# Chapter 1: Introduction

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1 1.1. Introduction to power processing 1.2. Some applications of power electronics 1.3. Elements of power electronics Summary of the course 2

2 1.1 Introduction to Power Processing Power input Switching converter Power output Control input Dc-dc conversion: Change and control voltage magnitude Ac-dc rectification: Possibly control dc voltage, ac current Dc-ac inversion: Produce sinusoid of controllable magnitude and frequency Ac-ac cycloconversion: Change and control voltage magnitude and frequency 3

3 Control is invariably required Power input Switching converter Power output feedforward Control input Controller feedback reference 4

4 High efficiency is essential 1 η = P out P in η 0.8 P loss = P in P out = P out 1 η 1 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 P loss / P out 5

5 A high-efficiency converter P in Converter P out A goal of current converter technology is to construct converters of small size and weight, which process substantial power at high efficiency 6

6 Devices available to the circuit designer Linearmode Switched-mode Resistors Capacitors Magnetics Semiconductor devices DT s T s 7

7 Devices available to the circuit designer Linearmode Switched-mode Resistors Capacitors Magnetics Semiconductor devices DT s T s Signal processing: avoid magnetics 8

8 Devices available to the circuit designer Linearmode Switched-mode Resistors Capacitors Magnetics Semiconductor devices DT s T s Power processing: avoid lossy elements 9

9 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) i(t) Ideal switch consumes zero power 10

10 A simple dc-dc converter example 100V Dc-dc R converter 5Ω I 10A V 50V Input source: 100V Output load: 50V, 10A, 500W How can this converter be realized? 11

11 Dissipative realization Resistive voltage divider 100V P in = 1000W 50V P loss = 500W R 5Ω I 10A V 50V P out = 500W 12

12 Dissipative realization Series pass regulator: transistor operates in active region 50V I 10A 100V P in 1000W linear amplifier R and base driver 5Ω P loss 500W V ref V 50V P out = 500W 13

13 Use of a SPDT switch 1 I 10 A 100 V 2 v s (t) R v(t) 50 V v s (t) DT s (1 D) T s t switch position: V s = D 14

14 The switch changes the dc voltage level v s (t) V s = D D = switch duty cycle 0 D 1 DT s (1 D) T s t switch position: T s = switching period f s = switching frequency = 1 / T s DC component of v s (t) = average value: V s = 1 T s 0 T s v s (t) dt = D 15

15 Addition of low pass filter Addition of (ideally lossless) L-C low-pass filter, for removal of switching harmonics: 100 V P in 500 W 1 2 v R s (t) C Choose filter cutoff frequency f 0 much smaller than switching frequency f s This circuit is known as the buck converter L P loss small i(t) v(t) P out = 500 W 16

16 Addition of control system for regulation of output voltage Power input Switching converter Load i v g v H(s) Sensor gain δ(t) Transistor gate driver δ Pulse-width modulator v c G c (s) Compensator Error signal v e Hv dt s T s t Reference input v ref 17

17 The boost converter 2 L 1 C R V 5 4 V D

18 A single-phase inverter 1 v s (t) 2 2 v(t) load 1 v s (t) H-bridge t Modulate switch duty cycles to obtain sinusoidal low-frequency component 19

19 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

20 A laptop computer power supply system Inverter Display backlighting v ac (t) i ac (t) Charger PWM Rectifier Buck converter Microprocessor Power management ac line input Vrms Lithium battery Boost converter Disk drive 21

21 Power system of an earth-orbiting spacecraft Dissipative shunt regulator Solar array v bus Battery charge/discharge controllers Dc-dc converter Dc-dc converter Batteries Payload Payload 22

22 An electric vehicle power and drive system ac machine ac machine Inverter Inverter control bus 3øac line 50/60 Hz Battery charger battery v b DC-DC converter µp system controller Low-voltage dc bus Vehicle electronics Inverter Inverter Variable-frequency Variable-voltage ac ac machine ac machine 23

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

24 Part I. Converters in equilibrium Inductor waveforms Averaged equivalent circuit v L (t) V R L D Ron D' V D D' R D D' : 1 DT s D'T s V t I V R switch position: i L (t) I i L (0) V L i L (DT s ) V L 0 DT s T s i L t Predicted efficiency 100% 90% 80% 70% % 0.05 η 50% R L /R = 0.1 Discontinuous conduction mode Transformer isolation 40% 30% 20% 10% 0% D 25

25 Switch realization: semiconductor devices The IGBT collector Switching loss transistor waveforms i A (t) Q r gate v A (t) i L emitter 0 0 t n Gate p n Emitter n p n diode waveforms i L 0 area Q r i B (t) v B (t) 0 t n - minority carrier injection t r p p A (t) = v A i A Collector area ~Q r area ~i L t r t 0 t 1 t 2 t 26

26 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

27 Part II. Converter dynamics and control Closed-loop converter system Averaging the waveforms Power input Switching converter Load gate drive v g (t) v(t) R feedback connection t transistor gate driver δ(t) δ(t) pulse-width modulator v c (t) compensator G c (s) v c voltage reference v ref v actual waveform v(t) including ripple averaged waveform <v(t)> Ts with ripple neglected t dt s T s t t Controller Small-signal averaged equivalent circuit v g (t) Id(t) V L g V d(t) 1 : D D' : 1 Id(t) C v(t) R 28

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

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