A New Approach for Impedance Tracking of Piezoelectric Vibration Energy Harvesters Based on a Zeta Converter - MDPI
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sensors
Article
A New Approach for Impedance Tracking of
Piezoelectric Vibration Energy Harvesters Based on a
Zeta Converter
Antonino Quattrocchi * , Roberto Montanini, Salvatore De Caro, Saverio Panarello ,
Tommaso Scimone, Salvatore Foti and Antonio Testa
Department of Engineering, University of Messina, 98166 Messina, Italy; roberto.montanini@unime.it (R.M.);
salvatore.decaro@unime.it (S.D.C.); saverio.panarello@unime.it (S.P.); tommaso.scimone@unime.it (T.S.);
salvatore.foti@unime.it (S.F.); antonio.testa@unime.it (A.T.)
* Correspondence: antonino.quattrocchi@unime.it; Tel.: +39-090-676-5513
Received: 19 September 2020; Accepted: 13 October 2020; Published: 16 October 2020
Abstract: Piezoelectric energy harvesters (PEHs) are a reduced, but fundamental, source of power
for embedded, remote, and no-grid connected electrical systems. Some key limits, such as low
power density, poor conversion efficiency, high internal impedance, and AC output, can be partially
overcome by matching their internal electrical impedance to that of the applied resistance load.
However, the applied resistance load can vary significantly in time, since it depends on the vibration
frequency and the working temperature. Hence, a real-time tracking of the applied impedance load
should be done to always harvest the maximum energy from the PEH. This paper faces the above
problem by presenting an active control able to track and follow in time the optimal working point of
a PEH. It exploits a non-conventional AC–DC converter, which integrates a single-stage DC–DC Zeta
converter and a full-bridge active rectifier, controlled by a dedicated algorithm based on pulse-width
modulation (PWM) with maximum power point tracking (MPPT). A prototype of the proposed
converter, based on discrete components, was created and experimentally tested by applying a sudden
variation of the resistance load, aimed to emulate a change in the excitation frequency from 30 to
70 Hz and a change in the operating temperature from 25 to 50 ◦ C. Results showed the effectiveness
of the proposed approach, which allowed to match the optimal load after 0.38 s for a ∆R of 47 kΩ and
after 0.15 s for a ∆R of 18 kΩ.
Keywords: piezoelectric generators; piezoceramic patches; energy harvesting; DC–DC power
converters; energy conversion efficiency; impedance matching
1. Introduction
Energy harvesting deals with the regeneration of surplus environmental energy and is attracting
an increasing interest, powered by the race towards the reduction of size and weight of electrical and
electronic devices. Today, energy harvesters are only starting to be considered as a viable alternative
to inexpensively supply different types of mobile, remote-controlled, or completely autonomous
devices, but, in a near future, one or more energy harvesters could be embedded into most consumer
electronic devices [1–3]. Electric energy can be obtained from waste energy of a different nature, such as
mechanical vibrations, electromagnetic fields, light, heat, and pressure. Among them, the mechanical
energy generated by residual vibrations is widely available in home, industrial, and vehicular
environments, making the development of vibrational energy harvesters one of the most promising
research fields, with the goal of turning wireless, wearable, and portable electronic devices into
self-supplied systems [4].
Sensors 2020, 20, 5862; doi:10.3390/s20205862 www.mdpi.com/journal/sensors
Sensors 2020, 20, 5862 2 of 13
Energy harvesters based on electromagnetic, piezoelectric, electrostatic, or electrochemical
principles have been developed in the last few years to convert vibrations into electric power, which can
be instantly used or stored. Among them, much attention is now being paid to piezoelectric devices,
because the piezoelectric effect, based on the ability of some crystals to generate an electromotive force
Sensors 2020,to
when subjected 20,ax FOR PEER REVIEW
mechanical stress, makes it possible to recover residual mechanical energy 2 of 13 from
many sources, such as human motion, machine vibrations, acoustic noises, and thermal waste [5–10].
Energy harvesters based on electromagnetic, piezoelectric, electrostatic, or electrochemical
These piezoelectric
principles havedevices can be used
been developed in several
in the last few years applications, takinginto
to convert vibrations advantage of their
electric power, which ability to
work ascaneither sensorsused
be instantly or actuators
or stored. [11,12].
Among them, However, the wideisdistribution
much attention now being paid of to
piezoelectric
piezoelectric energy
harvesters (PEHs)
devices, is currently
because burdened
the piezoelectric by some
effect, based key limits,
on the which
ability include
of some low to
crystals power density,
generate an poor
electromotive
conversion efficiencyforce when whenthey subjected
do not to worka mechanical
in resonance, stress,high
makes it possible
internal to recoverand
impedance, residual
AC output.
mechanical energy from many sources, such as human motion, machine vibrations, 2acoustic noises,
Piezoelectric crystals or powders feature a power density of only a few µW/mm , while the electrical
and thermal waste [5–10]. These piezoelectric devices can be used in several applications, taking
power generated by a single piezoelectric device is quite small, ranging from some µW to some tens of
advantage of their ability to work as either sensors or actuators [11,12]. However, the wide
mW. Hence, in order to fulfill theenergy
distribution of piezoelectric powerharvesters
requirements(PEHs)of is standalone systems,
currently burdened by such
some as keyGPS receivers,
limits,
wearablewhich
electronic
includedevices,
low power or wireless
density, poor sensors, practical
conversion piezoelectric
efficiency when they harvesters
do not work areintypically
resonance, made by
highmultiple
assembling internal impedance,
elementary anddevices.
AC output. Piezoelectricgenerators
Piezoelectric crystals or powders feature
that recover a power
energy density
from vibrations
are oftenofbased
only a onfewmechanical
µW/mm2, while the electrical
resonators, power
which generated
reach by a singleefficiency
an acceptable piezoelectriconlydevice
when is quite
working at
small, ranging from some µW to some tens of mW. Hence, in order to fulfill the power requirements
resonance [13].
of standalone systems, such as GPS receivers, wearable electronic devices, or wireless sensors,
Furthermore, the applied
practical piezoelectric electrical
harvesters load plays
are typically made anby important
assembling role in determining
multiple elementary the maximum
devices.
output power that can
Piezoelectric be extracted
generators from energy
that recover the PEH. fromAccording
vibrations to arethe theorem
often based of on maximum
mechanical power
transfer,resonators,
and in order whichto maximize the generated
reach an acceptable power,
efficiency it should
only when be very
working close to[13].
at resonance the internal impedance
Furthermore,
of the PEH. However, theoptimal
this applied electrical
resistance load
loadplays an important
is also a function roleofinthe
determining
vibrationthe maximum[14] and
frequency
output power that can be extracted from the PEH. According to the theorem of maximum power
it also depends on the working temperature [15]. Hence, changes in the excitation vibration or in the
transfer, and in order to maximize the generated power, it should be very close to the internal
environmental conditions leading to variation of the optimal resistance load should be appropriately
impedance of the PEH. However, this optimal resistance load is also a function of the vibration
faced byfrequency
the PEH[14] powerand itconverter
also depends in on
order to harvest
the working the maximum
temperature energy.
