energy harvesting from ambient vibrationsenergy harvesting from ambient vibrations fr´ed´eric...

IntroductionModelling of a piezoelectric energy harvester

An Example of inverter

Energy Harvesting from Ambient Vibrations

Frederic Giraud

L2EP – University Lille1

November 27, 2012

Frederic Giraud Master E2D2 University Lille1 - L2EP

Table of contents

1 IntroductionWhat is Energy Harvesting ?Generator TechnologiesSummary

2 Modelling of a piezoelectric energy harvesterPresentation of the systemEMR of the systemPower Extraction on a load resistor RL from harmonic oscillation

3 An Example of inverterIntroductionSSHI: Synchronized Switch Harvesting on Inductor

Frederic Giraud Master E2D2 November 27, 2012 2 / 40

What is Energy Harvesting ?Generator TechnologiesSummary

What is Energy Harvesting ?

We extract energy from an ambient and free source:

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than 1W.

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE

︷︸︸︷

EnergyConversion

We talk about Energy Harvesting or also energy scavenging

when the converted power is small, typically less than 1W.

η = P2P1

= 1− P1−P2P1

−→ Losses in the energy converter should be

as small as possible.

Objectives: Sensors Network

www.perpetuum.com

Gutierriez,A Heterogeneous Wireless IdentificationNetwork for the Localization of Animals Based onStochastic Movements

www.perpetuum.com

Gutierriez,A Heterogeneous Wireless IdentificationNetwork for the Localization of Animals Based onStochastic Movements

http://www.rfwirelesssensors.com, 2012

Roundy et Al.:A study of low level vibrations as a powersource for wireless sensor nodes.

Objectives: Power, just where you need it

http://enocean.com

Wireless

Reduce Cost, and isreconfigurable

Better Waste Cycle(Information fromEnocean)

http://enocean.com

Wireless

Innowattech’s systems produces power with vehicles

http://www.innowattech.com

http://enocean.com

Wireless

Innowattech’s systems produces power with vehicles

http://www.innowattech.com

The economist – April 28th 2007

Objectives: Marketing Purpose

Experience: Same Remotecontroller energized by humanpower, but with different packaging.

”No need for Batteries”

”Green” ”Fun”

54% of people Will choose the firstone because it is eco-friendly.(Jansen, Human power empirically explored)

Several projects are born fromthis fact: Metis Produces energyfrom dancers’ movements.

In Toulouse, the system VIHA

proposes Smart Tiles to energiesstreet lights.

The energy converter

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.

Generator

−Wind

−Light

−Vibrations

−Thermal

−...

SOURCE LOAD

︷︸︸︷

EnergyConversion

ElectricityElec.

Generator Inverter

Solar Harvesters:

This sensor measures IntraOccular Pres-sure http://cymbet.com

Handbag to recharge electronicdevices http://www.neubers.de

Solar Harvesters:

Solar Energy Harvester Evaluation Kit http://ti.com

Power and current asa function of voltage:

Solar Harvesters:

Solar Energy Harvester Evaluation Kit http://ti.com

Power and current asa function of voltage:

VMPPT strategies,require Energymanagement of thesystem

Thermoelectric

A Peltier module from http://www.tellurex.com

RDC IDC

Thermoelectric

RDC IDC

Thermoelectric

RDC IDC

Thermoelectric

RDC IDC

Thermoelectric

RDC IDC

Thermoelectric

RDC IDC

Temperature Gradient (residential). Lindsay Miller,http://uc-ciee.org

plumbing application from http://www.nextreme.com

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

1) Diode turns ON

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

1) Diode turns ON2) di

dt= 0 because e − vB = 0

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3) i = 0, diode turns OFF

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3〈i〉

3) i = 0, diode turns OFF

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3〈i〉

3) i = 0, diode turns OFF vB

〈i〉, P

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3〈i〉

〈i〉, P

P = 〈vB i〉 = vB〈i〉Frederic Giraud Master E2D2 November 27, 2012 10 / 40

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3〈i〉

〈i〉, P

Magnetic

stoppercoilstopper

e = −N dφdt

= N dφdx

e,vB, i

3〈i〉

〈i〉, P

Piezoelectric

An electronic lighter,http://freepatentsonline.com

Piezoelectric crystals

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Equivalent electrical circuit

