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

ECEN 5807 : Introduction 4

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

ECEN5807, Spring 2007

ECEN 5807 : Introduction 6

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

ECEN 5807 : Introduction 7

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

ECEN 5807 : Introduction 8

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

ECEN 5807 : Introduction 9

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 )

ECEN 5807 : Introduction 10

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

ECEN 5807 : Introduction 11

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

ECEN 5807 : Introduction 12

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

ECEN 5807 : Introduction 13

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%

ECEN 5807 : Introduction 14

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”

ECEN 5807 : Introduction 15

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)

Power Electronics Laboratory Lecture 11

ECEN 4517ECEN 5517

POWER ELECTRONICS AND PHOTOVOLTAIC POWER SYSTEM LABORATORYhttp://ece.colorado.edu/~ecen4517

• Photovoltaic power systems

• Power conversion and control electronics

PVPanel

85 W

Battery

Deep-dischargelead-acid

12 V, 56 A-hr

Inverter

120 V 60 Hz300 W

true sinewave

Charge control

DC-DC converterfor maximum powerpoint tracking and

battery charge profile

ACloads

DC loads

Digital control

Prerequisite: ECEN 4797 or ECEN 5797

Instructor: Prof. Bob Erickson

TAs: Mingyang Wang (Tuesday and Wednesday) and Mark Norris (Thursday).

Power Electronics Laboratory Lecture 12

Experiment 1 Direct Energy Transfer System

• Model PV panel• Investigate direct energy transfer system behavior• Investigate effects of shading• Observe behavior of lead-acid battery

Power Electronics Laboratory Lecture 13

Experiments 2 and 3Maximum Power Point Tracking

• Design and construct dc-dc converter• Employ microcontroller to achieve maximum power point tracking

(MPPT) and battery charge control

Power Electronics Laboratory Lecture 14

Experiments 4 and 5Add Inverter to System

• Build your own inverter system to drive AC loads from your battery• Step up the battery voltage to 200 VDC as needed by inverter• Regulate the 200 VDC with an analog feedback loop• Change the 200 VDC into 120 VAC

Power Electronics Laboratory Lecture 15

Mini-ProjectECEE Expo Competition

• Propose and build an upgrade to your system to improve efficiency, reliability, and energy capture

• Competition during ECEE Expo: capture the most energy with your system outside

Solar PowerCompetition and Expo

Awards given to the stand-alone solar power system demonstrating the highest efficiency and energy capture

Featuring Photovoltaics and

Power Electronics Laboratory

Classes ECEN 4517 and 5517

Thursday 4/30 9 a.m. to noon Herbst Plaza, CU Engr Center

Last year s competition poster