1. ENERGY HARVESTING: STATE OF THE ART

The ever-increasing number of advances in technology have shaped the world into a

place where we are more and more accustomed to being always connected; from our

phones to our homes and even cities, as electronic hardware circuitries become

cheaper and smaller and wireless communication more efficient, paradigms such as

Wireless Sensor Networks or the Internet of Things are now a reality. As they rely

heavily on wireless, “smart” devices, there is an emerging need to overcome the

energy problem: a lot of these devices are embedded and need to continuously run so

it is not efficient to use the connection to the power grid as it would be unpractical,

nor use batteries, for they would require proper maintenance. A possible solution that

has gained momentum in the past years is to use ambient energy sources and convert

them into electrical energy to recharge the batteries.

Large-scale ambient energy (e.g. solar, wind and tide), and large-scale technologies

are already widely used and constantly updated, especially in the light of the growing

concern for the environment, a hot topic right now. At the other end of the scale,

energy harvesting, although is not spread as much, has been the recurring object of

research efforts.

Energy Harvesting is a technique which aims to scavenge or recover the small

amounts of ambient energy that would otherwise be lost, with a consequent

significant economic and environmental impact. The captured energy is generally

very small (of the order of mJ) especially compared with the amount large scale

plants using ambient energy sources such as wind farms can achieve (order of several

hundreds of MJ). However, unlike the large-scale power stations that must be fixed at

a given location, Energy Harvesting devices for small-scale electronics are portable

and in the case of low power applications (such as nodes in Wireless Sensor

Networks, or medical devices embedded in the human body) could not only decrease

the dependency on conventional batteries, but even replace them.

It is easy to see that the environment is full of waste and unused ambient energy. Of

course, not all of it is suitable to all types of applications: for example, even if solar

energy is widely studied and there are a lot of technologies available to capture it, it

would not be optimal to use it in an indoor environment, as we can see from the table

1.1 [1], which reports the main available choices for ambient energy sources.

The best strategy would be to base the solution on whichever energy source is

available at the specific application areas.

Energy Source Performance Conversion Efficiency

Ambient Light 100mW/cm3 (outdoor)

10µW/cm3 (indoor)

15-20%

Thermal 60-135µW/cm3 <1%

Vibration 4µW/cm3 (human motion)

800µW/cm3(industrial

machines)

25-50%

Wind 1mW/cm2 0.5-10%

RF Wide Range, varies with

distance from RF source

50%

Table 1.1: ambient energy sources.

Adopting an Energy Harvesting based solution can bring many advantages:

1- Improve Efficiency: this technique recovers energy that otherwise would be

wasted and eliminates the need for operations such as battery maintenance;

2- Reduce Environmental Impact;

3- Enable new technology.

Given that these types of systems rely on renewables, they are affected by the same

problems that are characteristic of the large-scale plants; particularly, the main

concern is that the energy source is of fluctuating nature. This can cause damage to

the electrical load in correspondence of peak energy values and impair its ability to

continuously run when the energy is not available, as is the case of a solar energy

based system at night. These aspects must be taken in consideration in the design

phase of an EH system, for example inserting an appropriate solution for the energy

storage.

In an EH system, there are generally four main components: energy collection and

conversion mechanism (the actual energy harvester), electrical power

management/conditioning circuit, energy storage device, and electrical load (for

example, a wireless sensor node able to transmit the collected data). In this thesis, the

focus will be on the first element. In fact, in order to optimize the design of the

application, the choice of the EH technique is crucial: a summary of the main options

is reviewed in the following section.

1.1 TYPES OF AMBIENT ENERGY SOURCES

1.1.1 Solar Energy

This is certainly the most known of renewable energy sources. Energy can be

extracted to power electronic devices using tiny photovoltaic cells. Commercial off-

the-shelf solutions already exist and can be classified into two categories: single

crystal, with a conversion efficiency ranging from 15% up to 40%, and the cheaper

thin film, whose efficiency is 13% at the maximum. Form table 1.1 it can be seen

that this technique is attractive because of its high-power density (100mW/cm3)

available for direct sunlight at noon; however, this number drops dramatically when

indoor. Hence, to guarantee the requested value of extracted power, either (or both)

high efficiency conversion solutions and proper energy storage devices must be

adopted.