im is a current proportionalto the deformation speed

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

im is a current proportionalto the deformation speed

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

im is a current proportionalto the deformation speedComparison Magn. Piezo

Magnetic Piezo.Voltage source Current

sourceInductive capacitiveLarge Stroke Small

StrokeRemote action

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

StrokeRemote action

Roundy, A piezoelectric vibrationbased generator for wireless

electronics (2004)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

vim RL

StrokeRemote action

electronics (2004)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

vim RL

StrokeRemote action

electronics (2004)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

vim RL

StrokeRemote action

electronics (2004)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Energy ManagementEquivalent electrical circuit

vim RL

StrokeRemote action

electronics (2004)

Piezoelectric

Cantilever beam

w(t) = Wsin(ωt)

Energy ManagementEquivalent electrical circuit

vim RL

StrokeRemote action

electronics (2004)

There is no ”one fit all” solution

Each solution may be efficient in a certain range of Power.Meanwhile, shrinking Chips consumption come at a time when energy harvesting becomes efficient and practical

(source: IDtechex.com)

Table of contents

Presentation of the systemEMR of the systemPower Extraction on a load resistor RL from harmonic oscillation

Coordinates and assumptions

moving Case

Bender

moving Case

Bender

The bender is attached to a vibrating andrigid case,

moving Case

BenderM

A mass M is attached to increase powerharvesting,

moving Case

BenderM

w(t) is the deflection of the beam,

moving Case

BenderM

We define ℜ a fixed reference frame,

moving Case

BenderM

ℜℜ′

And ℜ′ a reference frame affixed to thevibrating case.

moving Case

Bender

−→F p→M

ℜℜ′

−→F p→m is the force of the Bender onto themass M.

moving Case

Bender

−→F p→M

ℜℜ′

The case is supposed to be controlled inposition, and we have yc = Asin(ωt) theamplitude of the case’s vibration.

moving Case

Bender

−→F p→M

ℜℜ′

Gravity is neglected, as well as Inertiamomentum of the bender,

moving Case

Bender

−→F p→M

ℜℜ′

Gravity is neglected, as well as Inertiamomentum of the bender,

Actuator electrical convention.

Equations

Dynamic of the mass M: Glossary

M the mass

f , the force onto M

A, vibration’s amplitude

ω, vibration’s pulsation

facc is the inertial force

i current of the device(actuator convention)

im motional current

fp inside piezo force

N Piezoelectric forcefactor (depends ongeometry)

fp Piezo internal force

fs Material internal elasticforce

Ks equivalent stiffness(depends on geometry)

Ds Viscous coefficient

Equations

Dynamic of the mass M:

dt2(w(t) + Asin(ωt)) = Fp→M = f

Glossary

M the mass

im motional current

Equations

Mw(t) = f +MAω2sin(ωt) = f + facc

Glossary

M the mass

im motional current

Equations

Electrical Behaviour: Capacitive

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

Piezoelectric effect

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

im derives from deflection: im = Nw

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

while v produces an internal forcefp = Nv

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

Material’s behaviour

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

The material is elastic: fs = Ks

∫wdt

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

∫wdt

With some friction inside:fs = Ks

∫wdt + Ds w

Glossary

M the mass

im motional current

Equations

v = 1Cb

∫(i − im)dt

∫wdt

With some friction inside:fs = Ks

∫wdt + Ds w

These actions are opposite to the PEeffect: f = fp − fs

Glossary

M the mass

im motional current

EMR of the system

(i − im)dt

︸︷︷︸

EMR of the system

(i − im)dt

︸︷︷︸

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

pe = v .i is the output power,

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

pe = v .i is the output power, pm = facc w is the mechanical input power

and both should be < 0

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

SM Comparison with a DC motor

Things are not so differerent.

