Resistive voltage divider

+– R

5Ω

+

V50V

–

Vg

100V

I10A

+ 50V –

Ploss = 500W

Pout = 500WPin = 1000W


Dissipative realization

Series pass regulator: transistor operates inactive region

+– R

5Ω

+

V50V

–

Vg

100V

I10A+ 50V –

Ploss ≈ 500W

Pout = 500WPin ≈ 1000W

+–linear amplifierand base driver

Vref


Use of a SPDT switch

+– R

+

v(t)50 V

–

1

2

+

vs(t)

–

Vg

100 V

I10 A

vs(t) Vg

DTs (1 – D) Ts

0

tswitch

position: 1 2 1

Vs = DVg


The switch changes the dc voltage level

D = switch duty cycle0 ≤ D ≤ 1

Ts = switching period

fs = switching frequency = 1 / Ts

Vs = 1Ts

vs(t) dt0

Ts

= DVg

DC component of vs(t) = average value:

vs(t) Vg

DTs (1 – D) Ts

0

tswitch

position: 1 2 1

Vs = DVg


Addition of low pass filter

Addition of (ideally lossless) L-C low-pass filter, forremoval of switching harmonics:

• Choose filter cutoff frequency f0 much smaller than switchingfrequency fs

• This circuit is known as the “buck converter”

+– R

+

v(t)

–

1

2

+

vs(t)

–

Vg

100 V

i(t)

L

C

Ploss smallPout = 500 WPin ≈ 500 W


Addition of control systemfor regulation of output voltage

δ(t)

TsdTs t

+–

+

v

–

vg

Switching converterPowerinput

Load–+

Compensator

vrefReference

input

HvPulse-widthmodulator

vc

Transistorgate driver

δ Gc(s)

H(s)

ve

Errorsignal

Sensorgain

i


The boost converter

+–

L

C R

+

V

–

1

2

Vg

D

0 0.2 0.4 0.6 0.8 1

V

5Vg

4Vg

3Vg

2Vg

Vg

0


A single-phase inverter

1

2

+–

load

+ v(t) –

2

1

Vg

vs(t)

+ –

t

vs(t) “H-bridge”Modulate switchduty cycles toobtain sinusoidallow-frequencycomponent


1.2 Several applications of power electronics

Power levels encountered in high-efficiency converters• less than 1 W in battery-operated portable equipment• tens, hundreds, or thousands of watts in power supplies for

computers or office equipment• kW to MW in variable-speed motor drives• 1000 MW in rectifiers and inverters for utility dc transmission

lines


A laptop computer power supply system

vac(t)

iac(t) Charger

PWMRectifier

Lithiumbattery

ac line input85–265 Vrms

Inverter

Buckconverter

Boostconverter

Displaybacklighting

Microprocessor

Powermanagement

Diskdrive


Power system of an earth-orbiting spacecraft

Solararray

+

vbus

–

Batteries

Batterycharge/discharge

controllers

Dc-dcconverter

Payload

Dc-dcconverter

Payload

Dissipativeshunt regulator


An electric vehicle power and drive system

3øac line

50/60 Hz

Batterycharger

battery

+

vb

–

Variable-frequencyVariable-voltage ac

Inverter

ac machine

Inverter

Inverter

ac machine

DC-DCconverter

µPsystem

controller

VehicleelectronicsLow-voltage

dc bus

control bus

ac machine ac machine

Inverter


1.3 Elements of power electronics

Power electronics incorporates concepts from the fields ofanalog circuitselectronic devicescontrol systemspower systemsmagneticselectric machinesnumerical simulation


Part I. Converters in equilibrium

iL(t)

t0 DTs Ts

IiL(0) Vg – V

L

iL(DTs)∆iL

– VL

vL(t)Vg – V

t– V

D'TsDTs

switchposition: 1 2 1

RL

+–Vg

D' RD

+ –

D' VDD Ron

R

+

V

–

I

D' : 1

Inductor waveforms Averaged equivalent circuit

D

η RL/R = 0.1

0.02

0.01

0.05

0.002

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Predicted efficiency

Discontinuous conduction modeTransformer isolation


Switch realization: semiconductor devices

Collector

p

n-

n np p

Emitter

Gate

nn

minority carrierinjection

collector

emitter

gate

The IGBT

t

iL

–Vg

0

iB(t)

vB(t)

area–Qr

0

tr

t

iL

Vg

0

iA(t)

vA(t)

Qr

0

t

area~QrVg

area~iLVgtr

t0 t1 t2

transistorwaveforms

diodewaveforms

pA(t)= vA iA

Switching loss


Part I. Converters in equilibrium

2. Principles of steady state converter analysis

3. Steady-state equivalent circuit modeling, losses, and efficiency

4. Switch realization

5. The discontinuous conduction mode

6. Converter circuits


Part II. Converter dynamics and control

+–

+

v(t)

