A review of renewable power generation using piezoelectric materials

This paper reviews and summarizes recently published journal articles on piezoelectricity and vibration energy harvesting using piezoelectric materials, covering key areas such as piezoelectricity, piezoelectric materials, harvesting kinetic (mechanical vibration) energy, piezoelectricity power generators, piezoelectricity modelling, charge collector / energy storage equipment. The emphasis is on renewable power generation using piezoelectric materials.

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A REVIEW OF RENEWABLE POWER

GENERATION USING PIEZOELECTRIC

MATERIALS Ojo E Olufisayo and Professor Freddie Inambao*

Mechanical Engineering, University of KwaZulu-Natal, Durban, South Africa

https://orcid.org/0000-0001-9922-5434

*Corresponding Author Email: inambaof@ukzn.ac.za

ABSTRACT

Piezoelectric materials are crystals that can convert energy associated with mechanical deformation into electrical energy This material is identified with higher energy density and stronger electromechanical coupling properties than other contemporary technologies Vibration, which is a cheap and common source of mechanical energy, is often encountered in our environments with good energy levels Therefore, the energy generated by the vibration of piezoelectric materials provides

an ideal energy solution for portable and wireless devices This paper reviews and summarizes recently published journal articles on piezoelectricity and vibration energy harvesting using piezoelectric materials, covering key areas such as piezoelectricity, piezoelectric materials, harvesting kinetic (mechanical vibration) energy, piezoelectricity power generators, piezoelectricity modelling, charge collector / energy storage equipment The emphasis is on renewable power generation using

piezoelectric materials

Keywords: Renewable energy harvesting, mechanical vibration, piezoelectric

materials

Cite this Article: Ojo E Olufisayo and Freddie Inambao, A Review of Renewable

Power Generation Using Piezoelectric Materials International Journal of Mechanical Engineering and Technology 10(12), 2020, pp 559-577

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=12

1 INTRODUCTION

In recent years, renewable energy sources have become popular in attempting to reduce global warming These energies are an alternative form of energy resource which can reduce the consumption of traditional energy resources like fossil fuels Typical renewable energy resources are wind, tidal waves, geothermal heat, solar, and rain [28] Piezoelectricity was first discovered by Pierre and Jacques Curie in the 1880s [29] They found that in asymmetrical crystals possessing a polar axis, the effect of compression parallel to the polar axis was to polarize the crystal, resulting in the generation of a positive charge on one side of the material and a negative charge on the other side of the material One of the innovative

ways to accomplish this is through harvesting unexploited and wasted energies in our environment The concept of renewable energy generation from human surroundings has stimulated renewed interest in piezoelectricity This renewable energy source is a self-sustainable system for generating electricity without depleting natural resources In the past two decades there has been a strong interest in converting mechanical energy from human motion to electrical energy This power can then be used to charge the battery in an electronic device or directly power a small, low-power circuit

The three main transduction methods for conversion of vibrations to electrical energy for self-powering devices are electromagnetic, electrostatic, and piezoelectric harvesters

2 PIEZOELECTRICITY

According to [1], piezoelectricity can be defined as the property of some dielectric materials that have developed a polarization as a result of being subjected to mechanical strain deformation This mechanical property (tension) in their view was produced by the liking force realignment of atoms and in so doing, producing polarization and thus an electric field

If this is reversed and a piezoelectric material not being compressed is exposed to an electric field, it will create a mechanical deformation in its lattice structure Considering the two applications, the reversal in the course of application of force, either by mechanical or electrical means, will generate a reversal in the direction of the residual effect [2] explains that the piezoelectric effect on piezoelectric material occurs in two forms: the first is the direct piezoelectric effect that describes the material‟s capacity to convert mechanical strain into electrical charge; the second is the converse effect, which is the capacity of a material to convert an applied electrical potential into mechanical strain energy (deformation) The direct piezoelectric effect is responsible for the material‟s ability to function as a sensor and the converse piezoelectric effect is responsible for its ability to function as an actuator The authors submitted that a material is deemed piezoelectric when it has this ability to convert electrical energy into mechanical strain energy, and likewise to transform mechanical strain energy into electrical charge According to [3], renewable energy which is harnessed from a natural source has evolved as the power source of the future due to diminishing fossil fuel and nuclear power sector volatility The authors state that renewable energy harvesting plants that can generate power at the kW or mW level are classified as macro energy harvesting technology Micro energy harvesting technology is centered on mechanical vibration such as: mechanical stress and strain; thermal energy from furnaces, heaters and friction sources; sunlight or room light; the human body; chemical or biological sources which generate mW

