Transcript
Fundamentals of Power Electronics Second edition Robert W. Erickson Dragan Maksimovic University of Colorado, Boulder
Fundamentals of Power Electronics
1
Chapter 1: Introduction
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
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Chapter 1: Introduction
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
Fundamentals of Power Electronics
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Chapter 1: Introduction
Control is invariably required
Power input
Switching converter
Power output
Control input feedforward
feedback Controller reference
Fundamentals of Power Electronics
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Chapter 1: Introduction
High efficiency is essential 1
η=
Pout Pin
η 0.8
1 –1 Ploss = Pin – Pout = Pout η 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
1.5
Ploss / Pout
Fundamentals of Power Electronics
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Chapter 1: Introduction
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
Fundamentals of Power Electronics
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Chapter 1: Introduction
+ –
Devices available to the circuit designer
DT
Resistors
Capacitors
Fundamentals of Power Electronics
Magnetics
7
T
s s Linearmode Switched-mode Semiconductor devices
Chapter 1: Introduction
+ –
Devices available to the circuit designer
DT
Resistors
Capacitors
Magnetics
T
s s Linearmode Switched-mode Semiconductor devices
Signal processing: avoid magnetics
Fundamentals of Power Electronics
8
Chapter 1: Introduction
+ –
Devices available to the circuit designer
DT
Resistors
Capacitors
Magnetics
T
s s Linearmode Switched-mode Semiconductor devices
Power processing: avoid lossy elements
Fundamentals of Power Electronics
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Chapter 1: Introduction
Power loss in an ideal switch
Switch closed: Switch open:
v(t) = 0
+
i(t) = 0
In either event: p(t) = v(t) i(t) = 0 Ideal switch consumes zero power
Fundamentals of Power Electronics
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i(t)
v(t) –
Chapter 1: Introduction
A simple dc-dc converter example I 10A + Vg 100V
Dc-dc converter
+ –
R 5Ω
V 50V –
Input source: 100V Output load: 50V, 10A, 500W How can this converter be realized?
Fundamentals of Power Electronics
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Chapter 1: Introduction
Dissipative realization
Resistive voltage divider I 10A + Vg 100V
+ –
+
50V –
Ploss = 500W
R 5Ω
V 50V –
Pin = 1000W
Fundamentals of Power Electronics
Pout = 500W
12
Chapter 1: Introduction
Dissipative realization Series pass regulator: transistor operates in active region +
I 10A
50V –
+ Vg 100V
+ –
linear amplifier and base driver Ploss ≈ 500W
Pin ≈ 1000W
Fundamentals of Power Electronics
–+
Vref
R 5Ω
V 50V –
Pout = 500W
13
Chapter 1: Introduction
Use of a SPDT switch I 10 A
1
+ Vg 100 V
+
2
+ –
vs(t)
R
– vs(t)
v(t) 50 V –
Vg Vs = DVg
switch position: Fundamentals of Power Electronics
DTs
0 (1 – D) Ts
t
1
2
1
14
Chapter 1: Introduction
The switch changes the dc voltage level
vs(t)
switch position:
Vg Vs = DVg
D = switch duty cycle 0≤D≤1
DTs
0 (1 – D) Ts
t
Ts = switching period
1
2
1
fs = switching frequency = 1 / Ts
DC component of vs(t) = average value: Vs = 1 Ts
Ts
vs(t) dt = DVg 0
Fundamentals of Power Electronics
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Chapter 1: Introduction
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
v(t)
– Pin ≈ 500 W
–
Ploss small
Pout = 500 W
•
Choose filter cutoff frequency f0 much smaller than switching frequency fs
•
This circuit is known as the “buck converter”
Fundamentals of Power Electronics
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Chapter 1: Introduction
Addition of control system for regulation of output voltage Power input
Switching converter
Load +
vg
+ –
i
v H(s)
– Transistor gate driver
Error signal ve
δ(t)
dTs Ts
Fundamentals of Power Electronics
–+
Pulse-width vc G (s) c modulator Compensator
δ
Sensor gain
Hv
Reference vref input
t
17
Chapter 1: Introduction
The boost converter
2
+
L 1
Vg
+ –
C
R
V –
5Vg 4Vg
V
3Vg 2Vg Vg 0 0
0.2
0.4
0.6
0.8
1
D Fundamentals of Power Electronics
18
Chapter 1: Introduction
A single-phase inverter vs(t) 1
Vg
+ –
+
2
– +
v(t)
–
2
1
load
“H-bridge”
vs(t)
t
Fundamentals of Power Electronics
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Modulate switch duty cycles to obtain sinusoidal low-frequency component
Chapter 1: Introduction
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
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Chapter 1: Introduction
A laptop computer power supply system
Inverter
iac(t) vac(t)
Display backlighting
Charger Buck converter
PWM Rectifier
ac line input 85–265 Vrms
Fundamentals of Power Electronics
Boost converter
Lithium battery
21
Microprocessor Power management Disk drive
