EE152 Green Electronics

Introduction Periodic Steady State Analysis

9/24/13

Prof. William Dally Computer Systems Laboratory

Stanford University

Today’s Agenda •  Course Logistics •  Why “Green Electronics” •  Periodic Steady-State Analysis

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About the Course •  Philosophy

–  Engineering to benefit society –  Learn Engineering Thinking and Engineering Methods –  Hands-on – learn by doing

•  7 Labs + Project •  6 HW Assignments •  2 Midterms

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Course at a Glance HW   Lab  

Lecture   Date   Topic   out   in   out   in   Lab  Descrip3on   Homework  Descrip3on  1   24-‐Sep  Introduc3on  to  Green  Electronics   1   1   Introduc3on  to  AVR  Microcontroller  2   26-‐Sep  Real-‐3me  embedded  soFware  

3   1-‐Oct  Boost,  Buck,  and  periodic  steady  state  analysis   2   1   2   1  AC  energy  meter   Periodic  Steady  State  

4   3-‐Oct  Power  MOSFETs,  SPICE  simula3on  5   8-‐Oct  Motors  and  Modeling   3   2   3   2  Motor  control  -‐  Matlab   Motor  Calcula3ons  6   10-‐Oct  Feedback  Control  7   15-‐Oct  Review  for  Midterm   3   4   3  Motor  control  -‐  Lab  8   17-‐Oct  PV  Cells,  Op3miza3on,  Finding  Peak  Power  

MT   17-‐Oct  Midterm  1  -‐  in  evening  9   22-‐Oct  Magne3cs   4   5   4  PV  power-‐point  tracker   Feedback  

10   24-‐Oct  Transformers  and  bridge  converters  11   29-‐Oct  Grounding  and  debugging   5   4   6   5  Power  supply  part  1/Project  Proposal  Magne3cs  design  12   31-‐Oct  Solar  Day  -‐  costumes  op3onal  13   5-‐Nov  Inverters   6   5   7   6  Power  supply  part  2   Bridge  converter  14   7-‐Nov  SoF  switching  15   12-‐Nov  Review  for  Midterm   6   P   7  Project  16   14-‐Nov  Guest  Lecture  1  MT   14-‐Nov  Midterm  2  17   19-‐Nov  Guest  Lecture  2   C1  18   21-‐Nov  Guest  Lecture  3  19   3-‐Dec  Wrapup  Lecture   C2  20   5-‐Dec  Project  Presenta3ons   P  Project  Report  Due  -‐  Website  

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Grading

6 Homeworks 15% 7 Labs 20% 2 Midterms 30% 1 Project 30% Participation 5%

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Collaboration •  May collaborate in groups of up to 4 on homework

assignments –  Turn in one assignment for the group. –  Give attribution for any outside assistance

•  Labs to be done in assigned groups of 2

•  Projects may be done in groups of up to 4

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Labs •  One lab each week

–  Assigned on Tuesday (9/24 for Lab 1) –  Must be demonstrated and signed off during your lab

session the following week •  Groups of two

–  If you have a partner lined up, put it on your lab sheet •  Lab will be open 7-10 several nights per week

–  Write down what evenings you are available –  We will assign you one evening for your checkoff

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Labs •  Introduction to AVR Microcontroller •  AC energy meter •  Motor control - Matlab •  Motor control - Lab •  PV power-point tracker •  Power Supply SPICE •  Power Supply Lab

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Project •  Proposal assigned Oct 29 (in parallel with lab 6) •  Project starts Nov 12 (after lab 7) •  Due December 5 •  Weekly checkpoints •  Significant investigation related to green electronics

–  Efficient power converter –  Soft switching –  Inverter –  Battery characterization –  Battery management –  New concept in PV control –  Three-phase motor control –  Energy-conservation via control –  ….

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Homeworks •  Assigned each Tuesday •  Due the following Tuesday •  OK to work in groups of up to 4

–  Turn in one solution and list all who participated –  Give attribution for any outside help

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Midterms •  Oct 17 and Nov 14 – in the evening •  Two hours each •  Covers all material up through previous lecture •  Open notes

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Why Green Electronics?

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1. Growing CO2 Emissions

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2. Finite Supply of Fossil Fuels

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Inefficient Use of Energy

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Green Electronics is Part of the Solution

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What is Green Electronics?

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Energy Conversion

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Photovoltaic System

Solar Panel

Solar Panel

Solar Panel

Solar Panel

Solar Panel

Solar Panel

Photovoltaic Array

PV Controller and Inverter

Batteries

400V DC 240V AC60 Hz

48V DC

To Grid

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Electric Car

Charger120/240V AC60 Hz

From Grid

Battery

Battery

Battery

Battery Pack

400V DC Motor Controller

AC Induction or Brushless PM Motor

400V DC

3-phase ACVariable Voltage

Variable Frequency

Resistive Load

User Interface

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Less Obvious

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Or

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A great vehicle to teach Engineering

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Interesting examples to teach methods •  Analyze – of a circuit or a system •  Synthesize – a circuit, a system, software •  Model – a physical thing •  Simulate – your system or circuit •  Optimize – efficiency, performance, cost, etc…

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Interrelating Topics •  Electronics •  Electro-mechanical system •  Thermal effects •  Magnetic components •  Power Semiconductors •  …

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Bugs have consequences

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Power Electronics + Intelligent Control

Intelligent Controller

Power Path

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Example Waveforms

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Periodic Steady State Analysis

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Buck Converter

L

V2

+-

iLV1

+-

a

b

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Periodic Steady State

L

V2

+-

iLV1

+-

a

b

Switch is periodic with cycle time tcy Separate behavior

Over one cycle of switch At frequencies much lower than fcy

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Periodic Steady State

L

V2

+-

iLV1

+-

a

b

Time is divided into cycles with period tcy State variables are the same at the beginning and end of each cycle