EMR of the system

(i − im)dt

︸︷︷︸

︷︸︸︷

fp = Nv, im = Nw

(f − facc )dt

︸︷︷︸

︷︸︸︷

f = fp − fs︷︸︸︷

fs = Ks

wdt + Ds w

SM Comparison with a DC motor

Things are not so differerent.

Asumption

facc = MAω2sin(ωt) for harmonic oscillations

Asumption

complex notation: x is the complex phasor of x(t), meansx(t) = ℑ(x)

Asumption

complex notation: x is the complex phasor of x(t), meansx(t) = ℑ(x)since oscillations are harmonic, we will write:x = Xe jωt

Asumption

for steady state operation, X is constant, leading todxdt

= jωXe jωt

Asumption

= jωXe jωt

|x | = |X | = X

Asumption

= jωXe jωt

|x | = |X | = X

for example, f acc = MAω2e jωt and |f acc | = MAω2.

Asumption

= jωXe jωt

|x | = |X | = X

v = −RLi

Asumption

= jωXe jωt

|x | = |X | = X

v = −RLi

Asumption

= jωXe jωt

|x | = |X | = X

v = −RLi

v RLim

Asumption

= jωXe jωt

|x | = |X | = X

v = −RLi

v RLim

i And RL ≪ 1Cbω

, yieldsv ≃ −RLim

For an ideal generator (Ds = 0)

Mw = f + f acc

f = Nv − Ksw

Mw = f + f acc

f = Nv − Ksw

v = −RLim = −RLNw

Mw = f + f acc

f = Nv − Ksw

Mw + N2RLw + Ksw = f acc

Mw = f + f acc

f = Nv − Ksw

Mw + N2RLw + Ksw = f acc−→ RL acts as a damping

P2 = − 12RL|im|2

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

|im| = N |w | = ω.N.|facc|√(Ks−Mω

2)2+(N2RLω)2

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

(Ks−Mω2)2+(N2RLω)2

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

The vibrations should occur atgenerator’s resonance frequency

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

P2max RL ց

ω0 =√

We can harvest as muchpower as we want

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

P2max RL ց

ω0 =√

P2max ,Wmax

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

P2max RL ց

ω0 =√

P2max ,Wmax

We can harvest as muchpower as we want, at theexpense of largedisplacement of thebender’s tip

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

P2max RL ց

ω0 =√

P2max ,WmaxTechnological limit for Wmax

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

vmax = MAω2

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

vmax = MAω2

P1Max = 12 faccωWMax = (MAω2)2

N2RL= P2Max

P2max RL ց

ω0 =√

Mw = f + f acc

f = Nv − Ksw

P2 = − 12RL|im|2

2)2+(N2RLω)2

P2 = − 12

N2RLω2|facc |

P2Max = (MAω2)2

2N2RL, Wmax = MAω

vmax = MAω2

P1Max = 12 faccωWMax = (MAω2)2

N2RL= P2Max

P2max RL ց

ω0 =√

Assumtionnot valid

For a real generator (Ds 6= 0)

f = Nv − Ksw − Dsw

w =f acc

(Ks−Mω2)+jω(Ds+N2RL)

w =f acc

P2 = − 12RL|im|2

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ds+RLN2)ω2|f acc |

(Ks−Mω2)2+ω

2(Ds+N2RL)2

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P2, P1

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P2, P1

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

ω0 should still be the vibration’s pulsation.

P2, P1

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P2, P1

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P2, P1

Generator’s Power Losses

w =f acc

P2 = − 12RL|im|2

P2 = − 12

RLN2ω

2|f acc |2

(Ks−Mω2)2+ω

2(Ds+N2RL)2

P1 = − 12ℜ(f acc .w

P1 = − 12

(Ks−Mω2)2+ω

2(Ds+N2RL)2

Wmax = |facc |(Ds+N2RL)ω0

, P1max = 12

|f acc |2

Ds+N2RL,

P2max = 12

N2RL|f2acc |

(Ds+N2RL)2

P2, P1

Generator’s Power Losses

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

When RL ց, P1 ր, which is good, but thelosses increase as well: it exists an optimalvalue of RL which optimizes P2 for a givenvibration amplitude.

