ECEN 5807 Modeling and Control of Power Electronic Systemsecee.colorado.edu/~ecen5807/course_material/Introduction.pdf · ECEN 5807 Modeling and Control of Power Electronic Systems

ECEN 5807 : Introduction 1

ECEN 5807Modeling and Control of Power Electronic Systems

Instructor: Prof. Bob EricksonOffice telephone: (303) 492-7003

Fax: (303) 492-2758

Email: [email protected] web page

http://ece.colorado.edu/~ecen5807

TextbookErickson and Maksimovic, Fundamentals of Power Electronics,

second edition. Springer Science+Business, 2001.ISBN: 0-7923-7270-0http://ece.colorado.edu/~pwrelect/book/SecEd.html

Online course lectureshttp://engineeringonline.colorado.edu/TegrityUtils/

getCourseRSS.asp?courseId=ECEN5807091

ECEN5807, Spring 2007

Power Electronics Program at CU Boulder

ECEN5797Introduction to Power

Electronics

ECEN5807Modeling and Control of PE

Systems

ECEN5817Resonant and Soft-Switching

Techniques in PE

ECEN5517Power Electronics Lab

Fall semesters

Spring semesters

Alternate Spring semesters (2008)

Alternate Spring semesters (2007) Professional Certificate in

Power Electronics


Grading

Homework: 50%

Midterm exam: 17%Final exam: 33%


Required Software

Available to local students in ECE teaching labs (power electronics lab, circuits lab)

Spice simulatorFree version of Pspice or LTspice is sufficient

MATLAB/SimulinkStudent version is sufficientCan be purchased online or through CU Bookstore


Topics

1. Averaged switch modeling and simulation

CCM, DCM, and other examples. Computer simulation

2. Techniques of design-oriented analysis, with switching converter applications

Middlebrook s feedback and extra element theoremsInput filter designWriting complicated transfer functions by inspection

3. Current programmed control of PWM converters

4. Introduction to digital control of PWM converters

5. Rectifiers

• Rectifier harmonics in power systems

• Low harmonic PWM rectifiers and power factor correctors


1. Averaged switch modeling and simulation

Section 7.4, Chapter 11, and Appendix B

This approach has recently become quite popular

Can be applied to a wide variety of converters

We will use it to model CCM, DCM, and current programmed converters

Also useful for incorporating switching loss into ac model of CCM converters

Computer simulation of small-signal transfer functions

Objectives of simulation

PSPICE examples

ECEN5807, Spring 2007


2. Techniques of Design-Oriented Analysis

Chapter 10, Appendix C, and supplementary notes on webNull double injection methods for analysis of complex analog systems

Converter applicationsInput filter designExact analysis of a fifth-order converter system

Middlebrook s extra element theoremHow to easily determine the effect of an extra element on a circuit transfer

function, without starting the analysis all over again

The n extra element theoremHow to write complicated transfer functions by inspection, in rational form

Middlebrook s feedback theoremHow to easily construct the loop gain and closed-loop transfer functions of a

complex feedback circuit


Middlebrook’s Extra Element Theorem

Appendix C

How a given transfer function is modified by addition of an element:

vout(s)vin(s)

= G(s)Z(s)

1 +ZN(s)Z(s)

1 +ZD(s)Z(s)

Simple methods to find ZN(s) and ZD(s)

How to design circuit so that new element doesn t change anything:

Z( j ) > ZN( j )

Z( j ) > ZD( j )

Design oriented result: construct Bode plots of above impedances


Input filter design

• Filter can seriously degrade converter control system behavior

• Use extra element theorem to derive conditions which ensure that converter dynamics are not affected by input filter

• Must design input filter having adequate damping

+–

Inputfilter

Converter

T(s)

Controller

vgZo(s) Zi(s)

