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Introduction to Power ElectronicsECEN 4797/5797

Robert W. EricksonUniversity of Colorado, Boulder

Fall 2012

Lecture 1: August 27, 2012

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Introduction to Power ElectronicsECEN 4797/5797

�• Instructor: Prof. Bob Erickson�– Ofce: ECOT 356�– Telephone: (303) 492-7003�– Email: rwe@colorado.edu�– Ofce hours: MW 3:00 - 4:00 pm�– Telephone ofce hours: M 3:00 - 4:00 pm

�• Course web site:�– http://ece.colorado.edu/~ecen5797�– Includes lecture slides, handouts, homework

assignments, links to online lecture les�• Textbook:

�– Erickson and Maksimovic, Fundamentals of Power Electronics, second edition, Springer, ISBN 0-7923-7270-0.

�• Prerequisite:�– A 3-4 semester sequence of undergraduate EE circuits and electronics courses

(at Univ. of Colorado: ECEN 3250)

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Coursework in Power Electronicsat the University of Colorado

�• Power electronics courses�– ECEN 4797/5797 (this course): Intro to power electronics (Fall)�– ECEN 5807 Modeling and Control of Power Electronics Systems (Alt

Spring semesters, including S 13)�– ECEN 5817 Resonant and Soft-Switching Techniques in Power

Electronics (Alt Spring semesters, including S 14)�– ECEN 4517/5517 Power Electronics Laboratory (Spring)

�• Professional Certicate in Power Electronics�– ECEN 5797, 5807, and 5817

�• Formats for this course�– On-campus, for senior or graduate credit�– Web-based lectures: recorded with ECHO 360 system, with

viewing through the Flash viewer. For technical help, contact help@cuengineeringonline.colorado.edu (CAETE)

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Grading

�• Homework�– Due at beginning of class on date listed on Lecture Schedule web page�– Submit online via D2L dropbox; late homework not accepted�– Homework counts 50% of grade�– You may speak with others about the homework, but turn in your own work�– Homework and exam problems of additional depth and complexity for

those earning graduate credit; separately graded �• Exams

�– Midterm exam: one-week take-home exam, 17% of grade�– Final exam: ve-day take-home exam, 33% of grade�– See course schedule page for dates�– See course vitals page for details

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Desire-2-Learn (D2L) Site

learn.colorado.edu Log on with your campus IdentiKey

Dropbox for submission of homework and exams• Scan, save as pdf, then upload to the D2L dropbox• For on-campus students: a scanner is available within the SRC• Automatic deadline at beginning of class

A log of your grades for all assignments• When grading is complete, your grade will appear online• Running total of your overall course grade• Grader will post comments and annotations online

Homework solutions• Posted within D2L after submission deadline

Student discussion forum• You can post questions and discussions with your classmates• Normally questions will not be answered by Prof. Erickson• Posting of homework solutions in the forum is prohibited

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Off-campus students

• Viewing of lectures�– Lectures are normally available online by the end of the day of the on-

campus lecture• Assignments

�– Use the D2L site to upload your pdf le: same as for on-campus students�– Generally, by Friday the lectures will nish covering the material needed for

the homework assignment due the following Friday. So you can work the homework over the weekend. Professor Erickson will be available for telephone ofce hours on Monday afternoon, to answer any questions.

�– Check out the D2L student forums�– Due dates are the same as for the on-campus students

• Educational Ofcers�– Not needed

• See course vitals page�– Link to academic calendar for CAETE students, including add/drop

deadlines

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Key dates

• Drop deadlines�– September 12: last day to drop the course and receive full tuition refund, with

no W grade appearing on transcript�– October 10: last day to drop the course without petitioning the Dean s ofce

• Tentative exam dates�– Midterm exam: 1 week take-home exam. Available through D2L on Oct. 19,

due on Oct. 26.�– Final exam: Four day take-home exam. Available through D2L on Dec. 14,

due on Dec. 18.• Grades assigned in May appear on your permanent university

transcript• Campus holidays

�– Labor day: Sept. 3�– Fall break / Thanksgiving holiday: Nov. 19-23

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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

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1.1 Introduction to Power Processing

Dc-dc conversion: Change and control voltage magnitude

Ac-dc rectication: Possibly control dc voltage, ac current

Dc-ac inversion: Produce sinusoid of controllable magnitude and frequency

Ac-ac cycloconversion: Change and control voltage magnitude and frequency

Switchingconverter

Powerinput

Poweroutput

Controlinput

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Control is invariably required