or µW levels of power Micro energy harvesting is is an alternative to conventional macro renewable energy

Wireline Sensor Network systems (WSNs) and Micro Electromechanical Systems (MEMs) represent pressure electricity which is attributed to the properties of certain crystalline materials such as quartz, rochelle salt, tourmaline and barium titanate which develops electricity when subjected to pressure, a term known as the direct effect These same crystals can undergo deformation when subjected to an electric field, known as the converse effect The converse effect of these materials can be used as an actuator while the direct effect can be used as a sensor or energy transducer

[4] listed the benefits, advantages and applications of piezoelectricity as a proven and viable form of renewable energy as being:

 Long lasting operability

 No chemical disposal

 Cost saving

 Safety

 Maintenance free

 No charging points

 Inaccessible site operability

 Flexibility

 Applications otherwise impossible

Applications include:

 Environmental monitoring

 Habitat monitoring (light, temperature, humidity)

 Integrated biology

 Structural monitoring

 Interactive and control

 RFID, real time locator, TAGS

 Building, automation

 Transport tracking, car sensors

 Surveillance

 Pursuer-evader

 Intrusion detection

 Interactive museum exhibits

 Medical remote sensing

 Emergency medical response

 Monitoring, pacemaker, defibrillators

 Military and aerospace applications

3 HARVESTING KINECTIC (MECHANICAL) VIBRATION ENERGY

[5] defined piezoelectric energy harvesting as the conversion of energy absorbed by a transducer from the environment to usable electric voltage that can be either used immediately for actuation or otherwise stored in batteries for future or later usage The world is dynamically moving from the era of electrical equipment to electronic devices due to the energy crisis; the crisis is leading to a wanton voluntary reduction in global electrical power consumption, resulting in the evolution of micro and nano powered electronic circuits [3] established that piezoelectric energy harvesters are viable substitutions for the conventional battery The authors‟ explained that ultra-low power portable electronics and wireless sensors, which hitherto have been using conventional batteries as their power sources, have proven to

be unreliable as the life of these batteries are limited and very short compared to the working life of the devices themselves Therefore, the replacement or recharging of these batteries is cumbersome and sometimes absolutely impossible Consequent upon this, many researches have been instituted to study energy harvesting technology as a self-dependent power source for portable devices or wireless sensor network systems The authors‟ view on energy conversion recognized that human beings have already been using energy harvesting technology from time immemorial in the form of windmills, watermills, geothermal and solar energy which has helped in the research and development of micro energy harvesting technology

According to [6], the most extensively deployed method of harvesting mechanical energy

is piezoelectric energy conversion which utilizes the piezoelectric effect to convert time-dependent mechanical deformations into electricity The authors listed other methods for direct mechanical to electrical energy conversion including electromagnetic, electrostatic, and electroactive polymer generators Harvesting these wasted energies (thermal and mechanical) would contribute to more efficient and sustainable energy consumption This wasted

mechanical energy which is a by-product of objects in motion usually exists in the form of vibrations, shocks or strains Sources of this wasted mechanical energy include fluid flow, household appliances, industrial equipment, motor vehicles and structures such as buildings and bridges

According to [7], energy harvesting or scavenging is the process of seizing and

resourcefully utilizing wasted energy from naturally occurring energy sources, accumulating and storing it for immediate or future use Essentially, it is the conversion of ambient energy that exists in our environment into electrical energy