[15]. Hence, changes in the excitation
Thevibration
main scope or in theof the power converter
environmental conditions is leading
to turntothe PEH AC
variation of theoutput
optimalcurrent intoload
resistance a DC one
suitableshould be appropriately
for supplying faced by
electronic the PEHorpower
devices converter
batteries. Asinshown
order toin harvest
Figure the 1a,
maximum energy.way for
the easiest
connecting aThe main scopedevice
piezoelectric of the power
to a DC converter
load is istoto turn
use the PEH AC
a full-wave output
diode current
bridge. into a DCwhile
However, one diode
suitable for supplying electronic devices or batteries. As shown in Figure 1a, the easiest way for
rectifiers are simple and inexpensive, they are burdened by a quite low efficiency and they do not allow
connecting a piezoelectric device to a DC load is to use a full-wave diode bridge. However, while
impedancediode tuning.
rectifiers are simple and inexpensive, they are burdened by a quite low efficiency and they do
Actively
not allow controlled
impedanceswitching
tuning. converters may be used to improve the conversion efficiency,
but they involve
Actively higher costsswitching
controlled and power self-consumption,
converters may be used to thus improve a trade-off mustefficiency,
the conversion be foundbut between
they involve higher costs and power self-consumption, thus a trade-off
cost and energy yield. As shown in Figure 1b, resonant rectifiers have been proposed which exploit must be found between cost
switchingandresistor–inductor–capacitor
energy yield. As shown in Figure (RLC) 1b,circuits
resonanttorectifiers
optimally have been proposed
transfer power from whichaexploit
piezoelectric
switching resistor–inductor–capacitor (RLC) circuits to optimally transfer power from a piezoelectric
device to a diode rectifier. Active power devices are driven through self-synchronizing techniques,
device to a diode rectifier. Active power devices are driven through self-synchronizing techniques,
which do not do
which neednot external
need externalcontrol circuits,
control circuits,thus
thus reducing
reducing the theself-consumption
self-consumption [16–19].
[16–19]. A moreA more
effectiveeffective
approach relies on the exploitation of an active rectifier, which is
approach relies on the exploitation of an active rectifier, which is composed of the cascade composed of the cascade
connection of a diode bridge and a suitable DC–DC converter, as shown in Figure 1c.
connection of a diode bridge and a suitable DC–DC converter, as shown in Figure 1c.
(a) (b) (c)
Figure 1. Figure 1. Conditioning
Conditioning circuits
circuits forfor piezoelectric energy
piezoelectric energy harvesting based
harvesting on (a)
based ona (a)
full-wave diode diode
a full-wave
rectifier,rectifier, (b) a resonant rectifier, and (c) an active rectifier.
(b) a resonant rectifier, and (c) an active rectifier.
The DC–DC converter is tasked to regulate the DC output voltage and to draw the maximum
The DC–DC converter is tasked to regulate the DC output voltage and to draw the maximum
possible power from the piezoelectric device for a specific electrical load [20–25]. The maximum
possiblepower
power from point
working the piezoelectric device forthea output
is obtained by controlling specific
DCelectrical load to
current in order [20–25].
obtain anThe maximum
average
power working point is obtained by controlling the output DC current in order to obtain an average
Sensors 2020, 20, 5862 3 of 13
converter input impedance close to that leading to the maximum power transfer. Such an approach,
on the one hand, minimizes the number of sensors and the circuit self-consumption, but, on the
other hand, it requires the knowledge of the optimal input resistance, which is not constant, being a
function of the operating conditions. Buck, buck–boost, and flyback DC–DC converter topologies
have been used to realize active rectifiers for piezoelectric generators, all featuring an inductive power
transfer. Srinivasan et al. [26] used the principle of the buck–boost converter to achieve a bridgeless
configuration for impedance matching based on single-stage direct AC–DC conversion. The results
demonstrated that the harvested power is improved by the factors of 1.4 and 3.2 for single-input and
multiple-input configurations, respectively, as compared to the power harvested using a dual-output
rectifier. An alternative way to match the maximum power point can be provided by a step-down
piezoelectric transformer, which can be integrated in a cantilever structure, connected to a bidirectional
half-bridge converter [27].
All the above-mentioned schemes provide hardware configurations able to perform impedance
matching, but they do not allow impedance tracking. Hence, if the electrical load applied to the PEH
changes with time, they are no longer able to guarantee operation at the optimum working point.
In this paper, a new approach based on an active control is proposed to overcome this limitation,
ensuring that maximum harvested energy is always extracted by the PEH as the applied electrical
load undergoes variations due to changes in the excitation frequency or in the working temperature.
The proposed hardware employs a non-conventional AC–DC converter that integrates a single-stage
DC–DC Zeta converter and a full-bridge active rectifier. The implemented active control strategy
is based on pulse-width modulation (PWM) coupled with maximum power point tracking (MPPT).
The study presents results related to the effectiveness of the power optimization strategy; the operation
of the proposed energy harvesting converter was evaluated by forcing a sudden variation of the applied
resistance load. A preliminary characterization of the effect produced on the resistance load by a
change in the working frequency (from 30 to 70 Hz) and in the operating temperature (from 25 to 50 ◦ C)
was carried out. These data were then used to emulate the variation of the load in practical situations.
2. PEH Electro-Mechanical Characterization
2.1. Cantilever-Based Piezoelectric Generator
Tests were performed on a home-made cantilevered piezoelectric energy harvester (Figure 2a),
which consisted of a bendable piezoelectric patch (PZT, Physik Instrumente GmbH, Karlsruhe Germany,
mod. DuraAct P-876 A.12) glued onto a composite beam. The PZT was made of a modified lead
zirconate titanate powder (PIC255), enclosed into a polymeric case with dimensions of 61 mm × 35 mm
× 0.5 mm, which ensured a high resistance to cyclical loads [28]. It featured a piezoelectric material
thickness of 200 µm, a d31 charge coefficient of −180 pC/N, a capacitance of 90 nF, a blocking force of
265 N, a minimum lateral constriction of 650 µm/m, and a bending radius of 20 mm. The maximum
operating frequency was 1 × 104 Hz, the fatigue limit was up to 1 × 109 cycles, while the operating
temperature ranged from −20 to +150 ◦ C [14].
The cantilever beam was obtained by the manual layup of three layers of 0◦ /90◦ oriented fiberglass
and epoxy resin with dimensions of 105 mm × 35 mm × 1 mm. This type of generator shows a
symmetric structure during its deformation; therefore, the same quantity of charge is generated,
although with the opposite sign along two following half-periods of the vibration.
