Fundamentals of Power Electronics Chapter 1: Introduction1
Fundamentals of Power ElectronicsSecond edition
Robert W. EricksonDragan Maksimovic
University of Colorado, Boulder
Fundamentals of Power Electronics Chapter 1: Introduction2
Chapter 1: Introduction
1.1. Introduction to power processing1.2. Some applications of power electronics1.3. Elements of power electronics
Summary of the course
Fundamentals of Power Electronics Chapter 1: Introduction3
1.1 Introduction to Power Processing
Dc-dc conversion: Change and control voltage magnitudeAc-dc rectification: Possibly control dc voltage, ac currentDc-ac inversion: Produce sinusoid of controllable
magnitude and frequencyAc-ac cycloconversion: Change and control voltage magnitude
and frequency
Switchingconverter
Powerinput
Poweroutput
Controlinput
Fundamentals of Power Electronics Chapter 1: Introduction4
Control is invariably required
Switchingconverter
Powerinput
Poweroutput
Controlinput
Controller
reference
feedbackfeedforward
Fundamentals of Power Electronics Chapter 1: Introduction5
High efficiency is essential
High efficiency leads to lowpower loss within converter
Small size and reliable operationis then feasible
Efficiency is a good measure ofconverter performance
0 0.5 1 1.5
0.2
0.4
0.6
0.8
1
Ploss / Pout
ηη =Pout
Pin
Ploss = Pin – Pout = Pout1η – 1
Fundamentals of Power Electronics Chapter 1: Introduction6
A high-efficiency converter
A goal of current converter technology is to construct converters of smallsize and weight, which process substantial power at high efficiency
ConverterPin Pout
Fundamentals of Power Electronics Chapter 1: Introduction7
Devices available to the circuit designer
DTs Ts
Resistors Capacitors Magnetics Semiconductor devices
Linear-mode
+ –
Switched-mode
Fundamentals of Power Electronics Chapter 1: Introduction8
Devices available to the circuit designer
Signal processing: avoid magnetics
DTs Ts
Resistors Capacitors Magnetics Semiconductor devices
Linear-mode
+ –
Switched-mode
Fundamentals of Power Electronics Chapter 1: Introduction9
Devices available to the circuit designer
Power processing: avoid lossy elements
DTs Ts
Resistors Capacitors Magnetics Semiconductor devices
Linear-mode
+ –
Switched-mode
Fundamentals of Power Electronics Chapter 1: Introduction10
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)
Fundamentals of Power Electronics Chapter 1: Introduction11
A simple dc-dc converter example
Input source: 100VOutput load: 50V, 10A, 500WHow can this converter be realized?
+– R
5Ω
+
V50V
–
Vg
100V
I10A
Dc-dcconverter
Fundamentals of Power Electronics Chapter 1: Introduction12
Dissipative realization
Resistive voltage divider
+– R
5Ω
+
V50V
–
Vg
100V
I10A
+ 50V –
Ploss = 500W
Pout = 500WPin = 1000W
Fundamentals of Power Electronics Chapter 1: Introduction13
Dissipative realization
Series pass regulator: transistor operates inactive region
+– R
5Ω
+
V50V
–
Vg
100V
I10A+ 50V –
Ploss ≈ 500W
Pout = 500WPin ≈ 1000W
+–linear amplifierand base driver
Vref
Fundamentals of Power Electronics Chapter 1: Introduction14
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
tswitch
position: 1 2 1
Vs = DVg
Fundamentals of Power Electronics Chapter 1: Introduction15
The switch changes the dc voltage level
D = switch duty cycle0 ≤ 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
tswitch
position: 1 2 1
Vs = DVg
Fundamentals of Power Electronics Chapter 1: Introduction16
Addition of low pass filter
Addition of (ideally lossless) L-C low-pass filter, forremoval of switching harmonics:
• Choose filter cutoff frequency f0 much smaller than switchingfrequency 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
Fundamentals of Power Electronics Chapter 1: Introduction17
Addition of control systemfor regulation of output voltage
δ(t)
TsdTs t
+–
+
v
–
vg
Switching converterPowerinput
Load–+
Compensator
vrefReference
input
HvPulse-widthmodulator
vc
Transistorgate driver
δ Gc(s)
H(s)
ve
Errorsignal
Sensorgain
i
Fundamentals of Power Electronics Chapter 1: Introduction18
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
Fundamentals of Power Electronics Chapter 1: Introduction19
A single-phase inverter
1
2
+–
load
+ v(t) –
2
1
Vg
vs(t)
+ –
t
vs(t) “H-bridge”Modulate switchduty cycles toobtain sinusoidallow-frequencycomponent
Fundamentals of Power Electronics Chapter 1: Introduction20
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