It is worth stating that solar energy can be exploited also by means of heat carried by

the solar radiation.

1.1.2 Wind Energy

Like solar energy, wind energy is a subject that has been (and still is) widely studied

in relation to large-scale technologies, but unlike the former, despite its relatively

high power electric density, it has not been developed much for small-scale

applications. The few attempts that can be found in literature are oriented towards

design of small sensors that are able to work in remote and/or hostile environments,

more than for being embedded in the devices we use every day.

The investigated methods for wind energy conversion up to now take inspiration

from their large-scale counterparts, and consists of miniaturizing structures such as

windmills and anemometers in order to exploit the near linear relationship between

wind speed and frequency of rotation. The advantage of this choice is that it can rely

on years of research: this does in fact yield to an increased operational lifetime and

harvested power for devices that employ this solution; however, it comes at the cost

of a large size, higher energy conversion loss and a high overall cost. For this reason,

more recent research efforts [2] have been focused on integrating the existing

architectures with piezoelectric materials in order to obtain the same quantity of

harvested power but reducing dimensions and increasing conversion efficiency. The

main problem with this approach is that the robustness that usually is associated with

wind harvesting solution is reduced due to the great strain applied on the

piezoelectric, which deploy easily with stress and age.

1.1.3 Thermal Energy

Theoretically, thermal energy would seem like the better solution when designing

devices targeted to the industrial environment as wasted heat is present in abundance

in all types of system. Conversion can be based on Seebeck effect and

thermocouples, or exploiting the Pyroelectric effect (i.e. the property of certain

materials to present a temporary voltage following a temperature change). The

conversion efficiency of a thermal energy harvesting device is in any case related to

Carnot’s law:

� =���� − ����

����

Where ���� and ���� are the extreme values of the temperature gradient to which

the device is subjected, expressed in Kelvin.

Application of Carnot Law usually yields higher values of efficiency compared to the

actual ones, because of the characteristic efficiencies of the single devices that must

be taken into account that are well below the simple Carnot’s rule. Hence, at least for

now, the attainable electrical power density turns out to be a small fraction of the one

the material can offer with Carnot efficiency.

1.1.4 Radio Frequency

In the modern environment, there are multiple wireless sources of different

frequencies radiating in all directions, such as TV, mobile phone, WLAN, etc. So, it

is easy to think that they would made a good source for energy harvesting purposes.

For the conversion, an antenna or an array of antennae must be used: hence,

frequency selection is an important consideration to be made in the design phase.

The common choice would be GSM, as mobile phone signals are prevalent and

propagate well both in and out of buildings. Also, the distance from the RF source is

a very important parameter, since the antenna dimension depend on it. The extracted

power range is wide as it is dependent on the aforementioned parameters. As an

example, GSM900, yields about 7µW/cm3.

1.1.5 Vibration

Mechanical vibrations are attractive to use as a power source for low-power

electronics thanks to their power density and abundance in real environments. Since

the device object of this work exploits this type of energy, its characteristics will be

analysed more in detail in the following section.

1.2 ENERGY HARVESTING FROM VIBRATION

Mechanical vibration can come in various forms: seismic noise, human and vehicle

motion, vibrating systems such as electrical machinery. They can be frequency-

specific, like the case of rotating machines but they are more frequently random.

Vibrational Energy Harvesting is the conversion of kinetic energy present in the

environment into electrical energy. Actually, this conversion is articulated in two

steps: first, vibrations coming from the source are converted into the relative motion

between two elements, using systems such as mass-spring or cantilever beam: this is

needed because ambient vibrations are generally low in amplitude, so through this

step we exploit the resonance phenomenon of the oscillating mass-spring or

cantilever system, increasing the output harvested power. Then, there is the

conversion into electrical energy via electro-mechanical transducer. A traditional

mechanism of this type can be schematized as it shown in figure 1.1:

Figure 1.1: a simple energy harvesting system

In terms of energy balance, the input kinetic energy contained in the base vibration is

transmitted to the mechanism part of the energy is stored thanks to the mass-spring

dynamics, part is dissipated and part is converted into electrical energy. There are

different kinds of dissipative effects that can be relevant for a vibration harvester,

such as internal friction of the elements in the system and viscous friction due to the

mass moving within a gas, which contrast the mass movement; these phenomena are

taken into account with the presence of the damper.

