Lecture 1: introduction

Lecture 1: introduction
R. W. Erickson Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder ECEN 5807!
Modeling and Control of Power Electronics Systems
Instructor: Robert Erickson
• 
• 
• 
Offices: ECOT 356, ECEE 1B55
Email: [email protected]
Office hours:
Course web site:
• 
• 
http://ecee.colorado.edu/~ecen5807
Announcements, course materials, assignments
D2L course site
• 
• 
Log into https://learn.colorado.edu with your identikey
Course lectures, submission of assignments, solutions, grades, discussion forum
Textbook:
• 
ECEN 5807, Spring 2015
Erickson and Maksimovic, Fundamentals of Power Electronics, 2nd edition
1
Power Electronics Courses at the University of Colorado, Boulder
undergraduate
ECEN 3250
Circuits 3
ECEN 2260
Circuits 2
ECEN 2250
Circuits 1
graduate
ECEN 4797/5797
Intro to Power Electr.
ECEN 4517/5517
Power Electronics Lab
ECEN 4827/5827
Analog IC Design
ECEN3170
Energy Conversion
ECEN 4167/5737
Energy Conversion 2
Prerequisite for either ECEN 5807 or ECEN 5817: ECEN 5797
2
Professional
certificate in
power electronics
ECEN 5817
Res. and Soft-Sw. Tech
ECEN 5837
Mixed-Signal IC Design
ECEN 5737
AC Drives
ECEN 5017
Pwr Elect for Electric
Drive Vehicles
Coursera (MOOC): Introduction to Power Electronics
ECEN 5807, Spring 2015
ECEN 5807
Modeling and Control of
Power Electronics
Systems
Power management
Graduate
certificate in
electric drivetrain
technology
Assignments
Weekly homework sets, 50% of total grade
Midterm exam (open book/notes, take home), 17% of grade
Final exam (comprehensive, open book/notes, take home), 33% of grade
All assignments and due dates will be posted on course web site
You must scan your homework or exam into a pdf
•
•
•
•
Black-and-white, no color or grayscale
200-400 dpi is sufficient
Upload a single pdf file to the Dropbox in D2L
Due dates are typically at the start of Friday lecture; no late assignments will be accepted and the Dropbox will
close automatically
Due date and time for CAETE students and on-campus students are the same
ECEN 5807, Spring 2015
3
Required Software
A version of Spice
•  You can download LTSpice for free. See course Vitals page for a link
•  Examples in class will use LTSpice. PSpice files will also be linked on website.
MATLAB/Simulink
•  Available in most department labs
•  You can buy the student version from Mathworks
•  We will use: Matlab, Simulink, and the Control Systems Toolbox. The student version of Matlab includes all of
these and much more.
ECEN 5807, Spring 2015
4
Topics
1.  Simulation and averaged switch modeling
•  CCM, DCM, and other examples
•  Simulation
2.  Techniques of design-oriented analysis, with application to switched-mode converter systems
•  Middlebrook’s feedback and extra-element theorems
•  Input filter design
•  Writing complex transfer function expressions 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 rectifiers and power factor correction converters
ECEN 5807, Spring 2015
5
1. Simulation and Averaged Switch Modeling
•  Additional notes, Section 7.4, Chapter 11, and Appendix B
•  Averaged switch modeling is another approach to derive the averaged model of a PWM
converter.
• 
Well suited to Spice modeling of PWM converters
• 
We will use this approach to model CCM, DCM, and current-programmed converters
• 
Also useful for incorporation of ac losses (switching loss, core loss) into averaged models of PWM converters
•  Computer simulation of small-signal transfer functions
• 
• 
• 
ECEN 5807, Spring 2015
Objectives of simulation
Spice models
Simulink models
6
Averaged Switch Modeling and Simulation
ECEN 5807, Spring 2015
7
2. Techniques of Design-Oriented Analysis
Chapter 10, Appendix C, and supplementary notes on website
Null double injection methods for analysis of complex analog systems
• 
Converter applications
Input filter design
Exact analysis of a fifth-order converter system
• 
Middlebrook’s extra element theorem
How to easily determine the effect of an added element on a circuit transfer function, without starting the analysis
all over again
• 
The n extra element theorem
How to write complicated transfer functions by inspection, in rational form
• 
Middlebrook’s feedback theorem
How to easily construct the loop gain and transfer functions of a complex feedback circuit
ECEN 5807, Spring 2015
8
Q1
Q1
Q1
Q1
Now multiply
out and average over one period:
0 = VQ1 IQ1 + hṽQ1 (t)ĩQ1 (t)i
0 = VQ1 IQ1 + hṽQ1 (t)ĩQ1 (t)i
nd average over one period:
The transistor “consumes”
at DC,Theorem
Middlebrook’s
Extra power
Element
)ĩQ1 (t)i
The transistor
“consumes”power
poweratatthe
DC,switching
and “generates”
and “generates”
power
the switching
frequency.
The at
transistor
functions as an
nsumes” power at DC, frequency.inverter.
