25-06-2012, 12:00 PM
Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply
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Abstract
This paper describes an approach to harvesting electrical
energy from a mechanically excited piezoelectric element.
A vibrating piezoelectric device differs from a typical electrical
power source in that it has a capacitive rather than inductive source
impedance, and may be driven by mechanical vibrations of varying
amplitude. An analytical expression for the optimal power flow
from a rectified piezoelectric device is derived, and an “energy harvesting”
circuit is proposed which can achieve this optimal power
flow. The harvesting circuit consists of an ac–dc rectifier with an
output capacitor, an electrochemical battery, and a switch-mode
dc–dc converter that controls the energy flow into the battery. An
adaptive control technique for the dc–dc converter is used to continuously
implement the optimal power transfer theory and maximize
the power stored by the battery. Experimental results reveal
that use of the adaptive dc–dc converter increases power transfer
by over 400% as compared to when the dc–dc converter is not used.
Index Terms—Adaptive control, dc–dc conversion, energy harvesting,
low power, piezoelectric.
I. INTRODUCTION
THE need for a wireless electrical power supply has spurred
an interest in piezoelectric energy harvesting, or the
extraction of electrical energy using a vibrating piezoelectric
device. Examples of applications that would benefit from
such a supply are a capacitively tuned vibration absorber [1],
a foot-powered radio “tag” [2], [3], and a PicoRadio [4]. A
vibrating piezoelectric device differs from a typical electrical
power source in that its internal impedance is capacitive rather
than inductive in nature, and that it may be driven by mechanical
vibrations of varying amplitude and frequency. While there have
been previous approaches to harvesting energy generated by a
piezoelectric device [2], [3], [5], [6] there has not been an attempt
to develop an adaptive circuit that maximizes power transfer
from the piezoelectric device. The objective of the research
Manuscript received August 27, 2001; revised May 9, 2002. Recommended
by Associate Editor J. D. van Wyk. This paper was presented at the 42nd
AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials
Conference and Exhibit, Adaptive Structures Forum, Seattle, WA, April
16–19, 2001. This work was supported by the Pennsylvania State University,
Office of Naval Research, under Contract N00014–99-1–0450 and under a
Subcontract from the University of Florida.
G. K. Ottman is with the Applied Physics Laboratory, Johns Hopkins University,
Laurel, MD 20723 USA.
H. F. Hofmann is with the Department of Electrical Engineering, Pennsylvania
State University, University Park, PA 16802 USA (e-mail: hofmann@
engr.psu.edu).
A. C. Bhatt is with the Systems Design Engineering Department, Intel Corporation,
Santa Clara, CA 95054 USA.
G. A. Lesieutre is with the Department of Aerospace Engineering, Pennsylvania
State University, University Park, PA 16802 USA.
Publisher Item Identifier 10.1109/TPEL.2002.802194.
Fig. 1. Piezoelectric element model with ac–dc rectifier and load.
described herein was to develop an approach that maximizes the
power transferred from a vibrating piezoelectric transducer to
an electrochemical battery. The paper initially presents a simple
model of a piezoelectric transducer. An ac–dc rectifier is added
and the model is used to determine the point of optimal power
flow for the piezoelectric element. The paper then introduces an
adaptive approach to achieving the optimal power flow through
the use of a switch-mode dc–dc converter. This approach is
similar to the so-called maximum power point trackers used to
maximize power from solar cells [7]–[10]. Finally, the paper
presents experimental results that validate the technique.
II. OPTIMAL POWER FLOW OF PIEZOELECTRIC DEVICE
To determine its power flowcharacteristics, a vibrating piezoelectric
element is modeled as a sinusoidal current source
in parallel with its internal electrode capacitance . This model
will be validated in a later section. The magnitude of the polarization
current varies with the mechanical excitation level of
the piezoelectric element, but is assumed to be relatively constant
regardless of external loading. A vibrating piezoelectric
device generates an ac voltage while electrochemical batteries
require a dc voltage, hence the first stage needed in an energy
harvesting circuit is an ac–dc rectifier connected to the output
of the piezoelectric device, as shown in Fig. 1. In the following
analysis, the dc filter capacitor is assumed to be large
enough so that the output voltage is essentially constant;
the load is modeled as a constant current source ; and the
diodes are assumed to exhibit ideal behavior.
The voltage and currentwaveforms associated with the circuit
are shown in Fig. 2. These waveforms can be divided into two
intervals. In interval 1, denoted as , the polarization current is
charging the electrode capacitance of the piezoelectric element.
During this time, all diodes are reverse-biased and no current
flows to the output. This condition continues until the magnitude
0885-8993/02$17.00 © 2002 IEEE
670 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 5, SEPTEMBER 2002
Fig. 2. Voltage, current waveforms of piezoelectric element-rectifier circuit.
of the piezoelectric voltage is equal to the output voltage
. At the end of the commutation interval, interval 2 begins,
and output current flows to the capacitor and the load
(1)
By assuming , the majority of the current will be
delivered as output current
(2)
The dc component of can then be shown to be
(3)
The output power can be shown to vary with the value of the
output voltage as follows:
(4)
It can then be shown that the peak output power occurs when
(5)
or one-half the peak open-circuit voltage of the piezoelectric
element (see Appendix for complete analysis).
III. ENERGY HARVESTING CIRCUITRY
The magnitude of the polarization current generated by the
piezoelectric transducer, and hence the optimal rectifier voltage,
may not be constant as it depends upon the vibration level exciting
the piezoelectric element. This creates the need for flexibility
in the circuit, i.e., the ability to adjust the output voltage
of the rectifier to achieve maximum power transfer. To facilitate
the attainment of the optimal voltage at the output of the rectifier,
a dc–dc converter is placed between the rectifier output
and the battery as shown in Fig. 3. Typically the controller of
such a converter is designed to regulate the output voltage [11];
however, in this circuit the converter will be operated to maximize
power flow into the battery. If effective, the piezoelectric
element would be at peak power, which corresponds to the
output voltage of the rectifier being maintained at its optimal
value, approximately one-half the open-circuit voltage, as
described previously.
The purpose of this circuit is to maximize the power flowing
into the battery. As the battery voltage is essentially constant or
changes very slowly, this is equivalent to maximizing the current
into the battery, . By sensing this current, the duty
cycle can be adjusted to maximize it. A control scheme such as
this is general enough to be effective for many dc–dc converter
topologies. To illustrate the theoretical principles of maximum
power transfer and the control of the converter, a step-down or
buck converter will be discussed in this paper. Fig. 4 shows a
representation of the steady-state battery current – duty cycle
relationship using a step-down converter.
In order to achieve peak battery current, an appropriate
method of controlling the duty cycle is to incrementally
increase or decrease the duty cycle as determined by the slope
of the battery current curve, . The duty cycle is now the
sum of the present duty cycle and the increment
(6)
Where is the assigned rate of change of the duty cycle and
is the signum function which returns the sign of the quotient
.
Note a few features of this control: First, as the control algorithm
is based upon the sign of a rate of change, the duty cycle
must continuously change in practice. Ideally, once the controller
has settled, this will amount to small perturbations about
the optimal operating point. Furthermore, as the control algorithm
is based upon steady-state behavior of the piezoelectric element
and the dc–dc converter, a two-time-scale approach must
be used when designing the controller [12]. Using two-timescale
analysis techniques, convergence of the controller can be
assured provided the dynamics of the control algorithm are set
to be “slow” enough such that the piezoelectric device and converter
can be assumed to always be operating under steady-state
conditions. However, this also places limitations on the bandwidth
of the controller.
IV. CONTROL IMPLEMENTATION
The adaptive controller is implemented using a dSPACE
DS1102 controller board. The board includes a Texas Instruments
TMS320C31 floating-point digital signal processor
OTTMAN et al.: ADAPTIVE PIEZOELECTRIC ENERGY HARVESTING CIRCUIT 671
Fig. 3. Adaptive energy harvesting circuit.
Fig. 4. Steady-state battery current as function of duty cycle, energy harvesting
circuit with step-down converter.
(DSP), analog-to-digital (ADC) converters for sampling
measurements, and pulse-width modulated (PWM) signal
outputs for controlling the converter. The control algorithm
was developed in MATLAB 5.3 using the graphical interface
Simulink 3.0 and the Real-Time Workshop to generate the
controller code for the DSP.
Fig. 5 shows a block diagram of the controller implementation.
The initial duty cycle is set at 10% for circuit startup. The
resulting battery current is evaluated using a current-sense resistor
in series with the battery and sampled by an A/D converter.
The current signal is then low-pass filtered to attenuate noise
and reduce the current ripple effect caused by the switching of
the MOSFET. The derivative of the signal is then taken and divided
by the derivative of the duty cycle. Dividing the derivative
of the current by the derivative of duty cycle provides ,
which is used to determine the controller’s position on the battery
current–duty cycle curve shown in Fig. 4.
The sign of the quotient, , is used by a 0-threshold
block to increment the duty cycle by a set rate, in our case
21 millipercent/s (21-m%/s). This rate was determined to produce
a measurable change in battery current that could be
used to evaluate the effectiveness of the new duty cycle. The
resulting sign ( / ) of the division block, not its numerical
magnitude, is all that is used by the 0-threshold block to increase
or decrease the duty cycle. If either input signal would
be zero, resulting in a zero or undefined quotient, the threshold
block will decrease the duty cycle as a default. This default decrease
allows the control to migrate to lower duty cycle values
when the battery current might not be measurably changing,
as is the case of circuit startup. Experimentation showed that,
at a switching frequency of 1 kHz, the current changes little at
duty cycles above 10%, whereas optimal duty cycles occurred
around 3–5%.
The duty cycle is then filtered and used to generate the
PWM signal for the driver circuitry of the step-down converter.
The additional filtering of the PWM signal is necessary to
slow the rate of change of the duty cycle so the change in
current can be measured and evaluated. Without the LPF, the
controller is prone to duty cycle oscillations, as the perturbing
signal reacts faster than the finite settling time of the battery
current signal.
V. EXPERIMENTAL SETUP
A Quickpack® QP20W purchased from Active Control eXperts
(ACX), Cambridge, MA, was used as the piezoelectric energy
source. It is a two-layer device that generates an ac voltage
when vibrated in a direction perpendicular to its mid-plane. Device
specifications and diagram are shown in Fig. 6 along with
the piezoelectric element properties.
The experimental setup is shown in Fig. 7. The piezoelectric
device is secured to an electric-powered shaker, which provides
variable mechanical excitation in response to a sine wave input.
The magnitude of the mechanical excitation of the piezoelectric
element will be characterized by the open-circuit voltage that is
measured across the unloaded rectifier capacitor, . A small
mass was added to the free tip of the bimorph to enhance the
external stress and increase the tip deflection, thus providing a
larger open-circuit voltage.
The step-down converter consists of a MOSFET switch with
a high breakdown voltage rating, a custom wound inductor with
inductance of 10.03 mH, a Schottky diode, and a filter capacitor.
The voltage across the current-sense resistor is amplified
with a precision op-amp (powered by the 3 V battery), and then
sampled by the A/D converter on the controller card. The controller
card then generates thePWMsignal at the calculated duty
cycle that is fed to a high-side MOSFET driver. The driver was
powered by an external dc power supply. Due to the low power
levels expected from the piezoelectric element [2]–[4], [6], it is
assumed that the converter will operate in discontinuous current
conduction mode at the chosen switching frequency of 1 kHz.
Such a low switching frequency was chosen because switching
losses in the experimental setup comprised a significant fraction
of the power flow from the element.