ABSTRACT
Title of document: WIND-INDUCED VIBRATION ENERGY HARVESTING
USING PIEZOELECTRIC TRANSDUCERS COUPLED
WITH DYNAMIC MAGNIFICATION
Austin Baker, Kathryn Connolly, Lauren Dorsey, Ian Grissom,
Alden Grobicki, Kevin Keller, Chandan Kittur, Daniel
Konecki, Mark Lee, Timothy Lee, Boheng Ma, Edward
Mulhern, Andrea Ng, Mihir Patel.
Directed by: Professor Amr Baz
Department of Mechanical Engineering
Flexible cylindrical structures subjected to wind loading experience vibrations from
periodic shedding of vortices in their wake. Vibrations become excessive when the natural
frequencies of the cylinder coincide with the vortex shedding frequency. In this study,
cylinder vibrations are transmitted to a beam inside the structure via dynamic magnifier
system. This system amplifies the strain experienced by piezoelectric patches bonded to
the beam to maximize the conversion from vibrational energy into electrical energy. Real-
world applicability is tested using a wind tunnel to create vortex shedding and comparing
the results to finite element modeling that shows the structural vibrational modes. A
crucial part of this study is conditioning and storing the harvested energy, focusing on
theoretical modeling, design parameter optimization, and experimental validation. The
developed system is helpful in designing wind-induced energy harvesters to meet the
necessity for novel energy resources.
WIND-INDUCED VIBRATION ENERGY HARVESTING USING
PIEZOELECTRIC TRANSDUCERS COUPLED WITH DYNAMIC
MAGNIFICATION
by
Austin Baker, Kathryn Connolly, Lauren Dorsey, Ian Grissom, Alden
Grobicki, Kevin Keller, Chandan Kittur, Daniel Konecki, Mark Lee,
Timothy Lee, Boheng Ma, Edward Mulhern, Andrea Ng, Mihir Patel
Thesis submitted in partial fulfillment
of the requirements of the
Gemstone Program
2014
Advisory Committee:
Professor Amr Baz, Mentor
Professor Balakumar Balachandran
Professor Johan Larsson
Dr. Ronald G. Polcawich
Dr. Robert M. Proie
Professor Norman M. Wereley
Professor Miao Yu
c© Copyright by
Austin Baker, Kathryn Connolly, Lauren Dorsey, Ian Grissom, Alden
Grobicki, Kevin Keller, Chandan Kittur, Daniel Konecki, Mark Lee,
Timothy Lee, Boheng Ma, Edward Mulhern, Andrea Ng, Mihir Patel.
2014
ACKNOWLEDGEMENTS
We would like to thank our mentor, Dr. Amr Baz, and his graduate students, Dr.
Mostafa Nouh and Mohamed Raafat and the other members of his lab. We would also like
to thank our librarian, Nedelina Tchangalova. We want to acknowledge the ACCIAC and
the Maryland Sustainability Fund. In addition, we want to give a huge thanks to all of the
Gemstone staff. We want to recognize all of our family and friends who have supported
us along the way.
ii
Table of Contents
List of Figures vii
List of Tables x
1 Introduction 1
2 Literature Review 7
2.1 Energy Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Piezoelectricity . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.3 Vortex Induced Vibrations . . . . . . . . . . . . . . . . . . . . . 13
2.1.4 Unimorph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.5 Dynamic Magnification . . . . . . . . . . . . . . . . . . . . . . 18
2.1.6 Related Research . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Energy Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.1 Rectifier Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
iii
2.3.1 Battery Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.2 Supercapacitor Systems . . . . . . . . . . . . . . . . . . . . . . 28
2.3.3 Supercapacitor and Li-ion Battery Hybrid System . . . . . . . . . 30
2.3.4 Control Circuitry . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3 Harvesting 35
3.1 Harvesting Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Prototype Fabrication . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.2 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . 37
3.1.3 Vibrometer and Shaker Testing . . . . . . . . . . . . . . . . . . . 38
3.1.4 Wind Tunnel Testing . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.5 Performance without Magnifier . . . . . . . . . . . . . . . . . . 40
3.1.6 Performance with Magnifier . . . . . . . . . . . . . . . . . . . . 41
3.2 Harvesting Results and Discussion . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . 42
3.2.2 Shaker Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3 Vibrometer Testing . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.4 Wind Tunnel Testing . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.5 Harvesting Discussion . . . . . . . . . . . . . . . . . . . . . . . 51
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Conditioning 54
4.1 Conditioning Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.1.1 Construction of the Rectifier Circuit Models . . . . . . . . . . . . 54
iv
4.1.2 Tuning of the Rectifier Circuits . . . . . . . . . . . . . . . . . . 56
4.1.3 Running pSpice Simulations . . . . . . . . . . . . . . . . . . . . 59
4.1.4 Evaluating the Simulation Results . . . . . . . . . . . . . . . . . 60
4.1.5 Construction of the Physical Rectifier Circuits . . . . . . . . . . . 61
4.1.6 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.1.7 Collecting Experimental Data . . . . . . . . . . . . . . . . . . . 64
4.1.8 Derivations for Piezoelectric Analog Model . . . . . . . . . . . . 66
4.2 Conditioning Results and Discussion . . . . . . . . . . . . . . . . . . . . 69
4.2.1 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.2.2 Conditioning Discussion . . . . . . . . . . . . . . . . . . . . . . 74
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5 Storage 80
5.1 Storage Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.1.1 Battery Selection and Initial Testing . . . . . . . . . . . . . . . . 80
5.1.2 Charging System . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.1.3 Battery Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.4 Energy Measurement . . . . . . . . . . . . . . . . . . . . . . . . 85
5.1.5 Calculation of Efficiency from Measurements . . . . . . . . . . . 86
5.1.6 Supercapacitor Hybrid System . . . . . . . . . . . . . . . . . . . 87
5.2 Storage Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.1 Initial Setup Results . . . . . . . . . . . . . . . . . . . . . . . . 88
5.2.2 Final Setup Results . . . . . . . . . . . . . . . . . . . . . . . . . 89
v
5.2.3 Storage Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Integration 97
6.1 Integration Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.4 Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7 Conclusion 102
Glossary 104
Bibliography 108
Appendices 116
vi
List of Figures
1.0.1 U.S. Carbon Emissions from 1990-2010 . . . . . . . . . . . . . . . . . . 1
1.0.2 Breakdown of U.S. carbon emissions by industry . . . . . . . . . . . . . 2
1.0.3 Breakdown of U.S. energy consumption . . . . . . . . . . . . . . . . . . 4
1.0.4 Map of U.S. wind speeds . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Piezoelectric effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Phase Diagram for PZT . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.3 Effect of cyclic loading on PZT strain value . . . . . . . . . . . . . . . . 11
2.1.4 Relationship between cyclic loading of PZT and crack growth length . . 12
2.1.5 Vortex formation behind a bluff body . . . . . . . . . . . . . . . . . . . 13
2.1.6 Effect of Reynold’s number on vortex formation . . . . . . . . . . . . . 14
2.1.7 VIVACE converter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.8 Circuit model of a piezoelectric unimorph . . . . . . . . . . . . . . . . . 18
2.1.9 Dynamic magnification system . . . . . . . . . . . . . . . . . . . . . . 19
2.1.10Piezoelectric harvester designed by Dr. Francis Moon . . . . . . . . . . 21
2.2.1 Conditioning Circuit diagrams . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1 Specific power and energy of different batteries . . . . . . . . . . . . . . 28
vii
2.3.2 Power density and energy density for different storage systems . . . . . . 30
3.1.1 Wiring diagram of the piezoelectric harvester . . . . . . . . . . . . . . . 36
3.1.2 CAD render of the piezoelectric harvester prototype . . . . . . . . . . . 37
3.1.3 Ling/LDS V408 V-408 Low Force Vibration Shaker . . . . . . . . . . . 39
3.1.4 Correlation between wind velocity and fan frequency . . . . . . . . . . . 40
3.2.1 Bending modes of the beam with baseline configuration . . . . . . . . . 41
3.2.2 Bending modes of the beam with dynamic magnification . . . . . . . . . 42
3.2.3 Sine sweep of the beam in the baseline system . . . . . . . . . . . . . . 44
3.2.4 Sine sweep of the cylinder in the baseline system . . . . . . . . . . . . . 44
3.2.5 Displacement color map of baseline beam . . . . . . . . . . . . . . . . . 45
3.2.6 Displacement color map of the beam with dynamic magnification . . . . 46
3.2.7 Fast-Fourier transform of the output voltage of the baseline harvester . . 48
3.2.8 Peak voltage for two elastomers at optimal flow velocity . . . . . . . . . 49
3.2.9 Peak voltage for two elastomers after optimal flow velocity . . . . . . . . 50
4.1.1 pSpice schematic for the SEH circuit. . . . . . . . . . . . . . . . . . . . 55
4.1.2 pSpice schematic for the SSHI-P circuit. . . . . . . . . . . . . . . . . . 57
4.1.3 Bode plot for gain and phase shift of differentiator . . . . . . . . . . . . 58
4.1.4 Effect of RVAL value on voltage . . . . . . . . . . . . . . . . . . . . . . 60
4.1.5 Image of resistor box . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.1.6 SEH circuit setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.1.7 Image of piezoelectric shaker setup for conditioning testing . . . . . . . 63
4.1.8 Schematic for measuring a signal with the DAQ . . . . . . . . . . . . . 65
viii
4.1.9 Input voltage from the piezoelectric stripe . . . . . . . . . . . . . . . . . 66
4.1.10Diagram of model used to simulate the piezoelectric analog . . . . . . . 67
4.1.11Piezoelectric analog model calibration . . . . . . . . . . . . . . . . . . . 69
4.2.1 Piezoelectric analog model voltage vs load resistance . . . . . . . . . . . 71
4.2.2 Piezoelectric analog model power vs load resistance . . . . . . . . . . . 72
4.2.3 Simulated output voltage for SEH and SSHI-P . . . . . . . . . . . . . . 73
4.2.4 Simulated output power for SEH and SSHI-P . . . . . . . . . . . . . . . 74
5.1.1 Boost converter configuration . . . . . . . . . . . . . . . . . . . . . . . 83
5.2.1 Breakout circuit designed for the MAX17710 . . . . . . . . . . . . . . . 89
5.2.2 Voltage profile of unexpected breakdown . . . . . . . . . . . . . . . . . 91
6.2.1 Voltage across piezoelectric element at 56 Hz . . . . . . . . . . . . . . . 99
6.2.2 Rectifier output for integrated circuit . . . . . . . . . . . . . . . . . . . 100
ix
List of Tables
4.1 SEH pSpice component legend . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 SSHI-P pSpice component legend . . . . . . . . . . . . . . . . . . . . . 56
4.3 SSHI-P fixed component values . . . . . . . . . . . . . . . . . . . . . . 57
4.4 SSHI-P fixed component values . . . . . . . . . . . . . . . . . . . . . . 64
4.5 Value of parameters in piezoelectric model . . . . . . . . . . . . . . . . . 68
4.6 Simulated and experimental peak power output . . . . . . . . . . . . . . 72
5.1 Discharge voltage ranges over time . . . . . . . . . . . . . . . . . . . . . 90
5.2 Discharge of the battery over 3 hours . . . . . . . . . . . . . . . . . . . . 92
x
1 Introduction
Undisciplined and minimally restrained use of the Earth’s natural resources for en-
ergy production has led to significant environmental damage. In order to reduce this en-
vironmental damage, great strides must be made in the field of renewable energy sources.
Energy is currently produced primarily by burning fossil fuels such as coal, natural gas,
and petroleum[50]. Although these processes are reliable energy sources, the natural re-
sources which drive them are finite[20]. The byproducts of these processes can result
in harmful climate changes including acid precipitation, stratospheric ozone depletion,
Figure 1.0.1: Carbon dioxide equivalent emitted by the US from 1990-2009.
1
Figure 1.0.2: CO2 emissions breakdown by industry in the U.S.
and the greenhouse effect[14]. According to the United States Environmental Protection
Agency, greenhouse gases trap heat in the atmosphere, and an estimated fifty percent
of this effect is attributed to the buildup of carbon dioxide[50]. Methane, chlorofluo-
rocarbons, halons, nitrous oxide, ozone, and peroxyacteylnitrate produced in industrial
processes make up the remaining fifty percent[14]. Because of the increasing amounts of
greenhouse gases being emitted into the atmosphere due to human activities, the overall
temperature of the earth is increasing over time. If current emission levels persist through
the end of this century, the temperature of the earth could increase 2.0 to 11.5 degrees
Fahrenheit above temperatures from the 1990s[50]. Climate variability has a detrimental
effect on many natural and human processes, such as agriculture, precipitation patterns,
and human health[1].
While methane, nitrous oxide, and hydrofluorocarbons are all greenhouse gases,
2
carbon dioxide, a byproduct of the burning of fossil fuels, makes up 83% of all the
greenhouse gas emissions in the United States[50]. Figure 1.0.1 illustrates the amount
of carbon dioxide released into the atmosphere from 1990 to 2009. Most of the carbon
dioxide emissions resulted from burning fossil fuels, mainly coal. While carbon dioxide
emissions have decreased since the early 2000s, a significant amount of the gas is still
emitting into the atmosphere to this day[50].
The majority of these greenhouse gas emissions are a result of the electric power
industry, which relies mostly on coal (Figure 1.0.2). Further exploration, development,
and utilization of alternative energy sources are crucial to making society’s energy depen-
dence more sustainable and less harmful to the environment.
The U.S. Energy Information Administration (EIA) defines renewable energy as
any source of energy that can regenerate and can be sustained indefinitely, and such
sources include solar power, geothermal energy, and wind energy. Recent reports by
the EIA state that from 2009 to 2011 renewable energy has only made an increase of 1%
in the its share of the total primary energy production, from approximately 8% to 9% of
the total energy consumed in the United States and 10.3% of the energy generated for
electricity consumption[50, 49].
Wind power is an excellent candidate for renewable energy. Wind energy can be
harvested at all times of the day, unlike solar power, which depends on the hours of day-
light. Also, though wind is present at all times of year, other energy sources such as
biofuels depend on seasonal variation and harvest yields. Among current renewable en-
ergy sources, wind power has had the least growth. According to the EIA, from 2009 to
2011, wind power experienced only a 2% increase for electricity produced from renew-
3
able sources (Figure 1.0.3)[49].
Most current wind energy harvesting devices are large turbines that utilize internal
moving mechanical parts and require maintenance. In addition, these large turbines are
centralized in the Midwestern United States due to the higher wind velocities that oc-
cur in that region (Figure 1.0.4). Wind turbines also cause problems for local wildlife,
endangering all flying animals and affecting their ecosystems.
The U.S. Department of Energy reported in April 2011 that areas with annual av-
erage wind speeds around 6.5 m/s and greater at a height of 80 meters are generally con-
sidered to have suitable wind resource for wind development. According to Figure 1.0.4
Maryland, along with a majority of other states, does not receive adequate wind speeds
Figure 1.0.3: Breakdown of energy consumption in the U.S.
