Energy Harvesting:
introduction
NiPS Summer School
July 7-12th, 2015
Fiuggi, Italy
Francesco Cottone
NiPS lab, Physics Dep., Università di Perugia, Italy
francesco.cottone at unipg.it
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 1
Summary
Energy harvesting applications and principles
Fundamentals of vibration energy harvesters
Beyond linear systems: linear and nonlinear
approaches
Conclusions
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 2
Energy harvesting applications
02/07/2014 - Belo Horizonte (Brazil)
(birdge collapse at FIAT factory)
Wireless Sensor Networks
Energy Harvesting could enable 90% of WSNs applications (IdTechex)
Environmental MonitoringStructural Monitoring
Transportation
Wearable sensing for health
applicationsEmergency medical response
Monitoring, pacemaker, defibrillators
Military applications
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• Ultra capacitors
• Rechargeable
Batteries
• Wireless Sensor
Node
• Piezoelectric
• Electrodynamics
• Photovoltaic
• Hydro Turbine
Wasted thermal energy
Electronic
device
Energy
Harvesting
Generator
Temporary
Storage
system
EM energy
Solar
Vibrations
Traffic
Hydro/wind
Power sources available from the ambient
RF
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Biochemical
Thermal
energy Radioactivity
Examples of energy harvesting systems
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Crystal radio - 1906
Sailing ship (XVI-XVII century)
Tree - vegetation
Self-charging
Seiko wristwatch
First automatic wristwatch,
Harwood, c. 1929 (Deutsches
Uhrenmuseum, Inv. 47-3543)
First automatic watch.
Abraham-Louis Perrelet,
Le Locle. 1776
Vibration energy harvesting versus
power requirements
Devic
e P
ow
er
Consu
mpti
on
Time
VEH
sPow
er
Densi
ty
Zero Power ??
100-300W/cm3 ?
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Vibration Energy Harvesters (VEHs): basics
Inertial generators are more flexible than direct-force devices because they require
only one point of attachment to a moving structure, allowing a greater degree of
miniaturization.
Load (ULP sensors, MEMS
actuators)
Bridge Diodes
Rectifier
Cstorag
e ZL
Vou
t
AC/DC
converter Vibration
Energy
Harvester
RL
Transducer
k
i
F(t)
zRL d
m
fe
k
i
Transducer
F(t)=mÿ
zd
m
fe
y
zinc oxide (ZnO) nanowires
Wang et al. 2008
Energy harvesting from
moth vibrations
Chang. MIT 2013
Energy Harvesting from dancing
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Vibration
Harvesting
Generator
Magnetostrictive
Piezoelectric
Electromagnetic
V
Moving magnet
Spring
Coil
(a) (b)
(c)
Electrostatic/Capacitive
Proof mass
Springs
Vb
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Vibration Energy Harvesters (VEHs): basics
Piezoelectric conversion
Unpolarized
Crystal
Polarized
Crystal
After poling the zirconate-titanate atoms are off center.
The molecule becomes elongated and polarized
9
Pioneering work on the direct
piezoelectric effect (stress-charge)
in this material was presented by
Jacques and Pierre Curie in 1880
In 1903 Pierre received the Nobel
Prize in Physics with his wife, Marie
Skłodowska-Curieand and Henri
Becquerel, for the research on the
radiation phenomena discovered by
Professor Henri Becquerel.
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone
Piezoelectric conversion
Man-made ceramics
• Barium titanate (BaTiO3)—Barium titanate was the
first piezoelectric ceramic discovered.
• Lead titanate (PbTiO3)
• Lead zirconate titanate (Pb[ZrxTi1−x]O3 0≤x≤1)—more
commonly known as PZT, lead zirconate titanate is
the most common piezoelectric ceramic in use
today.
• Lithium niobate (LiNbO3)
Naturally-occurring crystals
• Berlinite (AlPO4), a rare phosphate mineral that is
structurally identical to quartz
• Cane sugar
• Quartz (SiO2)
• Rochelle salt
Polymers
• Polyvinylidene fluoride (PVDF): exhibits
piezoelectricity several times greater than quartz.
Unlike ceramics, long-chain molecules attract and
repel each other when an electric field is applied.
direct piezoelectric effect
Stress-to-charge conversion
10
Biological
• Bones
• DNA !!!
