Energy Harvesting Throurgh Piezoelectric Materials

Rajeev Kumar

Energy Harvesting through Piezoelectric Material

Computational Intelligence Applications to Renewable Energy-2012

Rajeev KumarSchool of Engineering

IIT Mandi

1

Outlines of the presentation

�Introduction

�Energy Scavenging through Vibration

�Thermodynamic of piezoelectric material

�Piezoelectric Frequency Response

�Piezoelectric Energy Harvester

Computational Intelligence Applications to Renewable Energy-2012 2

�Piezoelectric Energy Harvester

�Engineering Design Process

�Finite Element Analysis of Layered Piezoelectric Ma terial

�Optimization of Piezoelectric Energy Harvester by G enetic Algorithm

Energy harvesting or the process of acquiring energy from thesurrounding environment has been a continuous humanendeavor throughout history.

Energy harvesting

Introduction


Need of Energy Harvesting

• Growing need for renewable sources of energy

• Proposes several potentially inexpensive and highly effective solutions

• Reduce dependency on battery power

Introduction (Cond..)


• Reduce dependency on battery power

• Complexity of wiring

• Increased costs of wiring

• Reduced costs of embedded intelligence

• Increasing popularity of wireless networks

• Limitations of batteries

• Reduce environmental impact

Available energy sources in the environment

Introduction (Cond..)


Available energy sources

Energy Scavenging through Vibration


Type Advantage Disadvantage

Piezoelectric 1. No separate voltage source2. Voltages of 2 to 10 Volts3. No mechanical stops4. Highest energy density

1. Micro fabrication processes are not compatible with standard processes and piezo thin films have poor coupling.

Electrostatic 1. Easier to integrate with 1. Separate voltage source

Energy Scavenging through Vibration (Cond..)


From this comparison it is clear that the most desirable conversion method resultsthat piezoelectric one which presents the major number of advantages. So, it is forthese reasons that this is currently the best choice to realize the micro vibrationdriven generator for energy harvesting to power sensor nodes.

Electrostatic 1. Easier to integrate with electronics and microsystems

2. Voltages of 2 to 10 Volts

1. Separate voltage source required

2. Mechanical stops needed

Electromagnetic 1. No separate voltage source2. No mechanical stops

1. Max. voltage of 0.1 volt2. Difficult to integrate with

electronics and microsystems

Examples of common vibration sources

Energy Scavenging through Vibration(Cond..)


Thermodynamic of piezoelectric material


Direct Piezo Effect:

The phenomenon of generation of a voltage under mechanical stress is referred to as the direct piezoelectric effect.

Thermodynamic of piezoelectric material ( Cond..)



The mechanical strain produced in the crystal under electric voltage is referred as converse piezoelectric effect.

Converse Piezoelectric Effect


The phenomenon of generation of a electric field, when thetemperature of the crystal is raised or lowered is referred to as thePyroelectric effect.

Pyroelectric Effect




Piezoelectric Material (Material with Piezoproperties )

:

Naturally occurring crystals : Berlinite (AlPO4), Cane sugar, Quartz, Rochelle salt, Topaz,Tourmaline Group Minerals, and dry bone (apatite crystals)

Man-made ceramics :Barium titanate (BaTiO3), Lead titanate (PbTiO3), Lead zirconate


Barium titanate (BaTiO3), Lead titanate (PbTiO3), Lead zirconatetitanate (Pb[ZrxTi1-x]O3 0<x<1) - More commonly known as PZT,Potassium niobate (KNbO3), Lithium niobate (LiNbO3), Lithiumtantalate (LiTaO3), Sodium tungstate (NaxWO3), Ba2NaNb5O5,Pb2KNb5O15

Polymer :Polyvinyledene fluoride (PVDF)

13

Polarization of Piezoelectric Material

Thermodynamic of piezoelectric material (Cond..)


Applications of Energy Harvesting through Piezoelectric Material

• The best-known application is the electricCIGARETTE LIGHTER: pressing the buttoncauses a spring-loaded hammer to hit apiezoelectric crystal, producing a sufficientlyhigh voltage electric current that flows acrossa small spark-gap, thus heating and ignitingthe gas.


the gas.

• Gas burners now have built-in piezo-basedignition systems .