Switchingconverter

Powerinput

Poweroutput

Controlinput

Controller

reference

feedbackfeedforward

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High efciency is essential

High efciency leads to low

power loss within converter

Small size and reliable operation

is then feasible

Efciency is a good measure of

converter performance0 0.5 1 1.5

0.2

0.4

0.6

0.8

1

Ploss

/ Pout

=Pout

Pin

Ploss= P

in�– P

out= P

out

1�– 1

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A high-efciency converter

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

size and weight, which process substantial power at high efciency

ConverterPin P

out

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Devices available to the circuit designer

DTsTs

Resistors Capacitors Magnetics Semiconductor devices

Linear-mode

+ �–

Switched-mode

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Devices available to the circuit designer

Signal processing: avoid magnetics

DTsTs

Resistors Capacitors Magnetics Semiconductor devices

Linear-mode

+ �–

Switched-mode

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Devices available to the circuit designer

Power processing: avoid lossy elements

DTsTs

Resistors Capacitors Magnetics Semiconductor devices

Linear-mode

+ �–

Switched-mode

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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)

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A simple dc-dc converter example

Input source: 100V

Output load: 50V, 10A, 500W

How can this converter be realized?

+�–

R5

+

V50V

�–

Vg

100V

I10A

Dc-dc

converter

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Dissipative realization

Resistive voltage divider

+�–

R5

+

V50V

�–

Vg

100V

I10A

+ 50V �–

Ploss = 500W

Pout = 500WPin = 1000W

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Dissipative realization

Series pass regulator: transistor operates in

active region

+�–

R5

+

V50V

�–

Vg

100V

I10A+ 50V �–

Ploss 500W

Pout = 500WPin 1000W

+�–linear amplifier

and base driverVref

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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

t

switchposition: 1 2 1

Vs = DVg

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The switch changes the dc voltage level

D = switch duty cycle

0 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

t

switchposition: 1 2 1

Vs = DVg

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Addition of low pass lter

Addition of (ideally lossless) L-C low-pass lter, for

removal of switching harmonics:

�• Choose lter cutoff frequency f0 much smaller than switching

frequency 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

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Addition of control systemfor regulation of output voltage

(t)

TsdTs t

+�–

+

v

�–

vg

Switching converterPowerinput

Load

�–+

Compensator

vref

Referenceinput

HvPulse-widthmodulator

vc

Transistorgate driver

Gc(s)

H(s)

ve

Errorsignal

Sensorgain

i

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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

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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

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1.2 Several applications of power electronics

Power levels encountered in high-efciency converters

�• less than 1 W in battery-operated portable equipment

�• tens, hundreds, or thousands of watts in power supplies for computers or ofce equipment

�• kW to MW in variable-speed motor drives

�• 1000 MW in rectiers and inverters for utility dc transmission

lines

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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

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Power system of an earth-orbiting spacecraft

Solararray

+

vbus

�–

Batteries

Batterycharge/discharge

controllers

Dc-dcconverter

Payload

Dc-dcconverter

Payload

Dissipativeshunt regulator

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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

P

systemcontroller

Vehicleelectronics

Low-voltagedc bus

control bus

ac machine ac machine

Inverter

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A standalone photovoltaic power system

The system constructed in ECEN 4517/5517 Power

Electronics and Photovoltaic Systems Laboratory

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1.3 Elements of power electronics

Power electronics incorporates concepts from the elds of

analog circuits

electronic devices

control systems

power systems

magnetics

electric machines

numerical simulation

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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

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 efciency

Discontinuous conduction mode

Transformer isolation

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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

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Part I. Converters in equilibrium

2. Principles of steady state converter analysis

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

4. Switch realization

5. The discontinuous conduction mode

6. Converter circuits

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Part II. Converter dynamics and control

+�–

+

v(t)

�–

vg(t)

Switching converterPowerinput

Load

�–+

R

compensator

Gc(s)

vref

voltagereference

v

feedbackconnection

pulse-widthmodulator

vc

transistorgate driver

(t)

(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

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Part II. Converter dynamics and control

7. Ac modeling

8. Converter transfer functions

9. Controller design

10. Input lter design

11. Ac and dc equivalent circuit modeling of the discontinuous

conduction mode

12. Current-programmed control

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Part III. Magnetics

i

�–i

3i

�–2i

2i

current

density 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

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Part III. Magnetics

13. Basic magnetics theory

14. Inductor design

15. Transformer design