Lecture 1: August 23, 2010
Introduction to Power Electronics
ECEN 4797/5797
Robert W. Erickson
University of Colorado, Boulder
Fall 2010
1
Introduction to Power Electronics
ECEN 4797/5797
• Instructor: Prof. Bob Erickson
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Office: ECOT 356
Telephone: (303) 492-7003
Email: rwe@colorado.edu
Office hours: Th 2:00 - 3:30 pm, W 3:00 - 4:00 pm
Telephone office 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 files
• 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) 2
Coursework in Power Electronics
at 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 11)
– ECEN 5817 Resonant and Soft-Switching Techniques in Power
Electronics (Alt Spring semesters, including S 12)
– ECEN 4517/5517 Power Electronics Laboratory (Spring)
• Professional Certificate in Power Electronics
– ECEN 5797, 5807, and 5817
• Formats for this course
– On-campus, for senior or graduate credit
– Web-based lectures (visit the CU Anywhere website at http://
caete.colorado.edu/courses/onlineaccessdetails.aspx)
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Grading
• Homework
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Due at beginning of class on date listed on Lecture Schedule web page
Late homework not accepted
Homework counts 50% of grade
You may speak with others about the homework, but turn in your own work
Password-protected solutions on web site
Homework and exam problems of additional depth and complexity for
those earning graduate credit; separately graded • Exams
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Midterm exam: one-week take-home exam, 17% of grade
Final exam: five-day take-home exam, 33% of grade
See course schedule page for dates
See course vitals page for details
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Off-campus students
• Assignment due dates
– One week grace period allowed for all assignments and exams
– Late homework not accepted beyond the one-week grace period
• How to submit your work: mail, email, or fax
– Fax option: ECEE Department fax 303-492-2758. On cover page, clearly direct to
Prof. Erickson.
– Email: send to Prof. Erickson at rwe@colorado.edu
Scan instructions: black-and-white (no grayscale or color!), 200-300 dpi, with all
pages in a single pdf file. Other file/scan formats not accepted.
– Mail: send to: Prof. R. Erickson, ECEE Department, University of Colorado, Boulder
CO 80309-0425. Must be postmarked by due date.
• Exam options
– Send email to Prof. Erickson on your desired start date. Prof. Erickson replies with
exam as email attachment. You fax or email completed exam directly to Prof.
Erickson by due date. No Educational Officer (EO) required.
– Second option: your company EO receives the exam from CAETE, then administers
the exam to you.
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Key dates
• Drop deadlines
– September 8: last day to drop the course and receive full tuition refund, with
no “W” grade appearing on transcript
– October 6: last day to drop the course without petitioning the Deans office
• Tentative exam dates
– Midterm exam: 1 week take-home exam. For on-campus students: handed
out Oct. 22, due in class on Oct. 29. One week grace period allowed for
CAETE students.
– Final exam: Five day take-home exam. For on-campus students: handed out
Dec. 10, due in Prof. Ericksons office on Dec. 15. One week grace period
allowed for CAETE students.
• Grades assigned in December appear on your permanent
university transcript
• Campus holidays
– Labor day: Sept. 6
– Fall break / Thanksgiving holiday: Nov. 22-26
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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
7
1.1 Introduction to Power Processing
Power
input
Switching
converter
Power
output
Control
input
Dc-dc conversion:
Ac-dc rectification:
Dc-ac inversion:
Change and control voltage magnitude
Possibly control dc voltage, ac current
Produce sinusoid of controllable
magnitude and frequency
Ac-ac cycloconversion: Change and control voltage magnitude
and frequency
8
Control is invariably required
Power
input
Switching
converter
Power
output
Control
input
feedforward
feedback
Controller
reference
9
High efficiency is essential
1
=
Pout
Pin
0.8
1 –1
Ploss = Pin – Pout = Pout 0.6
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
0.4
0.2
0
0.5
1
Ploss / Pout
10
1.5
A high-efficiency converter
Pin
Converter
Pout
A goal of current converter technology is to construct converters of small
size and weight, which process substantial power at high efficiency
11
+
–
Devices available to the circuit designer
DT
Resistors
Capacitors
Magnetics
12
T
s
s
Linearmode
Switched-mode
Semiconductor devices
+
–
Devices available to the circuit designer
DT
Resistors
Capacitors
Magnetics
Signal processing: avoid magnetics
13
T
s
s
Linearmode
Switched-mode
Semiconductor devices
+
–
Devices available to the circuit designer
DT
Resistors
Capacitors
Magnetics
Power processing: avoid lossy elements
14
T
s
s
Linearmode
Switched-mode
Semiconductor devices
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
15
v(t)
–
i(t)
A simple dc-dc converter example
I
10A
+
Vg
100V
+
–
Dc-dc
converter
R
5
V
50V
–
Input source: 100V
Output load: 50V, 10A, 500W
How can this converter be realized?