• Battery-less wireless doorbell push button

• The armed forces toyed with the idea ofputting piezoelectric materials in soldiers bootsto power radios and other portable electronicgear

• Several nightclubs,mostly in Europehave alreadybegun to powertheir strobes andstereos using theforce of hundreds

Applications of Energy Harvesting through Piezoelectric Material ( Cond..)


force of hundredsof people poundingon piezoelectriclined dance floors

16


• Several gyms, notable in Portland and a few other places arepowered by a combination of piezoelectric set ups and generatorsset up on stationary bikes.


• Laying piezoelectric crystalarrays underneath sidewalks,stairwells, and pretty much anyother high traffic area to powerstreet lights.



• Piezoelectric Powered MusicInstruments



Applications of Energy Harvesting through Piezoelectric Material (Cond..)

• Capitalizing on the friction and heat created bywalking, running and even just wearing jeans,engineers from Michigan TechnologicalUniversity, Arizona State University devised away to use this type of generated energy tocharge portable electronic devices, like iPodsandmobilephones.


andmobilephones.

• Biomechanical Energy Harvester

• Energy harvesting byPiezoelectric windmills

20

Identify the need or problem

Research the need or problem

Modify to improve the design if needed

Engineering Design Process


Develop possible solutions

Select the best solutionsConstruct a

prototype

Test and evaluate the prototype

Detailed Design

Analyze the problem

Detailed Design

Optimization of the problem

Detailed Drawing of the problem

Engineering Design Process (Contd..)


the problem

Piezoelectric Energy Harvester Model

The electromechanical model of this structure can be represented


The electromechanical model of this structure can be represented by the following set of differential equations

[ ]{ } [ ]{ } [ ] [ ][ ] [ ]( ){ } { } [ ]{ }θθφφφφ umuuuuuuuu kFqkkkkqcqmsss 2

11 +=+++ −&&&

[ ][ ] [ ]{ } [ ]{ }auu asskkkk φθ φφφφ φθ

−− −1

2

1

{ } [ ] [ ]{ } [ ]{ }

+= − qkkk us sss φθφφφ θφ2

11

Harvested power

Piezoelectric Frequency Response

Piezoelectric energy harvester is only effective under a narrowbandwidth of excitation frequency. If the excitation frequency shiftsfrom this band, the power density of the harvester will significantlydecrease


•If the excitation frequency shifts from this band, the power densityof the harvester will significantly decrease.

•Different strategies have been used to enhance the harvestingperformances when the vibration source has a larger frequencybandwidth.

Piezoelectric Energy Harvester Model ( Cond..)


•One of them is to use an array of harvesters which consists ofmultiple harvesters having different resonance frequencies in orderto increase the harvested power on a wider frequency bandwidth.However, this leads to a harvester having a higher volume, whichdecreases its power density (mW.cm-3).

•Therefore Design optimization is required



�The cost function of this first optimization problem is to maximizethe mean power density over a certain frequency bandwidth.�The power density is defined as the ratio of the harvested Powerand the harvester volume


Objective function


{ } [ ] { } [ ] { } { } Θ−−= kkkk EeQ λεσ

Direct Piezoelectric effect

Constitutive relation

Finite Element Modeling

Converse piezoelectric effect


Direct Piezoelectric effect

{ } [ ] { } { } { } { } Θ++= kk

T

kk PEbeD ε

For a non piezoelectric layer

{ }oek

=

−

{ } { }0=kP { } { }oE k =

Where [ ] [ ] [ ] [ ] [ ][ ]θε TTTeTe kokvkΤ=

[ ] [ ] [ ] [ ]vkvk TbTb Τ=

{ } [ ] { }kvk pTp Τ=

[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ]θεεθ TTTQTTTQ ΤΤΤ=

Finite Element Modeling (Cond..)


{ } [ ] [ ] [ ] { }kkok TTT λλ εθΤΤΤ=

[ ]εT

][ oT

[ ]θT

[ ]vT

[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ]θεεθ TTTQTTTQ kokkok =

Strain transformation matrix

Ply orientation transformation matrix

Rotational transformational matrix

Vector transformation matrix

[ ]

( ) ( )

( ) ( )

−−

−−

=

12

2112

2

2112

212

2112

212

2112

1

00000

000000

000011

000011

G

vv

E

vv

Evvv

Ev

vv

E

Q

{ }

=

012

3

2

1

λλλλ

λ

{ }

=

3

2

1

p

p

p

p

Elastic stiffness coefficients matrix Stress coefficients vector

Pyroelectric coefficients vector



13

23

12

00000

00000

00000

SFG

SFG

G

0

0

{ }

=

363534333231

262524232221

161514131211

eeeeee

eeeeee

eeeeee

e

{ }

=

13

23

12

3

2

1

τττσσσ

σ [ ]