4
Figure 1.0.4: Average wind speeds across the U.S.
in order to viably utilize wind as an alternative energy source. To most effectively utilize
regional differences in renewable resources, these resources will require implementation
primarily on a local level in order to provide enough energy for the population[13]. While
wind turbines require high wind velocities, there are practical alternatives for wind energy
harvesting at lower wind velocities.
One possible implementation of an energy harvester uses piezoelectric materials to
harvest energy from vibrations induced on a dynamically magnified bluff body by vortex
induced shedding. This design lowers the required wind speed for energy harvesting
dramatically, while the use of piezoelectrics as the energy converting element reduces
the need for maintenance. Renewable energy sources throughout the nation comprise a
minority of all energy produced in the U.S. In this study, a case is presented for using
5
piezoelectric-based wind energy harvesters because of their simplicity, reliability, and
high conversion efficiency at low wind speeds.
6
2 Literature Review
The design of a new type of energy harvester is split into three categories, each
of which addresses a separate component of the harvester: the energy harvesting device,
the electrical conditioning circuitry, and the storage system. Extensive literature review
in the fields respective to each of these categories has guided the design process of each
subsystem.
2.1 Energy Harvesting
The design for the wind energy harvesting device is based on research for the best
piezoelectric materials and on a structure that requires a minimal amount of maintenance
and moving parts. The literature review includes research of specific piezoelectric ma-
terials, an examination of the properties compatible with the proposed application, the
plausibility of an efficient, real world application based on wind data, the phenomenon of
vortex induced vibrations (VIV), and the coupling of vibrations with dynamic magnifica-
tion.
7
2.1.1 Piezoelectricity
Piezoelectric materials possess the unique ability to convert between electrical and
mechanical energy. The piezoelectric effect occurs in certain materials when a mechanical
stress is applied, causing the electrical charges in the molecules of the material to develop.
As the material is deformed, the molecules realign in a manner that forms a surface charge
density leading to voltage (Figure 2.1.1).
Figure 2.1.1: Piezoelectric effect
The converse piezoelectric effect is observed when an electrical charge is applied
to a piezoelectric material[35]. The molecules are electrically inclined to create a dipole,
thus causing a physical change in shape as the molecules realign. Piezoelectricity was
first discovered in 1880 when the brothers Pierre and Paul-Jacques Curie observed that
mechanical stress in certain materials such as tourmaline, cane sugar, topaz, and quartz
resulted in the production of electric charge in the material. In 1881, Gabriel Lippmann
predicted the converse effect using thermodynamic principles [4]. These properties can be
found in crystalline materials such as quartz, bone, dentine, and sugar cane[35]. In mod-
ern day research and applications, piezoelectric materials are preferred for the immediacy
8
and simplicity of the transduction mechanism between the mechanical and electrical field
[4]. The use of piezoelectric materials requires minimal incorporation of moving and
quickly degrading parts.
Although there is a variety of piezoelectric materials, two types were considered
for this design: ceramics and polymers. Ceramics, such as lead zirconate titonate (PZT),
were first used as piezoelectric materials in 1947. PZT has now become the most com-
monly utilized ceramic piezoelectric material[42]. Although the piezoelectric properties
of polymers were discovered in 1924, they were not used until the 1950s when researchers
studied the strong piezoelectric properties of polyvinylidenefluoride (PVDF)[42]. Both
materials have their advantages and disadvantages. Piezoceramics have a large strain re-
sponse and therefore a high voltage output with piezoelectric constants of about 200 to
400 pC/N. The ceramics, however, are brittle and suffer from both high loss factors and
highly hysteretic behavior [33, 38]. PVDF is much more flexible and can be modified
easily to different dimensions of size and thickness, though it suffers from a lower piezo-
electric constant of about 10 pC/N[33]. Despite the structural advantages of polymers,
ceramics deliver greater voltage in response to mechanical strain, which is a primary goal
of this design. Both materials were considered in this study to determine the best combi-
nation of the two for a specific range of wind velocities and frequencies.
2.1.2 Fatigue
Many piezoelectric materials were researched for the optimal electromechanical
properties of an energy harvester. For use in sensors and actuators, piezoelectric materi-
9
als must have low dielectric and mechanical losses since the energy dissipation from these
factors can change the physical properties of the material. They must also have high elec-
tromechanical coupling coefficients, which indicates a high conversion efficiency from
mechanical strain to electrical charge[9].
Figure 2.1.2: Crystal phases of PZT[9]
For most applications of PZT (Pb[ZrxTi1−x]O3 0 ≤ x ≤ 1), the ideal performance
occurs at the boundary between the tetragonal and rhombohedral perovskite phases, as
seen in Figure 2.1.2. This is where the piezoelectric coefficients reach their maximum due
to a peak in the spontaneous polarization, which is directly proportional to the intrinsic
piezoelectric coefficient. In addition, the almost degenerate states of the tetragonal and
rhombohedral structure allow the domains within the grains to be reoriented and aligned
10
through exposure to an electric field or by direct electrical poling. This reorientation
maximizes the extrinsic piezoelectric contributions [9].
Figure 2.1.3: Strain value for PZT after cyclic loading
By substituting hardener or acceptor ions with lower valence states into the PZT
system, the properties can be modified and diverge to hard or soft PZT. Hard PZT ex-
hibits low losses and a high quality factor, but it only has modest values for the dielectric
constant and piezoelectric coefficient. Alternatively, soft PZT exhibits a high dielectric
constant and piezoelectric coefficient, but also exhibits high losses. Differences between
the macroscopic properties of hard and soft PZT are caused by domain wall motion in
piezoceramics [17].
The strain value increases with increasing cyclic loading, and settles after 50× 104
cycles for the PZT ceramics, as seen in the Figure 2.1.3. The endurance limit for PZT
11
is at a stress amplitude of 180 MPa[39]. Figure 2.1.4 shows how crack growth length is
affected by frequency of the load. The fatigue crack growth length increased nonlinearly
during the cyclic loading, reaching its maximum at 5 kHz.
Figure 2.1.4: Cracks form in PZT during cyclic loading.
Electrically fatigued PZT with cyclic bipolar loading shows a large number of mi-
crocracks in the microstructure in regions near the surface, with the bulk showing no
observable cracking. The loss in the polarization due to fatigue cracking can be regained
by removing the affected surface layer to expose the internal bulk, meaning that these re-
gions are largely responsible for the degradation of piezoelectric properties in PZT. After
removing the load to 0 V the strain value becomes zero for PZT ceramics[34].
12
2.1.3 Vortex Induced Vibrations
Vortex induced vibrations(VIVs) occur when a bluff body rests in a flow within a
range of Reynolds numbers from an approximate minimum value of 40 to an approximate
maximum of 3× 105 (Figure 2.1.5).
Figure 2.1.5: Vortex formation behind a bluff body[18]
Within these Reynolds numbers the flow splits apart so that the layers closest to the
body start curving around behind it [11]. These layers, known as free shear layers, turn
in opposite directions around the body [11]. As shown in Figures 2.1.6 and 2.1.5, these
layers alternate in feeding a vortex until the vortex’s rotation pulls the opposite shear layer
across the object, thereby shedding the vortex and commencing the creation of the next
vortex[18]. The end result is that vortices are created on alternating sides of the bluff body
with a repeating frequency. The frequency at which the vortices are created is known as
the shedding frequency and is dependent on the bluff body and the Strouhal number of
the fluid [11].
The formation and shedding of a vortex causes the bluff body to experience unequal
13
Figure 2.1.6: Air flow around a bluff body with varied Reynolds numbers[32]
pressures from different sides, leading the body to move back and forth perpendicular to
the flow. This oscillating motion is greatest when the shedding frequency is equal to
the natural oscillating frequency of the object[11]. These vibrations can be harvested by
various means, including the use of piezoelectric materials and conventional mechanical
generators[10, 46].
Vortex shedding from an oscillating bluff body is significantly different from that
14
of a fixed bluff body. In fact, the principles by which the incoming flow interacts with the
bluff body alter when motion is either externally induced or vortex-induced[7]. One of the
problems with vortex shedding on an oscillating bluff body is the difficulty in modeling
the distributed force exerted by the fluid along the length of the body[8]. The oscillatory
motion of the body makes analysis of the resultant force complex, so Bearman et al. uti-
lized finite element modeling (FEM) of the bluff body in order to ensure the accuracy of
the analysis. The bluff body and fluid involved in this study were a flexible cylinder and
water and the primary quantities examined included the fluid forces and the lift and drag
coefficients. The results of the study show that, based on a predetermined FEM, a force
distribution analysis along the surface of a bluff body is plausible. Despite its success, the
study emphasized that it utilized indirect measurement methods, and more direct mea-
surement methods remain unavailable. Although the FEM provided solid groundwork in
terms of a place to start for initial modeling, the exact details of the force distribution still
require more clarity [8].
One example of a modern vortex-induced power harvester is the VIVACE converter
developed at the University of Michigan [10]. The converter consists of a series of cylin-
ders placed within a current of water, shown in Figure 2.1.7, which oscillate vertically
like pistons in a motor, creating either usable electricity or hydraulic energy. The main
fault with this project is that constant acceleration and deceleration of the cylinders caused
by their oscillating motion, combined with friction between the parts, eventually damage
the unit. Using piezoelectric materials to convert vortex induced vibrations into electricity
eliminates the need for moving parts.
15
Figure 2.1.7: Model of the VIVACE converter[10]
2.1.4 Unimorph
The ceramic unimorph cantilever beam was identified as the most relevant design
for the purpose of this project. The beam is fixed on one end and free on the other end, and
the ceramic piezoelectric material is attached on top of the beam close to the fixed end.
This ensures the highest strain because it is the location of the largest bending moment. A
proof mass is also applied in order to increase the strain during the vibration[48]. Power
is given by
P =
mξA2
ω
(
ω
ωN
)


(
2ξ
ω
ωN
)2
+
(
1−
(
ω
ωN
)2
)2


−1
(2.1.1)
where P is power, m is the mass, ξ is the damping coefficient, ω is the operating fre-
quency, ωN is the natural frequency, and A is amplitude of the acceleration. The optimal
16
resonance power, when the operating frequency equals the natural frequency, is given by
P =
mξA2
4ωNξ2
(2.1.2)
The natural frequency is determined by calculating the transverse stiffness and effective
mass using
k0 = W
[
Gbh3b
12
+ 2G
(
h3p
12
+
hp(hp + hb)2
4
)](pi
L
)4
(
L
2
)
(2.1.3)
meff = mproof +
WL
2
(ρbhb + 2ρphp) (2.1.4)
ωN =
√
k0
meff
(2.1.5)
where W and L are the width and length respectively. G is the young’s modulus, h is the
thickness and ρ is the density. The subscript b denotes the beam and the p denotes the
ceramic piezoelectric material. The length, width, thickness, and proof mass need to be
optimized to match the operating frequency in order to get the largest power.
The piezoelectric unimorph can be modeled as a circuit as shown in Figure 2.1.8
where the energy conversion is modeled as a charge source. The piezoelectric ceramic
acts like a capacitor(Cp), and the parallel resistance(Rd) models the dielectric leakage.
This is then used to charge a storage device. The electric power is given by the following
equation.
Pelec = CpV
2
peakfd (2.1.6)
The peak voltage is the voltage at maximum compression of the ceramic where fd is
the operating frequency. The efficiency of the conversion from electrical to mechanical
energy is given by the following equation.
ν =
CpV 2peak
Fd
(2.1.7)
17
Figure 2.1.8: Circuit model of a piezoelectric unimorph[48]
F is force and d is displacement. The efficiency can be experimentally determined. Using
this efficiency and the resonance power, the peak voltage can be predicted.
2.1.5 Dynamic Magnification
The basics of simple harmonic motion lead into the concept of dynamic magnifi-
cation. The main differential equation governing a simple harmonic oscillator is given
by
mx¨(t) + cx˙(t) + kx(t) = f(t) (2.1.8)
where m is the mass of the oscillator, c is the viscous damping coefficient for the system,
k is the oscillator stiffness and f(t) is the applied force with respect to time[19].
These properties lead to the following relations:
ω0 =
√
k
m
(2.1.9)
ξ =
c
2mωN
(2.1.10)
where ωN is the natural frequency and ξ is the damping ratio.After substitution of Eq. 2.1.9
18
and Eq. 2.1.10 into Eq. 2.1.8 the following is obtained
x¨(t) + 2ξωN x˙(t) + ω
2
Nx(t) =
f(t)
m
(2.1.11)
Figure 2.1.9: Dynamic magnification system configuration
The main structure in the system is referred to as the tube and the beam-mass sys-
tem used to magnify the oscillations is referred to as the auxiliary beam or simply the
beam. This beam configuration is demonstrated in Figure 2.1.9. The concept of dynamic
magnification is similar to the idea of a tuned mass damper. The difference, however,
lies in choosing auxiliary beam properties that will generate maximum amplitude in the
oscillations of the auxiliary beam rather than dampen the amplitude of the primary beam
oscillations.
In previous experiments, there has been success in magnifying both the system’s
first mode, as done by Aldraihem and Baz, and in the magnification of multi-mode oscil-
19
lations, as in the experiments conducted by Zhou et al[2, 51]. In the latter experiments, the
addition of an optimized tuned mass damper increased the harvested energy to 25.5 times
that of a single beam energy harvester[19]. This maximum magnification was achieved
by adjusting the length of the auxiliary beam and the mass attached to auxiliary beam
until both the primary and auxiliary structure had the same natural frequency.
In the single mode experiments conducted by Aldraihem and Baz, it was shown that
the maximum energy harvested can be magnified by a factor of 20 using a tuned dynamic
magnifier. This maximum was reached by adjusting the auxiliary beam properties until it
resonated with the primary beam.
With preliminary figures for the dimensions of the primary structure and the aux-
iliary beam, it is possible to complete a comprehensive finite element analysis where the
structure is theoretically tuned by adjusting the proof mass and the length of the auxiliary
beam[51].
2.1.6 Related Research
While the design of the prototype and dynamic magnification system described in
this report is novel, piezoelectric energy harvesting research is both an established and
rapidly growing field. At Cornell University, Dr. Francis Moon leads a team of under-
graduate engineering students in designing a piezoelectric energy harvester comprised
of an array of foam masses on cantilevers that vibrate in wind. In Figure 2.1.10 below,
the energy harvester is positioned on the roof of a building to maximize wind exposure
and energy harvested. The team from Cornell sees a future for similar arrays since the
20
design is both more space efficient and less expensive than traditional wind energy har-
vesters like turbines. In addition to using piezoelectric materials to harvest the vibrational
energy, the team is examining the feasibility of an electromagnetic apparatus for energy
conversion. This option could also be a viable opportunity for future research for the
harvester constructed by Team PRESSURE[27].