As for the transducer, it is simply represented by a block with an input (mechanical,

from the movement of the mass) and two output terminals accompanied by signs plus

and minus, thus indicating the existence of a voltage difference V (electrical output).

It can be implemented according to a particular conversion technique: these

VIBRATING BODY

k

d

m

OSCILLATOR

TRANSDUCER

+ -

techniques can be classified into three groups, basing on the physical principle they

exploit:

1. Electrostatic: they use a variable capacitor so to generate charges from the

relative motion between the capacitor’s plates. They are well suited for

MEMS (Micro Electro Mechanical System) level type of application, have a

good output voltage and are long-lasting. However, they need an external

power source and yield relatively low power density at small scale.

2. Electromagnetic: based on electromagnetic induction, they exploit the

relative motion between a coil and a magnetic mass; as opposing to precedent

group, these devices do not need an external power source, but they are

inefficient at MEMS scale for they require a large mass displacement

3. Piezoelectric: based on the use of piezoelectric materials, they are well

adapted to miniaturization without the need of an output voltage source, but

they can be very expensive and are affected by ageing.

In particular, we will focus on the third category. Before going into detail with a

possible configuration, let us illustrate the basic characteristics of piezoelectric

materials.

1.2.1 Piezoelectric Materials

Piezoelectric transducers are based on the property of piezoelectric materials of

accumulating charges when stressed (direct effect) and to strain in case of the

application of an electrical signal (inverse effect). This property arises from the

presence of asymmetry in the crystalline lattice-like ionic structure of the material,

resulting in the presence of polarized dipoles: when an electrical field is applied, they

are displaced by electrostatic forces, with a subsequent mechanical deformation of

the whole piece.

This effect occurs naturally in quartz crystals, but can be induced in other materials,

such as asymmetric polymers and specially formulated ceramics consisting mainly of

Lead, Zirconium, and Titanium. Regarding the latter case, it must be stated that these

types of materials show an initially random orientation of dipoles leading to a null

polarization. Hence, in order to obtain a preferential polarization axis, a polarization

process is required.

The material is first heated to its Curie temperature. Then, a voltage field of a

sufficient strength is applied in the desired direction, forcing the ions to realign along

the excitation field axis. Finally, keeping the field constant, the material is cooled

down to its original temperature.

Figure 1.2: domain alignment in LZT [3]

In a piezoelectric material, mechanical and electrical quantities are related according

to the following equations:

� = �� + ���

� = ��� + ��

Where:

o D is the Electric Flux Density;

o T is the Stress;

o S is the Strain;

o E is the electric field;

o �� is the electrical permittivity for a constant stress T;

o �� is the compliance (inverse of Young module) for an applied field E;

o d is the piezoelectric constant, expressed in [C/N].

In real devices, the above relations must be considered for the six possible axis: 3 for

stress due to compression/expansion and 3 for torsional stress.

Figure 1.3: stress axes.

[��] = ���,��[��] + ���,��[��]

[��] = [��,�][��] + [��,�][��]

With

��, � = 1, … ,6

�, �, � = 1,2,3 ��,� = ��,� ; ��,� = 0 ��� � ≠ �

Where the first index indicates the polarization axis and the second the stress

direction.

So, the two equation model the polarization and the strain of the material,

respectively. As we can see, both are the result of the sum of mechanical and

electrical contribution. For a non-piezoelectric material, of course, the strain would

depend only on mechanical quantities while the polarization only on electrical ones.

In particular, d, which ties the material polarization with the applied stress, is a

parameter whose evaluation is crucial in order to choose the right material for the

desired energy harvesting application. Other important characteristic material

quantities are:

o ��, the piezoelectric voltage coefficient, defined as �

�� , which ties the voltage

V across the electrodes (separated by gap l) with the stress, as shown by the

following equation:

� = ����

o k, coupling factor, which describes the conversion between mechanical and

electrical energy, and can be defined in terms of the other parameters, as

���

����

Some properties for common piezoelectric material are reported in table 1.2.