=

3

2

1

00

00

00

b

b

b

b

6

5SF = shear correction factor =

Piezoelectric coefficient matrix

Stress vector Dielectric constant matrix

[ ] ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )

+++++++++

=

233223322332323232

122112211221212121

33333323

23

23

22222222

22

22

11111121

21

21

222

222

222

lnlnnmnmmlmlnnmmll

lnlnnmnmmlmlnnmmll

lnlnnmnmmlmlnnmmll

lnnmmlnml

lnnmmlnml

lnnmmlnml

Tε

[ ]

[ ][ ]

[ ][ ]

=

θ

θ

θ

θ

θ

t

t

t

t

T

000

000

000

000

Strain transformation matrixRotational transformation matrix

Transformation matrices



( ) ( ) ( )

+++ 311331133113131313 222 lnlnnmnmmlmlnnmmll

[ ]

=

333

222

111

000

000

000

000100

000010

000001

nml

nml

nmltθ

[ ]

−

−−

−

=

cs

sc

sccscs

cscs

cssc

To

0000

0000

00022

000100

000

000

22

22

22

[ ]

=

333

222

111

nml

nml

nml

Tv

Ply orientation transformation matrix

θθ

sin

cos

==

s

c nml ,, Direction cosines between local and global axis

Vector transformation matrix

zyx ′′′ ,, ζηξ ,,zyx ,,

9-node degenerate shell elementThree Co-ordinate system

Shape Function

( )( )11)1(4

1 −+++= iiiiiN ηηξξηηξξ

( )1

i=1,2,3,4



( ) )1(12

1 2iiN ηηξ +−=

( )( )iiN ξξη +−= 112

1 2

( )22 1)1( ηξ −−=iN

i=5,7

i=6,8

i=9

+

=

bottomi

i

i

topi

i

i

middlei

i

i

z

y

x

z

y

x

z

y

x

2

1

Nodal Coordinates



bottomtopmiddle

−

=

=

bottomi

i

i

topi

i

i

ii

i

i

i

z

y

x

z

y

x

tn

m

l

V1

3

3

3

3

r

( ) ( ) ( )( ) 2/1222ibottomitopibottomitopibottomitopi zzyyxxt −+−+−=

9-node degenerate shell element

iii

i

middlei

i

i

ii VtN

z

y

x

N

z

y

x

32

rζ∑∑ +

=

Relation between the Co-ordinate systems



∑

∑

=

==

=9

13

3

9

1

3

3

3

3

iii

ii

i

VN

VN

n

m

l

Vr

r

r

3

3

1

1

1

1Vi

Vi

n

m

l

V r

rrr

×

×=

= 13

2

2

2

2 VV

n

m

l

Vrrr

×=

=

Displacement Field

iii

i

npi

i

innel

ii VHN

z

y

x

N

z

y

x

3

r

∑∑ +

=



ii kk

oki ttH2

ζ+=

( ) [ ]

−+

=

∑= i

iii

i

i

innel

ii VVH

w

v

u

N

w

v

u

βα

ζηξ 211

,rr

{ } [ ] { }eeu

i

i

i

i

i

nnel

iiiiii

iiiii

iiiii

e qNw

v

u

HNnHNnN

HNmHNmN

HNlHNlN

w

v

u

u =

−−−

=

= ∑

αβ12

12

12

00

00

00

Displacement & Strain Field

ε

∂∂∂

x

u



{ }

=

zx

yz

xy

z

y

x

εεεεεε

ε

∂∂+

∂∂

∂∂+

∂∂

∂∂+

∂∂

∂∂∂∂∂

z

u

x

wy

w

z

vx

v

y

uz

wy

vx

=

oi

oi

nnel ziiziii

yiiyiii

xiixiii

v

u

gngnN

gmgmy

N

glglx

N

−∂

∂

−∂

∂

−∂

∂

12

12

12

00

00

00


Strain Field


{ }( ) ( )

( ) ( )

( ) ( )

[ ] { }ee

i

i

oi

oinnel

i

ziixiiziixiiii

yiiziiyiiziiii

xiiyiixiiyiiii

ziizii

qBw

v

glgnglgnx

N

z

N

gngmgngmy

N

z

N

gmglgmglx

N

y

N

gngnz =

++−

∂∂

∂∂

++−∂

∂∂

∂

++−∂

∂∂

∂

−∂=∑

αβ

ε

1122

1122

1122

12

0

0

0

00

Thermal field

nnelnnel

HNN ϕ∑∑ +Θ=Θ

�Temperature distribution is taken linear within the element.