Figure 2.1.10: An undergraduate researcher adjusts the piezoelectric array
2.2 Energy Conditioning
The power harvesting capabilities of piezoelectric harvesters have improved through
optimization of the conditioning circuits. The current produced directly from a piezoelec-
tric energy harvester is not easily stored, as electrical energy is best stored by a direct
current (DC). Therefore, the alternating electrical output from the harvester must be con-
ditioned by a rectifier circuit to produce stable DC output. The rectifier circuit serves as
21
an efficient and effective intermediary between the harvesting and storage components of
the harvester.
2.2.1 Rectifier Circuits
Early designs for rectifier circuits utilized diodes and capacitors to convert alter-
nating current to direct current. These conditioning circuits employed standard passive
diode rectification to condition signals. However, conditioning circuits that utilize active
rectification, which adds switching elements to the rectifier, were found to increase the
efficiency of power transfer by up to 400%. In these circuit designs, the switches are
typically synchronized with the vibrations of the harvester by monitoring the voltage on
the piezoelectric element of the harvester.
In most cases, the switches are turned on for high voltages to allow for energy
storage and turned off for low voltages to prevent loss[3]. These two types of rectifier
circuit designs are known as the standard energy harvester (SEH) and the synchronous
switch harvesting on inductor (SSHI). As seen in 2.2.1a, the SEH consists of a standard
full-bridge rectifier circuit coupled with a resistor and a capacitor in series.
The main goal of SSHI circuits is to synchronize the changes in voltage with the
changes in current in a piezoelectric material. In normal piezoelectric materials the ca-
pacitance will result in a -90◦ phase shift between the voltage and the current, so an SSHI
circuit uses an inductor and a switch to remove the phase shift[41]. The SSHI is formed
by placing a branch with an inductor and a switch in parallel or in series to the traditional
SEH circuit, as shown in 2.2.1b. The switch is thrown during the peak of the incoming
22
(a) SEH circuit diagram
(b) SSHI circuit diagram
Figure 2.2.1: Conditioning circuit diagrams[28]
voltage signal, allowing the inductor to resonate with the piezoelectric material’s capac-
itance, resulting in the inversion of the piezoelectric material’s voltage. This results in a
higher power output because the capacitor starts in a charged state which is related to the
inversion factor of the circuit[41].
One method of detecting the peak at which the switch should be thrown is through
the use of a differentiator. When the differentiated signal is zero, the voltage has reached
a peak. A simple differentiator can be devised using a resistor and capacitor, but suffers
from low gain, so a more effective design is one using an op-amp as a differentiator
and a Schmitt Trigger as a comparator. When powered by external sources, the design
experiences a 230% improvement when compared to the standard diode bridge. When
self-powered, the design experiences a 118% power improvement from the standard diode
bridge[28].
SEH, SSHI-series, and SSHI-parallel circuits have a number of advantages and dis-
advantages. For weakly coupled systems, both the SSHI-series and parallel circuits pro-
23
duce optimal power outputs which are much greater than the SEH method. For medium
range coupled systems, the peak power is comparable for all three circuits, though SSHI
is less sensitive to frequency changes[44]. For strongly coupled systems, all three meth-
ods have similar peak optimal power outputs. The series-SSHI circuit experiences a sig-
nificant loss in performance in weakly coupled systems when diode loss is accounted
for[31]. The SSHI circuit also has voltage losses due to switching circuitry, voltage gap,
and switching phase delay[41].
2.2.2 Impedance Matching
Maximum efficiency is obtained by using complete impedance versus incomplete
impedance matching. The difference between incomplete and complete impedance is
whether or not the reactive impedance is accounted for. Impedance can be divided into
two types: real and reactive. The reactive capacitance causes the voltage and current
coming from the mechanical system to be out of phase. The power of the system is
maximized when the phase between the current and the voltage is zero. This can only be
achieved through complete impedance matching. In order to obtain complete impedance
matching, the input impedance of the electrical transmission system must be the complex
conjugate of the output impedance of the mechanical system. Incomplete impedance
matching is when only the real part of the impedance is matched and the reactive part is
neglected. Using complete matching instead of incomplete matching can result in a 20%
increase in power [12]. Constrained matching is maximizing the harvesting power subject
to the constraints on the reactance of the electrical part, the resistance of the dissipative
24
component of the electrical part and the resistance of the harvesting component of the
electrical part. Constrained matching is more effective than free matching in a non-ideal
setting[30]
The real impedance from the mechanical system comes from the mechanical stress
as well as the resistive element of the piezoelectric material, while the reactive impedance
comes from the capacitive element of the piezoelectric material. This capacitive element
inherently shunts some of the current flow, causing a significant drop in output power.
One possible solution for correcting this impedance mismatch is to include an in-
ductor in parallel with the piezoelectric generator. However, there are numerous problems
that arise when considering this solution. Both the impedance of the inductor and the
impedance of the capacitor are frequency dependent, so any shift in frequency other than
the resonant frequency causes an impedance mismatch. Additionally, only uncharacter-
istically large inductances, typically over 1 H, completely cancel the capacitive element.
Generating such a large inductance would be impractical as the inductor’s size would be
large relative to the system[28].
Another possibility is joining a capacitive element in parallel with an even larger
external capacitor, which drastically reduces the amount of inductance necessary to cancel
the capacitive impedance. However, this setup has an extreme frequency dependence due
to the large capacitance. By adding the external capacitance, the system will generate
large reactive currents, forcing large losses in power[28].
25
2.3 Energy Storage
The final component of the energy harvester is the storage system. The storage sys-
tem must be capable of storing the energy rectified by the conditioning circuit. Potential
storage systems include batteries and supercapacitors controlled by smart chargers that
can prevent overdischarges and provide regulated outputs.
2.3.1 Battery Systems
Common rechargeable battery systems used for energy storage include lead acid
(Pb-acid), nickel metal hydride (NiMH), nickel cadmium (NiCd), sodium sulfur (NaS),
sodium metal hydride (NaMH), and lithium ion (Li-ion). Characteristics relevant to the
performance of a battery system include its energy capacity, power capacity, energy den-
sity, life span, operating temperature, and rate of self-discharge.
Energy capacity refers to the total energy that a battery can hold. Power capacity is
the maximum rate energy can be transferred into or out of the battery over time. Energy
density and power density are the energy and power capacities per unit volume, respec-
tively. High energy and power capacity are desirable in a battery. The life span of the
battery is the number of charge and discharge cycles the battery can be cycled through
before it must be replaced. The operating temperature is the optimum operating tempera-
ture of the battery. High temperatures decrease lifespan, while low temperatures decrease
battery capacity for most batteries. Rate of self-discharge is the amount of energy dissi-
pated from the battery over time when it is not connected to a load[16].
Each battery system has different storage properties. Lithium-ion, NiCd, and NaS
26
batteries have the highest power density among batteries. NiCd and Pb-acid batteries are
excellent pulsed power suppliers, but are large and heavy. In addition, NiCd and Pb-
acid batteries have high energy densities but are difficult to recharge. Since NiCd and
Pb-acid batteries are difficult to recharge, they do not perform well in applications where
the batteries require recharging many thousands of times in a lifespan. NaS batteries
are smaller and lighter than NiCd batteries[15]. They also have high energy density,
high cycling flexibility, low maintenance requirements, and high coulombic efficiency.
However, NaS batteries are sensitive to overcharging and overdischarging and operate at
very high temperatures, ranging from 270◦C - 350◦ C [16]. Their constant heat input
requirement is inconvenient and unrealistic for a self-sustaining system[15].
Li-ion batteries hold the greatest potential in terms of battery storage systems. Li-
ion batteries outperform NiMH, NiCd, and Pb-acid batteries in providing energy and
holding high specific power by at least a factor of 2.5, as shown in Figure 2.3.1 [16,
47]. They are particularly valuable because of their small size, light weight, high energy
density, as well as their high output voltages and high storage efficiency [16, 15]. Li-
ion batteries have a low self-discharge while not in use, one of the highest energy-to-
weight ratios, and suffer less from memory effect. In addition, they have a long life
cycle and rate capability [16]. The disadvantages of Li-ion batteries include high cost and
a self-damaging effect when deeply discharged. When this occurs, the battery lifetime
can drop to hazardously low levels[15]. Li-ion batteries prefer partial discharge to deep
discharge, which does not lower the energy capacity since they exhibit little memory
effect. Despite the disadvantages of Li-ion batteries, they remain the superior battery
device for the design.
27
Figure 2.3.1: Specific power and energy of different batteries[16]
2.3.2 Supercapacitor Systems
Supercapacitors, also known as ultracapacitors and electrochemical capacitors, have
been used successfully in a number of applications. Supercapacitors are used for regen-
erative braking in transportation vehicles, for consumer products such as cell phones and
cameras, and for solar and wind energy harvesters[26].
The structure of a supercapacitor allows for capacitances 100 to 1000 times greater
than those of traditional capacitors[5, 22]. Their large capacitance makes supercapac-
itors a viable energy storage option for various applications. A supercapacitor can be
electrically modeled as two capacitors with an internal resistance in series; however, this
resistance is nominal compared to the internal resistance of a battery cell. Because of their
lower resistance, supercapacitors can have over ten times the power densities of normal
batteries[5].
While supercapacitors can operate in a relatively wide range of temperatures and
28
voltages, -40◦C to 85◦C and 0.8 to 2.0 volts per cell, they are operated well within these
ranges to prevent the lifetime from being significantly shortened[5, 25]. For every 100
mV or 10◦C that a supercapacitor is operated at above its rated voltage and tempera-
ture, the lifetime of the supercapacitor is halved[22]. In addition, if the supercapacitor
is operated outside its voltage range, chemical reactions may begin to occur, causing the
supercapacitor to act more like a battery. The oxidation and reduction reactions result in
the formation of impurities within the cell which decreases the lifetime and capacitance
of the supercapacitor[5].
Unlike batteries, which store energy through chemical reactions within the cell, su-
percapacitors physically store and transfer charge across the electrode plates. This means
that supercapacitors can last through hundreds of thousands of cycles, while batteries
have a significantly shorter lifetime[5]. The Ragone chart in Figure 2.3.2 below depicts
the relationship between energy density and power density for batteries and supercapaci-
tors. From this chart, it is evident that double layer supercapacitors store less energy than
batteries, but they can discharge at a much faster rate[29]. In addition, supercapacitors
have a power density in the range of 18 kW/kg, significantly higher than that of a Li-ion
battery. A supercapacitor’s ability to charge and discharge in tens of seconds is benefi-
cial for many applications, especially those in which there is a variable source and load,
such as harvesting energy from varying renewable energy sources like the sun and wind.
Batteries, on the other hand, take hours to fully charge or discharge. However, super-
capacitors lack an energy density as high as that of batteries; therefore, for large energy
storage needs batteries are more suitable[25].
Supercapacitors are a viable energy storage option over batteries due to their high
29
Figure 2.3.2: Power and energy density for different storage systems[29]
power density, wide operating temperature range, and long lifetime; however, there are
some disadvantages of supercapacitors that must also be considered. Supercapacitors are
ideal for applications requiring a rapid discharge, but not for those requiring slow and
steady power discharge. Many potential applications of a piezoelectric device require a
storage system to discharge energy at a steady rate. A supercapacitor is unable to store
a large amount of energy due to its low energy capacity, making it unsuitable as the sole
energy storage system[26].
2.3.3 Supercapacitor and Li-ion Battery Hybrid System
A hybrid system with both a Li-ion battery and a supercapacitor has the desirable
characteristics of both. Qualities such as the long lifetime and large range of operating
temperatures of supercapacitors are complemented by the high energy density of Li-ion
30
batteries. A Li-ion battery generally limits the longevity of a storage system. However,
using a supercapacitor to manage the charging of the Li-ion battery increases the lifetime
of the storage system[40]. Li-ion batteries typically undergo a charge cycle that begins
with a constant current charging period followed by a constant voltage charging period
until a full state of charge (SOC) is reached. The constant current charging period charges
70%-80% of the battery in 20%-30% of the total charge time, while the constant voltage
charging period charges the remaining 20%-30% in the remaining charge time. In order to
increase the longevity of a Li-ion battery, charging should occur at a constant, low current;
the number of charge/discharge cycles should be as low as possible; and the battery should
not undergo irregular charging in the constant voltage stage, as this decreases battery
lifetime[40].
A supercapacitor reduces the number of cycles experienced by the battery by smooth-
ing out the fluctuations in power from the source, thus extending the longevity of the sys-
tem. Coupling supercapacitors to the Li-ion battery in the storage system reduces the rate
capacity effect in the battery and increases the peak current that is provided to the load.
Repeated high current discharges also reduce battery lifetime and thereby the longevity of
the storage system. The supercapacitor can store energy from the battery during low load
periods and release the extra energy necessary during high load periods. This allows the
entire system to provide a higher overall peak discharge current while not exceeding the
peak discharge current allowed for the Li-ion battery[24]. Using such a system increases
the energy density of the system by up to 8% and extends the serviceable lifetime of the
storage system[43].
Energy density, mass, and cost are important considerations for sizing a supercapac-
31
itor in a hybrid system. A larger supercapacitor helps decrease the battery’s peak charge
and discharge rates, leading to a longer system lifespan; however, because supercapacitors
have a low energy density, the energy density of the system is also reduced[43]. A hybrid
system can achieve higher power than a battery or supercapacitor alone because higher
peak currents are produced when the two are coupled. A supercapacitor also increases the
energy storage capacity of the overall system by over 20% in pulsed or fluctuating loads
as compared with systems with only a Li-ion battery. This occurs because during pulsed
loads, the supercapacitor supports the voltage provided by the battery during the time that
the load draws current[24]. The overall capacity of the hybrid system as compared with a
battery without a supercapacitor remains relatively unchanged because the supercapacitor
can store little energy compared to the Li-ion battery.
The addition of a supercapacitor to a Li-ion battery not only increases the peak
current delivered, but also regulates the charge and discharge of the battery in order to
extend the battery lifetime, which decreases the total life cycle costs of the piezoelectric
harvesting system. When sizing the supercapacitor for a hybrid system, design factors
include peak load current, typical input power, and battery specifications.
2.3.4 Control Circuitry
A control circuit is important for regulating the power entering the energy storage
system. When energy enters the system, an initial capacitor or supercapacitor charges
up to a threshold voltage, after which charge is allowed to flow to the Li-ion battery.
The voltage of the battery is controlled to prevent overcharging the battery. When there
32
is insufficient input power to charge the battery, the voltage of the supercapacitor drops
significantly, so the cycle terminates. In the hybrid system, the charge on the battery is
preserved until the supercapacitor discharges below a threshold voltage and the battery
enters a discharge cycle to supply energy to the load[40]. A similar algorithm can be
used in energy management circuits to ensure the longevity of a Li-ion battery. Ongaro et
al. utilized this algorithm in an energy management and storage system for a photovoltaic
array, which also experiences varying input power depending on weather conditions. This
study found that the number of charge/discharge cycles decrease by a factor of four when
utilizing a supercapacitor and Li-ion hybrid system.
