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Fundamentals of Power Electronics Chapter 1: Introduction1

Fundamentals of Power Electronics

Robert W. EricksonUniversity of Colorado, Boulder


Chapter 1: Introduction

1.1. Introduction to power processing

1.2. Some applications of power electronics

1.3. 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 low power loss within converter

Small size and reliable operation is then feasible

Efficiency is a good measure of converter performance 0 0.5 1 1.5

0.2

0.4

0.6

0.8

1

Ploss / Pout

η

η =Pout

Pin

Ploss = Pin – Pout = Pout1η – 1


A high-efficiency converter

A goal of current converter technology is to construct converters of small size 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



DTs Ts


linear-mode

+ –

switched-mode

Signal processing: avoid magnetics



DTs Ts


linear-mode

+ –

switched-mode

Power processing: avoid lossy elements


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 in active region

+– R

5Ω

+

V50V

–

Vg

100V

I10A+ 50V –

Ploss ≈ 500W

Pout = 500WPin ≈ 1000W+–linear amplifier

and base driverVref


Use of a SPDT switch

+– R

+

v(t)50V

–

1

2

+

vs(t)

–

Vg

100V

I10A

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, for removal of switching harmonics:

+– R

+

v(t)

–

1

2

+

vs(t)

–

Vg

100V

i(t)

L

C

Ploss smallPout = 500WPin ≈ 500W

• Choose filter cutoff frequency f0 much smaller than switching frequency fs

• This circuit is known as the “buck converter”


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 switch duty cycles to obtain sinusoidal low-frequency component


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 computer power supply system

vac(t)

iac(t)

Rectifier

dc link

Dc-dcconverter

loads

regulateddc outputs

ac line input85-265Vrms

+

–


A spacecraft power system

Solararray

+

vbus

–

Batteries

Batterycharge/dischargecontrollers

Dc-dcconverter

Payload

Dc-dcconverter

Payload

Dissipativeshunt regulator


A variable-speed ac motor drive system

3øac line

50/60Hz

Rectifier

Dc link

+

vlink

–

Inverter

Ac machine

variable-frequencyvariable-voltage ac


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 mode

Transformer 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-signal averaged equivalent circuit


Part II. Converter dynamics and control

7. Ac modeling

8. Converter transfer functions

9. Controller design

10. Ac and dc equivalent circuit modeling of the discontinuous conduction mode

11. Current-programmed control


Part III. Magnetics

Φ

i

–i

3i

–2i

2i

2Φ

curr

en

td

en

sity 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

Po

t co

re s

ize

4226

3622

2616

2213

1811 1811

2213

2616

n1 : n2

: nk

R1 R2

Rk

i1(t)i2(t)

ik(t)

LM

iM(t)transformer design

transformer size vs. switching frequency

the proximity effect


Part III. Magnetics

12. Basic magnetics theory

13. Filter inductor design

14. 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

Ha

rmo

nic

am

plit

ud

e,

pe

rce

nt

of

fun

da

me

nta

l

THD = 136%Distortion factor = 59%

Pollution of power system by rectifier 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 of the ideal rectifier


Part IV. Modern rectifiers,and power system harmonics

15. Power and harmonics in nonsinusoidal systems

16. Line-commutated rectifiers

17. The ideal rectifier

18. Low harmonic rectifier modeling and control


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 = 20105

3.52

1.51

0.75

0.5

0.35

Q = 0.2

The series resonant converter

Dc characteristics

conductingdevices:

t

Vgvds1(t)

Q1

Q4

D2

D3

turn offQ1, Q4

commutationinterval

X

Zero voltage switching


Part V. Resonant converters

19. Resonant conversion20. Quasi-resonant converters

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