�Using the shape function the temperature of any point in the element can beuniquely given in terms of nodal temperature and gradient of the mid plane as



ii

iii

i HNN ϕ∑∑ +Θ=Θ

[ ] [ ] [ ] { } [ ] { }eeeei

innel

ii

i

innel

ii NNHNN θθ

ϕϕ φ+=

Θ

+

Θ

=Θ Θ∑∑ 00

are the mid plane temperature and gradient respectively at node iiΘ iϕ

{ } { }kpek BE φφ−=

Electric field in the kth piezoelectric layer within the element can be given as

l

Finite Element Modeling (Cond..) Electric Field


Where

{ }

=

3

3

31

n

m

l

tB

kpeφ

Thickness of kth piezoelectric layer

Electric potential of kth piezoelectric layer

kpt

kpφ

{ } { }kpek BE φφ−=

Electric field in the kth piezoelectric layer within the element can be given as

l

Finite Element Modeling (Cond..) Electric Field


Where

{ }

=

3

3

31

n

m

l

tB

kpeφ

Thickness of kth piezoelectric layer

Electric potential of kth piezoelectric layer

kpt

kpφ

{ } { } dAdzV k

A k

σεΤ

∫ ∫∑=2

1

Using the variational principle the potential energy is given as

Substituting various values


Strain energy


{ } [ ] { } { } [ ] { } { } [ ] { }[ ]eeueeeueeeuue kqkqqkqV θφ θφΤΤΤ −+=

2

1


where[ ] [ ] [ ] [ ]∑∫

=

Τ=nl

k V

ekeeuu dVBQBk1

[ ] [ ] [ ] { } [ ] [ ] { } [ ] [ ] { }

= ∫∫∫

ΤΤΤΤΤΤ

Vepe

Vepe

Vepeeu dVBeBdVBeBdVBeBk

npl φφφφ ...21

[ ] [ ] { } [ ] [ ] { } [ ]( )dVNBHNBknl

k Vekeekeeu ∑∫

=

ΤΘ

Τ +=1

ϕθ λλ

Finite Element Modeling (Cond..) Strain energy


{ }

=

nplp

p

p

e

φ

φφ

φ

.

.

.2

1

{ } { }dzdADEWA k

t

t

ee

k

k

∫∑ ∫−

Τ=1

2

1

The element electrical energy can be given as


Electrical energy


{ } [ ] { } { } [ ] { } { } [ ] { }eeeeeeeeuee kkqkW θφφφφ φθφφφ

ΤΤΤ −+−=2

1

2

1

2

1


where

[ ] [ ]Τ=eueu kk φφ

[ ]

{ } [ ] { }{ } [ ] { }

∫

∫Τ

Τ

Vepe

Vepe

dVBbB

dVBbB

φφ

φφ

.

2

1


Electrical energy


[ ]

{ } [ ] { }

=

∫Τ

Vepe

e

dVBbB

k

npl φφ

φφ

.

.

.

[ ]

{ } { } [ ] { } { } [ ]( ){ } { } [ ] { } { } [ ]( )

+

+

∫

∫Τ

ΘΤ

ΤΘ

Τ

Vepeepe

Vepeepe

dVNpBHNpB

dVNpBHNpB

φφφ

φφφ

22

11

Finite Element Modeling (Cond.)

Electrical energy


[ ]

{ } { } [ ] { } { } [ ]( )

+

=

∫Τ

ΘΤ

Vepeepe

V

e

dVNpBHNpB

k

nplnpl φφφ

φθ

.

.

.

( )( )∑∫=

++=nl

k V

k dVwvuT1

222

2

1&&&ρ


The element kinetic energy can be given as


Kinetic energy


kρ

{ } [ ] { }eeuue qmqT..