Another component of control circuitry is the boost or DC-DC step up converter,
which can greatly increase the effectiveness of a storage system. DC-DC converters are
commonly used to regulate the output from highly variable sources such as wind sources
and solar cells. Switch mode converters include boost converters, which step a voltage up,
buck converters, which step a voltage down, and buck-boost converters, which regulate a
voltage either higher or lower. Each uses a capacitor, an inductor, and a switch with other
components. The inductor or capacitor is used to store energy, which is released when
the switch changes position, thus enabling a higher output voltage to be realized from a
lower input voltage. The coupling inductor is crucial to the performance of the design,
and depending on the circuit, the power efficiency of the converter ranges between 67%
and 86%[37].
There are a variety of DC-DC converters commercially available that could be used
to integrate low voltage systems such as a supercapacitor with otherwise incompatible
voltages such as a battery. For example, Linear Technologies’ LTC3533 buck-boost con-
33
verter operates at input and output voltages of 1.8 V to 5.5 V with efficiencies of up to
96%. The LTC3785 is a similar device that has been shown to produce 3.3 V at 3 A
from a 2.7 V to 10 V input source with efficiencies as high as 96%[23]. The efficiency
and power consumption of the DC-DC converter are important factors to consider in the
design of the storage system.
34
3 Harvesting
The purpose of the harvesting system is to design an energy harvester that utilizes
piezoelectric materials to convert mechanical energy from vortex induced vibrations to
electrical energy. A comprehensive model of a system with dynamic magnification is gen-
erated to accurately simulate prototype behavior under varying conditions. Additionally,
the experimental performance of a dynamic magnifier is compared to that of a baseline
energy harvester.
3.1 Harvesting Methodology
In this section, fabrication of the prototype, testing facilities and experimental meth-
ods are discussed. CAD models, simulation parameters and instrument specifications are
presented. Finally, baseline and dynamic magnification configurations are explained.
3.1.1 Prototype Fabrication
In order to determine the transferability of theoretical results to real world appli-
cations, a small scale prototype harvester was constructed. To construct the prototype
leads were soldered to the top and bottom contacts of four 2.25” PZT-5H bimorphs. The
ceramic PZT-5H was purchased from APC International. These piezoelectric samples
35
were then secured to the top and bottom of a 10.75” acrylic magnifier beam using epoxy.
To harvest energy from all four piezoelectric elements, the elements were connected in a
manner such that their voltage potentials were summed. The inner surfaces were wired
to a ’positive’ lead, and the outer surfaces were wired to a ’negative’ lead. The bending
of the cantilever beam due to external vibrations caused the inner surfaces to be in com-
pression and the outer surface to be in tension. The corresponding setup can be seen in
Figure 3.1.1.
Figure 3.1.1: Wiring schematic of the piezoelectric harvester
The beam was then epoxied to a base plug as defined by the cantilever design.
In order to create dynamic magnification, a rubber ring design was selected to serve as
a sleeve for the base plug. Three different types of elastomer tubing purchased from
McMaster-Carr were cut to lengths of 3/8” (creating rings). To assemble the harvester,
the beam-plug-elastomer system was then inserted inside the free end of a cantilevered
plastic cylinder. The plastic cylinders for the harvester structure were purchased from
Uline Shipping Supply Specialists. At the fixed end of the cantilevered plastic cylinder,
the base contained a small sleeve for stabilization, and duct tape was used to further
secure the connection. The base for the cylinder and the base plugs were fabricated using
a rapid prototyping machine in the Mechanical Engineering Prototyping Lab (ProtoME).
The prototype base and plugs were custom designed using SolidWorks. The wire leads
36
from the ceramic piezoelectric were taped to the inner walls of the cylinder to reduce any
negative effects due to damping. A computer-aided design (CAD) model and a photo of
the prototype are shown in Figure 3.1.2.
Figure 3.1.2: Labeled CAD render of the harvester prototype
3.1.2 Finite Element Analysis
Following prototype fabrication, a CAD model was created in the engineering sim-
ulation software ANSYS to complete finite element analysis (FEA) of the structure. The
necessary material properties for each element were measured or determined from prior
research, and these physical dimensions and material properties were imported into AN-
SYS. The CAD model was virtually excited across a range of frequencies to determine
the theoretical natural modes of the beam, cylinder, and coupled beam-cylinder assembly.
These results were then compared with later experiments to determine the validity of the
experimental results.
37
3.1.3 Vibrometer and Shaker Testing
The highest voltage output is obtained when the structural frequency of the har-
vester is matched to the vortex shedding frequency. To test the natural modes of the beam
and cylinder, the energy harvester was fixed to a shaker device, as shown in Figure 3.1.3,
so that the beam was orthogonal to the shaking directional axis. This allowed the deter-
mination of the frequency of the first, second and third bending modes for both the beam
and the cylinder, which the harvester experiences when undergoing vortex shedding. A
dynamic signal analyzer, SR785 – 100 kHz 2-ch. FFT analyzer, was used to drive the
shaker at multiple frequencies. In addition, the signal analyzer was used initially to per-
form sine sweeps and obtain the frequencies of the natural bending modes of both the
beam and cylinder. These frequencies were then tested using a PSV-200, OFV-055, Scan-
ning Vibrometer. White reflective tape was applied along the desired test section, which
spanned the entire length of the beam or cylinder, so that the vibrometer could measure
the displacement corresponding to each of the measured frequencies. The results from
the laser vibrometer data were used to verify whether these frequencies correspond to the
correct bending modes.
3.1.4 Wind Tunnel Testing
The laboratory used for the wind tunnel testing of the prototype was the Edwin W.
Inglis ’43 Thermal Fluids Instructional Laboratory at the University of Maryland. Flow in
the wind tunnel was created by a large fan that could be set to different fan frequencies to
modulate the test-section wind speed, as seen in Figure 3.1.4. Wind velocities inside the
38
Figure 3.1.3: Ling/LDS V408 V-408 Low Force Vibration Tester/Shaker and labled ex-
perimental setup.
wind tunnel were measured using a flow meter. In Matlab, a linear regression of the data
points for all the wind velocities and fan frequencies correlated the wind velocity (m/s) to
fan frequency (Hz) as shown in Equation 3.1.1.
v(f) = 0.8456f − 2.9346 (3.1.1)
The first data set included the resonance frequency of the fully assembled cylinder-
beam harvester in the wind tunnel. These results were compared to the shaker results and
the value obtained in the FEA. Voltage output from the piezoelectric elements was taken
over a range of wind velocities from 7.7 m/s to 26.5 m/s.
39
Figure 3.1.4: Wind velocity (m/s) vs. fan frequency (Hz)
3.1.5 Performance without Magnifier
To obtain a baseline with which the theoretical results and the experimental dynamic
magnifier could be compared, a larger base plug was fabricated to fit in the free end of
the cantilevered cylinder without an elastomer. For testing, this prototype was placed in
the wind tunnel. Measuring voltage output on the signal analyzer across a range of wind
velocities resulted in a correlation between wind speed and piezoelectric voltage output.
In addition, for each wind speed, the signal analyzer showed an FFT plot for the voltage,
which revealed the different modes of the structure (structural frequencies) in addition to
the vortex shedding frequencies. Voltage output was maximized by determining where the
vortex shedding frequency matched the structural frequency. The voltage in the system
was measured across the internal impedance of the scope.
40
3.1.6 Performance with Magnifier
Dynamic magnification testing followed an identical procedure to that of the non-
magnified testing, except that the harvesting structure included the plug-beam subassem-
bly fitted inside an elastomer ring. The voltage outputs of both systems were later com-
pared to one another.
3.2 Harvesting Results and Discussion
In this section, the results from the finite element analysis are presented and dis-
cussed. The experimental results from the shaker and vibrometer testing are compared
with the theoretical simulations. Finally, the wind tunnel results are presented, and a dis-
cussion of the performance of the harvester evaluates the feasibility and success of the
design.
(a)
(b) (c)
Figure 3.2.1: This picture shows the first(a), second(b), and third(c) bending modes of the
beam with baseline configuration from ANSYS
41
(a)
(b)
(c)
Figure 3.2.2: This picture shows the first(a), second(b), and third(c) bending modes of the
beam with dynamic magnification from ANSYS
3.2.1 Finite Element Analysis
In order to validate the vibrometer and wind tunnel results, a computer model of the
harvester was constructed to determine the theoretical performance of the prototype. Both
baseline and dynamic magnification configurations were simulated to ensure that results
from both experiments could be supported theoretically. The code used in the ANSYS
simulation is included in the Appendix and the results are described below. The model
was excited at a continuous range of frequencies from 1 Hz to 200 Hz. The first four
modes of the cylinder and beam were determined and the most important modes shapes
are shown below. The first, second and third modes of the beam are the most important as
they exert the maximum strain on the piezoelectric material. The first three modes of the
beam in the baseline configuration are shown in Figure 3.2.1a, 3.2.1b, and 3.2.1c. Their
frequencies are 9 Hz (a), 34 Hz (b), and 76 Hz (c). The first three modes of the beam with
dynamic magnification are shown in Figure 3.2.2a, 3.2.2b, and 3.2.2c. Their frequencies
42
are 9 Hz (a), 34 Hz (b), and 80 Hz (c). The remainder of the peaks found in the ANSYS
testing are included in the Appendix.
3.2.2 Shaker Testing
After theoretical tests were completed to determine the bending modes of the pro-
totype, the constructed harvester was secured to a shaker for testing as described in the
methodology section of this paper. An initial sine sweep generated by the spectrum ana-
lyzer, and used to drive the shaker, allowed the determination of the frequencies where the
piezoelectric material experienced maximum voltage output. These excitation frequen-
cies were then evaluated using a scanning laser vibrometer to determine which modes the
peaks represented. The sine sweeps for the beam and cylinder in both the baseline and dy-
namic magnification configurations are shown in Figure 3.2.3 and Figure 3.2.4. Since the
cylinder did not have any piezoelectric material to measure the strain, an accelerometer
was utilized in the sine sweep to determine mode locations for the cylinder. In addition,
each of these figures contains a table that presents the theoretical bending modes deter-
mined by the FEA. The sine sweep for the beam showed peaks at 9, 18, 31, 57, 69, 79,
85 and 148 Hz. While the sine sweep peaks at 9, 31 and 85 showed promising correlation
to the results obtained in the finite element analysis, a definitive connection could not be
proved until the laser vibrometer measured the shape of the beam displacement at each of
these frequencies. The sine sweep for the cylinder showed peaks at 18, 31, 59, 70, 79 and
90 Hz. Although the modes did not align exactly due to unknown properties related to the
coupling of the beam-cylinder system, the third mode of the beam and the first mode of
43
the cylinder were close to each other. This finding was important for the eventual tuning
of the system in wind tunnel testing.
Figure 3.2.3: Sine sweep of the beam in the baseline system
Figure 3.2.4: Sine sweep of the cylinder in the baseline system
44
3.2.3 Vibrometer Testing
To demonstrate that the peaks determined in the shaker testing were the same peaks
shown in the finite element analysis, a scanning laser vibrometer was used to measure
precise beam displacement during excitation. The shaker was used to excite the beam
at each peak determined in the previous testing. Although the prototype was excited at
each peak determined by the sine sweep, only the major bending modes of the beam are
shown below. The remaining vibrometer data is included in the Appendix. The first set
of vibrometer data was taken with the baseline configuration. In figures below, the color
map shows the displacement of the beam at 7, 32 and, 60 Hz.
(a) (b)
(c)
Figure 3.2.5: Displacement color maps of the first(a), second(b), and third(c) bending
modes of the beam with baseline configuration
In Figure 3.2.6a the two dimensional color map verified the location of the first
45
bending mode of the beam at 9 Hz for the dynamic magnification configuration. In Fig-
ure 3.2.6b, the prototype was given an input excitation of 31 Hz and the vibrometer results
clearly show the presence of the second bending mode of the beam.The rest of the fre-
quencies present in the sine sweep showed ambiguous mode shapes, which are torsional
modes or superpositions of modes. The most accurate measurements are taken when
the displacements occur along the axis parallel to the laser. Torsion is more difficult to
measure and results in images that are more difficult to classify. Figure 3.2.6c shows the
closest response to a third mode found in the list of frequencies. The bending of the beam
closely resembles a superposition of the second and third modes at 69 Hz which makes it
difficult to determine the location of the third bending mode with the vibrometer.
(a) (b)
(c)
Figure 3.2.6: Displacement color maps of the first(a), second(b), and third(c) bending
modes of the beam with dynamic magnification
46
3.2.4 Wind Tunnel Testing
The final stage of testing involved placing the harvester in the wind tunnel in or-
der to determine the performance of the harvester in a real world application. Three
different harvester configurations were tested: baseline, elastomer A, and elastomer B,
where elastomer A and elastomer B had different stiffnesses. For wind tunnel testing, it
was hypothesized that dynamic magnification would cause the harvester to generate more
voltage than the baseline harvester system. Baseline wind tunnel testing results showed a
peak voltage output of 438 mV at a flow velocity of 12.9 m/s as shown in Figure 3.2.7. In
the baseline configuration, the Strouhal (vortex shedding) frequency was approximately
100 Hz at a flow velocity of 20.6 m/s and the structural frequency was approximately
55 Hz, but at the optimal flow speed of about 13 m/s, the Strouhal frequency aligned
with this structural frequency and the system experienced the highest level of vibrations,
and thereby the highest voltage output. The first bending mode of the cylinder, which is
excited at the Strouhal frequency, matches the third bending mode of the inner beam.
Using elastomer A, the peak voltage output from the harvester was 903 mV, while
using elastomer B, the peak voltage was 939 mV as shown in Figure 3.2.8a and Fig-
ure 3.2.8b. Both of these peaks were measured at a flow velocity of 19.1 m/s. As shown
in Figure 3.2.9, the voltage dropped at flow speeds greater than 19.1 m/s. Voltage outputs
at a greater range of flow velocities were also measured, and the plots of these results can
be found in the Appendix.
As projected, dynamic magnification resulted in more than double the voltage out-
put of the non-magnified harvester system as in the case of elastomer B, which experi-
47
Figure 3.2.7: Peak voltage output for the baseline harvester system without dynamic mag-
nification
enced a 509 mV increase. In the plots from all three setups, the harvester reached its peak
voltage output only at the optimal flow velocity and then subsequently decreased. This
was due to the phenomenon of the coinciding structural and Strouhal frequencies at the
optimal flow velocity that resulted in a voltage peak. This increased voltage output was
desired for the conditioning subgroup to harness and transform into storable electricity.
48
(a)
(b)
Figure 3.2.8: Peak voltage output for the harvester systems with elastomers A(a) and B(b)
49
(a)
(b)
Figure 3.2.9: Peak voltage output for the harvester systems with elastomers A(a) and B(b)
after optimal flow velocity
50
3.2.5 Harvesting Discussion
Although the results show promise for future piezoelectric integration into energy
harvesters, more research must be completed to determine the feasibility of this design.