Fundamentals of Power Electronics Chapter 1: Introduction21
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
Fundamentals of Power Electronics Chapter 1: Introduction22
Power system of an earth-orbiting spacecraft
Solararray
+
vbus
–
Batteries
Batterycharge/discharge
controllers
Dc-dcconverter
Payload
Dc-dcconverter
Payload
Dissipativeshunt regulator
Fundamentals of Power Electronics Chapter 1: Introduction23
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
µPsystem
controller
VehicleelectronicsLow-voltage
dc bus
control bus
ac machine ac machine
Inverter
Fundamentals of Power Electronics Chapter 1: Introduction24
1.3 Elements of power electronics
Power electronics incorporates concepts from the fields ofanalog circuitselectronic devicescontrol systemspower systemsmagneticselectric machinesnumerical simulation
Fundamentals of Power Electronics Chapter 1: Introduction25
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
η 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 efficiency
Discontinuous conduction modeTransformer isolation
Fundamentals of Power Electronics Chapter 1: Introduction26
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
Fundamentals of Power Electronics Chapter 1: Introduction27
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
Fundamentals of Power Electronics Chapter 1: Introduction28
Part II. Converter dynamics and control
+–
+
v(t)
–
vg(t)
Switching converterPowerinput
Load
–+R
compensator
Gc(s)
vrefvoltage
reference
v
feedbackconnection
pulse-widthmodulator
vc
transistorgate driver
δ(t)
δ(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-signalaveragedequivalent circuit
Fundamentals of Power Electronics Chapter 1: Introduction29
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 discontinuousconduction mode
12. Current-programmed control
Fundamentals of Power Electronics Chapter 1: Introduction30
Part III. Magnetics
Φ
i
–i
3i
–2i
2i
2Φ
curr
ent
dens
ity 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
Pot
cor
e si
ze
4226
3622
2616
2213
1811 1811
2213
2616
n1 : n2
: nk
R1 R2
Rk
i1(t)i2(t)
ik(t)
LM
iM(t)transformerdesign
transformersize vs.switchingfrequency
theproximityeffect
Fundamentals of Power Electronics Chapter 1: Introduction31
Part III. Magnetics
13. Basic magnetics theory
14. Inductor design
15. Transformer design
Fundamentals of Power Electronics Chapter 1: Introduction32
Part IV. Modern rectifiers,and power system harmonics
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%
Pollution of power system byrectifier current harmonics
Re(vcontrol)
+
–
vac(t)
iac(t)
vcontrol
v(t)
i(t)
+
–
p(t) = vac2 / Re
Ideal rectifier (LFR)
acinput
dcoutput
boost converter
controller
Rvac(t)
iac(t)+
vg(t)
–
ig(t)
ig(t)vg(t)
+
v(t)
–
i(t)
Q1
L
C
D1
vcontrol(t)
multiplier X
+–vref(t)
= kx vg(t) vcontrol(t)
Rsva(t)
Gc(s)
PWM
compensator
verr(t)
A low-harmonic rectifier system
Model ofthe idealrectifier
Fundamentals of Power Electronics Chapter 1: Introduction33
Part IV. Modern rectifiers,and power system harmonics
16. Power and harmonics in nonsinusoidal systems
17. Line-commutated rectifiers
18. Pulse-width modulated rectifiers
Fundamentals of Power Electronics Chapter 1: Introduction34
Part V. Resonant converters
L
+–Vg
CQ1
Q2
Q3
Q4
D1
D2
D3
D4
1 : n
R
+
V
–
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
M =
V /
Vg
F = fs / f0
Q = 201053.5
2
1.5
1
0.75
0.5
0.35
Q = 0.2
Q = 2010
53.5
21.5
10.75
0.5
0.35
Q = 0.2
The series resonant converter
Dccharacteristics
conductingdevices:
t
Vgvds1(t)
Q1
Q4
D2
D3
turn offQ1, Q4
commutationinterval
X
Zero voltageswitching
Fundamentals of Power Electronics Chapter 1: Introduction35
Part V. Resonant converters
19. Resonant conversion20. Soft switching
Fundamentals of Power Electronics Chapter 1: Introduction36
Appendices
A. RMS values of commonly-observed converter waveformsB. Simulation of convertersC. Middlebrook’s extra element theoremD. Magnetics design tables
21
345
CC
M-D
CM
1
+–
+
–
+–
C2
50 µH
11 kΩ500 µF
Vg
28 V
L
CR
vref
5 V
+12 V
LM324
R1
R2
R3 C3
R4
85 kΩ
1.1 nF2.7 nF
47 kΩ
120 kΩ
vz
–vyvx
Epwm
VM = 4 V
value = LIMIT(0.25 vx, 0.1, 0.9)
+
v
–
iLOAD1 2 3
4
5678
.nodeset v(3)=15 v(5)=5 v(6)=4.144 v(8)=0.536
XswitchL = 50 µΗfs = 100 kΗz
f
|| Gvg ||
–60 dB
–80 dB
0 dB
20 dB
5 Hz 50 Hz 5 kHz 50 kHz500 Hz
R = 3 Ω
R = 25 Ω
–40 dB
–20 dB
Open loop, d(t) = constant
Closed loop