H(s)

d

v

f

Gvd Gvd

0˚

– 360˚

– 540˚

0 dB

– 10 dB

20 dB

30 dB

100 Hz

40 dB

1 kHz 10 kHz

– 180˚

10 dB

Gvd

Gvd


Design of damped input filters that don’t degrade converter transfer functions

-20 dB

-10 dB

0 dB

10 dB

20 dB

1 kHz 10 kHz 100 kHz

Section 1alone

Cascadedsections 1 and 2

30 dB

ZN ZD

fo

+–vg

L1

n1L1R1

C1

L2

n2L2R2

C2

6.9 F

31.2 H

15.6 H1.9 0.65 2.9 H

5.8 H

11.7 F

Design criteria derived via Extra Element theorem:

Two-section damped input filter design:

Z( j ) > ZN( j )

Z( j ) > ZD( j )


Write the line-to-output transfer functionby inspection

+–

+–

L

RC

1 : D D' : 1Lf

RfCf

Cb

vg(t) I d(t)

(Vg – V)d (t)

I d(t)

Solution: use n extra element theorem

Example: buck-boost with input filter


3. Current Programmed Control

+–

Buck converter

Current-programmed controller

Rvg(t)

is(t)

+

v(t)

–

iL(t)

Q1

L

CD1

+

–

Analogcomparator

Latch

Ts0

S

R

Q

Clock

is(t)

Rf

Measureswitch

current

is(t)Rf

Controlinput

ic(t)Rf

–+

vref

v(t)Compensator

Conventional output voltage controller

• Chapter 12

• A very popular method for controlling PWM converters

• Transistor turns off when its current is(t) is equal to the control input ic(t)

• Simpler dynamics, more robust compensator

Switchcurrentis(t)

Control signalic(t)

m1

t0 dTs Ts

on offTransistor

status:

Clock turnstransistor on

Comparator turnstransistor off


Effect of current programming on transfer functionsBuck converter example

Gvd

Gvd

f

0˚

–90˚

–180˚

G

–20 dB

–40 dB

0 dB

20 dB

40 dB

10 Hz 100 Hz 10 kHz 100 kHz1 kHz

G

–60 dB

Gvc

Gvc

21

345

CCM-DCM1

+–

+–

35 H

100 F

Vg

12 V

L

C R

vc

+

v

–

iLOAD

CPM

control current 1 2

d

+–

+–

+–

iL RL1 2 3 4

d

Rf iL v(1)–v(3) v(3)

0.05

10

Rf = 1 fs = 200 kHzL = 35 Va = 0.6 V

Xcpm

Xswitch

fs = 200 kHzL = 35

EiE1 E2

Comparison of control-to-output transfer functions

Averaged switch model used in PSPICE simulations

CoPEC

5ECEN5807

Digitally Controlled Buck ConverterSimulink Model

• The buck converterblock is the same as in the continuous-time system

• Note the parts of the system that model the digital controller including:

– A/D converter

– Discrete-time compensator, and

– Digital PWM

Digital PWM

Discrete-time compensator

A/D converter


4. Modern rectifiers, power system harmonics, and low harmonic rectifiers

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%


The Ideal Rectifier

+–

1 : M(D)

Vg R

+

V

–

Re(vcontrol)

+

–

vac(t)

iac(t)

vcontrol

v(t)

i(t)

+

–

p(t) = vac2 / Re

Ideal rectifier (LFR)

acinput

dcoutput

Modeling the basic functions of ideal converters

Dc-dc converter: dc transformer

Ac-dc rectifier: “loss-free resistor”


Controlling a dc-dc converterto behave as an ideal rectifier

1 : M(d(t))

dc-dc converter

controller

d(t)

Rvac(t)

iac(t)+

vg(t)

–

ig(t)

ig

vg

+

v(t)

–

i(t)

C

Controller varies d(t) as necessary, to cause ig(t) to be proportional to vg(t)


Next lecture

Begin with circuit averaging and averaged switch modeling

Assignment: Read Sections 7.4 and 7.5

Documents

ECEN 5807 Modeling and Control of Power Electronic Systemsecee.colorado.edu/~ecen5807/course_material/Introduction.pdf · ECEN 5807 Modeling and Control of Power Electronic Systems