Fundamentals of Power Electronics Second PDF

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

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

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

Control is invariably required

Power input

Switching converter

Power output

Control input feedforward

feedback Controller reference

High efficiency is essential 1 out

Pin 0.8

Ploss = Pin – Pout = Pout 1 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

Ploss / Pout

1.5

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

+ –

Devices available to the circuit designer

DTs

Resistors

Capacitors

Magnetics

Ts

LinearSwitched-mode mode Semiconductor devices

+ –

Devices available to the circuit designer

DTs

Resistors

Capacitors

Magnetics

Ts

LinearSwitched-mode mode Semiconductor devices

Signal processing: avoid magnetics

+ –

Devices available to the circuit designer

DTs

Resistors

Capacitors

Magnetics

Ts

LinearSwitched-mode mode Semiconductor devices

Power processing: avoid lossy elements

Power loss in an ideal switch

Switch closed: Switch open:

v(t) = 0

+ i(t)

i(t) = 0

In either event: p(t) = v(t) i(t) = 0 Ideal switch consumes zero power

v(t) –

A simple dc-dc converter example I 10A

Vg 100V

+ –

Dc-dc converter

R

V 50V –

Input source: 100V Output load: 50V, 10A, 500W How can this converter be realized?

Dissipative realization Resistive voltage divider I 10A + Vg 100V

+ –

50V –

Ploss = 500W

R

V 50V –

Pin = 1000W

Pout = 500W

Dissipative realization Series pass regulator: transistor operates in active region I 10A

+ 50V –

Vg 100V

+ –

linear amplifier and base driver

–+ Vref

R

V 50V –

Use of a SPDT switch I 10 A

1

+ Vg 100 V

+

2

+ –

R

vs(t) – vs(t)

–

Vg Vs = DVg 0

switch position:

v(t) 50 V

DTs

(1 – D) Ts

t

1

2

1

The switch changes the dc voltage level

vs(t)

Vg Vs = DVg 0

switch position:

DTs

(1 – D) Ts

t

1

2

1

DC component of vs(t) = average value: Vs = 1 Ts

Ts

vs(t) dt = DVg 0

D = switch duty cycle 0≤D≤1 Ts = switching period fs = switching frequency = 1 / Ts

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

–

– P in

Ploss small

v(t)

Pout = 500 W

•

Choose filter cutoff frequency f0 much smaller than switching frequency fs

•

This circuit is known as the “buck converter”

Addition of control system for regulation of output voltage Power input

Switching converter

Load +

+ –

v H(s)

– Transistor

Error signal ve

Pulse-width vc modulator Compensator dTs Ts

t

+ –

vg

i

Reference vref input

Hv

Sensor gain

The boost converter 2

+

L 1

Vg

+ –

C

R

V –

5Vg 4Vg

V

3Vg 2Vg Vg 0 0

0.2

0.4

0.6

D

0.8

1

A single-phase inverter vs(t) 1

Vg

+ –

+

2

– +

v(t)

–

2

1

load

“H-bridge”

vs(t)

t

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

A laptop computer power supply system

i ac(t) vac(t)

ac line input 85–265 Vrms

Inverter

Display backlighting

Buck converter

Microprocessor

Charger PWM Rectifier

Lithium battery

Boost converter

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

An electric vehicle power and drive system ac machine

Inverter

ac machine

Inverter

control bus

battery

µP system controller

+ 3øac line 50/60 Hz

Battery charger

DC-DC converter

vb –

Low-voltage dc bus Inverter

Inverter

ac machine

ac machine

Variable-frequency Variable-voltage ac

Vehicle electronics

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

Part I. Converters in equilibrium Inductor waveforms vL(t)

Averaged equivalent circuit

DTs

t

1

2

0

+

Vg +–

V

I

R

–

1

iL(t) I iL(0)

D' : 1

D'Ts –V

switch position:

D' R D

+ –

Vg – V

D' VD

D Ron

RL

Predicted efficiency Vg – V L

100%

–V L DTs

0.002

90%

0.01

Ts

t

80%

0.02

70%

0.05

60% 50% 40%

Discontinuous conduction mode

30%

Transformer isolation

10%

20%

0% 0

0.1

0.2

0.3

0.4

0.5

D

0.6

0.7

0.8

0.9

1

Switch realization: semiconductor devices iA(t)

The IGBT

collector

Switching loss

transistor waveforms

Qr Vg

gate

vA(t)

iL

0

0

emitter

Emitter

t diode waveforms

iL

iB(t) vB(t)

Gate

0

0 t

n

p

n

n

np

p

area –Qr

n

–Vg

minority carrier injection

tr

p A(t)