In the experimental setup (Figure 2b), the PEH was locked at one end to a vise and to the stinger
of an electrodynamic shaker (Tira GmbH, Schalkau, Germany, mod. S 51) at the other end. The shaker
was driven by a power amplifier (Tira GmbH, Schalkau, Germany, mod. BAA 120) and a function
generator (Agilent Technologies Inc., Santa Clara, CA, USA, mod. 33220 A). An oscilloscope (Tektronix
Inc., Beaverton, OR, USA, mod. TDS 2014) equipped with a 10 MΩ probe was employed to measure the
PEH output voltage as the electrical load is varied, while a laser displacement transducer (MicroEpsilon
GmbH, Ortenburg, Germany, mod. ILD 2200-50) was used to measure beam deflection.
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(a) (b)
2. (a) Schematic
FigureFigure drawing
2. (a) Schematic drawingof the low-cost
of the low-costpiezoelectric
piezoelectric energy harvester(PEH)
energy harvester (PEH) used
used in this
in this workwork
and (b)and (b) setup
setup employed
employed forexperimental
for its its experimental characterization(the
characterization (the humidity
humiditygeneration
generationchamber
chamber is not
is not
shownshown this figure).(a)
in thisinfigure). (b)
Figure 2. (a) Schematic drawing of the low-cost piezoelectric energy harvester (PEH) used in this work
2.2. Effects
2.2. Effects of Vibration
of Vibration Frequency
Frequency andand Working
Working Temperature
Temperature
and (b) setup employed for its experimental characterization (the humidity generation chamber is not
The The electro-mechanical
shown
PEH PEH electro-mechanical
in this figure). behavior
behavior waswas investigated
investigated setting
setting the
the displacementamplitude
displacement amplitude of
ofthe
shakerthe shaker
stinger atstinger
2 mm, at 2 mm,
that that
is, ±1 mm is, from
±1 mm from
the the equilibrium
equilibrium position.
position. The PEH
The PEH output
output voltage
voltage across
2.2. Effects
across theofapplied
Vibration Frequency
electrical andwas
load Working Temperature
measured for different vibration frequencies and electrical
the applied electrical load was measured for different vibration frequencies and electrical resistance
resistance loads. Moreover, tests were also performed by varying the PEH temperature. Temperature
The PEH tests
loads. Moreover, electro-mechanical behavior was
were also performed investigated
by varying thesetting the displacement
PEH temperature. amplitude oftests
Temperature
tests were carried out by putting the PEH and associated electronics into a benchtop humidity
the shaker
were carried stinger
outchamber at
by putting 2 mm, that
the PEH is, ±1 mm from
and associated the equilibrium
electronics position.
into The
a benchtop PEH output
humidity voltage
generation
generation (Thunder Scientific Corp., Albuquerque, NM, USA, Model 2500) able to maintain
across the applied electrical load was measured for different vibration frequencies and electrical
chamber (Thunder
relative Scientific
humidity Corp.,
in the range of Albuquerque,
10–95% with 0.5% NM, USA, Model
uncertainty and a 2500) able toup
temperature maintain relative
to 70 °C with
resistance loads. Moreover, tests were also performed by varying the PEH temperature. Temperature
humidity
0.06 in
°Cthe range ofAll
uncertainty. 10–95% with
the tests were 0.5% uncertainty
carried out fixing and
RH toa temperature
45%. up to 70 ◦ C with 0.06 ◦ C
tests were carried out by putting the PEH and associated electronics into a benchtop humidity
uncertainty. AllPEH
The thepower
tests were
output carried
PPZT was outcalculated
fixing RH as to 45%.
follows:
generation chamber (Thunder Scientific Corp., Albuquerque, NM, USA, Model 2500) able to maintain
The PEHhumidity
relative power output PPZT of
in the range was calculated
10–95% as follows:
with 0.5% uncertainty and a temperature up to 70 °C with
= (1)
0.06 °C uncertainty. All the tests were carried out fixing
2
8 RH to 45%.
The PEH power output PPZT was calculated as vfollows: PZT
where vPZT is the PEH peak-to-peak outputPPZT = and
voltage RL is the electric resistance load, downstream (1)
8RL
of the PEH.
= (1)
where vPZTAisdetailed
the PEH analysis of the conversion
peak-to-peak output voltage and8ofRthe
efficiency PEH used in this work has been recently
L is the electric resistance load, downstream
published elsewhere by some of the authors of the present work [29].
of the where
PEH. vPZT is the PEH peak-to-peak output voltage and RL is the electric resistance load, downstream
Figure 3a shows the output power measured at fixed temperature (25 °C) as a function of the
of the PEH.
A detailed analysis of the conversion efficiency of the PEH used in this work has been recently
electrical load, for various working frequencies, while Figure 3b highlights the effects of varying the
published A detailed analysis
elsewhere by some of thethe
conversion efficiency of thework
PEH used
[29].in this work has been recently
working temperature. The of authors
PEH output of the
power present
increases with the vibration frequency fm and decreases
published
Figure elsewhere
3aoperating
shows the by some of
output powerthe authors of
measured the present
at fixed work [29].
temperature (25 ◦ C) as resistance
a function of the
with the temperature θPZT. For given values of fm and θPZT, an optimal load RL_opt
Figure 3a shows the output power measured at fixed temperature (25 °C) as a function of the
electrical
(fm, load,
θPZT) for various
exists that working
maximized frequencies,
the generatedwhilepower.
FigureSuch 3b highlights
an optimal theload
effects of varying
varies almost the
electrical load, for various working frequencies, while Figure 3b highlights the effects of varying the
working temperature.
hyperbolically The
with thePEH output
vibration power increases
frequency and almostwith the vibration
linearly frequency
with the working fm and decreases
temperature.
working temperature. The PEH output power increases with the vibration frequency fm and decreases
with the
withoperating temperature
the operating temperature θPZT
θPZT.. For
Forgiven
givenvalues
values of fof
m and θPZT, θan
fm and PZT , an optimal
optimal load resistance
load resistance RL_opt
RL_opt (f(fmm , θ ) exists that maximized the generated power.
, θPZT) exists that maximized the generated power. Such an optimal load varies
PZT Such an optimal load varies almost
almost
hyperbolically with the vibration frequency and almost linearly with the
hyperbolically with the vibration frequency and almost linearly with the working temperature. working temperature.
(a) (b)
Figure 3. (a) Effect of the vibration frequency on PEH output power (at a fixed temperature of 25 °C)
and (b) effect of the working temperature (while keeping the vibration frequency at 50 Hz).
(a) (b)
3. (a) 3.Effect
FigureFigure of the
(a) Effect vibration
of the frequency
vibration frequencyon
onPEH
PEH output power(at
output power (ata afixed
fixed temperature
temperature 25 ◦ C)
of 25of°C)
and
and (b) (b) effect
effect of theofworking
the working temperature
temperature (whilekeeping
(while keepingthe
the vibration
vibration frequency
frequency at at
5050
Hz).
Hz).