Harvesting kinetic energies is a sustainable method for producing electricity without depleting valued natural resources The main methods employed in kinetic energy harvesting are piezoelectric, electromagnetic, electrostatic or by using magnetostrictive materials Attention has been focused on harvesting of walking energy as one of the easiest and most reliable means of vibration energy harvesting, and then to explore and compare different technologies used for converting same to electricity, and identifying the most effective technology to be used in generating it There are numerous types of harvester that can be positioned on a user‟s body to harvest kinetic energy during walking Furthermore, some pavement slabs have been designed and produced for harvesting energy; these slabs with inbuilt harvesters are more dependable than body-located technologies for piezoelectricity harvesting, since they are independent of physiological parameters Piezoelectric transduction remains the most desirable and commonly accepted micro energy harvesting technology due

to its advantageous stance which includes simplicity, flexibility and availability despite producing less output current than electromagnetic transduction

Energy harvesting is one of the most favorable techniques that can be deployed to tackle ever increasing global energy demand problems without adverse residual effects on the environment Piezoelectric energy harvesting at the moment typically connotes micro- to milli-watts small power generation systems that have been developed as viable replacements for battery stored power It explores kinetic, thermal, solar or electromagnetic radiation sources to generate movement mainly in the form of vibrations which are later converted into electrical energy An energy harvester basically has three main components; the micro-generator for converting ambient energy into electrical energy, the voltage booster to pump up and regulate the generator voltage, and the storage element Since vibration powered generators are mainly resonant systems, maximum power is produced when the resonant frequency of the generators equals the ambient vibration frequency of the piezoelectric material Available are different types of vibration energy that can be harvested which are being studied by several researchers, including: human motion, ocean waves, harvesting strain from beam elements in critical structures etc Energy harvesting in the form of mechanical loading generated from the ground in the shape of compressive forces while people move across the floor, is a typical example of a sustainable method to generate electrical energy [8] pointed out that the performance of a piezoelectric energy harvester principally hinges on the piezoelectric properties of the material used to construct the generators

Usually, thin film piezoelectric materials display improved piezoelectric properties compared to bulky piezoelectric materials The usage of single crystals and nanomaterials (nanowires) has enhanced the power density and energy conversion efficiency which has resulted in improvement in the miniaturization of the device size while upholding a reasonable power output In spite of prodigious research efforts on these nanomaterials, there

is still a deficiency in the basic scientific understanding of and experimental research on piezoelectric and flexoelectric effects in single crystalline nanowires This gap in research at this fundamental level compromises fidelity of the mathematical algorithms deployed in

modeling and forecasting the piezoelectric potential mechanical to electrical energy conversion efficiency and device material optimization

A related task is research on the combination of piezoelectric and semiconducting effect which brings about the so-called piezotronic effect The scientific theory of the interaction between electron distribution and semiconductor band structures still call for additional research efforts While single crystal materials are believed to offer a better piezoelectric performance and offer enhanced power density compared to their bulk material counterparts, the costs of these materials remain exorbitantly high and occasionally hyper-inhibitive The existing construction methods of these generators and the associated device incorporation techniques at nano scale are not yet suitable for large scale processing, and research efforts in this regard will substantively lessen fabrication costs and assist in transforming piezoelectric energy harvesting from ordinary experimental curiosity into genuine engineered device achievement to power wireless sensors

4 PIEZOELECTRIC MATERIALS

According to [2], piezoelectric materials can play a pivotal role as mechanisms for energy harvesting, as they possess the ability to absorb energy from the environment and convert it to electrical energy that can then be deployed to drive electronic devices directly or indirectly Piezoelectric materials belong to a wider class of materials called ferroelectrics One of the essential behaviors of a ferroelectric material is that its molecular structure is arranged in such

a manner that the material exhibits a local charge separation, a situation known as an electric dipole All the way through the material configuration, the electric dipoles are arranged randomly and upon subjecting the material to heat energy above a particular point (the Curie temperature) and subject to an extreme electric field, the electric dipoles will re-orientate themselves relative to the applied electric field This process is known as poling As soon as the material is cooled, the dipoles will maintain their new orientation and the material at that moment is said to be poled Subsequent to the completion of the poling process, the material will then exhibit the piezoelectric effect [9] classified piezoelectric materials used in piezoelectricity energy generation into four basic groups namely: ceramics, composites, polymers and monocrystals Most experimental research conducted has found ceramics to be most commonly used, followed by composites, polymers and monocrystals