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

When RL ց, P1 ր, which is good, but thelosses increase as well: it exists an optimalvalue of RL which optimizes P2 for a givenvibration amplitude. It can be shown:

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

voltage is not so high.

P2, P1

, P1max = 12

|f acc |2

Ds+N2RL

P2max = 12

N2RL|f acc |2

(Ds+N2RL)2

RLopt =Ds

P2opt =|f acc |

P1opt =|f acc |

4Ds= 2.P2opt

voltage is not so high.

Assumption

not valid

P2, P1

Assumption

not valid

Assumption

not valid

Example

Device’s properties

N = 0.012N/V , Ks = 6300N/m, Cb = 300nF , Ds = 0.17Ns/m,M = 1g

Calculate for A = 0.1mm

the best working frequency,

the harvested P2 power in the bestcase,

the power of the source P1 in suchbest case,

the optimal resistor RL,

the deflection amplitude of the bender,

the voltage for this working point.

Validation

Is v = −RLim a validassumption?

Answers

The best working frequency is given by

f0 =12π

√63001.10−3 = 400Hz

Answers

f0 =12π

√63001.10−3 = 400Hz

For the best case, P2 is given by

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

Answers

f0 =12π

√63001.10−3 = 400Hz

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

For the best case P1 = 2.P2 = 928mW

Answers

f0 =12π

√63001.10−3 = 400Hz

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

The optimal resistor RLopt is given byRLopt =

N2 = 0,170,0122

= 1180Ω

Answers

f0 =12π

√63001.10−3 = 400Hz

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

N2 = 0,170,0122

= 1180Ω

The deflection Wmax is given by

= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!

Answers

f0 =12π

√63001.10−3 = 400Hz

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

N2 = 0,170,0122

= 1180Ω

= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!

The voltage is then given byvmax = NRLω0|w | = 0, 012.1180.2π.400.738.10−6 = 26V

Answers

f0 =12π

√63001.10−3 = 400Hz

P2 =|f acc |

8Ds= (1.10−3.1.10−4.(2π.400)2)2

8.0,17 = 464mW

N2 = 0,170,0122

= 1180Ω

= (1.10−3.1.10−4.(2π.400)2)2.0,17.2π.400 = 738µm!

The voltage is then given byvmax = NRLω0|w | = 0, 012.1180.2π.400.738.10−6 = 26V

ZCb = 1Cbω

= 12π.400.300.10−9 = 1990Ω ≈ RL, −→ Calculations

are NOT valid!

For a real Generator, Ds 6= 0 and v 6= −RLim

v RLim

We can show:v = − RL

1+jωRLCbim = −jωNRL

1−jωRLCb

1+(RLCbω)2wm

and we write: v = −jωNrLeqw − Nkeqw

v RLim

1−jωRLCb

1+(RLCbω)2wm

2 Cases to consider, since ω should be ω0:

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

rLeq ≃ RL and kLeq ≃ 0, no problem,just use the assumption

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

rLeq ≪ RL and kLeq is high, an otherstudy is needed

v RLim

1−jωRLCb

1+(RLCbω)2wm

ω0 ≪ 1RLCb

rLeq |dB , kLeq |dB

ω0 ≫ 1RLCb

rLeq |dB , kLeq |dB

rLeq ≪ RL and kLeq is high, an otherstudy is needed

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f accFrederic Giraud Master E2D2 November 27, 2012 23 / 40

Rule of the Thumb

Let Rb defined as RbCbω0 = 1, ω0 <1

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

rL ≃ RL ; keq ≃ 0 rL < RL ; keq ր

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3Rb4

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3Rb4

Rule of the Thumb

RLCb→ RL < Rb

P2/P2max

P2/P2Max

Rb1Rb2Rb3Rb4

Partial Conclusion

If Ropt < Rb

A resistor can recover the power optimally. But the study was notvalid for high RL. What happens for RL ≫ Rb?