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Periodic Steady State

L

V2

+-

iLV1

+-

a

b

Each cycle: switch in position a for ta, b for tb = tcy- ta

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Position a

L

V2

+-

iLV1

+-

a

b

VL =V1 −V2

ΔIa =taVLL

=ta V1 −V2( )

L

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Position b

L

V2

+-

iLV1

+-

a

b

VL = −V2

ΔIb =−tbV2L

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Waveforms

ip

i0

0 ta tcy=ta+tb

iL

a/b

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Periodic Steady State

ΔIa +ΔIb = 0ta V1 −V2( )

L+tb −V2( )L

= 0

ta V1 −V2( )+ tb −V2( ) = 0taV1 = ta + tb( )V2

V2 =ta

ta + tb

#

$%

&

'(V1 = DV1

L

V2

+-

iLV1

+-

a

b

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Periodic Steady State •  V2 = DV1 •  Only depends on duty factor D

–  Not on cycle time tcy –  Not on inductor value L –  They determine the “ripple”

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What if V2 ≠ DV1 ?

ΔI = ΔIa +ΔIb

ΔI =ta V1 −V2( )

L+tb −V2( )L

ΔI =tcyL

DV1 −V2( )

L

V2

+-

iLV1

+-

a

b

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Equivalent Circuit

L

V2+-

iL

DV1+-

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Transient Response

L

V2

iLV1

+-

a

b

R

C

+

_

V2(0) = 0, IL(0) = 0 . L = 10uH, C=0.1uF, R=8Ω, D=0.5 What is V2(t)? If V1(t>0) is 2V. Switching frequency is high enough you can ignore it.

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Equivalent Circuit

L

V2

iLDV1

+-

DR

C

+

_

ω =1LC

=1MHz

ζ =DR2

CL= 0.2

f = ω2π

=

Q = 12ζ

= 2.5

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Equivalent Circuit

L

V2

iLDV1

+-

DR

C

+

_

ω =1LC

=1MHz

ζ =DR2

CL= 0.2

f = ω2π

=

Q = 12ζ

= 2.5

ζ depends on duty factor!

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Sketch Response from f and Q

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Verify With Simulation

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

time µs

V 2

ω =1e+06ζ =0.2

f = 1.59e+05Q = 2.5

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With Current

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

time (µs)

V 2 (V

)

ω =1e+06ζ =0.2

f = 1.59e+05Q = 2.5

0 5 10 15 20 25 30 35 40

−0.1

−0.05

0

0.05

0.1

0.15

I L (V

)

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50% Overshoot

L

V2

iLV1

+-

a

b

R

C

+

_

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

time µs

V 2

ω =1e+06

ζ =0.2

f = 1.59e+05

Q = 2.5

Is this OK? What if your 5V power supply went to 7.5V on turn-on?

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50% Overshoot

L

V2

iLV1

+-

a

b

R

C

+

_

0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

time µs

V 2

ω =1e+06

ζ =0.2

f = 1.59e+05

Q = 2.5

Is this OK? What if your 5V power supply went to 7.5V on turn-on? It would fry all of your logic chips Control of switch-mode circuits prevents overshoot

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Matlab Model L=1e-5 ;!C=1e-7 ;!R=4 ; % DR!VI=2 ;!!dt=1e-8 ;!tsim=4e-5 ;!steps = ceil(tsim/dt) ;!!t=0 ;!vc=0 ;!il=0 ;!!% preallocate result arrays to speed simulation!tx=zeros(1,steps) ; vx=zeros(1,steps) ; ix = zeros(1, steps) ; !!for i=1:steps! vl = VI-vc-il*R ;! vc = vc+il*dt/C ;! il = il+vl*dt/L ;! tx(i) = t ; vx(i) = vc ; ix(i) = il ; % log variables! t=t+dt ;!end!

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0 5 10 15 20 25 30 35 400

0.5

1

1.5

2

2.5

3

3.5

time (µs)

V 2 (V

)

ω =1e+06ζ =0.2

f = 1.59e+05Q = 2.5

0 5 10 15 20 25 30 35 40

−0.1

−0.05

0

0.05

0.1

0.15

I L (V

)

Matlab Model L=1e-5 ;!C=1e-7 ;!R=4 ; % DR!VI=2 ;!!dt=1e-8 ;!tsim=4e-5 ;!steps = ceil(tsim/dt) ;!!t=0 ;!vc=0 ;!il=0 ;!!% preallocate result arrays to speed simulation!tx=zeros(1,steps) ; vx=zeros(1,steps) ; ix = zeros(1, steps) ; !!for i=1:steps! vl = VI-vc-il*R ;! vc = vc+il*dt/C ;! il = il+vl*dt/L ;! tx(i) = t ; vx(i) = vc ; ix(i) = il ;! t=t+dt ;!end!

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Caution! Simulation is not a substitute for

understanding

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Can the Buck Run Backwards?

L

V2+-

V1+-

a

b

iL

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Boost Converter

L

V2+-

V1+-

a

b

iL

V1 =V2Da

=V2

1−Db( )

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Boost Waveforms

ip

i0

t0 tb tcy

iL

b/a

tb ta

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Boost Transient Response (for f

Equivalent Circuit

kL

kV2 V1+-

kR

C

+

_

iL

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Summary: PWM, PSSA, Buck Boost •  Separate behavior into fast and slow

–  Fast – within switching cycle –  Slow – f

In Upcoming Lectures •  Application to motor control •  Realizing the switches

–  Power MOSFETs, Diodes, IGBTs –  and their imperfections

•  Realizing the inductors •  Using transformers •  Computing losses and efficiency •  Batteries and photovoltaic cells

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