Ceramic are the most commonly used materials in piezoelectric generator design PZT

cerama is a form of ceramic used in generators PZT is a mixed crystal of titanate and lead zirconate with the general formula (x)PbTiO3-(1-x)PbZrO3 The properties of piezoelectric ceramic PZT can be manipulated by modification of the percentage content of individual compounds comprising mixed crystal, x = (0 – 1) This enables the production of ceramics PZT with a diverse set of material constants Many PZT variations are used in generators with

no single ceramic PZT dedicated to generator design e.g PZT-5H, PZT-5A, PZT-PIC255, PZT-APC 841, PZT-APC 850, PZT-PPK11

Composites are materials made of piezoelectric materials of diverse shapes, polymer film, layers of adhesive and properly formed electrodes On parts of the composite layers that are fastened together by bolts are electrodes that properly fitted There are two types of composites that can be applied in generator design: PFC (piezoelectric fiber composite) and MFC (macro fiber composite) PFC is a composite consisting of circular piezoceramic fibers located in the layer of adhesive and on bolt-on parts of the polyimide film and electrodes MFC manufactured by Smart Materials Corp are primarily made of rectangular piezoceramic bars, distinguished by adhesive layers, polyimide film and an electrode on the bolt-on part Polymer materials are chemical substances comprising numerous component parts, prominent among polymers is polyvinylidene fluoride (PVDF) PVDF is a semi-crystal,

comprising a maximum of 50 % to 60 % of the crystal phase Piezoelectric properties of PVDF were discovered in the 1960s PVDF is generally applied as a foil so that it can be easily formed and shaped, compared to ceramics which are not

Monocrystal were invented a few years ago and are presently the most auspicious piezoelectric material in the piezoelectric generator field of research, as it is the most effective energy conversion material available There are two types of monocrystal materials that can

be used for generators: PZN-PT (Pb(Zn1/3Nb2/3)O3-PbTiO3) and PMN-PT ((Mg1/3 Nb2/3)O3-PbTiO3) It has been generally observed that PZN-PT and PMN-PT monocrystals have the highest efficiency when converting energy Composites or PVDF polymers are mostly used in research projects with ceramic generators Ceramic materials have been found

to be very effective in energy conversion, which is duly reflected in the high rates of electromechanical coupling coefficient However, they can be very fragile and are susceptible

to more wear as a result of fatigue compared to composites and polymers

[10] investigated piezoelectric ceramics with a microstructure texture experimentally prepared by tape casting of slurries containing a template SrTiO3 (STO) under external mechanical stress They established that STO-added specimens indicated excellent power compared to the STO-free specimen when a large stress was applied to the specimen

[11] analyzed aluminum nitride (AIN) as a piezoelectric material for piezoelectric energy harvesters because of their high resulting voltage level They reported a maximum output power of 60 µW for an unpackaged device at an acceleration of 2.0 g and at a resonance frequency of 572 Hz

[12] analyzed a piezocomposite composed of layers of carbon/epoxy, PZT ceramic and glass/epoxy to harvest energy They reported that piezocomposites have the potential to harvest energy subjected to vibration after numerical and experimental validation

5 PIEZOELECTRICTY POWER GENERATOR

[2] defined a power generator or harvesting as the process of obtaining the energy surrounding a system and transforming it into functional electrical energy Modern development in wireless technology and low-power electronics such as microelectromechanical systems have brought about renewed efforts in piezoelectricity research This development has led to the usage of piezoelectric materials which exploit the ambient vibrations of the surrounding system as a tool for power harvesting Piezoelectric materials are made of crystalline structures that enable them to convert mechanical strain energy into electrical charge, and also convert subjected electrical potential to mechanical strain This property offers these materials the capacity to absorb mechanical energy from their surroundings, usually in the form of ambient vibration, and convert it to electrical energy that can power other devices While the use of piezoelectric material is the foremost method

of generating/harvesting this energy, other methods exist, one of which is using conservative methods of electromagnetic transduction

