energy harvesting throurgh piezoelectric materials
DESCRIPTION
energy harvestingTRANSCRIPT
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Rajeev Kumar
Energy Harvesting through Piezoelectric Material
Computational Intelligence Applications to Renewable Energy-2012
Rajeev KumarSchool of Engineering
IIT Mandi
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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
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Energy harvesting or the process of acquiring energy from thesurrounding environment has been a continuous humanendeavor throughout history.
Energy harvesting
Introduction
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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..)
Computational Intelligence Applications to Renewable Energy-2012
• 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
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Available energy sources in the environment
Introduction (Cond..)
Computational Intelligence Applications to Renewable Energy-2012
Available energy sources
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Energy Scavenging through Vibration
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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..)
Computational Intelligence Applications to Renewable Energy-2012
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
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Examples of common vibration sources
Energy Scavenging through Vibration(Cond..)
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Thermodynamic of piezoelectric material
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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..)
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Thermodynamic of piezoelectric material ( Cond..)
The mechanical strain produced in the crystal under electric voltage is referred as converse piezoelectric effect.
Converse Piezoelectric Effect
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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
Thermodynamic of piezoelectric material ( Cond..)
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Thermodynamic of piezoelectric material ( Cond..)
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
Computational Intelligence Applications to Renewable Energy-2012
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)
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Polarization of Piezoelectric Material
Thermodynamic of piezoelectric material (Cond..)
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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.
Computational Intelligence Applications to Renewable Energy-2012 15
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
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• Several nightclubs,mostly in Europehave alreadybegun to powertheir strobes andstereos using theforce of hundreds
Applications of Energy Harvesting through Piezoelectric Material ( Cond..)
Computational Intelligence Applications to Renewable Energy-2012
force of hundredsof people poundingon piezoelectriclined dance floors
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Applications of Energy Harvesting through Piezoelectric Material ( Cond..)
• Several gyms, notable in Portland and a few other places arepowered by a combination of piezoelectric set ups and generatorsset up on stationary bikes.
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• Laying piezoelectric crystalarrays underneath sidewalks,stairwells, and pretty much anyother high traffic area to powerstreet lights.
Applications of Energy Harvesting through Piezoelectric Material ( Cond..)
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• Piezoelectric Powered MusicInstruments
Applications of Energy Harvesting through Piezoelectric Material ( Cond..)
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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.
Computational Intelligence Applications to Renewable Energy-2012
andmobilephones.
• Biomechanical Energy Harvester
• Energy harvesting byPiezoelectric windmills
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Identify the need or problem
Research the need or problem
Modify to improve the design if needed
Engineering Design Process
Computational Intelligence Applications to Renewable Energy-2012 21
Develop possible solutions
Select the best solutionsConstruct a
prototype
Test and evaluate the prototype
Detailed Design
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Analyze the problem
Detailed Design
Optimization of the problem
Detailed Drawing of the problem
Engineering Design Process (Contd..)
Computational Intelligence Applications to Renewable Energy-2012 22
the problem
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Piezoelectric Energy Harvester Model
The electromechanical model of this structure can be represented
Computational Intelligence Applications to Renewable Energy-2012
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
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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
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•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..)
Computational Intelligence Applications to Renewable Energy-2012
•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
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Piezoelectric Energy Harvester Model ( Cond..)
Computational Intelligence Applications to Renewable Energy-2012
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�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
Piezoelectric Energy Harvester Model ( Cond..)