16
Dissipative realization
Resistive voltage divider
I
10A
+
Vg
100V
+
–
+
50V –
Ploss = 500W
R
5
V
50V
–
Pout = 500W
Pin = 1000W
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Dissipative realization
Series pass regulator: transistor operates in
active region
+
I
10A
50V –
+
Vg
100V
+
–
linear amplifier
and base driver
Ploss 500W
–+
Vref
R
5
V
50V
–
Pout = 500W
Pin 1000W
18
Use of a SPDT switch
I
10 A
1
+
+
Vg
100 V
2
+
–
vs(t)
R
–
vs(t)
–
Vg
Vs = DVg
switch
position:
DTs
0
(1 – D) Ts
t
1
2
1
19
v(t)
50 V
The switch changes the dc voltage level
vs(t)
Vg
Vs = DVg
switch
position:
DTs
0
(1 – D) Ts
t
1
2
1
DC component of vs(t) = average value:
Vs = 1
Ts
Ts
vs(t) dt = DVg
0
20
D = switch duty cycle
0 D 1
Ts = switching period
fs = switching frequency
= 1 / Ts
Addition of low pass filter
Addition of (ideally lossless) L-C low-pass filter, for
removal of switching harmonics:
i(t)
1
+
Vg
100 V
+
–
+
L
2
vs(t)
C
R
–
Pin 500 W
v(t)
–
Ploss small
Pout = 500 W
•
Choose filter cutoff frequency f0 much smaller than switching
frequency fs
•
This circuit is known as the “buck converter”
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Addition of control system
for regulation of output voltage
Power
input
Switching converter
Load
+
+
–
v
H(s)
–
Transistor
gate driver
Error
signal
ve
Pulse-width vc G (s)
c
modulator
Compensator
(t)
dTs Ts
–+
vg
i
Reference
vref
input
t
22
Hv
Sensor
gain
The boost converter
2
+
L
Vg
1
+
–
C
R
V
–
5Vg
4Vg
V
3Vg
2Vg
Vg
0
0
0.2
0.4
0.6
D
23
0.8
1
A single-phase inverter
1
Vg
+
–
vs(t)
+
2
–
+
v(t)
–
2
1
load
“H-bridge”
vs(t)
t
24
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
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A laptop computer power supply system
Inverter
iac(t)
vac(t)
ac line input
85–265 Vrms
Display
backlighting
Charger
Buck
converter
PWM
Rectifier
Boost
converter
Lithium
battery
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Microprocessor
Power
management
Disk
drive
Power system of an earth-orbiting spacecraft
Dissipative
shunt regulator
+
Solar
array
vbus
–
Battery
charge/discharge
controllers
Dc-dc
converter
Dc-dc
converter
Payload
Payload
Batteries
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An electric vehicle power and drive system
ac machine
Inverter
ac machine
Inverter
control bus
battery
μP
system
controller
+
3øac line
50/60 Hz
Battery
charger
DC-DC
converter
vb
–
Low-voltage
dc bus
Inverter
Inverter
ac machine
ac machine
Variable-frequency
Variable-voltage ac
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Vehicle
electronics
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 fields of
analog circuits
electronic devices
control systems
power systems
magnetics
electric machines
numerical simulation
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Part I. Converters in equilibrium
Inductor waveforms
vL(t)
Averaged equivalent circuit
RL
t
–V
1
iL(t)
2
0
+
Vg – V
L
Vg
+
–
R
–
iL
Predicted efficiency
100%
–V
L
DTs
V
I
1
iL(DTs)
I
iL(0)
D' : 1
D'Ts
DTs
switch
position:
D' RD
+
–
Vg – V
D' VD
D Ron
0.002
90%
0.01
Ts
80%
t
0.02
70%
0.05
60%
50%
RL/R = 0.1
40%
Discontinuous conduction mode
30%
Transformer isolation
10%
20%
0%
0
0.1
0.2
0.3
0.4
0.5
D
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0.6
0.7
0.8
0.9
1
Switch realization: semiconductor devices
The IGBT
collector
Switching loss
iA(t)
transistor
waveforms
Qr
Vg
gate
iL
vA(t)
0
0
emitter
t
Emitter
diode
waveforms
Gate
iL
iB(t)
vB(t)
0
0
t
n
p
n
n
n-
p
area
–Qr
n
–Vg
minority carrier
injection
tr
p
pA(t)
= vA iA
area
~QrVg
Collector
area
~iLVgtr
t0
32
t1 t2
t
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
33
Part II. Converter dynamics and control
Closed-loop converter system
Power
input
Averaging the waveforms
Switching converter
Load
gate
drive
+
vg(t) +
–
v(t)
R
feedback
connection
–
(t)
compensator
pulse-width vc
Gc(s)
modulator
dTs Ts
v
averaged waveform <v(t)>T
s
with ripple neglected
voltage
reference vref
vc(t)
(t)
actual waveform v(t)
including ripple
–+
transistor
gate driver
t
t
t
t
Controller
L
Small-signal
averaged
equivalent circuit
vg(t)
+
–
+
–
1:D
Vg – V d(t)
I d(t)
D' : 1
+
I d(t)
C
v(t)
–
34
R
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 discontinuous
conduction mode
12.
Current-programmed control
35
Part III. Magnetics
n1 : n2
transformer
design
iM(t)
i1(t)
i2(t)
the
proximity
effect
LM
R1
R2
layer
2
current
density
J
Rk
4226
0.1
2616
2616
2213
2213
1811
0.08
0.06
1811
0.04
0.02
0
50kHz
100kHz
200kHz
250kHz
400kHz
Switching frequency
36
500kHz
1000kHz
Bmax (T)
Pot core size
3622
25kHz
2i
–i
layer
1
transformer
size vs.
switching
frequency
–2i
ik(t)
: nk
3i
layer
3
i
d
Part III. Magnetics
13.
Basic magnetics theory
14.
Inductor design
15.
Transformer design
37