= v A iA area ~QrVg

Collector

area ~iLVgtr t0

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

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

–

compensator pulse-width vc Gc (s) modulator

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

Small-signal averaged equivalent circuit

Vg – V d(t)

+ –

1:D

L

D' : 1 +

v g(t)

+ –

I d(t)

I d(t)

C

v(t) –

R

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

Part III. Magnetics n1 : n2

transformer design

iM(t)

i1(t)

i2(t)

the proximity effect

LM R1

R2

3i

layer 3

layer 2

–2i 2i –i

ik(t) layer 1

Rk

current density J

: nk

4226

Pot core size

3622

0.1

2616

2616 2213

2213 1811

0.08 0.06

1811

0.04 0.02 0 25kHz

50kHz

100kHz

200kHz

250kHz

Switching frequency

400kHz

500kHz

1000kHz

Bmax (T)

transformer size vs. switching frequency

d

Part III. Magnetics

13.

Basic magnetics theory

14.

Inductor design

15.

Transformer design

Part IV. Modern rectifiers, and power system harmonics

Pollution of power system by rectifier current harmonics

A low-harmonic rectifier system boost converter ig(t)

i(t) +

iac(t) vac(t)

+

L

vg(t)

D1 Q1

– vcontrol(t)

vg(t) multiplier

X

C

v(t)

R

– ig(t) Rs

PWM va(t)

– verr(t) 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

Harmonic number

15

17

19

Model of the ideal rectifier

vac(t)

2

p(t) = vac / Re Re(vcontrol)

i(t) + v(t) –

– ac input

dc output vcontrol

Part IV. Modern rectifiers, and power system harmonics

16.

Power and harmonics in nonsinusoidal systems

17.

Line-commutated rectifiers

18.

Pulse-width modulated rectifiers

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 2 3.5 5 10 Q = 20

0.2

0.4

0.6

0.8

1

F = fs / f0

1.2

1.4

1.6

1.8

2

conducting devices:

Q1 Q4 turn off Q1, Q4

X D2 D3 commutation interval

t

Part V. Resonant converters 19. 20.

Resonant conversion Soft switching

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

R2 R3

C3

8

7

vx VM = 4 V

50 Hz

6

500 Hz

f

5 kHz

50 kHz

–vy

5

–

–80 dB 5 Hz

C2

+12 V Closed loop

R

v –

–40 dB –60 dB

R1 4

Xswitch

–20 dB

+

C

3

4

0 dB

iLOAD

3

LM324

+

A. B. C. D.

z

Epwm value = {LIMIT(0.25 vx, 0.1, 0.9)} .nodeset v(3)=15 v(5)=5 v(6)=4.144 v(8)=0.536

vref + – 5V

R4

Chapter 2 Principles of Steady-State Converter Analysis

2.1. Introduction 2.2. Inductor volt-second balance, capacitor charge balance, and the small ripple approximation 2.3. Boost converter example 2.4. Cuk converter example 2.5. Estimating the ripple in converters containing twopole low-pass filters 2.6. Summary of key points

2.1 Introduction Buck converter 1

SPDT switch changes dc component

+ Vg

+

2

+ –

R

vs(t) –

Switch output voltage waveform Duty cycle D: 0≤D≤1

complement D′: D′ = 1 - D

vs (t)

–

Vg D'Ts

DTs

0 0 Switch position:

Ts

DTs 1

v(t)

2

t 1

Dc component of switch output voltage vs(t)

Vg area = DTsVg

0

0

DTs

Ts

Fourier analysis: Dc component = average value vs = 1 Ts

Ts

vs(t) dt

0

vs = 1 (DTsVg) = DVg Ts

t

Insertion of low-pass filter to remove switching harmonics and pass only dc component L

1

+ Vg

+

2

+ –

C

vs(t)

R

v(t)

–

–

V

s

= DVg

Vg

0 0

1

D

Three basic dc-dc converters (a) 1

L

1

2

+ –

Vg

C

R

v

M(D)

+

iL (t)

Buck

M(D) = D

0.8 0.6 0.4 0.2

–

0 0

0.2

0.4

0.6

0.8

1

D

(b)

5

2

M(D) = +

iL (t) 1

Vg

4

+ –

C

R

v

M(D)

Boost

L

1 1–D

3 2 1

–

0 0

0.2

0.4

0.6

0.8

1

0.6

0.8

1

D

D

(c)

0

0.2

0.4

0 1

Vg

+ –

+

2

iL (t)

C

R

v

L –

–1

M(D)

Buck-boost

–2 –3 –4 –5

M(D) = – D 1–D...