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Piezoelectric conversion
31 Mode
FV
+
-
3
1
2
• S = strain vector (6x1) in Voigt notation
• T = stress vector (6x1) [N/m2]
• sE = compliance matrix (6x6) [m2/N]
• cE = stifness matrix (6x6) [N/m2]
• d = piezoelectric coupling matrix (3x6) in Strain-Charge
[C/N]
• D = electrical displacement (3x1) [C/m2]
• e = piezoelectric coupling matrix (3x6) in Stress-Charge
[C/m2]
• = electric permittivity (3x3) [F/m]
• E = electric field vector (3x1) [N/C] or [V/m]
F33 Mode
V-
+
3
12
Strain-charge
t
E
T
S s T d E
D d T E
Stress-charge
E t
S
T c S e E
D e S E
11NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone
Conversion techniques comparison
Technique Advantages Drawbacks
Piezoelectric • high output voltages
• well adapted for
miniaturization
• high coupling in single
crystal
• no external voltage source
needed
• expensive
• small coupling for
piezoelectric thin films
• large load optimal
impedance required (MΩ)
• Fatigue effect
Electrostatic • suited for MEMS
integration
• good output voltage (2-
10V)
• possiblity of tuning
electromechanical
coupling
• Long-lasting
• need of external bias
voltage
• relatively low power
density at small scale
Electromagnetic • good for low frequencies
(5-100Hz)
• no external voltage source
needed
• suitable to drive low
impedances
• inefficient at MEMS scales:
low magnetic field, micro-
magnets manufacturing
issues
• large mass displacement
required.
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Human activity
Gorlatova, M et al (2013). Movers and shakers: Kinetic energy harvesting for the internet of things.
Example of vibration sources
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Example of vibration sources
Chicago North Bridge
http://realvibration.nipslab.org
Car in highway
Walking person
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A general model for VEHs
RL
k
i
coil
magnet
ÿ
z
Bz
Electromagnetic transduction Piezoelectric transduction
k
i
Piezo bar or cantilever beam
ÿ
z
RL
Seismic massmagnet
Vibrations
( )
( )
L
L c i L c
dU zmz dz V my
dz
V V z
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A general model for VEHs
22
0 2
2
2 2 2
( )2 ( )( )
e
c
L c c
PY m j
R j m d j k j
0
j ty Y e
( )
L
L c i L c
mz dz kz V my
V V z
LINEAR mechanical oscillator 21( )
2U z kz
2
0c c
Z mYms ds k
Vs s
Z mY
det A(s
c)
mY (sc)
ms3 (mc d)s2 (k
c d
c)s k
c
,
V mY
det A
cs
mY cs
ms3 (mc d )s2 (k
c d
c)s k
c
.
Hence, the transfer functions between displacement and voltage over input acceleration are given by
H
ZY(s)
Z
Y, (a) H
VY(s)
V
Y. (b) By substituting s=j in , we can calculate the electrical
power dissipated across the resistive load
Laplace transform
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Piezoelectric conversion
17
22 3131
11 33
.
. E T
El energy dk
Mech energy s
Electromechanical Coupling is an adimensional factor that provides the effectiveness of a
piezoelectric material. IT’s defined as the ratio between the mechanical energy converted and the
electric energy input or the electric energy converted per mechanical energy input
Characteristic PZT-5H BaTiO3 PVDF AlN
(thin film)
d33 (10-10 C/N) 593 149 -33 5,1
d31 (10-10 C/N) -274 78 23 -3,41
k33 0,75 0,48 0,15 0,3
k31 0,39 0,21 0,12 0,23
𝜀𝑟 3400 1700 12 10,5
Strain-charge Stress-charge
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 18
y(t)
z(t)
Mt
RL
i
strain
Lb
VL
Piezoelectric
plates
( )
L
L c i L c
mz dz kz V my
V V z
hp
hs
Piezoelectric layer
Subtrate layer
Le
Lm
Ep and Es are the Young’s modulus of
piezo layer and steel substrate
respectively
Piezoelectric conversion
31 2/ , ,
1 / , 1 / ,
p L
c L p i i p
kd h k R
R C R C
1 2
1 22
3 3
2
,
3 (2 )2, ,
3(2 )2
2
/, 2 ,
2 12 12
p
b m e
b m eb b m
s p b p s p b s
b p
k k k E
b l l lIk k
b l l ll l l
h h w h E E w hb I w h b
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Electromagnetic conversion
Equivalent circuit
i(t)
Ri
Lc
RL
RL
k
i
coil
magnet
ÿ
z
Bz
magnet
( )
L
L c i L c
mz dz kz V my
V V z
/ , ,
/ , / ,
L L
c L c i i c
Bl R Bl R
R L R L
𝑘𝑠𝑝
𝑘𝑠𝑡
𝑔0
𝑚𝑠
𝑅𝐿
𝑉0
𝑑
Mathematical modeling
2 2
2 2
( ),a i
d x dx dU x d ym c c m
dt dt dx dt
0( ) ,L
dR C V V U
dt
2 2
0 lim
2 2
0 lim
1 1( ) , for
2 2( )
1 1( ) ( ) , for
2 2
sp
sp st
k x C x U x x
U x
k k x C x U x x
Governing equations
MEMS electrostatic kinetic energy harvester
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• narrow bandwidth that implies
constrained resonant frequency-tuned
applications
• Non-adaptation to variable vibration
sources
• small inertial mass and high resonant
frequency at micro/nano-scale -> most
of vibration sources are below 100 Hz
Main limits of resonant VEHs
At 20% off the resonance
the power falls by 80-90%
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Beyond linear harvesting systems
Frequency tuning
Wu et al. 2008
Challa et al. 2008
Roundy and Zhang 2004
Piezoelectric cantilever with
a movable mass
Piezoelectric cantilever with magnetic tuning
Piezoelectric beam with a
scavenging and a tuning part
Zhu, et al. (2010). Sensors and Actuators A: Physical
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Beyond linear harvesting systems
Frequency tuning
Tang et al. 2010
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Multimodal Energy Harvesting
Beyond linear harvesting systems
Ferrari, M., et al. (2008). Sensors and Actuators A: Physical
Hybrid harvester with piezoelectric and electromagnetic transduction
mechanisms
Tadesse et al. 2009
Shahruz 2006
Piezoelectric cantilever arrays
with various lengths and tip masses
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H. Kulah and K. Najafi, IEEE Sensors Journal 8 (3), 261 (2008).