The experimental prototype utilized in the data collection was not as robust as expected,
leading to errors and inconsistencies in data collection. For example, securing the proto-
type in the wind tunnel required a very precise procedure. Changes in the position of the
prototype, as little as a millimeter, drastically changed the results. Although the results
were precise, a more robust prototype would lead to a higher voltage output. Through-
out testing the prototype was converted from the baseline configuration to the dynamic
magnification configuration multiple times for different sets of data. As the plug and
beam were separated, fatigue on the piezoelectric material and the beam may have led to
non-optimal testing conditions in the later data sets.
The scale of the energy harvester was limited by the dimensions of the wind tunnel
test environment. Specific parameters such as the length of the outer cylinder, the length
of the beam, and the size of the base were governed by the inner dimensions of the test
environment. Larger scale designs could be tested in a wind tunnel with a larger test envi-
ronment. These variations would utilize larger piezoelectric samples to harness vibrations
and produce more voltage.
In retrospect, approaching the project from a vibrational perspective and forgoing
wind tunnel testing to concentrate on shaker testing would have allowed for highly con-
trolled experimental conditions. However, the phenomenon of vortex shedding would be
completely absent in the proposed experimental setup.
51
One significant accomplishment described in the results is the similarity between
shaker data and the ANSYS model for the dynamic magnification configuration. With
an accurate model to describe prototype behavior over a wide range of frequencies, the
harvester can be tuned and modified to maximize output without having to construct mul-
tiple prototypes for testing. Another valuable conclusion is that a dynamically magni-
fied system generates considerably higher voltages than a non-magnified system. The
frequency responses for both systems showed similar trends within their optimal flow
velocity ranges, but the voltage output was over two times higher with dynamic magni-
fication. This significant improvement in output demonstrates the feasibility of dynamic
magnification in wind-induced energy harvesters.
3.3 Summary
The harvesting chapter describes the construction of the energy harvester and data
obtained from FEA, vibrometer/shaker testing, and wind tunnel testing. One of the pri-
mary goals was to determine the viability of dynamic magnification by assessing the
harvester’s performance in the presence of a flow. As such, the harvester was designed
to be interchangeable between a dynamically magnified configuration and a baseline con-
figuration. These two designs were tested extensively with FEA in order to determine the
theoretical natural modes of vibration for the structure. Next, the harvester was analyzed
physically for its modes of vibration using the vibrometer/shaker setup, which allowed for
verification of the FEA modeling. The matching between the FEA and the verification
testing indicated a high-fidelity model for the harvester structure. Based on the results
52
from wind tunnel testing, it was determined that the first bending mode of the cylinder,
which is excited at the Strouhal (vortex shedding) frequency, matches the third bend-
ing mode of the inner beam at the optimal flow velocity. Also, the results showed that
dynamic magnification generated over double the voltage output than the baseline config-
uration. One significant limitation of the design was the scale, in that a larger wind tunnel
test section would have allowed for a better design with more piezoelectric materials.
53
4 Conditioning
The purpose of the conditioning system is to efficiently convert the AC voltage from
the piezoelectric harvester to a DC voltage which can be stored in the storage subsys-
tem. This chapter details the methodology and results for the characterization of optimal
impedance conditions for the SEH and SSHI-P rectifier circuits. A comparision is made
between peak power outputs and corresponding impedance values for the SEH and SSHI-
P circuits. In addition, performance of the two rectifier circuits is analyzed with varying
capacitive loads.
4.1 Conditioning Methodology
In this section, the methodology for the design of the circuit simulation models, the
construction of the experimental setup, and the data collection procedure are described.
4.1.1 Construction of the Rectifier Circuit Models
In order to verify the results obtained from the experimental setup, it was necessary
to create simulated models of the rectification circuits that would be tested. Of the two
circuits constructed, the SEH required the least number of components. Figure 4.1.1
contains the schematic as used in the simulation.
54
Figure 4.1.1: pSpice schematic for the SEH circuit
All model numbers and corresponding values can be found in Table 4.1. While the
value of the capacitor ’C Smoothing’ appears to be fixed in the schematic above, it was
varied between runs. Initially, a capacitor value of 10 µF was used for two reasons: it pro-
vided sufficient control over voltage ripples and allowed for a suitable charge time. The
capacitance was later varied to ensure that the results remained consistent across a range
of capacitor values. The resistive load, ’R Load’ in the schematic, was the independent
variable during the simulated trial runs. The output voltage, and by extension the power,
were the dependent variables.
Model Name Component Value
D1N4148 Leaded Glass Diode N/A
R/ANALOG Resistor 1 kΩ – 100 MΩ
C/ANALOG Capacitor 10, 47, 100, 220 µF
Table 4.1: Model numbers, descriptions and values for the components of the SEH circuit
55
The SSHI-P circuit required far more components and tuning. The SSHI-P resem-
bles the SEH; however, it uses a peak-based switch. The switch needs to toggle for every
peak of the input signal. The design of such a switch is non-trivial and is frequency depen-
dent. The design in the schematic in Figure 4.1.2 was inspired by previous research[41].
A list of the model numbers and corresponding values can be found in Table 4.2.
Model Name Component Value
D1N4148 Leaded Glass Diode N/A
R/ANALOG Resistor 1 kΩ – 40 MΩ
C/ANALOG Capacitor 100 pF – 10 µF
L/ANALOG Inductor 100 mH
LT6003 Linear Technology Op-Amp N/A
LMC7215/NS Texas Instruments Comparator N/A
IRF7307 Dual N-P Channel MOSFET N/A
VDC/SOURCE Voltage Source ±3 V
Table 4.2: Model numbers, descriptions and values for the components of the SSHI-P
circuit
4.1.2 Tuning of the Rectifier Circuits
The fixed component values for the SSHI-P circuit were selected based on the de-
sired performance of the switch at the frequency of operation. The frequency of operation
was determined by the harvesting system and was given as approximately 78 Hz. A list
of the component values is given in Table 4.3.
56
Figure 4.1.2: pSpice schematic for the SSHI-P circuit
Component Value
Rin 100 kΩ
Cin 500 pF
Rfb 1 MΩ
Cfb 100 pF
R1 2 mΩ
R2 40 mΩ
V+,V− ±3 V
Table 4.3: Fixed component values for the SSHI-P circuit
The component labeled as ’Op Amp’ in Figure 4.1.2 takes the input signal and
outputs the signal’s derivative. For this circuit to function, the component values must be
selected so that the phase-shift of the circuit is 90◦ and the gain is sufficient for boosting
the output to a level that would trigger the square-pulse generator. The transfer function
57
and gain governing the differentiator is given by these equations[41]:
V0
Vin
=
−1
(Rin + 1sCin )(
1
Rfb
+ sCin)
(4.1.1)
Figure 4.1.3 shows the bode plot for both gain and phase shift of the differentiator.
For the target frequency of 78 Hz, the phase-shift is 87.54◦ and the gain is -28.19 dBm.
Figure 4.1.3: Bode plot for gain and phase shift of differentiator
The component labeled ’Comparator’ in Figure 4.1.2 acts as a square-pulse gener-
ator. It converts all positive values from the output of the differentiator to a rail value of
3 V and all negative values to -3 V. This creates a square-wave pulse which will drive the
NMOS and PMOS package, switching the inductor on and off. The component values for
the square-pulse generator determine the threshold voltages, VI and Vh that toggle the
output. This relationship is given by these equations[41]:
VI = V−
R1
R1 +R2
(4.1.2)
Vh = V+
R1
R1 +R2
(4.1.3)
58
Based on the values in Table 4.2, the threshold voltage to trigger the comparator
is ±286 mV. The final fixed value component is the inductor. The value of the inductor
governs the inversion time and factor for the voltage on the piezoelectric element. A
100 mH inductor was selected based on previous research[41]. This value of inductance
allows for a sufficient inversion time based on the low frequency of operation.
4.1.3 Running pSpice Simulations
Evaluation of the circuits was based on relative peak power outputs and the corre-
sponding real-valued load resistance. In order to determine the output power, the resistive
load was varied while measuring voltage across the load. After achieving steady-state, the
voltage across the load was then averaged over a duration of 2 seconds. In the case of the
active SSHI-P circuit, the calculation of power consumption by the circuit itself was also
necessary. This measurement was taken by recording the current drawn from the power
supplies present in the system for the duration of the averaging. Power consumed by the
SEH circuit is zero since there are no active elements.
In pSpice, component values can be parametrically swept by declaring them as
global variables. The value of ’R Load’ in Figure 4.1.1and Figure 4.1.2 is a global vari-
able named ’RVAL’. For each circuit, the value of RVAL was swept over a pre-set range,
from 1 kΩ to 60 kΩ while the voltage across the resistive load was measured. A sample
output from this process can be seen in the Figure 4.1.4.
59
Figure 4.1.4: Voltage across the resistive load over time for a sweep of different RVAL
values
4.1.4 Evaluating the Simulation Results
The data from the pSpice environment was next exported to Matlab. The voltages
across the time period were then time-averaged. The average power was finally calculated
based on the relationship:
Pavg =
V 2avg
R
(4.1.4)
While there is a capacitor in parallel with the resistor, the current that passes through
the capacitor can be approximated to zero after the system reaches steady-state. For the
60
SSHI-P circuit the power consumption was taken as:
Pconsumed = |Vsource|Iavg (4.1.5)
Finally, the total net power output was given as:
Pnet = (Pavg)− (Pconsumed) (4.1.6)
This process yielded the net power output from each circuit as a function of the
resistive load. The optimal load value is defined as the resistive load value for which the
net power is maximized for the given circuit.
4.1.5 Construction of the Physical Rectifier Circuits
The components used in constructing the circuit were the same as the simulated
components in the pSpice models. Simulation models and experimental components were
matched to improve the likelihood of the experimental data agreeing with the simulated
data. The only variation to the design involved the load resistance. A resistor box pro-
duced by Elenco, shown in Figure 4.1.5, was used in order to quickly sweep the load
resistance. This box can generate a resistance from 0 Ω to 11 MΩ in 1 Ω increments.
When laying out the components, a breadboard was used to connect the resistor box
and replace damaged or different valued components. A diagram of the constructed SEH
circuit is shown in Figure 4.1.6.
4.1.6 Experimental Setup
When preparing to collect data, it became apparent that there would not be enough
time to perform a full experimental test of both the SEH and SSHI-P circuits. Experi-
61
Figure 4.1.5: Variable resistor box
mental testing of the SEH circuit was prioritized, but simulated results from the SSHI-P
circuit were still included for comparison.
The rectifier circuits required testing using the output of a piezoelectric material,
but is difficult to model the mechanical and electrical properties of a piezoelectric element
using hardware components. An ideal case would be to perform testing with the output
of the harvesting device, when the device is placed in a wind tunnel. However, in order to
avoid a strict reliance on the harvesting data and to obtain consistent results, the circuits
were tested using a piezoelectric stripe actuator attached to a beam being driven by a
62
Figure 4.1.6: SEH circuit setup
shaker. By controlling the voltage gain and frequency of the shaker, AC voltage signals
were generated from the piezoelectric element at targeted frequencies and amplitudes.
Figure 4.1.7 contains an image of the piezoelectric beam shaker setup.
Figure 4.1.7: Piezoelectric shaker setup used to test the SEH circuit
The output from the piezoelectric stripe actuator acted as the input to the SEH
circuit. The piezoelectric element used for the experiments is a stripe actuator, model
no. 40-2010, produced by APC International. Table 4.4 gives the basic properties of the
63
piezoelectric stripe.
Length 60 mm
Width 20 mm
Thickness 0.7 mm
Total Deflection > 2.6 mm
Blocking Force > 0.5 N
Resonance 60 Hz
Capacitance 190 nF
Table 4.4: Fixed component values for the SSHI-P circuit
The output of the circuit was measured across the load using the National Instru-
ments data acquisition USB-6009 device (DAQ). A differential measurement across the
load was measured, transmitted to a laptop, and detected by LabVIEW software. This
software allowed the measurement and time-averaging of voltages over a period of time
before recording them to a text file for data analysis. The input leads to the DAQ device
were configured as recommended in the manual using the differential for floating signal
sources method. A schematic for this method is shown in Figure 4.1.8. High impedance
resistors (1 MΩ) were used in this experiment.
4.1.7 Collecting Experimental Data
A test consisted of two stages: calibrating the shaker and measuring voltage while
sweeping the load resistance. The shaker was calibrated in order to establish continuity of
data across tests. Calibration began by monitoring the open circuit voltage of the piezo-
64
Figure 4.1.8: Circuit diagram of the method used to measure a signal with the DAQ
device[36]
electric stripe. The input voltage to the shaker was of equal frequency and proportional
magnitude to the motion of the shaker and therefore of equal frequency and proportional
magnitude to the voltage of the piezoelectric stripe. The input voltage to the shaker was
first set to the target frequency of 78 Hz. Next, the voltage gain was increased until the
piezoelectric stripe produced 4 Vpk−pk signal. The shaker input voltage then remained
fixed for the rest of the test. Doing this calibration before each test run ensured that the
input to the conditioning circuit remained a fixed variable. Figure 4.1.9 shows the voltage
of the piezoelectric stripe nearing the end of the calibration phase.
The output of the piezoelectric stripe was then wired as an input to the SEH circuit
and the DAQ device was configured across the load in parallel with the resistor box. The
DAQ device then measured a DC voltage which was a function of the load resistance. A
data point was collected by setting the resistor box to the desired resistance, allowing a
few seconds for the circuit to reach steady state, and then running the data collection pro-
65
Figure 4.1.9: Input voltage from the piezoelectric stripe
gram in LabVIEW for 10 seconds. During this time, the program sampled the DC voltage
and then time averaged it to produce an average voltage. This voltage was then output to
a text file for later use. From here, the experiment continued by adjusting the resistor box
to produce a new load resistance and then repeating this process. This continued until all
desired data points were collected in the range between 1 kΩ and 100 kΩ. Typically data
points were in increments of 5 kΩ, or 2 kΩ for points near the peak.
4.1.8 Derivations for Piezoelectric Analog Model
In order to accurately simulate the piezoelectric output, several impedance values
were calculated based on data provided by the manufacturer. The 40-2010 stripe actuator
manufactured by APC International was used, and the model shown in Figure 4.1.10 was
used to simulate the piezoelectric analog. ∆Pp is the excitation force generated by the
shaker and Vp is the voltage that the piezoelectric stripe generates.
