Fundamentals of Power Electronics Chapter 1: Introduction1
Fundamentals of Power Electronics
Robert W. EricksonUniversity of Colorado, Boulder
Fundamentals of Power Electronics Chapter 1: Introduction2
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
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 low power loss within converter
Small size and reliable operation is then feasible
Efficiency is a good measure of converter performance 0 0.5 1 1.5
0.2
0.4
0.6
0.8
1
Ploss / Pout
η
η =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 small size 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
DTs Ts
Resistors Capacitors Magnetics Semiconductor devices
linear-mode
+ –
switched-mode
Signal processing: avoid magnetics
Fundamentals of Power Electronics Chapter 1: Introduction9
Devices available to the circuit designer
DTs Ts
Resistors Capacitors Magnetics Semiconductor devices
linear-mode
+ –
switched-mode
Power processing: avoid lossy elements
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 in active region
+– R
5Ω
+
V50V
–
Vg
100V
I10A+ 50V –
Ploss ≈ 500W
Pout = 500WPin ≈ 1000W+–linear amplifier
and base driverVref
Fundamentals of Power Electronics Chapter 1: Introduction14
Use of a SPDT switch
+– R
+
v(t)50V
–
1
2
+
vs(t)
–
Vg
100V
I10A
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, for removal of switching harmonics:
+– R
+
v(t)
–
1
2
+
vs(t)
–
Vg
100V
i(t)
L
C
Ploss smallPout = 500WPin ≈ 500W
• Choose filter cutoff frequency f0 much smaller than switching frequency fs
• This circuit is known as the “buck converter”
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 switch duty cycles to obtain sinusoidal low-frequency component
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 computer power supply system
vac(t)
iac(t)
Rectifier
dc link
Dc-dcconverter
loads
regulateddc outputs
ac line input85-265Vrms
+
–
Fundamentals of Power Electronics Chapter 1: Introduction22
A spacecraft power system
Solararray
+
vbus
–
Batteries
Batterycharge/dischargecontrollers
Dc-dcconverter
Payload
Dc-dcconverter
Payload
Dissipativeshunt regulator
Fundamentals of Power Electronics Chapter 1: Introduction23
A variable-speed ac motor drive system
3øac line
50/60Hz
Rectifier
Dc link
+
vlink
–
Inverter
Ac machine
variable-frequencyvariable-voltage ac
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 mode
Transformer 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-signal averaged equivalent 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. Ac and dc equivalent circuit modeling of the discontinuous conduction mode
11. Current-programmed control
Fundamentals of Power Electronics Chapter 1: Introduction30
Part III. Magnetics
Φ
i
–i
3i
–2i
2i
2Φ
curr
en
td
en
sity 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
Po
t co
re s
ize
4226
3622
2616
2213
1811 1811
2213
2616
n1 : n2
: nk
R1 R2
Rk
i1(t)i2(t)
ik(t)
LM
iM(t)transformer design
transformer size vs. switching frequency
the proximity effect
Fundamentals of Power Electronics Chapter 1: Introduction31
Part III. Magnetics
12. Basic magnetics theory
13. Filter inductor design
14. 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
Ha
rmo
nic
am
plit
ud
e,
pe
rce
nt
of
fun
da
me
nta
l
THD = 136%Distortion factor = 59%
Pollution of power system by rectifier 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 of the ideal rectifier
Fundamentals of Power Electronics Chapter 1: Introduction33
Part IV. Modern rectifiers,and power system harmonics
15. Power and harmonics in nonsinusoidal systems
16. Line-commutated rectifiers
17. The ideal rectifier
18. Low harmonic rectifier modeling and control
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 = 20105
3.52
1.51
0.75
0.5
0.35
Q = 0.2
The series resonant converter
Dc characteristics
conductingdevices:
t
Vgvds1(t)
Q1
Q4
D2
D3
turn offQ1, Q4
commutationinterval
X
Zero voltage switching
Fundamentals of Power Electronics Chapter 1: Introduction35
Part V. Resonant converters
19. Resonant conversion20. Quasi-resonant converters