Power Electronics

Fundamentals of Power Electronics Robert W. Erickson 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

2

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

3

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

η=

Pout Pin

1

η

1 –1 Ploss = Pin – Pout = Pout η

0.8

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

5

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

6

Chapter 1: Introduction

+ –

Devices available to the circuit designer

DT

Resistors

Capacitors

Fundamentals of Power Electronics

Magnetics

7

T

s s linearswitched-mode mode Semiconductor devices

Chapter 1: Introduction

+ –

Devices available to the circuit designer

DT

Resistors

Capacitors

Magnetics

T

s s linearswitched-mode 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 linearswitched-mode mode Semiconductor devices

Power processing: avoid lossy elements

Fundamentals of Power Electronics

9

Chapter 1: Introduction

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

+ v(t) –

Ideal switch consumes zero power

Fundamentals of Power Electronics

i(t)

10

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

11

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

Vref

R 5Ω

V 50V –

Pin ≈ 1000W

Fundamentals of Power Electronics

–+

Pout = 500W

13

Chapter 1: Introduction

Use of a SPDT switch

I 10A

1

+ Vg 100V

+

2

+ –

vs(t)

R

–

vs(t)

v(t) 50V –

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)

Vg Vs = DVg 0

switch position:

(1 – D) Ts

DTs 1

t

2

1

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

DC component of vs(t) = average value:

Vs = 1 Ts

Ts 0

vs(t) dt = DVg

Fundamentals of Power Electronics

15

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 100V

+ –

+

L

2

vs(t)

C

– Pin ≈ 500W

R

v(t) –

Ploss small

Pout = 500W

•

Choose filter cutoff frequency f0 much smaller than switching frequency fs

•

This circuit is known as the “buck converter”

Fundamentals of Power Electronics

16

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 Vg

1

+ –

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

1

Vg

+ –

vs(t) +

2

– +

v(t)

–

2

1

load

“H-bridge”

vs(t)

t

Fundamentals of Power Electronics

19

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

20

Chapter 1: Introduction

A computer power supply system

regulated dc outputs +

iac(t) vac(t)

Dc-dc converter

Rectifier

– ac line input 85-265Vrms

Fundamentals of Power Electronics

dc link

21

loads

Chapter 1: Introduction

A spacecraft power system

Dissipative shunt regulator + Solar array

vbus – Battery charge/discharge controllers

Dc-dc converter

Dc-dc converter

Payload

Payload

Batteries

Fundamentals of Power Electronics

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Chapter 1: Introduction

A variable-speed ac motor drive system

variable-frequency variable-voltage ac

+ 3øac line 50/60Hz

Rectifier

Inverter vlink –

Ac machine Dc link

Fundamentals of Power Electronics

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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

24

Chapter 1: Introduction

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

Averaged equivalent circuit RL

DTs

1

iL(t)

t

2

0

+

Vg – V L

Vg

+ –

R

–

ΔiL

Predicted efficiency 100%

–V L DTs

V

I

1

iL(DTs)

I iL(0)

D' : 1

D'Ts –V

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

25

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

Gate

iL

iB(t) vB(t)

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

26

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

Fundamentals of Power Electronics

27

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 Gc(s) modulator

dTs Ts

v averaged waveform Ts with ripple neglected

voltage reference vref

vc(t)

δ(t)

actual waveform v(t) including ripple

–+

transistor gate driver

t

t

t

t

Controller

L

Small-signal averaged equivalent circuit

vg(t)

Fundamentals of Power Electronics

+ –

+ –

1:D

Vg – V d(t)

I d(t)

D' : 1 + 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.

Ac and dc equivalent circuit modeling of the discontinuous conduction mode

11.

Current-programmed control

Fundamentals of Power Electronics

29

Chapter 1: Introduction

Part III. Magnetics n1 : n 2

transformer design

iM(t)

i1(t)

the proximity effect

i2(t)

LM R1

R2

–2i 2Φ

layer 2

ik(t)

2i –i Φ

layer 1

Rk

i

d

current density J

: nk

3i

layer 3

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

Fundamentals of Power Electronics

30

Chapter 1: Introduction

Part III. Magnetics

12.

Basic magnetics theory

13.

Filter inductor design

14.

Transformer design

Fundamentals of Power Electronics

31

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

vg(t) multiplier

X

C

v(t)

R

–

– vcontrol(t)

+

D1

ig(t) Rs

PWM va(t)

v (t) +– err Gc(s) vref(t) = kx vg(t) vcontrol(t) compensator

Harmonic amplitude, percent of fundamental

100%

controller

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

32

Chapter 1: Introduction

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

33

Chapter 1: Introduction

Part V. Resonant converters The series resonant converter Q1

Q3

D1

L

D3

C

1:n +

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 0.4 0.3

Dc characteristics

0.5

0.35

0.6

0.2 0.1 0

1

0.5 0.75 1 1.5 2 3.5 5 10 Q = 20

0

1.5

conducting devices:

Q1 Q4 turn off Q1, Q4

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 = f s / f0

Fundamentals of Power Electronics

34

Chapter 1: Introduction

Part V. Resonant converters 19. 20.

Resonant conversion Quasi-resonant converters

Fundamentals of Power Electronics

35

Chapter 1: Introduction