The transistor functions as an
Appendix
C inverter. V I = hṽ (t)ĩ (t)i
ower at the
switching
Q1 Q1
Q1
Q1
nsistor functions
as an Vfunction
How a transfer
modified
hṽQ1is(t)
ĩQ1 (t)i by addition of an extra element Z(s):
Q1 IQ1 = G(s)
0
1
Z
(s)
N
BBB 1 +
CCC
!
(t)i
0
1
Q1
BBB
CCC
ZN (s)
vout (s)
Z(s)
B
C
BBB CC
CCC
! BBB 1 +
= G(s)
CCC ZD (s) CC
B
B
vout (s)
B
Z(s)
v
(s)
B
Z(s)!1
[email protected] 1 CC+
CA
in
BBB
0
1
=
G(s)
C
ZN (s) C
BB
CCC Z(s)
B
Z
(s)
vin (s)
D
CCC
Z(s)!1 B
! BBB 1 +
@1 +
A
BBB
Z(s) CCC
Z(s)
BBB
CCC
D (s) C
!1 B
[email protected] 1 + ZSimple
CA methods to find ZN(s) and ZD(s) using null double injection
Z(s) to design circuits so that the extra element doesn’t significantly change G(s):
How
k
kZ( j!)k
kZN ( j!)k
kZ( j!)k
kZD ( j!)k
kZ( j!)k
kZD ( j!)k
Design-oriented result: construct Bode plots of above equations, and use to shape Z(s)
ECEN 5807, Spring 2015
9
Input filter design
Input
filter
design
Input Filter Design
Gvd
H(s)
H(s)
vg
vg +
–
+
–
Input
filter
Input
filter
Gvd
Zo(s)
Zo(s)
Zi(s)
Zi(s)
40 dB
40 dB
30 dB
30 dB
20 dB
Converter
v
Converter
v
T(s)
Gvd
Gvd
Gvd
20 dB
10 dB
10 dB
0 dB
0 dB
– 10 dB
d
Gvd
Gvd
0˚
Gvd
0˚
– 180˚
– 10 dB
– 180˚
– 360˚
T(s)
Controller
d
Controller
100 Hz
1 kHz
f
100 Hz
1 kHz
• Filter
canseriously
seriously
degrade
control system behavior f
•  Input
filter can
degrade
controlconverter
system
and cause
instability
• behavior
Filter can
seriously
degrade converter control system behavior
– 360˚
– 540˚
10 kHz
– 540˚
10 kHz
• Use extra element theorem to derive conditions which ensure that converter
•  Usedynamics
Extra Element
derive conditions
ensure that input filter does not disrupt dynamics of
areTheorem
not affected
by inputthat
filter
• control
Use system
extra element theorem to derive conditions which ensure that converter
arefilter
not
affected
by input
filter damping
•dynamics
Must
design
input
filter
having
adequate
•  Must
design
input
having
adequate
damping
10
• Must design input filter having adequate
damping
ECEN 5807, Spring 2015
degrade converter transfer functions
Design of Input Filters that Do Not Degrade Converter Transfer Functions
Design criteria derived via Extra
Element
Design
criteriatheorem:
derived via Extra Element
Two-section damped input filter
design: damped input filter design:
Two-section
Theorem:
30 dB
ZD
ZN
R2
n2 L 2
0.65
2.9 H
R1
1.9
n1L1
15.6 H
20 dB
fo
10 dB
L2 5.8 H
Cascaded
sections 1 and 2
vg +
–
Section 1
alone
L1 31.2 H
C2
11.7 F
0 dB
-10 dB
Z( j ) > Z N ( j )
-20 dB
1 kHz
ECEN 5807 : Introduction
ECEN 5807, Spring 2015
10 kHz
100 kHz
9
11
Z( j ) > Z D( j )
C1
6.9 F
Write the line-to-output transfer function
by inspection
Write the line-to-output
transfer function by inspection
Example: buck-boost with input filter
Example: buck-boost with input filter
Lf
1:D
(V g – V)d (t)
D' : 1
+
–
vg (t) +
–
L
Rf
Cf
I d(t)
I d(t)
Cb
Solution: use n extra element theorem
Solution: use n extra element theorem
ECEN 5807, Spring 2015
12
10
C
R
• Chapter 12
iL(t)
+
Q1
• Control
A very
popular method for
3. Current3.Programmed
Current-Programmed
Control
v(t)
C
D1
Buck converter
L
turns off when its
•  Chapter 12
current
i
(t)
is
equal
to
the
s
•
A
very
popular
method
for
•  A very popular method for controlling PWM converters
controlling
converters
control
(t) is(t) is equal to a
•  Transistor
turnsPWM
offinput
when
itsiccurrent
Q1
vg(t) +
–
Clock
Rf
0
Measure
switch
current
v(t)
C
D1
signal ic(s)
•control
Transistor
turns off when its
• Simpler
dynamics,
more
•  Simpler
dynamics,
more
robust
compensator
current is(t) is equal to the
robust
control
input icompensator
c(t)
S Q
is(t)
+
Rf –
Clock
R
0
Analog
is(t)Rf comparator
• Simpler dynamics,
robust compensator
Latch
S Q
R
Current-programmed controller
Analog
comparator
ic(t)Rf
Control signal
more
ic(t)
Ts
+
–
m1
Latch
Current-programmed controller
Compensator
Compensator
vref
m1
Switch
current
is(t)
0
v(t)
Transistor
0
status:
Transistor
status:
vref
on
Clock turns
Conventional
output voltage
controller
Conventional
output voltage
controller
ECEN
5807
: Introduction
ECEN
5807, Spring
2015
ntroduction
Control signal
Switch
ic(t)
current
is(t)
v(t)
+
–
Control
input
R
–
Ts
+
–
(t)Rf
• Transistor
• Chapter
12
iL(t)
+
is(t)
(t)Rf
controlling PWM converters
R
–
is(t)
ure
tch
ent
ntrol
input
L
is(t)
dTs
dTs
Ts
on
off
Comparator turns
off
Clock turns
Comparator turns
transistor
on off transistor
transistor on
transistor
11
11
13
Ts
off
t
t
Buck converter example
Effect of current programming on converter transfer functions!