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3. Design of Energy Harvesting Single-Stage Converter
3. Design of Energy
Sensors 2020, Harvesting
20, x FOR PEER REVIEW Single-Stage Converter 5 of 13
When cyclically loaded, piezoelectric harvesters generate an AC voltage whose amplitude is a
When cyclically loaded, piezoelectric harvesters generate an AC voltage whose amplitude is a
3. Design
function of theof vibration
Energy Harvesting
frequency Single-Stage
(Figure 4).Converter
In practical applications of PEHs, a power converter is
function of the vibration frequency (Figure 4). In practical applications of PEHs, a power converter is
usually When
connected downstream
cyclically to achieve
loaded, piezoelectric different but correlated tasks. Its first purpose is to rectify
usually connected downstream to achieve harvesters
different butgenerate an ACtasks.
correlated voltageItswhose amplitude
first purpose is istoarectify
and stabilizeofthe PEH output voltage, thus 4).
making the PEH itself suitable for supplying an electronic
andfunction
stabilize the thePEH
vibration frequency
output voltage,(Figure In practical
thus making the PEHapplications of PEHs,
itself suitable fora supplying
power converter is
an electronic
device or aconnected
usually battery. Consequently, it should
downstream to achieve be able
different butto step uptasks.
correlated or down thepurpose
Its first input voltage
is to rectifywith the
device or a battery. Consequently, it should be able to step up or down the input voltage with the goal
goaland stabilize the
to increase thePEH output
energy voltage, thus
efficiency, making
adapting thePEH
the PEHimpedance
itself suitable
tofor supplying
a given an electronic
electrical load.
to increase the energy efficiency, adapting the PEH impedance to a given electrical load.
device or a battery. Consequently, it should be able to step up or down the input voltage with the
goal to increase the energy efficiency, adapting the PEH impedance to a given electrical load.
Figure 4. Typical PEH output voltage (in magenta) and output current (in cyan).
Figure 4.4.Typical
Figure TypicalPEH
PEH output voltage(in(in
output voltage magenta)
magenta) andand output
output current
current (in cyan).
(in cyan).
A further task comes directly from the results of the previous section and, specifically, from the
need A to further
A further
match task
and task comes
trackcomesthedirectly
directly
resistancefrom
from theat
the
seen results
results ofof
the outputthetheofprevious
previous
the PEH section
section
as itand, and, specifically,
specifically,
varies with from
time. fromway,
Inthe
this the
need
the needto matchoutput
maximum to match and track
and track
power thewould
the resistance
resistance seen at the
seen at
be guaranteed the output the
output
whatever of of the
the PEH PEH assource
as
excitationit it varies
varies with with
time.
or the time. In this
In this
environmental
way,way,the the maximumoutput
maximum output power
power would
would be
be guaranteed
guaranteed whatever
whatever the theexcitation sourcesource
excitation or the or the
temperature. In principle, a two-stage converter topology including a diode rectifier and a suitable
environmental
environmental temperature.In
temperature. In principle,
principle, aatwo-stage converter topology including a diodediode
rectifier
DC–DC converter should be appropriate totwo-stage
achieve this converter
goal. Atopology
possibleincluding
solution isa that rectifier
shown in
and a
and a suitablesuitable DC–DC
DC–DC converter
converter should
should be appropriate
be appropriate to achieve
to achieve this goal. A
this goal. A possible solution
possible is
solutionthe is
Figure 5a, where the front end is a full-bridge diode rectifier. This configuration
that shown in Figure 5a, where the front end is a full-bridge diode rectifier. This configuration is used
is used to convert
that shown
AC input in Figure
voltage 5a,
intoinput where
a DCvoltage the
voltage, front end is a full-bridge diode rectifier. This configuration is used
to convert the AC intowhich
a DC is stabilized
voltage, which byisastabilized
suitable capacitor.
by a suitable The second The
capacitor. stage is a
to convert
Zeta the AC input voltagethe into a DC DC voltage, which is stabilized by alike
suitable capacitor. The
second stage is a Zeta converter, which regulates the output DC voltage. However, a circuit like this twice
converter, which regulates output voltage. However, a circuit this processes
second
the output stage
processes is a Zeta
power,
twice the converter,
thus reducing which
the
output power, regulates
conversion
thus reducing thetheoutput
efficiency. To DC voltage.
overcome
conversion However,
this
efficiency. drawback, a circuit
To overcome like this
a single-stage
this
processes
drawback,
topology twice
based the
a single-stageoutput
on a Zeta topology power,
converterbased thus
wason reducing
a Zeta devised
instead the conversion
converter(Figurewas instead efficiency.
5b). devised To overcome
(Figure 5b).
The proposed The is
solution this
a
drawback,
proposeda solution
modification single-stage topologysingle-switch
is a modification
of the conventional based
of theon a Zeta
Zetaconverter
conventional was
[30].instead
single-switch
converter Zeta devised
converter
Indeed, (Figure
[30].
introducing Indeed,
an 5b). The
active
proposed
rectifier, thesolution
introducing original isDC–DC
an active a rectifier,
modification ofisthe
the original
converter conventional
DC–DC
turned converter
into single-switch
an AC–DC is turned into an
converter. Zeta converter
AC–DC [30]. Indeed,
converter.
introducing an active rectifier, the original DC–DC converter is turned into an AC–DC converter.
(a) (b)
Figure 5. 5.Power
Figure conversion
Power conversion circuits
circuits based based on rectifier
on a diode a diode andrectifier and
a standard Zetaa converter:
standard(a)Zeta converter:
two-stage
converter and
(a) two-stage converter(a)and (b)
(b) proposed single-stage
proposedconverter.
single-stage converter. (b)
Figure 5. Power conversion circuits based on a diode rectifier and a standard Zeta converter: (a) two-stage
As shown
As shown in in Figure5b,
Figure 5b,aafull-bridge
full-bridge active
activerectifier replaces
rectifier replacesthethe
single switch
single present
switch in thein
present basic
the basic
converter
Zeta and (b)
converter. proposed
This has a single-stage
multiple converter.