Chapter 1: Introduction
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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Chapter 1: Introduction
An electric vehicle power and drive system
ac machine
Inverter
ac machine
Inverter
control bus
battery
µP system controller
+ 3øac line
Battery charger
50/60 Hz
DC-DC converter
vb –
Low-voltage dc bus Inverter
Inverter
ac machine
ac machine
Vehicle electronics
Variable-frequency Variable-voltage ac
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Chapter 1: Introduction
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
Fundamentals of Power Electronics
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Chapter 1: Introduction
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%
η
50%
RL/R = 0.1
40%
Discontinuous conduction mode
30% 20%
Transformer isolation
10% 0% 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
D
Fundamentals of Power Electronics
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Chapter 1: Introduction
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
iL
iB(t) vB(t)
Gate
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
Fundamentals of Power Electronics
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t1 t2
t
Chapter 1: Introduction
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
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Chapter 1: Introduction
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
–
δ(t)
compensator pulse-width vc G (s) c modulator
δ(t)
v averaged waveform Ts with ripple neglected
voltage reference vref
vc(t)
dTs Ts
actual waveform v(t) including ripple
–+
transistor gate driver
t
t
t
t
Controller
L
Small-signal averaged equivalent circuit
+ –
1:D
Vg – V d(t)
D' : 1 +
vg(t)
Fundamentals of Power Electronics
+ –
I d(t)
I d(t)
C
v(t)
R
–
28
Chapter 1: Introduction
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
Fundamentals of Power Electronics
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Chapter 1: Introduction
Part III. Magnetics n1 : n2
transformer design
iM(t)
i1(t)
i2(t)
the proximity effect
LM R1
R2
3i
layer 3
–2i 2Φ
layer 2
2i –i
ik(t)
Φ layer 1
Rk
d
current density J
: nk
i
4226
Pot core size
3622
0.1
2616
2616 2213
2213 1811
0.08 0.06
1811
0.04
Bmax (T)
transformer size vs. switching frequency
0.02 0 25kHz
50kHz
100kHz
200kHz
250kHz
400kHz
500kHz
1000kHz
Switching frequency
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Chapter 1: Introduction
Part III. Magnetics
13.
Basic magnetics theory
14.
Inductor design
15.
Transformer design
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Chapter 1: Introduction
Part IV. Modern rectifiers, and power system harmonics Pollution of power system by rectifier current harmonics
A low-harmonic rectifier system boost converter i(t)
ig(t) +
iac(t) vac(t)
L
vg(t)
Q1
– vcontrol(t)
vg(t) multiplier
X
+
D1 C
v(t)
R
– ig(t)
Rs
PWM va(t)
v (t) +– err Gc(s) vref(t) = kx vg(t) vcontrol(t) compensator controller
Harmonic amplitude, percent of fundamental
100%
100% 91%
80%
THD = 136% Distortion factor = 59%
73%
60%
iac(t) +
52%
40%
32% 19% 15% 15% 13% 9%
20% 0% 1
3
5
7
Ideal rectifier (LFR)
9
11
13
15
17
19
Model of the ideal rectifier
vac(t)
2
p(t) = vac / Re Re(vcontrol)
+ v(t) –
– ac input
Harmonic number
i(t)
dc output vcontrol
Fundamentals of Power Electronics
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Chapter 1: Introduction
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
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Chapter 1: Introduction
Part V. Resonant converters The series resonant converter Q1
L
Q3
D1
C
1:n
D3
+ Vg
+ –
R
Q2
–
Q4
D2
V
Zero voltage switching
D4
1
vds1(t)
Q = 0.2
Vg
0.9 Q = 0.2
0.8 0.35
M = V / Vg
0.7
0.75
0.5
0.2 0.1 0
1
0.5
0.4 0.3
Dc characteristics
0.5
0.35
0.6
0.75 1 1.5 2 3.5 5 10 Q = 20
0
1.5
conducting devices:
Q1 Q4 turn off Q 1, Q 4
X D2 D3
t
commutation interval
2 3.5 5 10 Q = 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
F = fs / f0
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Chapter 1: Introduction
Part V. Resonant converters 19. 20.
Resonant conversion Soft switching
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Chapter 1: Introduction
Appendices RMS values of commonly-observed converter waveforms Simulation of converters Middlebrook’s extra element theorem L 1 2 Magnetics design tables 50 µH 2 CCM-DCM1
+ – 5
28 V
20 dB
|| Gvg ||
1
Vg
Open loop, d(t) = constant
–20 dB
–60 dB –80 dB 5 Hz
8
R = 25 Ω
Closed loop
vx
50 Hz
500 Hz
5 kHz
85 kΩ
R3
C3
120 kΩ 6
vz
–vy
LM324
1.1 nF
+12 V 5
vref + –
value = {LIMIT(0.25 vx, 0.1, 0.9)}
f
C2
2.7 nF
Epwm
50 kHz
v –
7
VM = 4 V
R
R2
L = 50 µΗ fs = 100 kΗz
–40 dB
R1 11 kΩ 4
Xswitch
R=3Ω
+
C
3
4
0 dB
iLOAD
3
500 µF
+ –
A. B. C. D.
R4 47 kΩ
5V
.nodeset v(3)=15 v(5)=5 v(6)=4.144 v(8)=0.536
Fundamentals of Power Electronics
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Chapter 1: Introduction