Objective function
Computational Intelligence Applications to Renewable Energy-2012
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{ } [ ] { } [ ] { } { } Θ−−= kkkk EeQ λεσ
Direct Piezoelectric effect
Constitutive relation
Finite Element Modeling
Converse piezoelectric effect
Computational Intelligence Applications to Renewable Energy-2012 28
Direct Piezoelectric effect
{ } [ ] { } { } { } { } Θ++= kk
T
kk PEbeD ε
For a non piezoelectric layer
{ }oek
=
−
{ } { }0=kP { } { }oE k =
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Where [ ] [ ] [ ] [ ] [ ][ ]θε TTTeTe kokvkΤ=
[ ] [ ] [ ] [ ]vkvk TbTb Τ=
{ } [ ] { }kvk pTp Τ=
[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ]θεεθ TTTQTTTQ ΤΤΤ=
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012
{ } [ ] [ ] [ ] { }kkok TTT λλ εθΤΤΤ=
[ ]εT
][ oT
[ ]θT
[ ]vT
[ ] [ ] [ ] [ ] [ ] [ ] [ ][ ]θεεθ TTTQTTTQ kokkok =
Strain transformation matrix
Ply orientation transformation matrix
Rotational transformational matrix
Vector transformation matrix
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[ ]
( ) ( )
( ) ( )
−−
−−
=
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
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012
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
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[ ] ( ) ( ) ( )( ) ( ) ( )( ) ( ) ( )
+++++++++
=
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
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012
( ) ( ) ( )
+++ 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
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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
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 32
( ) )1(12
1 2iiN ηηξ +−=
( )( )iiN ξξη +−= 112
1 2
( )22 1)1( ηξ −−=iN
i=5,7
i=6,8
i=9
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+
=
bottomi
i
i
topi
i
i
middlei
i
i
z
y
x
z
y
x
z
y
x
2
1
Nodal Coordinates
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 33
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
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iii
i
middlei
i
i
ii VtN
z
y
x
N
z
y
x
32
rζ∑∑ +
=
Relation between the Co-ordinate systems
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 34
∑
∑
=
==
=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
×=
=
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Displacement Field
iii
i
npi
i
innel
ii VHN
z
y
x
N
z
y
x
3
r
∑∑ +
=
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 35
ii kk
oki ttH2
ζ+=
( ) [ ]
−+
=
∑= i
iii
i
i
innel
ii VVH
w
v
u
N
w
v
u
βα
ζηξ 211
,rr
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{ } [ ] { }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
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 36
{ }
=
zx
yz
xy
z
y
x
εεεεεε
ε
∂∂+
∂∂
∂∂+
∂∂
∂∂+
∂∂
∂∂∂∂∂
z
u
x
wy
w
z
vx
v
y
uz
wy
vx
=
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oi
oi
nnel ziiziii
yiiyiii
xiixiii
v
u
gngnN
gmgmy
N
glglx
N
−∂
∂
−∂
∂
−∂
∂
12
12
12
00
00
00
Finite Element Modeling (Cond..)
Strain Field
Computational Intelligence Applications to Renewable Energy-2012 37
{ }( ) ( )
( ) ( )
( ) ( )
[ ] { }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
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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
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 38
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
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{ } { }kpek BE φφ−=
Electric field in the kth piezoelectric layer within the element can be given as
l
Finite Element Modeling (Cond..) Electric Field
Computational Intelligence Applications to Renewable Energy-2012 39
Where
{ }
=
3
3
31
n
m
l
tB
kpeφ
Thickness of kth piezoelectric layer
Electric potential of kth piezoelectric layer
kpt
kpφ
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{ } { }kpek BE φφ−=
Electric field in the kth piezoelectric layer within the element can be given as
l
Finite Element Modeling (Cond..) Electric Field
Computational Intelligence Applications to Renewable Energy-2012 40
Where
{ }
=
3
3
31
n
m
l
tB
kpeφ
Thickness of kth piezoelectric layer
Electric potential of kth piezoelectric layer
kpt
kpφ
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{ } { } dAdzV k
A k
σεΤ
∫ ∫∑=2
1
Using the variational principle the potential energy is given as
Substituting various values
Finite Element Modeling (Cond..)
Strain energy
Computational Intelligence Applications to Renewable Energy-2012 41
{ } [ ] { } { } [ ] { } { } [ ] { }[ ]eeueeeueeeuue kqkqqkqV θφ θφΤΤΤ −+=
2
1
Substituting various values
where[ ] [ ] [ ] [ ]∑∫
=
Τ=nl
k V
ekeeuu dVBQBk1
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[ ] [ ] [ ] { } [ ] [ ] { } [ ] [ ] { }
= ∫∫∫
ΤΤΤΤΤΤ
Vepe
Vepe
Vepeeu dVBeBdVBeBdVBeBk
npl φφφφ ...21
[ ] [ ] { } [ ] [ ] { } [ ]( )dVNBHNBknl
k Vekeekeeu ∑∫
=
ΤΘ
Τ +=1
ϕθ λλ
Finite Element Modeling (Cond..) Strain energy
Computational Intelligence Applications to Renewable Energy-2012 42
{ }
=
nplp
p
p
e
φ
φφ
φ
.
.
.2
1
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{ } { }dzdADEWA k
t
t
ee
k
k
∫∑ ∫−
Τ=1
2
1
The element electrical energy can be given as
Finite Element Modeling (Cond..)
Electrical energy
Computational Intelligence Applications to Renewable Energy-2012 43
{ } [ ] { } { } [ ] { } { } [ ] { }eeeeeeeeuee kkqkW θφφφφ φθφφφ
ΤΤΤ −+−=2
1
2
1
2
1
Substituting various values
where
[ ] [ ]Τ=eueu kk φφ
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[ ]
{ } [ ] { }{ } [ ] { }
∫
∫Τ
Τ
Vepe
Vepe
dVBbB
dVBbB
φφ
φφ
.
2
1
Finite Element Modeling (Cond..)