aftermath. First, the PEH output current is processed by two
Zeta converter. This has a multiple aftermath. First, the PEH output current is processed by two power
power devices instead of three, reducing the power losses. Second, the active rectifier can be designed
devices instead ofFigure
three, reducing the power
activelosses. Second, thethe
active rectifier can be designed to
toAs shownain
generate very low5b, a full-bridge
voltage drop, avoiding rectifier replaces
the efficiency reduction single switch
caused, present
especially oninlow
the basic
generate a very low voltage drop, avoiding the efficiency reduction caused, especially
Zeta converter. This has a multiple aftermath. First, the PEH output current is processed by two on low voltage
circuits, by the instead
power devices diode fixed voltage
of three, drop.the
reducing Finally,
power the activeSecond,
losses. rectifier,
theunlike
activethe diodecan
rectifier rectifier that is
be designed
to generate a very low voltage drop, avoiding the efficiency reduction caused, especially on low
Sensors 2020, 20, x FOR PEER REVIEW 6 of 13
Sensors 2020,
voltage 20, 5862by the diode fixed voltage drop. Finally, the active rectifier, unlike the diode rectifier
circuits, 6 of 13
that is a highly nonlinear load, can be driven to behave as a resistance. On the contrary, an active
rectifier requires
Sensors 2020, 20,ax suitable control system, which leads to extra costs and power self-consumption
FOR PEER REVIEW 6 of 13 if
a highly nonlinear load, can be driven to behave as a resistance. On the contrary, an active rectifier
compared with a diode rectifier. However, in the present case, this disadvantage is nearly removed,
requires a suitable
voltage control
circuits, by the system, which
diode fixed leads
voltage to extra
drop. costs
Finally, the and
activepower self-consumption
rectifier, unlike the diodeifrectifier
compared
because the active rectifier replaces the switch of the conventional Zeta converter; thus, no additional
with athatdiode
is a rectifier. However,
highly nonlinear load,incan thebepresent
driven to case, thisas
behave disadvantage
a resistance. On is nearly removed,
the contrary, because
an active
control circuitries are needed. Moreover, the full-bridge driver circuit can be simplified by using a
rectifier
the active requires
rectifier a suitable
replaces thecontrol
switchsystem, which leads to Zeta
of the conventional extra converter;
costs and power thus,self-consumption
no additional control if
couplecompared
of NPN with and aPNPdiode bipolar
rectifier.junction
However, transistor (BJT)case,
in the driver
present devices disadvantage
in a totem-pole configuration for
circuitries are needed. Moreover, the full-bridge circuitthiscan be simplified is nearly removed,
by using a couple
each leg.
becauseFinally, an
the active automatic
rectifier input
replaces current
the switch shaping
of the is achieved
conventional by operating
Zeta converter; the converter
thus, no additional in
of NPN and PNP bipolar junction transistor (BJT) devices in a totem-pole configuration for each leg.
discontinuous conduction
control circuitries mode (DCM).
are needed. Moreover, This
themakes no longer
full-bridge driver necessary
circuit can abecurrent
simplifiedcontrol loopawith
by using
Finally, an automatic input current shaping is achieved by operating the converter in discontinuous
related current
couple sensing
of NPN anddevices,
PNP bipolarenablingjunctionthe transistor
use of a simple pulse-width
(BJT) devices modulation
in a totem-pole (PWM) strategy
configuration for
conduction mode (DCM). This makes no longer necessary a current control loop with related current
each leg. duty
with constant Finally, an automatic
cycle input current
δ = ton/Ts (where shaping
ton is the opening is achieved
time andbyTsoperating the converter
is the switching period) in and
sensing devices, enabling
discontinuous conduction the mode
use of(DCM).
a simple Thispulse-width
makes no modulation
longer necessary (PWM)
a current strategy
control with
loop constant
with
switching frequency fs.
duty cycle
related δcurrent
= ton /Tsensing
s (where ton is enablingthe opening the usetime and Tspulse-width
is the switching period) andstrategy
switching
The DCM operation ofdevices,
the proposed converter of ais
simple
described in Figure modulation (PWM)
6. In powering mode, the
frequency fs .
with constant duty cycle δ = ton/Ts (where ton is the opening time and Ts is the switching period) and
input voltage vPZT(t) is applied to inductors L1 and L2, which are charged, as well as the coupling
The DCMfrequency
switching operation fs. of the proposed converter is described in Figure 6. In powering mode,
capacitor C. Specifically, in the positive half-period of vAC(t), the switches S3 and S4 are turned off
The DCM
the input voltage operation
vPZT of the proposed
(t) is applied to inductors converter
L1 and is described
L2, whichinare Figure
charged,6. In powering
as well asmode, the
the coupling
and the other
input switches
voltage v (t)S1isand S2 are
applied to turned on,
inductors L1while
and during
L2, which the
aresecond
charged, half-period
as well as of vcoupling
the AC(t), S1 and
capacitor C. Specifically, in the positive half-period of vAC (t), the switches S3 and S4 are turned off and
PZT
S2 arecapacitor
turned off and S3 andinS4the
C. Specifically, arepositive
turnedhalf-period
off. In free-wheeling
of vACthe the mode,
(t), secondswitches S1,S3S2, andS3,S4 and turned
S4 are turned
the other switches S1 and S2 are turned on, while during half-period of are
vAC (t), S1 offand S2
off, while
and thetheother
diode Db conducts.
switches S1 and S2 The areenergy
turned stored
on, whilein during
the previous
the secondstephalf-period
from the coupling
of vAC(t), S1capacitor
and
are turned off and S3 and S4 are turned off. In free-wheeling mode, S1, S2, S3, and S4 are turned off,
C is transferred
S2 are turned to off
L1,andwhile L2 supplies
S3 and S4 are turned the battery. When all the
off. In free-wheeling energy
mode, S1, S2, stored
S3, andin L2 is transferred
S4 are turned
while the diode Db conducts. The energy stored in the previous step from the coupling capacitor C is
off, while the diode Db conducts. The energy stored in the previous
to the battery, the converter enters into the idle mode. The currents through the inductors become step from the coupling capacitor
transferred
C isand to L1, while
transferred to L1,L2while
supplies the battery.
L2 supplies WhenWhen
the battery. all theallenergy
the stored
energy in L2
stored in is
L2transferred
is transferred to the
constant the coupling capacitor C is charged to the battery voltage.
battery,
to the converter
the battery, theenters intoenters
converter the idle intomode.
the idleThe currents
mode. throughthrough
The currents the inductors become
the inductors constant
become
and the coupling capacitor C is charged to the battery
constant and the coupling capacitor C is charged to the battery voltage. voltage.
(a) (a) (b)(b)
FigureFigure
Figure 6. (a)6.Powering
6. (a) (a) Powering
Powering mode
modemode with
with
with v(t)
vvAC
AC AC(t)
(t) >>0>00(up)
(up)and
(up) and vvvAC
and AC(t) <
< 00 (down);
(down);(b)
(b)free-wheeling mode
free-wheeling (up),(up),
mode
AC (t) < 0 (down); (b) free-wheeling mode (up),
idle idle mode
mode (down).
(down).
idle mode (down).
The resulting inductors and input currents are schematically shown in Figure 7.
The resulting inductors and input currents are schematically
schematically shown
shown in
in Figure
Figure 7.
7.
Figure 7. Inductors and input currents.
Sensors 2020, 20, 5862 7 of 13
Sensors 2020, 20, x FOR PEER REVIEW 7 of 13
The following mathematical dissertation
Figure is and
7. Inductors referred
input to [31]. Assuming a constant duty cycle
currents.
operation on each half-cycle of the vibration, the average value on a switching period Ts of the PZT
Thepower
output following mathematical
PPZT (t) dissertation
is given by the following:is referred to [31]. Assuming a constant duty cycle
operation on each half-cycle of the vibration, the average value on a switching period Ts of the PZT
2
output power PPZT(t) is given by the following: vPZT 1
!
1
PPZT (t) = + (2)
2 2fs L1 L2
1 1
( )= + (2)
The converter is seen by the PEH as a controllable2 resistance RL (δ), given by the following:
The converter is seen by the PEH as a controllable resistance RL(δ), given by the following:
2 fs L1 L2
RL (δ) = 2 (3)
( ) = ( L1 + L2 ) δ
2
(3)
( + )
In order to maximize the energy yield, the electrical resistance should be adapted to cope with
In order to maximize the energy yield, the electrical resistance should be adapted to cope with
variations in vibration frequency and temperature, as already highlighted in Figure 3a,b. The optimal
variations in vibration frequency and temperature, as already highlighted in Figure 3a,b. The optimal
duty cycle δopt can be determined by setting RL (δ) = RL_opt (fm , θPZT ), as follows:
duty cycle δopt can be determined by setting RL(δ) = RL_opt (fm, θPZT), as follows:
s
22fs L1 L2
δopt = = (4)
(4)
((L1 ++L2 ))RLopt ( (fm , ,θPZT )
In principle, RRL_opt
Inprinciple, L_opt(fm(f,mθ θPZT
, PZT ) can
) can bebe estimatedbybymeasuring
estimated measuringthe
thevibration
vibrationfrequency
frequencyand
andthethe
temperaturefrom
temperature fromFigure
Figure3a,b,3a,b,asasshown
shownin inFigure
Figure8.8.However,
However,this
thisapproach
approachisisquite
quiteimpractical
impracticalsince
since
ititwould
wouldrequire
requireaapreliminary
preliminaryfull fullcharacterization
characterizationofofthe
thePEH
PEHdevice.
device.
(a) (b)
Figure
Figure8.8.Effect
Effectofof(a)
(a)the
thevibration
vibrationfrequency
frequencyand
and(b)
(b)the
thetemperature
temperatureon
onthe
theoptimal
optimalduty cycleδδopt
dutycycle ..
opt
AAmore
moreviable
viableand andgeneral
general approach
approach consists
consists of adapting
of adapting thethe
duty duty δ in δorder
cycle
cycle in order to force
to force the
the PEH
PEH to always
to always operate operate
at itsatoptimal
its optimal working
working point.point. An MPPT
An MPPT algorithm,
algorithm, basedbased on a perturb
on a perturb and
and observe
observe (P&O)(P&O)
approach approach
[32], was[32],thus
was developed.
thus developed. Thechart
The flow flow ischart is displayed
displayed in Figure
in Figure 9a. The 9a.
The adjustment step is one-half of the vibration period, being triggered
adjustment step is one-half of the vibration period, being triggered by the detection of vPZT by the detection of v PZT (t) zero
(t) zero
crossings.InInpractice,
crossings. practice,the theoutput voltagevvPZT
outputvoltage (t)(t)isissampled,
PZT sampled,low-pass
low-passfiltered,
filtered,squared,
squared,and andprocessed
processed
byan
by anintegrator,
integrator,which
whichisisresetresetat ateach
eachzero
zero crossing.
crossing.The Theresult
resultisisdivided
dividedby byRRLL, ,which
whichisisobtained
obtained
fromEquation
from Equation(2), (2),toto compute
compute thethe average
average PEH PEH output
output powerpower
overover a half-period
a half-period of theofvibration.
the vibration.
The
The obtained
obtained valuevalue is compared
is compared withwiththatthat computed
computed in the
in the previous
previous step.
step. Based
Based onon
the thegradient
gradientofofthe the
output power, the duty cycle is then updated. The converter control system is very simple, being ofof
output power, the duty cycle is then updated. The converter control system is very simple, being
thepredictive
the predictivetype,
type,as asshown
shownin inFigure
Figure9b.
9b.
Sensors 2020, 20, 5862 8 of 13
Sensors 2020, 20, x FOR PEER REVIEW 8 of 13
(a) (b)
Figure 9. (a)
(a) Flowchart
Flowchart of
of the
the perturb
perturb and
and observe
observe (P&O)
(P&O) maximum
maximum power
power point
point tracking
tracking (MPPT)
(MPPT)
algorithm and (b) converter control system with MPPT.
Considering almost
almostconstant
constantthethePEH
PEHoutput voltage
output along
voltage the switching
along period
the switching Ts , theTssmall-signal
period , the small-
based linearization of Equation (1), around a generic equilibrium point
signal based linearization of Equation (1), around a generic equilibrium (P δ
point0 (PPZT0, δ0), following:
PZT0 , ), gives the gives the
following:
v2 δ0 1
!
1
∆PPZT = PZT 2 + G (s)∆δ = FδP (s)∆δ (5)
∆ = fs 0 L11 + L12 d ( )∆ = ( )∆ (5)
−sTs
1 − sT2 s
Gd ( s ) = e ≈ 1 sT (6)
( )= 1 + 2 s2
(6)
where ∆PPZT and ∆δ are power and duty cycle disturbances,1 + respectively, while Gd (s) deals with the
2
delay caused by PWM.
where ΔPPZT and Δδ are power and duty cycle disturbances, respectively, while Gd(s) deals with the
According to the scheme of Figure 5a, a single-stage AC–DC converter based on a Zeta topology
delay caused by PWM.
was then designed, featuring the technical specifications reported in Table 1.
According to the scheme of Figure 5a, a single-stage AC–DC converter based on a Zeta topology
was then designed, featuring the technical specifications reported in Table 1.
Table 1. Single-stage Zeta converter technical data. BJT, bipolar junction transistor.
PZT MaxTable 1.Battery
Single-stage Zeta converter
Switching No. oftechnical
Power data. BJT, bipolar junction
Inductor transistor.Coupling
Inductor
Diode
Peak Voltage Voltage Frequency Switches L1 L2 Capacitor
No. of
PZT Max 20
Peak
V Battery
5V Switching
50 kHz 4 BJT 1 N4008 Inductor
100 µH Inductor
100 µH Coupling
100 µF
Power Diode
Voltage Voltage Frequency L1 L2 Capacitor
Switches
20 V 5 V 50 kHz
The power consumption of the whole system 4 BJT mainly
1 N4008
includes 100
thatµH 100 microcontroller
from the µH 100 µF and
from the switches. In detail, the microcontroller is set to operate in low consumption mode, i.e.,
The power consumption of the whole system mainly includes that from the microcontroller and
using 10 µW. The average power consumption of the DC–DC converter is about 80 µW.
from the switches. In detail, the microcontroller is set to operate in low consumption mode, i.e., using
10 µW. The average
4. Validation Tests power consumption of the DC–DC converter is about 80 µW.
Figure 10Tests
4. Validation displays schematically the operating principle of the proposed active control strategy
and single-stage DC–DC power conversion. Based on this scheme, a test bench was created to carry out
Figure 10tests
experimental displays
aimed schematically the operating
at demonstrating the correct principle of the
functioning ofproposed active
the proposed control as
approach strategy
either
and
the vibration frequency or the working temperature was changed suddenly. In the figure, thetoPEH
single-stage DC–DC power conversion. Based on this scheme, a test bench was created carryis
out experimental
coupled tests
to a digital aimedwhile
rheostat, at demonstrating
the converter the correct functioning
is cascade-connected to of the proposed approach
a programmable gain voltageas
either the vibration
amplifier. frequency
This assembly or the
enables an working temperature
easy emulation wasarrays
of larger changed madesuddenly. In the
of multiple figure,
PEHs, the
either
PEH is coupled
connected to a or
in parallel digital rheostat,
in series while
[33,34]. The the converter
converter is cascade-connected
supplies the battery, whichtoinaturn
programmable
powers the
gain voltage amplifier.
converter control system. This assembly enables an easy emulation of larger arrays made of multiple
PEHs, either connected in parallel or in series [33,34]. The converter supplies the battery, which in
turn powers the converter control system.
Sensors 2020, 20, x FOR PEER REVIEW 9 of 13
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Sensors 2020, 20, x FOR PEER REVIEW 9 of 13
Figure 10. Schematic representation of the operating principle of the proposed active control strategy
Figure 10. Schematic representation of the operating principle of the proposed active control strategy
based on
Figure 10. aaSchematic
single-stage DC–DC converter.
representation of the operating principle of the proposed active control strategy
based on single-stage DC–DC converter.
based on a single-stage DC–DC converter.
vPZT(t) and iPZT(t) signals are shown in Figure 11a. It can be highlighted that both presented a
vPZT (t) and iPZT (t) signals are shown in Figure 11a. It can be highlighted that both presented a
high-frequency
vPZT(t) and icomponent
(t) signalsthat
are had to be
shown eliminated
Figure 11a.by
in eliminated low-pass
It can filtering, resulting
be highlighted that bothin the signals
high-frequency component
PZT that had to be by low-pass filtering, resulting inpresented a
the signals
displayed in
high-frequency Figure 11b.
component that had to be eliminated by low-pass filtering, resulting in the signals
displayed in Figure 11b.
displayed in Figure 11b.
(a) (b)
(a) Plots of(a)
Figure 11. (a) output voltage
voltage vvPZT
PZT (in
(in cyan)
cyan) and
and output current iPZT (b)
PZT (in
(in green)
green) versus
versus time and
(b) filtered
Figure signals
11. (a) Plotsof
signals ofthe
of theoutput
output
output voltage
voltage
voltage vPZT
vPZTv(in(incyan)
PZT cyan)
(in andand
cyan)
and of the
of output
output the current
output
current (iniPZT
iPZTcurrent (in
green) green).
iPZT (in green).
versus time and
(b) filtered signals of the output voltage vPZT (in cyan) and of the output current iPZT (in green).
Figure 12a,b shows the transistor currents and the inductor currents according to the working
Figureexplained
condition in Figure
12a,b shows 6, measured
the transistor by means
means
currents of
of Hall
and the Hall probes.
probes.
inductor currents according to the working
condition explained in Figure 6, measured by means of Hall probes.
Sensors 2020, 20, 5862 10 of 13
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Sensors 2020, 20, x FOR PEER REVIEW 10 of 13
(a) (b)
12. (a) Plots
Figure 12. Plots of
of switching
switching
(a) currents iiS1
currents and iiS2
S1 (in green) and S2 (in magenta); (b) plots of switching
(b) switching
currents L1 (in
currents iiL1 (in green)
green) and
and iiL2
L2 (in
(inmagenta).
magenta).
Figure 12. (a) Plots of switching currents iS1 (in green) and iS2 (in magenta); (b) plots of switching
5. Discussion iL1 (in green) and iL2 (in magenta).
currents
5. Discussion
PEHs
5. in
in the
Discussion
PEHs the form
form of of cantilever
cantilever beams beams are are widely
widely used used for for generating
generating energy energy fromfrom low-frequency
low-frequency
vibrating
vibratingPEHs structures.
structures.
in the form To
To of harvest
harvest
cantileverthe maximum
thebeamsmaximum are widelyenergy
energy from
usedfrom the piezoelectric
the piezoelectric
for generating energy from element,
element, impedance
low-frequencyimpedance
matching
matching with the applied
withstructures.
vibrating the applied load
To load
harvest is required.
is required.
the maximum However,
However,
energy as as was
fromwasthe shown
shown in Figure
in Figure
piezoelectric 3, the resistance
resistance load
3, the impedance
element, load
depends
depends on
on both
matching withthe
both the vibration
the applied load
vibration frequency
is required.
frequency and
and the
the working
However, as wastemperature;
working shown in Figure
temperature; therefore, the
the variation
3, the resistance
therefore, load of
variation of
one of these
depends two
on quantities
both the leads
vibration to a
frequencyshift of
and the
the optimal
working working
temperature;
one of these two quantities leads to a shift of the optimal working point. In practical applications, it point. In
therefore,practical
the applications,
variation of
it one of these
is isunlikely
unlikely that two
thatthe quantities
theexcitation
excitation leads
isispureto aharmonic
pure shift of theor
harmonic optimal
orthat
thatthe working
the working
working point. In practical applications,
temperature
temperature remains constant.
remains it
constant.
is
Therefore, unlikely that the excitation is pure harmonic or that the working temperature remains constant.
Therefore, some some way way to to track
track and and match
match the the optimal
optimal working
working point point should
should be be thought
thought of of ifif maximum
maximum
power Therefore,
harvesting some hasway to to
be track and match the optimal working point should be thought of if maximum
achieved.
power harvesting has to be achieved.
power harvesting has to be achieved.