Partial Conclusion

If Ropt < Rb

A resistor can recover the power optimally. But the study was notvalid for high RL. What happens for RL ≫ Rb?

If Ropt > Rb

The power is not well extracted because P2 < P2max . Thishappens for high damped mechanisms.A simple resistor cannot recover the power optimally (and this isdue to Cb).

What happens if Ropt < Rb and RL ≫ Rb?

resonance is shifted

rLeq = RL

1+(RLCbω)2≃ RL

(RLCbω)2

keq = RLω2RLCb

1+(RLCbω)2≃ 1

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f acc leads to:

ω′0 =

√Ks+N2keq

resonance is shifted

rLeq = RL

1+(RLCbω)2≃ RL

(RLCbω)2

keq = RLω2RLCb

1+(RLCbω)2≃ 1

((Ks + N2keq)−Mω2) + jω(Ds + N2rLeq)w = f acc leads to:

ω′0 =

√Ks+N2keq

Another optimal resistor

The optimal power is harvested is N2rLeq = Ds , leading to:N2RL

(RLCbω′0)

2 = N2

Ks+N2Cb

RLopt2 = N2

C2bKsM

(1+ N2

KsCb)=

RL(log)

P2/P2Max

RL(log)

P2/P2Max

RLopt2

Conclusion

For the realistic case, there is one or two resistive loads whichallow to extract the maximum of power,

RL(log)

P2/P2Max

RLopt2

Conclusion

There exist an optimal frequency which may vary if RL is veryhigh,

RL(log)

P2/P2Max

RLopt2

P2/P2max

Conclusion

For highly damped structure, a simple resistor is not optimal.

RL(log)

P2/P2Max

RLopt2

P2/P2max

ω0 ≃ N2

P2/P2Max

Conclusion

For highly damped structure, a simple resistor is not optimal.

→ we always want to harvest the maximum of power!

RL(log)

P2/P2Max

RLopt2

P2/P2max

ω0 ≃ N2

P2/P2Max

Table of contents

IntroductionSSHI: Synchronized Switch Harvesting on InductorConclusion

Introduction

im > 0

Introduction

im > 0v

Introduction

im > 0v

Introduction

im > 0v

vL = RLim which is > 0and v = −vL = −RLim

Introduction

im > 0v

im < 0

Introduction

im > 0v

im < 0v

Introduction

im > 0v

im < 0v

Introduction

im > 0v

im < 0v

vL = −RLim which is > 0again, and

v = vL = −RLim

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

The current is rectified, but we still havev = −RLim: Power harvesting depends on RL

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

Moreover, it is still not optimal if Ropt > Rb.

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

Moreover, it is still not optimal if Ropt > Rb.

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

Moreover, it is still not optimal if Ropt > Rb.This is why, some want to compensate for Cb:

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

This is a bad solution because it works only forω0 (what if the frequency shifts?), and theInductor is large (because ω0 usually is small)

Introduction

im > 0v

im < 0v

v = vL = −RLim

T0 = 1

This is a bad solution because it works only forω0 (what if the frequency shifts?), and theInductor is large (because ω0 usually is small)−→Non linear Techniques

Why Synchronized

H bridge

Why Synchronized

Strategy: v = −Ropt im leads tofpN= −Ds

N2Nw or, fp = −Dsw .

Why Synchronized

vrefiref

N2Nw or, fp = −Dsw .This shows that v should be controlled.

Why Synchronized

vrefiref

N2Nw or, fp = −Dsw .This shows that v should be controlled.SSHI does this withefficiency.

How it works

LC oscillations

How it works

LC oscillations

How it works

LC oscillations

How it works

LC oscillations

How it works

LC oscillations Switched inductor

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

How it works

v , i+v

RLvLCF

How it works

v , i+v

RLvLCF

v , iI , im, vL

How it works

v , i+v

RLvLCF

v , iI , im, vL

How it works

v , i+v

RLvLCF

v , iI , im, vL

How it works

v , i+v

RLvLCF

v , iI , im, vL

How it works

v , i+v

RLvLCF

v , iI , im, vL

on off on off on off on off

Switching is synchronized on w , or

im = Nw .