Buck converter example
Comparison of control-to-output
Comparison
of control-to-output transfer functions
transfer functions
Averaged switch model used in
Averaged
model used in spice simulations
PSPICEswitch
simulations
40 dB
1
G
G
+
–
12 V
Gvc
5
0 dB
2 CCM-DCM1
Vg
Gvd
3 iL
35 H
1
20 dB
L
2
4 iLOAD
RL
+
0.05
100 F
fs = 200 kHz
L = 35
–
3
4
d
Gvd
0˚
CPM
–90˚
Gvc
10 Hz
100 Hz
1 kHz
10 kHz
–180˚
100 kHz
f
ECEN 5807, Spring 2015
Xcpm
d
–60 dB
14
control
current
Rf iL
vc
+
–
Ei
1
2
v(1)–v(3)
+
E1 +
–
–
v(3)
E2 +
–
v
10
–20 dB
–40 dB
R
C
Xswitch
Rf = 1
fs = 200 kHz
L = 35
Va = 0.6 V
Digitally Controlled Buck Converter!
Digitally Controlled
BuckModel
Converter
Simulink
Simulink Model
CoPEC
• The
buckconverter
converter
•  Buck
block is same as in
continuous-time
block
is the same assystem
in•  the
continuousNote
the parts of the system that model
digital controller, including:
timethesystem
•  A/D
converter
• Note the
parts
of the
system•  that
model compensator
Discrete-time
the digital
controller
•  Digital
PWM
including:
– A/D converter
– Discrete-time
compensator, and
– Digital PWM
Digital PWM
A/D converter
Discrete-time
compensator
ECEN 5807, Spring 2015
15
5
odern rectifiers,
power
system
harmonics,
4. Modern
Rectifiers,
Power
System Harmonics, and LowHarmonic Rectifiers
and low harmonic rectifiers
•  The traditional peak-detection rectifier injects
very large harmonic currents into the ac
power line.
•  At substantial power levels, this type of
rectifier is not allowed
Harmonic amplitude,
percent of fundamental
100%
100%
91%
80%
THD = 136%
Distortion factor = 59%
73%
60%
52%
40%
32%
19% 15% 15%
13% 9%
20%
0%
1
3
5
7
9
11
13
15
17
19
Harmonic number
ECEN 5807, Spring 2015
16
The Ideal Rectifier
The Ideal Rectifier
Modeling
the basic
Modeling
the basic functions
of idealfunctions
converters
of ideal converters
DC-DC
Dc-dcconverter:
converter:
AC-DC
Ac-dcrectifier:
rectifier:
DCtransformer
transformer
dc
“Loss-free resistor”
iac(t)
1 : M(D)
Vg
+
–
R
+
+
V
vac(t)
–
–
Ideal rectifier (LFR)
2
p(t) = vac / Re
Re(vcontrol)
+
v(t)
dc
output
vcontrol
17
i(t)
–
ac
input
ECEN 5807, Spring 2015
“loss-free resistor”
Controlling a dc-dc converter
to
behave
as
an
ideal
rectifier
Controlling a DC-DC Converter to Behave as an Ideal Rectifier
dc-dc converter
ig(t)
1 : M(d(t))
+
iac(t)
vac(t)
i(t)
+
vg(t)
v(t)
–
–
d(t)
ig
controller
vg
Controller varies d(t) as necessary, to cause ig(t) to be proportional to vg(t)
Controller varies d(t) as necessary, to cause ig(t) to
be proportional to vg(t)
ECEN 5807, Spring 2015
18
C
R
Next Lecture
Begin with circuit averaging and averaged switch modeling
Assignment: read Sections 7.4 and 7.5
ECEN 5807, Spring 2015
19
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertisement