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Behavioral modeling of a piezoelectric harvester with adaptive energy-investment for improved battery charging

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Tales Luiz Bortolin
Tales Luiz Bortolin
Tales Luiz Bortolin
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André Luiz Aita
André Luiz Aita
André Luiz Aita
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Abstract and Figures

This work describes the behavior of a piezoelectric energy harvesting system that uses a single inductor and the concept of energy investment for the whole of building a behavioral model for the harvester and a high-level system analysis approach. The harvester modules and control were specified and described in Verilog-A to fully model the energy harvester operation. Simulation results have shown the harvesting mechanism based on the concept of energy-investment and model accuracy, and the effect of the invested energy on the battery charging profile, highlighting the trade-off a constant energy investment time poses to the harvester, unable to meet the requirements a non-constant input vibration sets to system. An adaptive energy investment time based on a P&O algorithm was proposed to cope with this trade-off and added to the harvester model. Performed simulations with adaptive energy investment have shown improved energy harvesting, and that such improvement increases as the input power increases, since the system can tune the energy investing mechanism to the input vibrations.
Generic piezoelectric energy harvester block diagram
Generic piezoelectric energy harvester block diagram
… 
Proposed P&O Algorithm. The investment time τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} is perturbed and, afterwards, the variation of VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} (ΔVBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta V_{BAT}$$\end{document}) is observed, every harvesting cycle K
Proposed P&O Algorithm. The investment time τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} is perturbed and, afterwards, the variation of VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} (ΔVBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta V_{BAT}$$\end{document}) is observed, every harvesting cycle K
… 
VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} for different IPZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{PZ}$$\end{document} with adaptive τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} and without investment (τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document}=0), showing a higher energy investment performance for higher input vibrations (IPZ=12μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{PZ}=12~\upmu$$\end{document}A)
VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} for different IPZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{PZ}$$\end{document} with adaptive τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} and without investment (τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document}=0), showing a higher energy investment performance for higher input vibrations (IPZ=12μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$I_{PZ}=12~\upmu$$\end{document}A)
… 
Voltages VPZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{PZ}$$\end{document} and VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document}, and τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} (time range from 2.4 to 2.6 s is in detail) are shown focusing on the instants when the harvester disables the investment and right after the reinvestment (V1 on both figures), due to vibration level fading. The reinvestment and investment (in this order) are enabled back after (@V2)
Voltages VPZ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{PZ}$$\end{document} and VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document}, and τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} (time range from 2.4 to 2.6 s is in detail) are shown focusing on the instants when the harvester disables the investment and right after the reinvestment (V1 on both figures), due to vibration level fading. The reinvestment and investment (in this order) are enabled back after (@V2)
… 
Voltage VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} (same as in Fig. 12) with and without investment. Investment time τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} and ΔVBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta V_{BAT}$$\end{document} are detailed. With adaptive investment time, battery charging profile is improved when compared to reinvestment only
+9
Voltage VBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_{BAT}$$\end{document} (same as in Fig. 12) with and without investment. Investment time τI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _{I}$$\end{document} and ΔVBAT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta V_{BAT}$$\end{document} are detailed. With adaptive investment time, battery charging profile is improved when compared to reinvestment only
… 
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Behavioral modeling of a piezoelectric harvester with adaptive energy-
investment for improved battery charging
Tales Luiz Bortolin
1
•Andre
´Luiz Aita
2
Received: 6 April 2020 / Revised: 30 June 2020 / Accepted: 21 August 2020 / Published online: 14 September 2020
Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
This work describes the behavior of a piezoelectric energy harvesting system that uses a single inductor and the concept of
energy investment for the whole of building a behavioral model for the harvester and a high-level system analysis
approach. The harvester modules and control were specified and described in Verilog-A to fully model the energy harvester
operation. Simulation results have shown the harvesting mechanism based on the concept of energy-investment and model
accuracy, and the effect of the invested energy on the battery charging profile, highlighting the trade-off a constant energy
investment time poses to the harvester, unable to meet the requirements a non-constant input vibration sets to system. An
adaptive energy investment time based on a P&O algorithm was proposed to cope with this trade-off and added to the
harvester model. Performed simulations with adaptive energy investment have shown improved energy harvesting, and that
such improvement increases as the input power increases, since the system can tune the energy investing mechanism to the
input vibrations.
Keywords Piezoelectric energy harvesters Energy-investing harvesters Verilog-A behavioral modeling and simulation
Perturb and observe algorithm
1 Introduction
The same technological evolution that allows the design of
continuously smaller micro-sensors and microcircuits for
e.g. IoT (Internet of Things), also imposes limitations to
their operation, as the batteries required to supply them are
also very small, with very limited energy capacity [1].