How it works

v , i+v

RLvLCF

Operating point: calculate vL from im

1st Harmonic assumption: P = 12

RL≃ 1

4VLImπ

, VL = 4πRL Im

v , iI , im, vL

im = Nw .

How it works

v , i+v

RLvLCF

Operating point: calculate vL from im

1st Harmonic assumption: P = 12

RL≃ 1

4VLImπ

, VL = 4πRL Im

SSHI controls v and synchronises it, but doesn’t impose fp = −Ds w .

v , iI , im, vL

im = Nw .

Conclusion

Performances

SSHI can extract energy more efficiently than a resistor whendamping is important,

P2/P2Max

Conclusion

Performances

But Power extraction still depends on the load,

P2/P2Max

Conclusion

Performances

But Power extraction still depends on the load,

Needs to measure bender’s deflection w(t).

P2/P2Max

General conclusion

In this presentation, applications of Energy Harvesting were shown.The modelling of a piezoelectric generator has shown that thepower source needs an adaptation:

in frequency,

in load.

to maximize the harvested poer.The key energy management rules were presented through theanalysis of the EMR of the system. A typical power electroniccircuit was also presented, but the bibliography shows a lot ofexample.

References I

S Adhikari, M I Friswell, and D J Inman, Piezoelectric energy harvesting from broadband random vibrations,

Smart Materials and Structures 18 (2009), no. 11, 115005.

R. G Ballas, H. F Schlaak, and A. J Schmid, Closed form analysis of piezoelectric multilayer bending

actuators using constituent equations, The 13th International Conference on Solid-State Sensors, Actuatorsand Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS ’05, vol. 1, IEEE, June 2005,pp. 788– 791 Vol. 1.

R. Djugum, P. Trivailo, and K. Graves, A study of energy harvesting from piezoelectrics using impact forces,

The European Physical Journal Applied Physics 48 (2009), no. 1, 11101.

Daniel Guyomar, Gal Sebald, Sbastien Pruvost, Mickal Lallart, Akram Khodayari, and Claude Richard,

Energy harvesting from ambient vibrations and heat, Journal of Intelligent Material Systems and Structures20 (2009), no. 5, 609 –624.

Aman Kansal, Jason Hsu, Sadaf Zahedi, and Mani B. Srivastava, Power management in energy harvesting

sensor networks, ACM Transactions on Embedded Computing Systems 6 (2007), 32–es.

Elie Lefeuvre, Adrien Badel, Claude Richard, and Daniel Guyomar, Piezoelectric energy harvesting device

optimization by synchronous electric charge extraction, Journal of Intelligent Material Systems andStructures 16 (2005), no. 10, 865 –876.

H. Lhermet, C. Condemine, M. Plissonnier, R. Salot, P. Audebert, and M. Rosset, Efficient power

management circuit: From thermal energy harvesting to above-IC microbattery energy storage, IEEEJournal of Solid-State Circuits 43 (2008), no. 1, 246–255.

References II

G. A. Lesieutre, G. K. Ottman, and H. F. Hofmann, Damping as a result of piezoelectric energy harvesting,

Journal of Sound and Vibration 269 (2004), no. 3-5, 991–1001.

D. Niyato, E. Hossain, M. M Rashid, and V. K Bhargava, Wireless sensor networks with energy harvesting

technologies: a game-theoretic approach to optimal energy management, IEEE Wireless Communications 14(2007), no. 4, 90–96.

Shad Roundy, Paul Kenneth Wright, and Jan M. Rabaey, Energy scavenging for wireless sensor networks:

with special focus on vibrations, Springer, 2003.

G. Sebald, E. Lefeuvre, and D. Guyomar, Pyroelectric energy conversion: Optimization principles, IEEE

Transactions on Ultrasonics, Ferroelectrics and Frequency Control 55 (2008), no. 3, 538–551.

Qing-Ming Wang and L. E Cross, Constitutive equations of symmetrical triple layer piezoelectric benders,

IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control 46 (1999), no. 6, 1343–1351.

End of the presentation

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