[13] conducted an investigation relating to the rudiments of a generator that converts mechanical energy to electrical energy utilizing a piezoelectric vibrator and a steel ball The effect of the various characteristics of the piezoelectric vibrator was also investigated In simulating the generation mechanism, an electrical equivalent model was introduced The essential modes of bending vibration for two models were calculated: Model A (the transducer with the steel ball) and Model B (the transducer only) The admittance characteristics of each model were measured and it was confirmed that the peak frequencies

of the system equals the vibration modes It was also confirmed that the calculated waveform

of the output voltage was similar to the measured one, therefore confirming the model to have provided an accurate simulation of the output voltage An efficiency curve of the model was

drawn for different input mechanical energies, and it was determined that as the potential energy of the ball increased, the maximum efficiency decreased A larger chunk of the applied energy was reverted back to the steel ball in the form of kinetic energy thereby triggering bouncing off of the plate The conclusion thereafter was that the energy generated would be large if the steel ball had vibrated with the piezoelectric plate instead of bouncing off after the impact This scenario was simulated and it was resolved that a maximum efficiency of 52% could be achieved The characteristic effects of the piezoelectric vibrator were studied and it was concluded that the system efficiency increased as the mechanical quality factor and the electromechanical coupling coefficient increased while the dielectric loss decreased

[14] analyzed the efficiency of stacked piezoelectric material in terms of electric power generation An analytical model was considered and it was recommended that the basic challenge of generating electrical energy from piezoelectric material is that most of the generated energy in the system is held or stored and subsequently returned to the excitation source that originally triggered the charge to be generated This occurrence may be specifically problematic when a piezoceramic is positioned parallel to a capacitor in series with the applied load It was therefore recommended that the maximum efficiency of power generation can be realized by reducing the total amount of energy stored in the piezoelectric material The efficiency of this model was investigated across a spectrum of frequencies and resistive values, and it was concluded that at frequencies above 100 Hz, the efficiency of the stack actuator was insignificant and that the maximum efficiency occurred at 5 Hz This obtained frequency is far lower when compared to the first mechanical and electromechanical resonances of the stack, which occurred at approximate frequencies of 40 kHz and 60 kHz, respectively It was also recorded that the frequency of the maximum efficiency was low due

to the relative energetic structure of the stack Also recorded was that the stack efficiency intensely depended on the excitation frequency, while the load resistance had a low effect on

it

According to [15] the piezoelectric transducer, which is a key component of a generator,

is designed to generate electric voltage in response to thermal, electrical, mechanical and electromagnetic input The authors concentrated on energy generation for low-powered circuits with a PZT energy harvester Nano and micro watts of power can be produced from

PZT harvesters by applying mechanical, thermal, electrical, light and fluid input Mechanical

is considered to be the most efficient input compared to other input options, because it is readily available and can be tapped easily from the environment The conversion of this mechanical energy from waste vibrations into electrical energy can be achieved through electromagnetic, piezoelectric, or electrostatic transduction mechanisms The piezoelectric transduction generator is the most effective and efficient mechanism for microelectronics, wireless sensors, and nano electronics because it can be easily fabricated and one is able to harvest or generate energy at variable frequencies This theory was first discovered by Pierre andJacques Curie in 1880 as having a direct effect, that is conversion of mechanical energy to electrical energy, as expressed in Equation (1) and a converse effect i.e., the conversion of electrical energy to mechanical energy, as expressed in Equation (2)

Di = e0ij Ej + ddim Ơm (1)

Ek = dcjk Ej + SEkm Ơm (2) where Di is the dielectric displacement vector, Ek is the strain vector, Ej is the applied electric field vector, Ơm is the stress vector, ddim and dcjk are piezoelectric coefficients for direct and converse effects of piezoelectricity respectively, e0ij is the dielectric permittivity at constant stress, and SEkm is the elastic compliance matrix at constant electric field