This paper
ThisThis paper faced
faced thisthis problem by exploiting an active an control strategy based on abasednon-conventional
paper faced thisproblem
problem by by exploiting
exploiting an activecontrol
active control strategy
strategy based on aon a non-
non-
AC–DC
conventional converterAC–DC that integrates
converter a DC–DC Zeta converter and a full-bridge active rectifier.
conventional AC–DC converterthat thatintegrates
integrates aa DC–DC DC–DCZeta Zetaconverter
converter andand a full-bridge
a full-bridge activeactive
To
rectifier. prove the effectiveness of the proposed approach, a prototype of the converter was created
rectifier.
and tested Towith
To prove the
prove a cantilever
effectiveness
the effectiveness PEH. ofofFigure
the 13a,b shows
theproposed
proposed approach,
approach, the transient
a aprototype
prototype and
of of steady-state
the the converter
converter response
was was
created of the
created
single-stage
and converter
tested with a for a
cantilever sudden
PEH. change
Figure in
13a,bthe applied
shows the resistance
transient
and tested with a cantilever PEH. Figure 13a,b shows the transient and steady-state response of the load
and (which
steady-state actually
response mayof occur
the if
either the working
single-stage frequency
converter for a or temperature
sudden change in changes).
the applied Based
resistance
single-stage converter for a sudden change in the applied resistance load (which actually may occur on the
load results
(which reported
actually in
may Figure
occur 3a,b,
we if either
induced
if either the
the workingworking
a stepped frequency
change
frequency inortemperature
or thetemperature
resistance changes).
load from
changes). Based
Based15on to
onthe
62
theresults
kΩ toreported
results emulate
reported in aFigure
change
in 3a,b,in3a,b,
Figure the
working we induced
frequency a stepped
from 70change
to 30 in
Hz, the resistance
and from 28 load
to from
46 kΩ, 15 to to 62
emulatekΩ toa emulate
change ain change
the in the
temperature
we induced a stepped change in the resistance load from 15 to 62 kΩ to emulate a change in the
from working 50 frequency
◦ C. In both
25 tofrequency from 70 to 30self-adaption
Hz, and fromcapability28 to 46 kΩ, oftothe emulate a change in the temperature
working fromcases, 70 to the 30 Hz, and from 28 to 46 kΩ, single-stage
to emulate AC–DC
a change in converter
the temperature can be
from 25 to 50 °C. In both cases, the self-adaption capability of the single-stage AC–DC converter can
observed,
frombe which
25observed,
to 50 °C. In allows the
bothallows PEH
cases,the to always
thePEH operate
self-adaption at its optimal working point, generating maximum
which to always capability
operate at of its the single-stage
optimal workingAC–DC converter can
point, generating
power (see Figure
be observed, 3a,b). Reducing the to
amplitude of the forced variation (i.e., the width of ∆R) only
maximum power (see Figure 3a,b). Reducing the amplitude of the forced variation (i.e., the width generating
which allows the PEH always operate at its optimal working point, of ΔR)
affects
maximum theaffects
only time
power tsthe
needed
(see Figure
time tby the converter
3a,b).
s needed Reducing to the
by the converter reach the
amplitude steady-state
to reach ofthe condition,
thesteady-state
forced variationas it(i.e.,
condition, canas beitwidth
the observed
can beof ΔR)by
comparing
only observed Figure
affects the 13a, in
time ts needed
by comparing which ∆R
Figure by is
13a,the 47 kΩ
in which and t
ΔR is 47
converter s is 0.38
tokΩ reachs, and
and the Figure 13b,
steady-state
ts is 0.38 in
s, and Figure which
condition, ∆R
13b, in which equals
as itΔR 18 kΩ
can be
and tequals
observeds equals 0.15
by18comparing
kΩ and s. ts equalsFigure 0.15
13a,s. in which ΔR is 47 kΩ and ts is 0.38 s, and Figure 13b, in which ΔR
equals 18 kΩ and ts equals 0.15 s.
(a) (b)
Figure 13. (a) Load resistance adaption (15–62 kΩ) coping with a vibration frequency variation from 30
(a)
to 70 Hz; (b) load resistance adaption (28–46 kΩ) coping with a PZT operating (b)temperature variation
from 25 to 50 ◦ C.Sensors 2020, 20, 5862 11 of 13
While the variability of the environmental temperature might be rather limited, this may not be
the case as far the vibration frequency is concerned, as PEHs are usually called to work in a broadband
excitation scenario, where multiple vibration frequencies coexist simultaneously. As shown in Figure 3,
if we consider the PEH operating in optimal load matching at a temperature of 25 ◦ C, without any
adaptive compensation a variation of 30 Hz (from 30 to 60 Hz) of the vibrational frequency causes a
−120% decrease in the generated power. On the contrary, at a fixed frequency of 50 Hz and optimum
load, increasing the temperature from 25 to 50 ◦ C produces only a −8% variation.
A specific consideration must be taken into account about the resonant frequency of the PEH
since at resonance, as is well known, piezoelectric energy harvesters always generate the highest
power [14,28]. In our tests, the tip of the cantilever was connected to the shaker (see Figure 2b) and it
was forced to move with a fixed amplitude (it was not allowed to freely oscillate). Hence, it makes no
sense to deal with resonance. It is noteworthy to highlight that this setup was deliberately chosen to
study the intrinsic characteristics of the PEH rather than those of the assembly (which are function
of the geometry of the system and of the actual constraint conditions). Moreover, the resonance
condition is irrelevant for the performance of the proposed converter, as it adapts the impedance of
the load whatever the working frequency. Letting the PEH work in resonance condition would only
produce a higher generated power, without influencing the adaptative logic of the proposed power
conversion scheme.
6. Conclusions
This paper presented an original approach, based on a single-stage AC–DC converter, aimed
at tracking the optimal working point of piezoelectric energy harvesters. The proposed converter
topology, based on an active control, consists of an AC–DC converter that integrates a DC–DC Zeta
converter and a full-bridge active rectifier.
The study showed that the proposed strategy adapts the resistance seen by the PEH to the
change in working conditions, allowing the piezoelectric harvester to always operate at its optimal
working point, whatever the applied vibration frequency and/or the temperature, hence increasing the
conversion efficiency.
To accomplish this, an active rectifier and a PWM strategy were used to control the designed
converter, putting into evidence the fact that the optimal duty cycle is influenced by either the PEH
excitation frequency or the working temperature. A dedicated algorithm of maximum power point
tracking, based on a perturb and observe (P&O) approach, was developed. The validation tests
highlighted the effectiveness of the proposed active controlled approach as the applied resistance load
underwent a sudden change of up to 47 kΩ.
The proposed conversion topology introduces many advantages in the PEH electrical management,
as shown in Figure 5b. The use of a full-bridge active rectifier allows to reduce the number of devices
that process the current and the power losses. Moreover, a full-bridge active rectifier has a linear
behavior, can be simplified using a couple of NPN and PNP BJT devices in a totem-pole configuration
for each leg, and can replace the switch of conventional Zeta converters. For this latter reason,
no additional control circuitries are needed. Total power consumption of the proposed converter is
only 80 µW. This is much less than the minimum power generated by a single PEH, that is, 0.64 mW at
30 Hz as a resistance load of 62 kΩ is considered (see Figure 3a). Moreover, the power consumption of
the converter does not depend on the number of PEHs that can be connected, in a parallel configuration,
downstream to the converter. In this case, only the losses moderately increase because of the higher
current. It is noteworthy to observe that a similar power consumption is expected if a conventional
converter (without tracking capability) is used. Finally, since the converter operates in discontinuous
conduction mode, it does not use a current control loop but it exploits pulse-width modulation, which is
the core of the impedance tracking procedure. This guarantees a simpler and more accurate operation
of the converter, since, unlike the voltage that easily reaches tens of V, the current supplied by a PEH is
of the order of tens of µA.You can also read