Although these microcircuits might be designed to work
with an ultra-low power consumption, this only helps to
extend their operating life-time, without however elimi-
nating the need to replace the source of energy, eventually
[2]. Since the replacement of these batteries is impractical
in many situations due to technical reasons or costs, e.g.
smart-dust or biomedical implants [3,4], the challenge is
therefore to keep these systems running autonomously.
As the vibrations are abundant in many environments,
solutions for electrical energy harvesting from piezoelec-
tric transducers [5,6] have emerged as promising alterna-
tives [7]. And many challenges concerning the design of
these circuits remain unaddressed showing a promising
field of study.
This work, however, instead of looking for novel cir-
cuits and solutions, contributes differently, developing a
behavioral model for a particular harvester, providing an
alternative approach for the analysis and eventual design of
such systems. This is in turn well-aligned with other works,
e.g. switched power converters, which look for different
analysis and design methodologies [8,9] for fast and still
accurate circuit behavior evaluation. The use of either
Verilog-A or AMS or a mixed approach of these system
level hardware description languages with electrical net-
lists is also often observed [9,10] and was chosen for this
work.
&Andre
´Luiz Aita
aaita@inf.ufsm.br
Tales Luiz Bortolin
taleslbd@gmail.com
1
Post-graduation Course on Computer Science - PPGCC,
Federal University of Santa Maria - UFSM, Santa Maria, RS,
Brazil
2
Department of Electronics and Computing, Federal
University of Santa Maria - UFSM, Santa Maria, RS, Brazil
123
Analog Integrated Circuits and Signal Processing (2021) 106:249–259
https://doi.org/10.1007/s10470-020-01708-8(0123456789().,-volV)(0123456789().,-volV)
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
ResearchGate has not been able to resolve any citations for this publication.
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The Internet of Things (IoT) urges for development and pervasive deployment of energy-autonomous integrated remote sensing nodes. Microsystems-based (i.e. MEMS) Energy Harvesting (EH) seems to be a key-enabling technology to face such a challenge, and environmental vibrations are a source of energy commonly available in domestic, industrial and public contexts. A major limitation of standard vibration Energy Harvesters (EHs) is the power conversion performance typically pronounced just around the fundamental mechanical resonant frequency (narrowband device). In this work, we introduce a resonator design concept named Four-Leaf Clover (FLC). Having several mechanical Degrees Of Freedom (DOFs), the FLC EH-MEMS exhibits several resonant modes in the frequency range from around 200 Hz up to several kHz. Thereafter, it is capable to convert mechanical into electric energy efficiently in a wide frequency range of vibrations (wideband device). The FLC EH-MEMS design concept discussion is corroborated by simulations and experimental measurements that verify its performance and, in turn, that provide support to the contribution it can bring to self-powered integrated sensing nodes in the IoT scenario.
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This work analyzes a piezoelectric energy harvesting system that uses a single inductor and the concept of energy investment. The harvester behavior, with special focus on its control logic module and state machine, is fully described and modeled in Verilog-A. The needed sensors and control variables were also identified and modeled. Simulation results have shown the correct behavioral modeling of the piezoelectric energy harvester system and proposed control, highlighting the harvesting mechanism based on the concept of energy-investment and the effect of the energy invested on the characteristics of the battery charging profile. The speed of the behavioral simulations when compared to electrical ones and the obtained model accuracy, have shown a reliable and prospective higher-level design approach.
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A single-inductor 0.35 μm CMOS energy-investing piezoelectric harvester
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Although miniaturized piezoelectric transducers usually derive more power from motion than their electrostatic and electromagnetic counterparts, they still generate little power. The reason for this is that the electromechanical coupling factor is low, which means the damping force that tiny transducers impose on vibrations (when drawing power) is hardly noticeable. The single-inductor 0.35 μm CMOS piezoelectric harvester proposed in this paper counters this deficiency by investing energy from the battery into the transducer. The idea is to strengthen the electrostatic force against which vibrations work. This way, the circuit draws more power from the transducer, up to 79 μW from a 2.7 cm piezoelectric cantilever that is driven up to 0.25 m/s 2. Of the 79 μW drawn at 0.25 m/s 2 when investing 91 nJ of battery energy, the system outputs 52 μW, which is 3.6 times more output power than the 14.5 μW that a full-wave bridge rectifier with zero-volt diodes at its maximum power point can deliver from the same source. With 630 nW lost to the controller, power-conversion efficiency peaks at 69% when the harvester outputs 46 μW of the 67 μW it draws from the transducer at 0.25 m/s 2 when investing 0.8 nJ of battery energy.
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