A typical PEH is made up of three key components:

 The piezoelectric patch This is responsible for the converting of environmental input (e.g vibration, fluid structure interaction (FSI), biomechanical, etc.) into alternating current

 The storage unit This is usually a super capacitor or a battery which is responsible for the storage of the charge generated by the PEH;

 The modulating circuit This is responsible for conversion of AC into DC

The storage unit may be ignored in order to use generated energy directly from the PEH

[16] analyzed further that the power generation ability of piezoelectric energy harvesters (PEH) does not only relate to the piezoelectric material properties, the vibration magnitude and the succeeding conditioning circuit, but also to the fixation modes and the prescribed adjustment methods A commercially inclined piezoelectric ceramic plate (PCP) in simply supported beam fixation mode and cantilever beam fixation mode were both evaluated using finite element simulations and comprehensive experiments The two methods of adjusting the natural frequency of PCP were evaluated and compared, and as a result, some procedures were suggested for the application of PCPs according to the simulation and experimental results which revealed that:

 The simply supported beam fixation mode is appropriate for environments where the exciting frequency exceeds 50 Hz, while the cantilever beam fixation mode is suitable for a condition where the exciting frequency is below 50 Hz

 The maximum generation power of a PCP generated in simply supported beam fixation mode is higher than that in cantilever beam fixation mode

 Regulating the mass block weight affixed to the PCP can alter the natural frequency of the PCP more efficiently than the length-width ratio can do

[8] explains that in their research ambient mechanical vibrations were harvested and transformed to beneficial electrical energy which could then either be stored in a storage element or be delivered directly to the load Energy storage is a crucial component of the energy harvesting system because it is a conduit of stability between the energy source and the load that offers a continuous energy flow from an otherwise variable environmental source The power interface circuits align the harvested energy to permit the charging of low capacitor batteries or supercapacitors and also provide compatibility with the load requirements For a sensor node that is fully powered by ambient energy, the generated mean

power (Pg) must be higher than or equal to the mean consumed power (Pc):

Where Pg is the generated mean power and Pc is the mean consumed power

As earlier pointed out, the power used by a wireless sensor node is usually a few tens to hundreds of milliwatts When this is compared to the power output of MEMS piezoelectric energy harvesters with a range of a microwatt to tens of microwatts, it is apparent that energy harvesting will not be able to continuously power the sensor node This therefore led to the basic question of in what way can the power consumption of the wireless sensor node be decreased so that the energy harvesting would be able to handle the supply requirements? The answer to this concern is practically realized by what is called „duty cycling‟, a phenomenon which permits the sensor to function in a spasmodic regime instead of a continuous form In this approach, wireless sensor nodes are fundamentally designed to function in an extremely

low duty cycle (D), with average power consumption in an active mode (P), and low power consumption while in sleep (or idle) mode, (P active) This alternating operation of the sensor

node has been conditioned in a way that the monitoring procedure of the wireless sensor network is not compromised The average power used up by the sensor node can be calculated by:

Where Pc is the average power used, Psleep is the low power consumption in sleep mode, D is the low duty cycle and Pactive is the average power consumption in active mode

From Eqs (3) and (4) it can be deduced that if the duty-cycle (D) is diminished, and the

sensor node is put to the sleep mode for most of the time and again stimulated to perform sensing and communication when required, this will lead to a pronounced decrease in the average power consumption of the wireless sensor node Thus, careful choice of a suitable duty cycle is required in designing of the power management algorithms

Vibrations from ambient energy sources are variable in nature, and there are occasions

and circumstances when P g < P c In order to deal with this, a collector or storage element such as a supercapacitor or a thin film battery is required For any subjective protracted period

of time, T, a long-term storage (E storage ) element must be designed to satisfy the condition of:

mean power and Pc is the mean consumed power

The authors described piezoelectric micropower generator and nanogenerator design to be

a multidisciplinary area with problems emanating from basic physics, material science, mechanical engineering, and electrical engineering This multidisciplinary methodology and model is considered the most reliable means of designing piezoelectric energy harvesting devices, but much work still needs to be done to advance the power output of piezoelectric generators to equal the requirements of wireless sensor devices This task can be solved by selecting piezoelectric material with the best piezoelectric properties, device geometries, and power electronics to stabilize the power output