66
(a)
(b)
Figure 4.1.10: Schematic showing model used to simulate the piezoelectric analog(a) and
its realization in pSpice(b)
The electrical domain governs the electrical properties of the piezoelectric mate-
rial, while the mechanical domain corresponds to physical properties. The transformer
with turns ratio φ corresponds to the electro-mechanical transduction coefficient. The
following relationships model the system:
MD =
mp
A2R
=
ρlwt
A2R
(4.1.7)
Y31 =
k231K
T 0
d231
(4.1.8)
CD =
Y31AR
1
(4.1.9)
67
φ =
−dA
CD
(4.1.10)
k =
d2A
CpCD
(4.1.11)
CPB = (1− k
2)Cp (4.1.12)
These relationships can be derived from the basic constitutive equations for a piezo-
electric material. It was necessary to account for the mechanical domain of the harvester
as well as the electrical domain. If the mechanical domain of the harvester was not mod-
eled and coupled to the electrical domain then power drawn from the harvester would
not have an effect on the excitation of the harvester. For a real piezoelectric harvester,
power drawn from the harvester dampens the motion of the harvester. The coupling of
the mechanical and electrical domains, modeled by the transformer in the circuit analog,
determines the strength of the interaction between the domains.
AR 1.2 mm2 CD 2.261× 10−13 m4s2/kg
Cp 190 µF CpB 164.86 nF
d31 −125× 10−12 m/V dA −125× 10−12 C/N
K−1 1275 k .3638
l 60 mm MD 4433.33 kgm−4
mp 6.384 g t .7 mm
w 20 mm Y31 8.84× 1010 N/m2
0 8.85× 10−12 F/m ρ 7.6 g/cm3
φ 552.9 Pa/V
Table 4.5: Value of parameters in piezoelectric analog model
The simulation needed to be calibrated in a similar manner to previous experiments
68
in order to have comparable data. This calibration was done by placing an AC voltage
source at the input of the piezoelectric analog circuit to simulate ∆Pp, as can be seen in
Figure 4.1.11. The source was then swept at a constant frequency in order to determine
what input voltage corresponded to the appropriate 2 V open circuit voltage on the output.
In addition, the DAQ was modeled with a differential measurement across two 1 MΩ
resistors.
Figure 4.1.11: Excitation voltage and output amplitude of the piezoelectric analog model
4.2 Conditioning Results and Discussion
This section presents and analyzes the data obtained through the methods outlined
in the previous section.
69
4.2.1 Data Analysis
The experimentally determined data was compared to data sets generated using
the piezoelectric analog model[6]. Using this model, a reliable simulation of the piezo-
bimorph output was generated by using electro-mechanical coupling factors based on the
properties of the piezoelectric stripe actuator.
Validation of the data consisted of several factors. A non-linear relationship must be
observed between the output voltage and load resistance. In addition, there must exist an
absolute maximum power output as a function of load resistance. The maximum power
output for both the experimental data and simulation data must fall within the same range
of load resistances. Finally, the power output from the simulated data and the experimen-
tal data must be comparable.
Figure 4.2.1 shows the voltage across the load as a function of the load resistance.
Data was collected across several smoothing capacitor values in order to ensure that the
data was consistent. Both the simulated data and the experimental data exhibited a non-
linear relationship, across all capacitor values. As the load resistance increased, the volt-
age began to level off. This relationship is key to ensuring that an absolute maximum
power output exists. If the voltage is linear, the power output would exhibit a quadratic
non-decreasing relationship instead.
Once the average voltage as a function of the load resistance was obtained, average
power was calculated using Equation 4.2.1:
P = V I =
V 2
R
(4.2.1)
70
Figure 4.2.1: Output voltages of the piezoelectric analog model as a function of source
resistance for various smoothing capacitor values
Figure 4.2.2 shows the relationship between output power and load resistance. For both
simulated and experimental sets, an absolute maximum exists for all cases. In addition,
the peak power is obtained within a narrow band of resistance values.
Table 4.6 contains the peak power value and corresponding resistance value for all
sets. The peaks from each set fall within approximately 2 kΩ of one another.
71
Figure 4.2.2: Output power of the piezoelectric analog model as a function of source
resistance for various smoothing capacitor values
Capacitor Value Data Set Peak Power Load Resistance
10 µF
Experimental 13.85 µW 23242 Ω
Simulated 17.56 µW 21354 Ω
47 µF
Experimental 13.64 µW 22855 Ω
Simulated 17.66 µW 21267 Ω
100 µF
Experimental 13.65 µW 22778 Ω
Simulated 17.67 µW 21270 Ω
220 µF
Experimental 13.55 µW 23259 Ω
Simulated 17.68 µW 21254 Ω
Table 4.6: Simulated and experimental peak power output and optimal resistance for
multiple capacitors
72
Figure 4.2.3: Simulated output voltage for SEH and SSHI-P circuits
Figure 4.2.3 shows simulated output voltage for the SEH and SSHI-P circuits over a
load resistance range of 1 kΩ to1 MΩ. The simulated results show that the output voltage
for the SSHI-P circuit increases as the load resistance increases. The output voltage for
the SSHI-P circuit is also greater than that of the SEH circuit for all load resistances in the
tested range. The results of the output power simulation show that the output power for
the SSHI-P circuit is in fact significantly lower than the output power of the SEH circuit.
Figure 4.2.4 shows the simulated output power for the SEH and SSHI-P circuits
over load resistances ranging from 1 kΩ to 1 MΩ. This simulation takes into account
power losses from active sources. Despite a higher output voltage for the SSHI-P circuit,
the output power is significantly lower than that of the SEH circuit. In fact, the net output
73
Figure 4.2.4: Simulated output power for SEH and SSHI-P circuits
power for the SSHI-P circuit is only positive for a small range of load resistances. For the
majority of the load resistances tested in this simulation, the overall power generated by
the SSHI-P circuit is negative as it consumes more power than it generates.
4.2.2 Conditioning Discussion
When reviewing the data, there are three main factors for consideration. The first
consideration is what role the smoothing capacitance played in the power output. The
results in Table 4.6 indicate that varying the smoothing capacitor at low frequencies has
a very small, arguably negligible, effect on a system of this size and scale. The peak
power varies only by 0.12 µW at most between capacitor values for the simulated data
74
sets and by 0.3 µW for the simulated data sets. Furthermore, the simulated data suggest
a small peak power increase with an increase in capacitance while the experimental data
saw a small loss in peak power output as capacitance values grew larger. This discrepancy
is most likely due to the inability of the current pSpice model to account for real-world
losses. Several of the modeled components, including the capacitors and inductors will
produce losses in the physical world. For simplicities sake, the model does not factor in
these losses. The losses themselves might be simulated by placing resistors of appropriate
values in series with the components. However, since not all of these resistances are easily
calculable, they were omitted altogether. In addition to the peak power, the corresponding
load resistances too were minimally impacted. All load resistance values for the simulated
set were within 100 Ω of one another. For the experimental data, the largest difference
between optimal load resistances for varying capacitances was found to be less than 600
Ω, showing that the capacitor value had minimal impact on the optimal load resistance.
The second consideration for data revision was how accurate the simulation mod-
els were in predicting the peak output power and corresponding load resistance. When
comparing the experimental and simulated data for a given smoothing capacitance value,
it can be seen that the voltage and power levels differ. In all cases, the simulated data
set predicted a higher voltage and a higher power than what was obtained through exper-
imentation. There are a few reasons why the levels of voltage and power were different
between the simulated data and the experimental data. As previously stated, the model
does not factor in real-world losses for theoretically lossless components, such as capac-
itors and inductors. In addition to this, any inaccuracies for component values hinder the
models ability to predict outputs accurately. For components such as the inductors and
75
capacitors, component value tolerances were small and well defined due to strict manufac-
turing standards. The component value of concern was the load resistance. The resistance
box used as the load was not precise. When measured with a digital multi-meter, toler-
ances as large as 10% from their stated values. These component inaccuracies make it
difficult to accurately simulate and predict voltage and power outputs. While the output
levels make are not predicted with a high level of precision, the model does provide a good
metric for predicting the load resistance which will produce a peak power output. For all
smoothing capacitor data sets, the optimal load resistance between the experimental run
and the simulated run fell within approximately 2 kΩ of each other. Since variations in
the load resistance by 2 kΩ near the optimal value will result in only minor power output
fluctuations, this is considered to be a success.
The third and final consideration for data revision was the overall performance of
the SEH circuit when compared to the SSHI-P circuit. The results of the simulations for
output voltage and output power for the SEH and SSHI-P circuits across varying load
resistances differ. Power is related to voltage by the equation I = V
2
R . The output voltage
for the SSHI-P circuit is higher than that of the SEH circuit, which suggests that the out-
put power generated by the SSHI-P circuit is greater than the output power generated by
the SEH circuit. However, the data generated by the output power simulation shows that
the net output power generated by the SSHI-P circuit is in fact negative. This apparent
contradiction is explained by the fact that the net power output factors in power consump-
tion from active sources. The SSHI-P circuit uses an active switch which consumes more
power than the circuit outputs. While this data suggests that SEH is a better option, it is
important to consider scale and the overall switch design of the SSHI-P circuit. With a
76
higher input voltage source and a more efficient switch design, the SSHI-P circuit would
produce a much higher output power. For this experiment, the input voltage source was
limited by the scale of the harvesting device and the efficiency of the switch was not opti-
mal but chosen for the ease of implementation in the pSpice environment. Diode selection
also plays a critical role in determining overall performance. The SSHI-P circuit uses a
standard silicon diode with a forward voltage drop of 0.7 V. The reason this diode was
selected over a Schottky diode, which has a forward voltage drop of 0.3 V, was due to the
lower leakage current. Schottky diodes have a larger leakage current which diminishes the
efficacy of the voltage inversion that occurs during the switch time of the SSHI-P circuit.
The SEH circuit is not bound by this necessity and thus would see an overall increase in
power output if a Schottky diode was used in place of a standard silicone diode. Since
this experiment was not about the role of diode selection, it was decided to use a standard
silicone diode for both circuits for consistency.
Taken altogether, the results of simulated and experimental data yield a number of
conclusions. In its current state, the model is not an accurate predictor of power output
for a piezoelectric harvesting device. Despite this, the model has proved to be a useful
tool and metric in predicting an optimal load resistance for a piezoelectric harvester, given
the parameters of the piezoelectric element and the input force. Being able to predict an
optimal load resistance is important in the proper selection of a storage device. Should
a storage device?s input impedance match the optimal impedance of the harvesting and
condition device, the maximum amount of power is able to be stored. In terms of the
performance of the SEH and SSHI-P circuits for this application, the SEH proved to be
a more efficient choice, as it generated more power for the same input. Future work and
77
research would revolve around being able to more accurately model real-world losses so
that simulations can not only predict the optimal load resistance, but the project power
output. Furthermore, the SSHI-P circuit would be revisited with the focus of designing a
more efficient switch in order to make it a viable alternative to the SEH circuit.
4.3 Summary
The conditioning chapter summarizes the modeling, testing, and results related to
the production of the conditioning subsystem. The goal of the conditioning system is to
efficiently convert the AC output from the piezoelectric harvester to a DC input for the
storage subsystem. The first step towards meeting this goal was to create pSpice models
of the Piezoelectric harvester and the SEH and SSHIP-P rectifier circuits. Next, the SEH
circuit was physically constructed on a breadboard for testing. The input voltage signal
was generated by a PZT patch bonded to a beam, which was driven by a shaker. This
set-up was used to determine the SEH circuit’s optimal load resistance at the harvester’s
optimal oscillation frequency and to validate the pSpice models. A series of experiments
were carried out by setting the piezoelectric material’s output to four volts peak to peak,
then sweeping through a range of load resistances to determine which value produced the
greatest output power. In addition, the experiments were repeated for varying values of a
smoothing capacitor to determine what effect the capacitance had on the power output and
optimal load resistance. Once the data had been collected, the model’s predictions were
compared to the real world results. The simulations proved to be effective in estimating
the optimal load resistance, but were a poor predictor for output power. By carrying
78
out these tests we were able to determine that the SEH circuit with a load resistance of
approximately 22-23 kΩ is the most efficient design and gives an output of about 13.5
µW. Furthermore, based on the simulation outputs, the SEH circuit proved to be a more
efficient design when compared to the SSHI-P. The scale of our harvester design proved
to be a limiting factor in obtaining an improvement with the active rectification scheme.
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5 Storage
The storage system aims to efficiently store input energy from the conditioning
circuit into an energy storage device and deliver this energy to a load. Many storage
systems and charging circuits are considered. The experimental process is outlined in the
methodology, and the successes and challenges are presented in the results and discussion.
5.1 Storage Methodology
In this section, the selection of the battery and test circuitry is described. A method
to quantify the efficiency of the different storage systems is presented. Configurations
using supercapacitors are evaluated, and a final design for the hybrid system is chosen.
5.1.1 Battery Selection and Initial Testing
The storage subgroup developed several systems to compare the charging and dis-
charging efficiencies from low power sources. The first stage of the research consisted
of gathering the proper components to begin the modeling, building, and testing of the
storage systems. The initial specifications were determined from estimates of the output
levels from the energy harvester and conditioning circuit. The output voltage of the rec-
tifying circuit was originally estimated to be less than 1 V with a power on the order of
80
microwatts, assuming a perfect impedance match. Therefore, the research goal of storage
device testing was to determine the most efficient storage device that could charge with a
low input voltage of less than 1 V but power a load at a higher voltage.
The initial battery chosen for storage device testing was the ML614-TZ2 lithium-
ion coin battery produced by FDK America, rated at 3 V. It had a capacity of 3.4 mAh, a
discharge rate of 15 ?A, and a standard charge current of 15 µA. It weighed 0.17 g. The
second battery, also chosen for its high power capabilities, was the MEC202-22P THIN-
ERGY lithium-ion battery. It was rated at 4.1 V with a 3.9 V nominal output voltage.
It had a capacity of 2.2 mAh, a discharge rate of 0.75 mA, and a maximum continuous
discharge current of 90 mA. Its internal resistance was 22 Ω. The 4.1 V THINERGY
battery weighed more than the 3 V coin battery, at 0.975 g.
In addition to lithium-ion batteries, a supercapacitor-lithium ion hybrid system was
investigated as a plausible storage device design. The ESHSR-0100C0?002R7 superca-
pacitor designed by NessCap Cp Ltd was chosen for storage device testing. It had a
capacitance of 100 F and was rated at 2.7 V with a surge voltage of 2.85 V. It had a rated
current of 21.4 A, a maximum current of 58.7 A, and a maximum leakage current of 1.7
mA. It was designed for 500,000 life cycles. Under DC voltage, its maximum internal
resistance was 13 mΩ. In addition, it weighed 22.5 g.
5.1.2 Charging System
A commercial-off-the-shelf (COTS) energy-harvesting charger and protector de-
signed by Maxim Integrated was chosen to charge the lithium ion battery and used appro-
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priately according to the data sheet. The MAX17710 was specially designed to manage
poorly regulated sources with voltages as low as 0.75 V while preventing the battery from
charging to voltages that would otherwise shorten the lifetime of the cell.
The MAX17710 charging chip used in the storage subsystem is able to charge a
4.1 V battery using input voltages that are typically 0.75 V but can be as low as 0.485
V through the use of a boost regulator. It can operate using an input power anywhere
between 1 µW and 100mW. The charging voltage is limited to a maximum of 4.125 V to
prevent overcharging. If the voltage of the battery drops below 2.15 V, the chip enters an
undervoltage lockout mode to prevent overdischarge and possible damage to the battery.