Electrical energy
Computational Intelligence Applications to Renewable Energy-2012 44
[ ]
{ } [ ] { }
=
∫Τ
Vepe
e
dVBbB
k
npl φφ
φφ
.
.
.
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[ ]
{ } { } [ ] { } { } [ ]( ){ } { } [ ] { } { } [ ]( )
+
+
∫
∫Τ
ΘΤ
ΤΘ
Τ
Vepeepe
Vepeepe
dVNpBHNpB
dVNpBHNpB
φφφ
φφφ
22
11
Finite Element Modeling (Cond.)
Electrical energy
Computational Intelligence Applications to Renewable Energy-2012 45
[ ]
{ } { } [ ] { } { } [ ]( )
+
=
∫Τ
ΘΤ
Vepeepe
V
e
dVNpBHNpB
k
nplnpl φφφ
φθ
.
.
.
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( )( )∑∫=
++=nl
k V
k dVwvuT1
222
2
1&&&ρ
Substituting various values
The element kinetic energy can be given as
Finite Element Modeling (Cond..)
Kinetic energy
Computational Intelligence Applications to Renewable Energy-2012 46
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
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[ ] ∑
−−−
=nnel
iiiiii
iiiii
eu
HNnHNnN
HNmHNmN
HNlHNlN
N 12
12
00
00
00
Finite Element Modeling (Cond..)
Kinetic energy
Computational Intelligence Applications to Renewable Energy-2012 47
−iiiiii HNnHNnN 1200
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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
Computational Intelligence Applications to Renewable Energy-2012 48
{ } [ ] { } [ ] { }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
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∫ =+f
o
t
t
s dtWL 0)(δ ( )∫ =++−f
o
t
t
se dtWWVT 0δδδδ
Using Hamilton’s principle
Finite Element Modeling (Cond..)
Computational Intelligence Applications to Renewable Energy-2012 49
The governing equation for an element can be written as
[ ] { } [ ] { } [ ] { } [ ] { } { }emeeueeueeuueeuu Fkkqkqm =−++ θφ θφ 2
1&&
[ ] { } [ ] { } [ ] { } { }eqeeeeeeu Fkkqk =+− θφ φθφφφ 2
1
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[ ]{ } [ ]{ } [ ]{ } { } [ ]{ } [ ]{ }kkFkqkqm φθφ −+=++ 1..
• Sensors and actuators are present
• vector can be partitioned
• No charge accumulates on the sensor layer
Finite Element Modeling (Cond..)
Governing equations
Computational Intelligence Applications to Renewable Energy-2012 50
[ ]{ } [ ]{ } [ ]{ } { } [ ]{ } [ ]{ }auussuuuuu askkFkqkqm φθφ φθφ −+=++
2
1..
[ ]{ } [ ]{ } [ ]{ } { }021 =+− θφ θφφφφ sss
kkqk su
[ ]{ } [ ]{ } [ ]{ } { }aaaa qau Fkkqk =+− θφ θφφφφ 2
1
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Sensor equation
{ } [ ] [ ]{ } [ ]{ }
+= − qkkk us sss φθφφφ θφ2
11
Finite Element Modeling (Cond..)
Governing equations
Computational Intelligence Applications to Renewable Energy-2012 51
Actuator equation
[ ]{ } [ ]{ } [ ] [ ][ ] [ ]( ){ } { } [ ]{ }θθφφφφ umuuuuuuuu kFqkkkkqcqmsss 2
11 +=+++ −&&&
[ ][ ] [ ]{ } [ ]{ }auu asskkkk φθ φφφφ φθ
−− −1
2
1
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Flowchart of Genetic Algorithm
Computational Intelligence Applications to Renewable Energy-2012
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Computational Intelligence Applications to Renewable Energy-2012
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Computational Intelligence Applications to Renewable Energy-2012
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Computational Intelligence Applications to Renewable Energy-2012
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Computational Intelligence Applications to Renewable Energy-2012
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Computational Intelligence Applications to Renewable Energy-2012
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Optimization of Piezoelectric Energy Harvester
Computational Intelligence Applications to Renewable Energy-2012
Maximize
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Optimization of Piezoelectric Energy Harvester(Cond.. )
Material Properties
Computational Intelligence Applications to Renewable Energy-2012
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Simulation parameters for the genetic algorithm optimization
Optimization of Piezoelectric Energy Harvester(Cond.. )
Computational Intelligence Applications to Renewable Energy-2012
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Results of optimization problem
Computational Intelligence Applications to Renewable Energy-2012
Harvest a power 75% higher
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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.
Computational Intelligence Applications to Renewable Energy-2012
�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
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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
Computational Intelligence Applications to Renewable Energy-2012
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
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Thank you
Computational Intelligence Applications to Renewable Energy-2012 64