[3] in their work noted that the enhanced technique of vibrational energy harvesting with piezoelectric materials has led to the need to develop a scavenging energy device Generally, harvesting vibrational piezoelectric energy depends on the induced power from mechanical vibrations with varying amplitude, leading to induced output voltage with alternating current (AC) from the piezoelectric elements Many piezoelectric harvesters designed earlier have shown that the power produced from such a device must be rectified Diverse rectifiers have been studied and recommended, including vacuum tube diodes, mercury arc valves, silicon-based switches and solid state diodes The simplest approach to rectifying alternating input is

to connect the piezoelectric harvester with a P-N junction diode, but this can only work in half input wave In order to achieve full wave rectification of a vibrating piezoelectric device, a bridge-type rectifying circuit with 4 diodes is required In the search to improve the power harvesting circuit efficiency, many efforts have been recorded to modify the rectifying circuit Engaging a buck-boost DC-DC converter with intelligence to track the power generator‟s dependence with the acceleration and vibration frequency of a piezoelectric device, a lofty efficiency of 84% was recorded Furthermore, to improve the conversion efficiency of the bridge-type rectifying circuit, the synchronized charge extraction method with inductor was introduced, thereby leading to an increase in the harvested power by a factor of 4 [17] analyzed the actual energy flow that is behind numerous energy conversion practices like parallel synchronized switch harvesting on inductors (SSHIs) and series SSHI for piezoelectric vibration energy scavenging and introduced the pyroelectric effect which extracts energy due to temperature variation [18] suggested energy production using a

mechanically excited unimorph piezoelectric membrane transducer under dynamic conditions and predicted a new SSHI to improve the harvested power by the piezoelectric transducer of

up to 1.7 mW, which would be adequate to supply a large range of low consumption sensors

6 PIEZOELECTRICITY MODELLING

According to [2], the mechanical and electrical behavior of a piezoelectric material can be modeled by two linearized constitutive equations The direct effect and the converse effect may be modeled by the subsequent matrix equations (IEEE Standard on Piezoelectricity, ANSI Standard 176-1987):

Direct piezoelectric effect:

{D} = [e]T {S} + [αs] {E} (6) Converse piezoelectric effect

In Eqs (6) and (7), {D} is the electric displacement vector, {T} is the stress vector, [e] is the dielectric permittivity matrix, [CE] is the matrix of elastic coefficients at constant electric field

strength, {S} is the strain vector, [S] is the dielectric matrix at constant mechanical strain, and

{E} is the electric field vector

After the poling of the material, an electric field may be introduced to prompt expansion

or contraction of the material, and this electric field may be introduced at any point along the surface of the material, thereby resulting in a potentially variable stress and strain generation However, the piezoelectric properties must include a sign convention to expedite this capability to apply electric potential in three directions

Piezoelectric material can be universally categorized for two cases; the first is the stack configuration which operates in the -33 mode and the second is the bender that operates in the -13 mode The sign convention concludes that the poling direction is always in the “3” direction, and with this assumption, the two modes of operation can be understood In the -33 mode, the electric field is applied in the “3” direction and the material is strained in the poling

or “3” direction In the -31 mode, the electric field is applied in the “3” direction and the material is strained in “1” direction or perpendicular to the poling direction These two modes

of operation are essential when describing the electromechanical coupling coefficient that

occurs in two forms: the first is the actuation term d, and the second is the sensor term g The term g refers to the sensing coefficient for a bending element poled in the “3” direction and

strained along “1”

According to [3], coupled electro-mechanical behavior of piezoelectric materials can be modelled by these two linearized constitutive equations:

Direct piezoelectric effect

Converse piezoelectric effect

Ek = dcuc E1 + SEƠm (9)