The chip draws 1 nA of current from the battery when in standby, and supplies 625 nA of
charging current when input power is supplied. The physical dimensions of the chip are
3 mm by 3 mm by 0.5 mm, so a printed circuit board was designed to facilitate building
the external circuitry of the system. The battery must reach a minimum voltage of 3.7
V before the PCKP (unregulated output) pin can be activated and power supplied to the
load. The AE pin controls whether charge is delivered to the load, and must be pulsed
with a minimum of 1.13 V in order to supply current to the load. It terminates the current
supplied to the load when the AE pin is grounded.
The external components were chosen in order to operate the charger in its boost
regulator mode, enabling a boost converter for harvesting sources providing approxi-
mately 1 µW. The names of the pins and the associated passive component values for
this mode of operation are shown in Figure 5.1.1. When a source is present, a 47 µF
capacitor is charged until the voltage on the FB pin exceeds 0.75 V. Internal circuitry then
pulls the LX pin low to force current through the inductor. An internal oscillator releases
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the LX pin, causing the voltage on the LX pin to rise and exceed the voltage on the CHG
pin. This eventually causes a buildup of voltage on the 0.1 µF capacitor on the CHG pin.
The oscillator repeats this process at 1 MHz with a 90% duty cycle. Thus an input of less
than 1 V is boosted to a level suitable for charging the battery. An overcharge is detected
when CHG exceeds 4.5 V, at which point the boost converter limits its output in order to
return CHG to a safe level.
Figure 5.1.1: Boost converter configuration for the MAX17710 Integrated Circuit
The outputs are enabled through the control of the AE pin. In shutdown mode, the
charger cannot provide power until a charge source is present. The system uses 1 nA
of quiescent battery current. The MAX17710 determines that a charge source is present
when the CHG pin exceeds 4.15 V, which causes 625 nA of current to be provided to the
battery. Startup is achieved by pulsing the AE pin or holding it at a logic high value, a
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minimum of 1.13 V, which enables power flow to the unregulated output pin. This startup
can result in failure if the voltage on the PCKP pin is less than 2.15 V and collapses to 0
V or in success if the voltage on PCKP rises above 3.7 V. During the active period, 725
nA of current is drawn from the battery to supply the necessary power. Only after the
output voltage falls below 2.15 V will an under-voltage lockout occur, causing the system
to return to the original shutdown state. Otherwise, the output pin will be delivered power
depending on the state of AE. After AE is grounded, the output is turned off and after AE
is held at a logic high, the output is turned on.
In order to test the charging system with breadboard components and power sup-
plies, a printed circuit board (PCB) with the footprint of the chip and breakout pins was
designed using Eagle PCB Design Software. The design has holes that were spaced with
a 0.1 inch pitch. Two traces of the chip layout were fabricated on 40 mm by 80 mm PCBs.
The integrated circuits were placed onto the board using a heat reflow soldering station.
Once the circuitry was constructed on the breadboard, ribbon cable attached to the pins in
the accessible holes allowed for full integration of the chip.
5.1.3 Battery Efficiency
In order to determine the efficiency of the 4.1 V THINERGY battery in the context
of the storage system a modified form of the quick test method was used[21]. Efficiency
of the battery was determined by measuring the amount of energy input into the system
during charging, compared to the amount of energy discharged to a load during discharg-
84
ing. This allowed for the calculation of efficiency by
η =
Ed
Ec
(5.1.1)
where η is the efficiency, Ed is the discharge energy, and Ec is the charge energy.
5.1.4 Energy Measurement
The quick test method uses three voltage parameters, V0, V1, and V2, in addition
to three time parameters, t1, t2, and t3. The battery was charged to an initial voltage
of V0. Next, the battery was charged from V0 to V1. The time required to charge the
battery from V0 to V1 was recorded as t1. The power supply was set to a constant 1 V
during the charging process, and an ammeter was used to monitor the current leaving the
power supply. When V1 was reached, charging was stopped and the battery was allowed
to discharge through the load attached to the unregulated output of the chip. The battery
was discharged to a voltage, V2, below that of V0. Discharging was timed and recorded
as t2. While the battery was discharging, the ammeter was used to monitor the current
leaving directly from the battery, and the oscilloscope was used to monitor the voltage
drop across the battery. When the voltage of the battery dropped to V2, discharging was
stopped. At this point charging was resumed and timed until voltage V0 was reached
again. The time for the battery to charge from V2 to V0 was recorded as t3. Just as with
the charging process from V0 to V1, the current leaving the power supply was measured
again with an ammeter and the power supply was set to a constant voltage. The target
parameters for the quick test were as follows: V0 = 3.8 V, V1 = 4.1 V, and V2 = 3.5 V.
85
5.1.5 Calculation of Efficiency from Measurements
The quick test results can be used to calculate both the energy used in charging,
Ec, as well as the energy used in discharging, Ed. From Ec and Ed the efficiency of the
battery, η, is calculated.
To calculate the charge energy, the power P (t) is determined by multiplying the
instantaneous current I(t) by the voltage provided by the power supply, V ,
P (t) = I(t) ∗ V (5.1.2)
If P (t) is integrated over the amount of time necessary to charge the battery then the
charging energy can be calculated as
∫ T
0
P (t)dt = Ec =
∫ t1+t3
0
I(t) ∗ V dt (5.1.3)
where Ec is the energy needed to charge the battery.
The energy discharged by the battery can be calculated in a similar way. During the
discharge of the battery, the current and voltage can be recorded and multiplied together
to determine the power discharged.
P (t) = I(t) ∗ V (t) (5.1.4)
I(t) is the current out of the battery as a function of time as recorded by the ammeter, V (t)
is the voltage drop across the battery as a function of time as recorded by the oscilloscope,
and P (t) is the power output of the battery as a function of time. If this function is
integrated over the amount of time spent discharging the battery, the energy discharged,
86
Ed, can be calculated as
∫ T
0
P (t)dt = Ed =
∫ t2
0
I(t) ∗ V (t)dt (5.1.5)
As described in Equation 5.1.1, the charge and discharge energy are used to calcu-
late the efficiency of the battery in the setup, η.
5.1.6 Supercapacitor Hybrid System
A battery-supercapacitor hybrid system was designed and its efficiency compared
to that of the battery alone. From common configurations for a battery-supercapacitor
hybrid storage system, the passive system was chosen because of its low manufacturing
costs and relatively robust nature. In this configuration, a supercapacitor was attached
in parallel with the battery so that the supercapacitor can absorb pulsed inputs of energy
to extend battery lifetime. Although an active configuration using a DC-DC converter
could improve the efficiency of the storage system, it was likely that the converter would
consume more power than was available given the relatively low power output from the
piezoelectric harvester[29]. The passive configuration slows down battery aging because
the transient power is delivered by the supercapacitor, not the battery[45].
To test the passive configuration of the battery-supercapacitor storage system, the
circuit was connected to a DC power supply using the same method as the battery system.
The quick test method was utilized to test the efficiency of the hybrid system. The hybrid
system had the same properties as the battery-only system, so the same method was valid
for testing the hybrid system.
87
5.2 Storage Results and Discussion
In this section, the selection of the battery and test circuitry is described. A method
to quantify the efficiency of the different storage systems is presented. Configurations
using supercapacitors are considered, and a final design for the hybrid system is chosen.
5.2.1 Initial Setup Results
All tests were performed using MAX17710 chips soldered onto the PCB breakout
circuit shown in Figure 5.2.1. The PCB was connected to all other components on a
breadboard.
The first test using the MAX17710 chip used the 3 V lithium ion battery. Using a 1
V power supply, the battery was charged to 4.1 V and remained at this SOC as long as the
power supply remained connected. However, once the power supply was disconnected,
the battery immediately dropped to 3 V, the maximum voltage rating for the battery. The
battery could not be discharged while connected to the MAX17710 chip because the
unregulated output could not reach the threshold of 3.7 V, causing the voltage to collapse.
The next test was performed with the 3 V battery and a 100 F supercapacitor in a
passive parallel configuration. When the supercapacitor was first placed into the bread-
board with the power source disconnected, the battery voltage dropped immediately to 0
V. When the power supply was turned on, the battery and supercapacitor system charged
at a much slower rate compared to the battery-only system. The charging time frame rose
from seconds to hours. To test whether the supercapacitor was fully charged, the super-
capacitor was removed from the circuit and returned to the circuit. There was no drop
88
Figure 5.2.1: Breakout circuit designed for the MAX17710 in Eagle PCB Design.
in the battery voltage after the supercapacitor was reconnected, indicating that no charge
was flowing from the battery to the supercapacitor. This verified that the supercapacitor
was fully charged and was not receiving any more charge from the battery.
5.2.2 Final Setup Results
Due to the inability to discharge the 3 V lithium ion battery directly from the inte-
grated circuit, new 4.1 V batteries were purchased. The MAX17710 chip that was used
in the charging circuit was designed for a 4.1 V battery, like the THINERGY battery,
89
which resolved the issue with the discharge enable threshold. This allowed the battery to
discharge into the load when the controlling AE pin was pulsed high. The voltage reading
across the LED read 2 V even when the battery was fully charged. This occurred because
the LED had an upper voltage limit. A 5 kΩ resistor was placed in series with the LED so
that the voltage drop could be monitored across both the resistor and the LED, providing
an accurate voltage reading for the load. In addition, the discharge current was calculated
by measuring the voltage across the resistor and dividing by the resistance, eliminating
the need for an ammeter.
Once there was a reliable method for reading the voltage across both the battery
and the load using an oscilloscope, the THINERGY batteries were discharged, and their
discharge profiles were monitored. Table 5.1 displays the range of voltages as a function
of elapsed time for both the voltage drop across the battery and across the load. During
this test, the input DC power supply was disconnected.
Elapsed Time (hours) 0:00 0:08 0:14 0:23 0:24
Vbatt low 3.64 3.56 3.52 3.48 Breakdown
Vbatt high 3.68 3.64 3.60 3.56 Breakdown
VPCKP low 3.20 3.00 3.00 2.96 Breakdown
VPCKP high 3.20 3.16 3.12 3.04 Breakdown
VPCKP Average 3.20 3.08 3.06 3.00 Breakdown
VLED 2.00 2.00 2.00 2.00 Breakdown
Id (mA) 0.240 0.216 0.212 0.200 Breakdown
Table 5.1: Discharge voltage ranges as a function of time for the battery and load
Vbatt was the voltage drop across the battery. VPCKP was the voltage drop across
90
the unregulated output pin. VLED was the voltage drop across the LED. The discharge
current, Id, was calculated from the results.
From Table 5.1, there is a steady decline in voltage across both the battery and the
load. The voltage decrease was observed across both the battery and load over the period
of 24 minutes, indicating that the battery was discharging into the load. The voltage drop
across the LED remained constant because the LED had a voltage limit of 2 V, and the
load voltage remained above this limit for the duration of the test. At 24 minutes into the
discharge cycle, there was an unexpected voltage breakdown of the unregulated output
observed on the oscilloscope. See Figure 5.2.2 for the breakdown profile.
Figure 5.2.2: This graph shows the voltage profile for the unexpected voltage breakdown.
The next trial used another fully charged THINERGY battery. In this trial, begin-
ning and end voltages were recorded over a three hour period. The load was kept constant
from the previous setup, a 5 kΩ resistor in series with the LED. This load resulted in dis-
charge currents between 0.2 and 0.24 mA. The battery was disconnected and reconnected
91
to the circuit between the 2:58 and 3:00 time points. Table 5.2 shows the voltages that
were recorded.
Elapsed Time (Hours:Minutes) 0:00 2:58 3:00
Vbatt low 4.04 2.40 3.60
Vbatt high 4.08 2.48 3.70
VPCKP – 1.80 –
VLED 2.00 1.80 –
Table 5.2: Discharge of the battery over a period of three hours
The voltage of the battery decreased significantly over the course of the three hours,
indicating that it could drop below the breakdown voltage threshold. However, when the
battery was disconnected from the circuit and reconnected, the voltage across the battery
rose again to a higher voltage.
The quick test voltage parameters V0, V1, and V2 were determined by charging
and discharging the 4.1 V THINERGY battery. V0 was determined to be 3.25 V, V1 to
be 4.10 V, and V2 to be 2.44 V. The quick test method was attempted with a discharged
battery with an initial voltage of 2.44 V. After 1 minute and 47 seconds (t3), the battery
voltage rose to the V0 voltage. The voltage continued climbing to 3.6 V, where the voltage
reading on the oscilloscope plateaued. Therefore, the quick test method was unable to be
completed, and t1 and t2 were not collected. Upon later testing of the battery with a
multimeter, it was discovered that the voltage had increased to 4.1 V.
It was determined that the 4.1 V THINERGY battery was able to discharge with
the MAX17710 chip and a small load over three hours. A 1 V DC power supply was able
92
to partially recharge the battery. However, after attempting the quick test method, the
voltages of the batteries dropped below 3 V. This damaged the batteries, and they could
not be charged above 1.68 V. In addition, some of the batteries experienced mechanical
failure when wires were soldered to the leads for testing.
5.2.3 Storage Discussion
It was determined that the first battery setup with the 3 V lithium ion battery and
the final battery setup with the 4.1 V THINERGY battery were successful at charging the
batteries using a 1 V input.
In the first charging circuit using the 3 V lithium ion batteries, many aberrant re-
sults were observed. This battery was rated to charge to a maximal SOC of 3 V, but the
MAX17710 chip was meant for charging batteries with a voltage rating of 4.1 V. In addi-
tion the supercapacitors tested in conjunction with the 3 V batteries were rated at 2.7 V.
The discrepancies between these key components caused damage to the storage system.
Over the course of testing, all of the 3 V batteries used were degraded due to overcharg-
ing. This required a periodic replacement of batteries and made the results from different
trials incomparable because of different states of degradation between the batteries. The
supercapacitors did not degrade, but were all operating above their safe operation limit.
In order to achieve the target functionality, additional circuitry in the form of a DC-DC
converter or a different supercapacitor could be used to match the voltages of the battery
and supercapacitor.
Two main issues were observed in discharging the batteries through the MAX17710
93
chip to a load. First, the 3 V battery had too low of a voltage rating to switch the inte-
grated circuit into the discharge state, which has a threshold of 3.7 V on the PCKP pin.
Second, the circuit was unable to discharge into a simple diode load because the LED had
a maximum voltage of 2 V. The limit of the LED prevented PCKP from rising to 3.7 V.
By placing a resistor in series with the LED charge was allowed to build up at the PCKP
pin, and the chip was then able to transition the circuit into a discharge state.
