Fundamentals of Power Electronics

Fundamentals of Power Electronics Second edition Robert W. Erickson Dragan Maksimovic University of Colorado, Boulder

Fundamentals of Power Electronics

1

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


2


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


3


Control is invariably required

Power input

Switching converter

Power output

Control input feedforward

feedback Controller reference


4


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


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


6


+ –

Devices available to the circuit designer

DT

Resistors

Capacitors


Magnetics

7

T

s s Linearmode Switched-mode Semiconductor devices


+ –


DT

Resistors

Capacitors

Magnetics

T


Signal processing: avoid magnetics


8


+ –


DT

Resistors

Capacitors

Magnetics

T


Power processing: avoid lossy elements


9


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


10

i(t)

v(t) –


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?


11


Dissipative realization

Resistive voltage divider I 10A + Vg 100V

+ –

+

50V –

Ploss = 500W

R 5Ω

V 50V –

Pin = 1000W


Pout = 500W

12


Dissipative realization Series pass regulator: transistor operates in active region +

I 10A

50V –

+ Vg 100V

+ –

linear amplifier and base driver Ploss ≈ 500W

Pin ≈ 1000W


–+

Vref

R 5Ω

V 50V –

Pout = 500W

13


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


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


15


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”


16


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


–+

Pulse-width vc G (s) c modulator Compensator

δ

Sensor gain

Hv

Reference vref input

t

17


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


A single-phase inverter vs(t) 1

Vg

+ –

+

2

– +

v(t)

–

2

1

load

“H-bridge”

vs(t)

t


19

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


20


A laptop computer power supply system

Inverter

iac(t) vac(t)

Display backlighting

Charger Buck converter

PWM Rectifier

ac line input 85–265 Vrms


Boost converter

Lithium battery

21

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


22


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


23


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


24


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


25


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


26

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


27


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)


+ –

I d(t)

I d(t)

C

v(t)

R

–

28


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


29


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


30


Part III. Magnetics

13.

Basic magnetics theory

14.

Inductor design

15.

Transformer design


31


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


32


Part IV. Modern rectifiers, and power system harmonics

16.

Power and harmonics in nonsinusoidal systems

17.

Line-commutated rectifiers

18.

Pulse-width modulated rectifiers


33


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


34


Part V. Resonant converters 19. 20.

Resonant conversion Soft switching


35


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


36