–

vg(t)

Switching converterPowerinput

Load

–+R

compensator

Gc(s)

vrefvoltage

reference

v

feedbackconnection

pulse-widthmodulator

vc

transistorgate driver

δ(t)

δ(t)

TsdTs t t

vc(t)

Controller

t

t

gatedrive

actual waveform v(t)including ripple

averaged waveform <v(t)>Tswith ripple neglected

+– I d(t)vg(t)

+–

LVg – V d(t)

+

v(t)

–

RCI d(t)

1 : D D' : 1

Closed-loop converter system Averaging the waveforms

Small-signalaveragedequivalent circuit


Part II. Converter dynamics and control

7. Ac modeling

8. Converter transfer functions

9. Controller design

10. Input filter design

11. Ac and dc equivalent circuit modeling of the discontinuousconduction mode

12. Current-programmed control


Part III. Magnetics

Φ

i

–i

3i

–2i

2i

2Φ

curr

ent

dens

ity J

dlayer1

layer2

layer3

0

0.02

0.04

0.06

0.08

0.1

Switching frequency

Bm

ax (T)

25kHz 50kHz 100kHz 200kHz 250kHz 400kHz 500kHz 1000kHz

Pot

cor

e si

ze

4226

3622

2616

2213

1811 1811

2213

2616

n1 : n2

: nk

R1 R2

Rk

i1(t)i2(t)

ik(t)

LM

iM(t)transformerdesign

transformersize vs.switchingfrequency

theproximityeffect


Part III. Magnetics

13. Basic magnetics theory

14. Inductor design

15. Transformer design


Part IV. Modern rectifiers,and power system harmonics

100%91%

73%

52%

32%

19% 15% 15% 13% 9%

0%

20%

40%

60%

80%

100%

1 3 5 7 9 11 13 15 17 19

Harmonic number

Har

mon

ic a

mpl

itud

e,pe

rcen

t of f

unda

men

tal

THD = 136%Distortion factor = 59%

Pollution of power system byrectifier current harmonics

Re(vcontrol)

+

–

vac(t)

iac(t)

vcontrol

v(t)

i(t)

+

–

p(t) = vac2 / Re

Ideal rectifier (LFR)

acinput

dcoutput

boost converter

controller

Rvac(t)

iac(t)+

vg(t)

–

ig(t)

ig(t)vg(t)

+

v(t)

–

i(t)

Q1

L

C

D1

vcontrol(t)

multiplier X

+–vref(t)

= kx vg(t) vcontrol(t)

Rsva(t)

Gc(s)

PWM

compensator

verr(t)

A low-harmonic rectifier system

Model ofthe idealrectifier


Part IV. Modern rectifiers,and power system harmonics

16. Power and harmonics in nonsinusoidal systems

17. Line-commutated rectifiers

18. Pulse-width modulated rectifiers


Part V. Resonant converters

L

+–Vg

CQ1

Q2

Q3

Q4

D1

D2

D3

D4

1 : n

R

+

V

–

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

M =

V /

Vg

F = fs / f0

Q = 201053.5

2

1.5

1

0.75

0.5

0.35

Q = 0.2

Q = 2010

53.5

21.5

10.75

0.5

0.35

Q = 0.2

The series resonant converter

Dccharacteristics

conductingdevices:

t

Vgvds1(t)

Q1

Q4

D2

D3

turn offQ1, Q4

commutationinterval

X

Zero voltageswitching


Part V. Resonant converters

19. Resonant conversion20. Soft switching


Appendices

A. RMS values of commonly-observed converter waveformsB. Simulation of convertersC. Middlebrook’s extra element theoremD. Magnetics design tables

21

345

CC

M-D

CM

1

+–

+

–

+–

C2

50 µH

11 kΩ500 µF

Vg

28 V

L

CR

vref

5 V

+12 V

LM324

R1

R2

R3 C3

R4

85 kΩ

1.1 nF2.7 nF

47 kΩ

120 kΩ

vz

–vyvx

Epwm

VM = 4 V

value = LIMIT(0.25 vx, 0.1, 0.9)

+

v

–

iLOAD1 2 3

4

5678

.nodeset v(3)=15 v(5)=5 v(6)=4.144 v(8)=0.536

XswitchL = 50 µΗfs = 100 kΗz

f

|| Gvg ||

–60 dB

–80 dB

0 dB

20 dB

5 Hz 50 Hz 5 kHz 50 kHz500 Hz

R = 3 Ω

R = 25 Ω

–40 dB

–20 dB

Open loop, d(t) = constant

Closed loop

Fundamentals of Power Electronics...Fundamentals of Power Electronics Chapter 1: Introduction20 1.2...

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