D.G. Lee et al. IEEE porc. (2007)
Frequency-up conversion
Jung, S.-M. et al. (2010). Applied Physics Letters
Beyond linear harvesting systems
Le, C. P., Halvorsen (2012). Journal of Intelligent Material Systems and
Structures
Impact electrostatic MEMS generator
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Burrow, S.G and Clare, L.R. IEEE porc. (2007)
Nonlinear systems
Beyond linear harvesting systems
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009).
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2 0 1 2
2 2 3/2
1( , )
2 2 ( )eff
M MU x K x
x
Magneto-elastic potential
Governing equations of a single-DOF
piezo-magnetoelastic model
( , ) ( ) ( ) ( ) ( ) ( )
1( ) ( ) ( );
eff v
c L p
U xmx t x t K x t K V t my t
x
V t V t K x t R C
Mechanical vibrations
Piezoelectric beam
x
ÿ
m
Opposing magnets
Vout
Cottone, F., H. Vocca & L. Gammaitoni. PRL, 102 (2009).
Beyond linear harvesting systemsNonlinear systems for vibration energy harvesting
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Bistable oscillators for vibration energy harvesting
Resonant monostableBistable: inter-well and
intra-well oscillations
Bifurcation point
x
U(x,)
=25mm
x
U(x,)
Cottone, F., H. Vocca & L. Gammaitoni, Nonlinear Energy Harvesting. PRL, 102 (2009).NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 28
Bistable oscillators for vibration energy harvesting
Resonant monostableBistable: inter-well and
intra-well oscillations
Bandwith enhancement
when interwell jumps occur
x
U(x,)
=25mm
x
U(x,)
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Buckled beam piezoelectric harvesters
Snapping between buckled states
Cottone, F., Gammaitoni, L., Vocca, H., Ferrari, M., & Ferrari, V. (2012). Smart materials and structures, 21(3), 035021
stretching
bending
stretching
PP
Bistable oscillators for vibration energy harvesting
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 30
L L
x
L0
z
w(x,t)
hp
hs
Steel support
Piezoelectric layer
V (t)ip(t) Cp RL
RL
b
zk+1
zk
P
Buckled piezoelectric beams
1( , ) ) ( , )(w x t w v x tx
stretching
bending
stretching
0( ) (1 cos(2 / )) / 2x h x L
the initial buckling shape function is
P
by applying Euler-Lagrange equations
( ), ( )d d
F t I tdt q q dt
L L L L
gives two coupled second order nonlinear differential equations
governing the motion of the piezoelectric buckled beam
Where the output voltage is related to the flux linkage
0 1
33 2 1 0
2
,
2 2 .L p P P
V V
k kV V
R C C C
mq cq k q k k q k z
q qq
P
V
Bistable oscillators for vibration energy harvesting
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Experimental and numerical results
Cottone, F., L. Gammaitoni, H. Vocca, M. Ferrari & V. Ferrari (2012) Smart materials and structures, 21, 2012.
Bistable oscillators for vibration energy harvesting
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Nonlinear electromagnetic generators for wide
band vibrational energy harvesting
2 2
3
2 2
( ) 1 ( ) ( )( ) ( ) ( ) ,
d q dq d yq q V
d Q d d
2( )( )
1,
em
dV dqV k
d d
0 / ( )R L 2 2
2
1 1
( ).em
c c
Blk
k L k L
22
1 0
pzkk C
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Nonlinear electromagnetic generators for wide
band vibrational energy harvesting
Bandwidth
enhancement of 2.5x
with bistability at 0,2 grms
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Université Paris-Est, ESIEE Paris,
Silicon MEMS electrostatic harvesters.
• Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F. and T. Bourouina. IEEE TRANSDUCERS 2013.
• R., Guillemet, Basset., P, Galayko, D., Cottone, F., Marty, F. and T. Bourouina. Conf. Proceeding IEEE MEMS 2013.
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MEMS electrostatic kinetic energy harvester
MEMS electrostatic kinetic energy harvester
Basset, P., Galayko, D., Cottone, F., Guillemet, R., Blokhina, E., Marty, F., & Bourouina, T. (2014). Journal of Micromechanics and Microengineering
24(3), 035001
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013). 2013 Transducers & Eurosensors.
Guilllemet, R., Basset, P., Galayko, D., Cottone, F., Marty, F., & Bourouina, T. (2013).
Micro Electro Mechanical Systems (MEMS), 2013 IEEE 26th International Conference on (pp. 817-820): IEEE.
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F. Cottone, P. Basset Université Paris-Est, ESIEE Paris,
Silicon MEMS-based electrostatic harvesters.
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MEMS electrostatic kinetic energy harvester
Cottone, F., Basset, P., Guillemet, R., Galayko, D., Marty, F., & Bourouina, T. (2013).
Transducers & Eurosensors.
MEMS electrostatic kinetic energy harvester
Basset, P., Galayko, D., Cottone, F., Guillemet, R., Blokhina, E., Marty, F., &
Bourouina, T. (2014). JMM 24(3), 035001.
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Velocity-amplified mulitple-mass EM VEH
1 1 2 1 22
1 2
( 1) ( )i if
e m v m em vv
m m
the final velocity of the smaller mass is
v2f = 2v1f − v2i.
In the case of equal but opposite initial velocities
v2f = − 3v2i,
which represents a gain factor of 3x in velocity.
if 𝑒 = 1 and in the limit of m1 / m2 → ∞,
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Electromagnetic generators
Electromagnetic generators
For a series of n−bodies of progressively
smaller mass that impact sequentially,
the velocity gain is proportional to n.
(Rodgers et al., 2008)
, 1
1,0
2 , 1
1(1 ) 1
1
nk k
n
k k k
eG e
r
Velocity-amplified mulitple-mass EM VEH
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Velocity-amplified mulitple-mass EM VEH
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Electromagnetic generators
Velocity-amplified mulitple-mass EM VEH
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Electromagnetic generators
Velocity-amplified mulitple-mass EM VEH
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Electromagnetic generators
Moving coil
Gap magnet
expansions (iron)
High Q-factor
springs
Linear low friction
guides
Base for clamping
Top cap
NdFeB Magnets
University of Limerick (Ireland) and Bell-Labs Alcatel (USA).
F. Cottone, G. Suresh, J. Punch - “Energy Harvesting Apparatus Having Improved Efficiency”. US Patent n.
8350394B2
Prototype 2 with transversal magnetic flux
Velocity-amplified mulitple-mass EM VEH
NiPS Summer School 2015 – July 7-12th -Fiuggi (Italy) – F. Cottone 44
Electromagnetic generators
Moving coil
Gap magnet
expansions (iron)
High Q-factor
springs
Linear low friction
guides
Base for clamping
Top cap
NdFeB
Magnets
Velocity-amplified mulitple-mass EM VEH
University of Limerick (Ireland) and Bell-Labs Alcatel (USA).
F. Cottone, G. Suresh, J. Punch - “Energy Harvesting Apparatus Having
Improved Efficiency”. US Patent n. 8350394B2
Prototype 2 with transversal flux linkage
Improvement up to a
factor 10x
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Electromagnetic generators
Comparison of various approaches
Zhu, D., Tudor, M. J., & Beeby, S. P. (2010).
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Performance metrics
Mitcheson, P. D., E. M. Yeatman, et al. (2008). Proceedings of the IEEE 96(9): 1457-1486.
Bandwidth figure of merit
Frequency range within which the output
power is less than 1 dB
below its maximum value
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Conclusions
o Marriage between Energy harvesting systems and Zero-power
Technology will enable autonomous WSN applications
o Energy harvesting systems can be improved by:
o Nonlinear dynamic: Bistable systems, freqeuncy-up converters,
impacting masses, electrostatic softening
o Innovative electro-active materials (electrets, lead-free piezo)
o Miniaturization
o Zero-Power Technology has plenty of room for improvement at
level of
o Low-consumption components,
o Efficient conditioning.
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Current technical challenges
o Miniaturization issues
o Improvements of piezoelectric-material properties
o Improving capacitive design
o Increasing magnetic filed in micro magnets
o Research on electrets materials
o Efficient conditioning electronics
o Efficient Integrated design
o Power-aware operation of the powered device
o Target applications
o Tailoring the WSN technology to specific applications
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