2

1 Τ

=

where

density of kth layer

[ ] [ ] [ ]∑∫=

Τ=nl

k Veueukeuu dvNNm

1

ρ

[ ] [ ] [ ]∑∫=

Τ=nl

k Veueukeuu dvNNm

1

ρ

[ ] ∑

−−−

=nnel

iiiiii

iiiii

eu

HNnHNnN

HNmHNmN

HNlHNlN

N 12

12

00

00

00


Kinetic energy


−iiiiii HNnHNnN 1200

Where

Work done by the external force and electrical charge is given as

{ } { } { } { }eqeeme

s FFqW ΤΤ += φ

{ } [ ] { } [ ] { }epueseuem fNdsfNF ΤΤ += ∫ { } { } { } dsfBF

eqeeq ∫Τ= φ

Finite Element Modeling (Cond..) Work done


{ } [ ] { } [ ] { }epues

seuem fNdsfNF += ∫

1

{ } { } { } dsfBFeq

seeq ∫=

2

φ

{ }esf

{ }epf

{ }eqf

Element surface force intensity vector

Element point load vector

Element surface electrical charge density vector

∫ =+f

o

t

t

s dtWL 0)(δ ( )∫ =++−f

o

t

t

se dtWWVT 0δδδδ

Using Hamilton’s principle



The governing equation for an element can be written as

[ ] { } [ ] { } [ ] { } [ ] { } { }emeeueeueeuueeuu Fkkqkqm =−++ θφ θφ 2

1&&

[ ] { } [ ] { } [ ] { } { }eqeeeeeeu Fkkqk =+− θφ φθφφφ 2

1

[ ]{ } [ ]{ } [ ]{ } { } [ ]{ } [ ]{ }kkFkqkqm φθφ −+=++ 1..

• Sensors and actuators are present

• vector can be partitioned

• No charge accumulates on the sensor layer


Governing equations


[ ]{ } [ ]{ } [ ]{ } { } [ ]{ } [ ]{ }auussuuuuu askkFkqkqm φθφ φθφ −+=++

2

1..

[ ]{ } [ ]{ } [ ]{ } { }021 =+− θφ θφφφφ sss

kkqk su

[ ]{ } [ ]{ } [ ]{ } { }aaaa qau Fkkqk =+− θφ θφφφφ 2

1

Sensor equation

{ } [ ] [ ]{ } [ ]{ }

+= − qkkk us sss φθφφφ θφ2

11


Governing equations


Actuator equation

[ ]{ } [ ]{ } [ ] [ ][ ] [ ]( ){ } { } [ ]{ }θθφφφφ umuuuuuuuu kFqkkkkqcqmsss 2

11 +=+++ −&&&

[ ][ ] [ ]{ } [ ]{ }auu asskkkk φθ φφφφ φθ

−− −1

2

1

Flowchart of Genetic Algorithm







Optimization of Piezoelectric Energy Harvester


Maximize

Optimization of Piezoelectric Energy Harvester(Cond.. )

Material Properties


Simulation parameters for the genetic algorithm optimization

Optimization of Piezoelectric Energy Harvester(Cond.. )


Results of optimization problem


Harvest a power 75% higher

Conclusion

�Fromthe overview, it is quite clear that piezoelectric energyharvesting has great potential at micro level and some veryimportant part of applications are still in the research anddevelopment stage.


�The ability of piezoelectric equipment to convert motionfrom human body into electrical power is remarkable.

�It is a great hope that energy harvesting will rule the nextdecade in the technical field

62

1. M. Raju, “Energy Harvesting, ULP meets energy harvesting: A game-changing combination for design engineers,” Texas Instrument White Paper, Nov. 2008

2. R.J.M. Vullers, V. Leonov, T. Sterken, A. Schmitz, “Energy Scavengers For Wireless Intelligent Microsystems,” Special Report in Microsystems & Nanosystems, OnBoard Technology, June 2006

3. Imec, “Design for analog and RF technologies and systems,” www.imec.be

References


63

3. Imec, “Design for analog and RF technologies and systems,” www.imec.be4. Imec, “Micropower generation and storage,” www.imec.be5. F. Whetten, “Energy Harvesting Sensor Systems – A Proposed Application

for 802.15.4f, ” DOC: IEEE802.15-09/0074-00-004f6. C. Cossio, “Harvest energy using a piezoelectric buzzer,” EDN, pg.94-96,

March 20, 2008

Thank you


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Energy Harvesting Throurgh Piezoelectric Materials

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