Crystal

(Quartz)

Ceramic

(Barium

Titanate)

Polymer

(Polyvinylidene

Fluoride)

Density [Kg*m-3] 7.5 5.7 1.78

Relative Permittivity

��/��

1200 1700 12

Piezoelectric Constant

��� [C/N]

110 78 23

Voltage Constant

��� [V*m/N]

10 5 216

Electromechanical Constant ��� 30 21 12

Table 1.2 [3]: Piezoelectric properties.

1.3 PIEZOELECTRIC ENERGY HARVESTER: LINEAR VS NONLINEAR APPROACH

Going back to the system presented in figure 1.1, we can easily derive a

mathematical model of its mechanical behaviour referring to the classical Newtown

equation of motion:

�� +��(�)

��+ �� = �(�) (1.1)

Where:

o � is the mass;

o �, � and � are the mass displacement, velocity and acceleration, respectively;

o �(�) is the potential energy of the system;

o �� is the dissipated energy modelled by the damper;

o �(�) is the stochastic source modelling the external input mechanical

vibrations.

Particular attention must be focused on potential energy; its expression depends on

the geometry of the device and its dynamics. In this case, it is related to the presence

of the spring, hence is linear and equal to �

����. This makes the device fall into the

category of linear energy harvesters. Another device of this group, much more used,

is the so-called cantilever beam configuration, schematized below, in figure 1.4:

Figure 1.4: cantilever beam architecture for energy harvesting

Δx

+

-

PZT

Vibrating Wall

In this case, the bending of the beam is the equivalent of the movement of the spring:

in particular, the position of complete bending of the beam corresponds to a complete

extension/compression of the spring.

Being linear, both system show resonant behaviour: in short, resonance is a

phenomenon that occurs when the system is driven by an external force whose

frequency is equal to the resonance frequency of the system, and it maximizes its

response (figure 1.5).

This means the system would be efficient only when incoming energy is distributed

around its resonant frequency.

This is not a desirable feature when dealing with vibration energy harvesting

because, as previously stated, except for very specific cases (i.e. devices mounted on

rotating machines), vibrations are distributed over a wide frequency spectrum, with

significant predominance of low frequency components, which are very difficult to

deal with, especially if we want a small device.

Figure 1.5 Resonant EH frequency response.

100

101

102

103

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

Magnitude (

dB

)

System Response

Frequency (rad/s)

For this reason, research efforts have been aimed in two different directions:

1- design of linear devices whose resonant frequency is appropriately “tuned” to

better match the spectral distribution of the available energy in the application

environment, or

2- design of a nonlinear device.

As for the first approach, the idea is to tune the resonant frequency of the device

according to the specific application. This can be done by acting on device

characteristic parameters such as the length or the stiffness of the cantilever beam, or

of the spring. However, this is not a good solution because ambient condition might

change, thus the device would need to be retuned, and this is not easy to do, for

resonant frequency depends on its physical parameters, and changing them in most

cases would mean to completely redesign the harvester.

Based on the discussion made so far, it has become clear that linear resonant

vibration harvesters present drawbacks that limit seriously their application: they can

harvest energy only in a narrow frequency band, and to increase the efficiency, this

band would have to become narrower, as we would need to amplify the oscillator

frequency response. One of the proposed solution for this problem was to use

oscillator arrays in order to cover a large frequency range by overlapping their

responses. However, while this method does widen the frequency spectrum, the

overall harvested power is decreased. In addition, there are problems in maintaining

the resonant behaviour when scaling down the dimension. All of this implies that this

kind of device might not be the better solution for harvesting vibration, which bring

us to the second point of the above list: the nonlinear harvester.

This is not a well-defined category, but intuitively, we could say that the search for

the best solution in terms of non-resonant systems should start from the potential

energy function �(�) which can be considered one of the most important part of the

design for it acts as a dynamical energy storage facility (before transduction) for the

mechanical oscillator. We already know that the proposed potential function must

respect the condition:

�(�) ≠1

2���

Meaning nonlinear devices are all those whose potential energy is not quadratically

dependent on the displacement variable of interest. In this regard, various research

papers have investigated possible different solutions. Specifically, it emerged that the

better performance is given by oscillators which possess either a bistable or a

monostable behaviour.

Concerning the device topology and structure, nonlinearities can be introduced in

various ways: changing the geometry of the springs/cantilever beam, inserting

material nonlinearities, inducing stress or electromagnetic coupling with external

fields.