The supercapacitor configurations were unsuccessful primarily due to voltage in-
compatibility between the supercapacitor and the rest of the devices. It was also deter-
mined that it would not be meaningful to test the supercapacitor as a standalone storage
device. Due to the different electrical characteristics and efficiency considerations of bat-
teries and supercapacitors, a supercapacitor cannot replace a battery in a circuit. When
the supercapacitor was connected in parallel with the 3 V battery, the battery immediately
discharged into the supercapacitor and its voltage dropped to 0 V. In addition, the hy-
brid system took much longer to charge than the standalone battery. The supercapacitor
presented a large capacitance that dramatically increased the RC time constant and the
charging time of the system. The system was unable to charge completely and the output
was not at a suitable level for the MAX17710. Therefore without a DC-DC converter, the
supercapacitor hybrid is unsuitable for this application.
Acquisition of the 4.1 V THINERGY batteries fixed several of the charging prob-
lems originally encountered. This battery allowed for the successful transition of the
charging circuit into and out of the discharge state. The higher voltage rating of the
batteries allowed the voltage on the PCKP pin to reach 3.7 V. In order to control the tran-
sition into the discharge state the AE pin was manually pulsed to Vbatt. The discharging
94
state was terminated by pulsing AE to ground. A complete standalone charging device
would incorporate a low power micro-controller in order to control this signal. Data was
successfully collected on the charge and discharge function for the THINERGY batter-
ies. During discharge the unregulated output consumed 0.22 mA and after three hours the
voltage dropped below the safe discharge rating of the battery, causing permanent damage
to the THINERGY batteries.
One of the problems observed during testing was that the voltage at the PCKP pin
collapsed unexpectedly during some testing periods and no longer provided current to the
load. This may have occurred because the battery had passed below its safe discharge
voltage and could no longer provide a current to the load. This result was inconsistent
because during another trial the battery did not stop discharging causing concern as to the
susceptibility of the circuitry to external influences. Many of the problems encountered
resulted from manipulation of the measurement leads from the oscilloscope during test-
ing runs, which caused disturbances to the circuit and disrupted proper function of the
circuitry and battery. The leads on the THINERGY batteries were also very fragile and
mechanical failure of the leads resulted in a functional loss of the batteries.
A similar experiment could be repeated with different testing circuitry and moni-
toring devices. The oscilloscope used for monitoring the circuit had inherent offsets of up
to 0.5 V, which may have led to inaccurate readings during testing. Using an oscilloscope
that can simultaneously measure and record data in an external file would allow future
experiments to produce more accurate charging profiles. In addition, methods should be
devised to prevent mechanical failures of the THINERGY battery.
95
5.3 Summary
The storage chapter summarizes the testing and results carried out in the devel-
opment of the energy storage subsystem. The research on designing an energy storage
system capable of charging from a low voltage source while providing power to a load
of a high voltage began with the acquisition of two different batteries, the 3 V ML614-
TZ21 and 4.1 V THINERGY MEC202-17P lithium ion batteries, and a charge regulating
microchip, MAX17710. In addition to these two test configurations, a supercapacitor
battery hybrid storage system was tested using the 2.7 V, 100 F supercapacitor and the 3
V lithium ion battery in a passive parallel configuration. The MAX17710 was chosen to
act as the charge regulator for each of the experimental setups. A modified version of the
quick test method was used to determine the efficiency of the setups with a 1 V DC source
and an LED and resistor for the load. During this testing it was shown that the regulatory
circuitry was able to charge both battery systems and the supercapacitor hybrid system.
However, the 3 V battery and the supercapacitor hybrid system were not able to enter the
discharge state using the MAX17710 circuitry. When comparing these two systems it was
also seen that the battery supercapacitor hybrid system took longer to complete charging.
The 4.1 V THINERGY battery was able to pass the threshold voltage to enable discharge
to a load through the designed charging circuit. The use of the 4.1 V THINERGY battery
provided the expected testing results and corrected several problems seen when running
tests on the other storage devices. It also allowed for the determination that the storage
system, including the MAX17710 microchip and the 4.1 V THINERGY battery, achieved
close to ninety percent efficiency early in its life cycle.
96
6 Integration
After the completion of subsystem research, further testing was conducted to in-
tegrate the harvesting, conditioning, and storage systems. Tests were conducted to de-
termine the maximum power output from and possible sources of loss in the integrated
harvester-conditioning system. Finally, tests were conducted to determine how much rec-
tified energy was able to be stored in the conditioning-storage system.
6.1 Integration Testing
Following subsystem testing, the integrated harvester-conditioning system was placed
in the wind tunnel to observe how much power was generated. The setup for the har-
vester was similar to the configuration described in the harvesting methodology. Since
the beam was permanently epoxied to the baseline plug, only baseline testing could be
performed. Further attempts to separate the plug risked damage to the piezoelectric ele-
ment and beam.
The fan frequency was swept in order to determine the frequency with the highest
AC output voltage of the piezo. Once this frequency had been obtained, the fan frequency
was set and the output of the piezoelectric element was wired to the SEH circuit. Using
procedures described in the conditioning system methodology, the load resistance of the
97
SEH circuit was swept in order to determine the optimal resistance which would corre-
spond to a maximum power output. Voltage was measured using the DAQ. The smoothing
capacitor for this test was fixed at 10 µF.
Another test setup was designed to integrate the conditioning circuit with the stor-
age subsystem. As in previous experiments, a beam with piezoelectric material excited
by the shaker was used as input for the conditioning circuit. The excitation frequency
was 78 Hz and the open circuit voltage of the piezoelectric beam was set to 4 Vpk−pk.
The conditioning circuit replaced the power supply used in experiments with the storage
system. A 4.1 V THINERGY battery which was discharged to 1.8 V was used as a test
cell. Both the output voltage of the conditioning circuit and the voltage of the battery was
monitored as the cell charged after activating the shaker.
6.2 Data Analysis
At the optimal fan frequency, the voltage across the piezoelectric element had a
frequency of 56 Hz and an amplitude of 350 mV. This value agrees with the location and
magnitude of the voltage peak in previous baseline testing. Figure 6.2.1 shows a trace of
the voltage across the piezoelectric element at the optimal fan frequency.
After connecting the SEH circuit and performing a load resistance sweep, several
observations were made. Regardless of the load resistance, the output voltage did not
change. This voltage remained at a level of 30 mV or 10% of our input voltage. Fig-
ure 6.2.2 shows the output from the rectifier circuit when connected to a load of 1kΩ.
With a 4 Vpk−pk input signal and a perfect impedance match with minimal power
98
Figure 6.2.1: Voltage across piezoelectric element at 56 Hz
loss, the output from the conditioning circuit was expected to be a DC voltage of 0.7
V. However, with the storage system connected to the conditioning circuit, a 4 Vpk−pk
input signal produced a DC output of 0.25 V. This 0.25 V output served as the input to
the storage system. This voltage was too low to activate the charging mechanism in the
MAX17710 chip, so the battery did not charge.
6.3 Discussion
The output voltage of the integration baseline testing agreed with results obtained
from previous baseline testing. Regardless, at voltages below 400 mV, there isn’t enough
voltage to bias the diodes which make up the full wave rectifier. As such, there is no
meaningful relationship between input and output voltages. The 30 mV output can most
likely be explained by a bias voltage from the measuring device. Without being able
to correctly bias the diodes, there is no way to generate a voltage and load resistance
relationship. Based on dynamic magnification testing under optimal conditions, a higher
99
Figure 6.2.2: Rectifier output for integrated circuit
output voltage suitable for the conditioning circuit can be achieved.
The results from integrating the conditioning circuit with the storage system indi-
cate that the impedance mismatch between the two circuits caused losses that prevented
proper charging of the battery. The optimal output from the conditioning circuit was 0.7
V when connected to a resistive load, but only 0.25 V was received, which was 65%
less than expected. An impedance matching network should be incorporated into future
research to ensure optimal power transfer between systems.
6.4 Potential Applications
At the power levels produced in the prototype testing phase it is clear that the cur-
rent harvester design will not be the solution to the global energy crisis. However, it is
important to understand and appreciate the need for such a design is low power appli-
cations. The rapidly growing field of microelectromecanical systems often involve low
power devices that could utilize the harvester power output. Additionally, bridge and
100
building sensors without grid access could now draw power from a piezoelectric energy
harvester and be used to monitor fires, fatigue, mechanical stress and other structural vital
signs. The harvester could be used in even more remote applications such as crop sensors
in the center of large fields and mountain or forest sensors that measure climate data.
101
7 Conclusion
This study successfully demonstrated dynamic magnification, determined a method
to find an optimal load given a piezoelectric voltage input, and designed a storage system
for low-voltage applications. Further research can be conducted to improve harvester and
circuitry design. Scale was a limiting factor in the effectiveness of the energy harvesting
system. The design of the energy harvester was limited by the dimensions of the wind
tunnel test environment. The integration testing was hindered by insufficient voltage gen-
erated by the energy harvester. This insufficient voltage also greatly limited the design
of the storage system by reducing the ability to use the stored energy for practical ap-
plications and preventing the use of multiple active circuitry components in the design.
Utilizing more piezoelectric material, whether by increasing the number or size of har-
vesters, would increase the voltage output. The SSHI-P rectifying circuit would become
a potentially viable option with a larger voltage output from the harvester. In addition, the
storage system could consist of additional components including a DC-DC converter and
a microcontroller which consume power from the source but would reduce limitations
that were observed in the storage design.
Further research could focus on integration of an energy harvester with a rectifying
circuit and a storage system at the onset of experimentation. To focus on an integrated
102
system, the impedance of the rectifying circuit would need to be closely matched to the
impedance of the storage system in order to store energy. Additional research could
involve testing the integrated system solely on a shaker. By focusing on shaker testing
instead wind tunnel testing, experimental data would be more reliable because the input
variables such as frequency and vibrational intensity would be easily controlled.
Piezoelectric energy harvesting utilizing dynamic magnification through wind-induced
vibrations is a novel concept that can benefit from continued research. Investigation into
this type of renewable energy can have a positive impact on low flow velocity wind energy
harvesting. Crucial elements of this research include determining the reliability of piezo-
electrics for these applications and assessing the feasibility of these energy harvesters.
The research presented here can serve as a foundation for future exploration of piezoelec-
tric wind energy harvesters.
103
Glossary
Energy Harvesting
Cyclic loading - portions of the system are exposed to fluctuating loads continually in
order to determine the effects on a material over time
Degenerate states - two or more states are degenerate if they have the same energy level,
so the system is equally likely to be in either state
Dielectric - electrical insulator that can be polarized by aligning domains with an applied
electric field
Domain wall - a gradual reorientation of magnetic moments forming a boundary between
magnetic domains
Endurance limit - the maximum stress which can be applied to a material for an infinite
number of stress cycles without resulting in failure of the material.
Magnetic domain - a region of uniform magnetization, with all individual magnetic mo-
ments of the atoms alligned in the same direction
Rhombohedral - three equal aces and oblique angles
Tetragonal - rectangular prism
Energy Conditioning
Alternating current (AC) - a flow of electric charge that periodically reverses direction
Capacitor - a passive two-terminal electrical component used to store energy in an elec-
tric field. Capacitors are widely used in circuits for blocking direct current while passing
104
alternating current
Coupling (weak, strong) - the transfer of electrical energy from one circuit segment to
another
Diode - a two-terminal electrical component with low resistance to current flow in one
direction and high resistance to current flow in the other
Direct current (DC) - a flow of electric charge that only flows in one direction
Full-bridge rectifier – a rectifier circuit that uses four diodes connected in a closed-loop
bridge to produce the desired output
Gain - the measure of the ability of a circuit to increase the power of a input signal.
Impedance - the measure of the opposition to the passage of current when voltage is ap-
plied to a circuit.
Inductor - a passive electrical component that stores energy in a magnetic field.
Phase shift - In a sinusoidal wave, a phase shift describes a wave with an offset starting
angle.
Rectifier - a circuit which converts AC current into DC current.
Standard energy harvester (SEH) - a rectifier circuit that consists of a standard full-
bridge rectifier coupled with a resistor and capacitor in series
Synchronous switch harvesting on inductor (SSHI) - a rectifier circuit that is formed
by placing a branch with an inductor, a switch, and a resistor in parallel (SSHI-parallel)
or in series (SSHI-series) to the traditional SEH circuit
105
Energy Storage
Coulombic efficiency - the amount of battery charge output to input
Depth of discharge - the amount that a battery can ideally be discharged without ad-
versely affecting other properties of the battery
Energy capacity - the amount of energy a battery can hold in total
Energy density - the capability to deliver energy over its volume: how much electricity
a system can store as compared to the space it takes up
Life span - the number of charge and discharge cycles that it can undergo before it needs
to be replaced
Memory effect - when a battery’s maximum energy capacity drops after being repeatedly
charged but only partially discharged since the battery remembers only the lower energy
capacity
Operating temperature - the ideal temperature at which the battery will charge and dis-
charge, without adversely affecting any other properties of the battery
Power capacity - the maximum rate of energy transfer over time
Power density - the power per volume of battery
Pulse width modulation – a manner of delivering energy through a succession of pulses
rather than a continuously varying signal
Rate of self-discharge - the amount of energy that is dissipated over time when the batter
is not connected to anything
Rate capacity effect - an effect that causes degradation of the battery discharge efficiency
under high load currents
106
State of charge – the percent of the total energy capacity contained in a battery at an
instantaneous moment of time
107
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Appendices
115
Figure .0.1: FEM showing the 4th bending mode of the inner beam at 191 Hz in the
baseline configuration
116
Figure .0.2: FEM showing the 1st bending mode of the outer cylinder at 191 Hz in the
baseline configuration
117
Figure .0.3: FEM showing the 2nd bending mode of the outer cylinder at 191 Hz in the
baseline configuration
118
Figure .0.4: FEM showing the 1st torsional bending mode of the inner beam at 171 Hz in
the baseline configuration
119
Figure .0.5: FEM showing the 4th bending mode of the inner beam at 191 Hz with dy-
namic magnification
120
Figure .0.6: FEM showing the 1st bending mode of the outer cylinder at 191 Hz with
dynamic magnification
121
Figure .0.7: FEM showing the 2nd bending mode of the outer cylinder at 191 Hz with
dynamic magnification
122
Figure .0.8: FEM showing the 1st torsional bending mode of the inner beam at 171 Hz
with dynamic magnification
123
Figure .0.9: Peak voltage output for the harvester system with elastomer A for flow ve-
locities ranging from 12.3-14 m/s
124
Figure .0.10: Peak voltage output for the harvester system with elastomer A for flow
velocities ranging from 14.8-16.5 m/s
125
Figure .0.11: Peak voltage output for the harvester system with elastomer A for flow
velocities ranging from 19.9-21.6 m/s
126
Figure .0.12: Peak voltage output for the harvester system with elastomer B for flow
velocities ranging from 9.7-11.4 m/s
127
Figure .0.13: Peak voltage output for the harvester system with elastomer B for flow
velocities ranging from 12.3-14 m/s
128
Figure .0.14: Peak voltage output for the harvester system with elastomer B for flow
velocities ranging from 14.8-16.5 m/s
129
Figure .0.15: Peak voltage output for the harvester system with elastomer B for flow
velocities ranging from 19.9-21.6 m/s
130