Efficiency measurement in piezoelectric
vibration energy harvesters
P. M. Weaver, M. K. Rokosz, P. Woolliams, M. G. Cain, M. Stewart
National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK email paul.weaver@npl.co.uk
1. Abstract / Introduction
3. Performance and Efficiency
Vibrational energy harvesters convert energy from vibrations and
movement in the environment into electrical energy which can
be used to power a device such as a wireless sensor node. The
energy source is often considered as “waste” energy and energy
harvesting performance is typically characterised by power
output under specified conditions of vibration amplitude and
frequency. This takes no account of the energy extracted from,
or available from, the source. This is important where account
needs to be taken of the loading of the source by the harvester.
This includes “parasitic” harvesting where the energy derived from
the source is not “free” or wasted, and use of the energy harvester
increases the power consumed by the source. Examples include
human or vehicle powered applications where it is the availability
of the energy source rather than energy saving that is the main
motivation. It is also important in situations where the power
from the source is limited. In these cases, the ratio of power out to
power in, or the efficiency needs to be known.
The performance of an energy harvesting device is often
characterised by the measurement of its electrical output under
a specified set of conditions e.g. specification of the input
acceleration amplitude (base amplitude) and measurement of
the electrical output into a known resistive load. However, even
with this relatively simple setup, the performance characteristics
depend in a complex way on the base acceleration amplitude,
the load resistance and the design of the energy harvester. This is
illustrated in Figure 2 which shows how the harvested power for a
vibrating cantilever / tip mass energy harvester depends on both
frequency and amplitude of the vibration.
Measuring efficiency is more complex than measuring power
out under well-defined vibration conditions, because of the
requirement to measure the power transferred from the source
to the energy harvester. Often the harvested power is a small
fraction of the total power delivered by the system.
Figure 1. Schematic diagram of an energy harvesting system
To understand the operation of an energy harvester and how to
optimise performance in a particular vibrational environment and
powering a particular electrical load we need to know:
• The characteristics of the energy source,
• The way in which energy is transferred from the source to the
energy harvester,
• The electromechanical conversion in the energy harvesting
transducer,
• How the energy is transferred from the energy harvester to the
electrical load.
Losses can be incurred, not just within the energy harvesting
transducer [1], but at all stages in this process. It is clear that the
effectiveness of the transducer is not the only factor, and that
performance can be dominated by losses in the transfer of energy
across these system boundaries.
6. Efficiency Measurement
Two methods for measuring efficiency were employed. The first
method extends an approach originally described by Cho [6]
based on the decay of an impulse excitation of a piezoelectric
cantilever. Rather than a dropping ball we employ an impulse
excitation from the vibration motor, thus enabling automation of
parameter sweeps. The oscillation was allowed to decay to zero
amplitude (figure 5).
given by Eq.4, depends on the phase angle between the force
and displacement. The output power is given by Eq.5, and the
efficiency is the ratio of the power out to the power in (Eq.6).
(4)
(5)
(6)
Figure 5. Impulse excitation displacement and voltage for 97 kΩ load.
Figure 3. Schematic diagram of piezoelectric cantilever vibration harvester and
strain generation.
Piezoelectric vibration harvesters generate charge from strain in a
piezoelectric material created by the inertia of a suspended mass
undergoing acceleration. This is commonly achieved through
the use of a piezoelectric cantilever as shown in Figure 3. A
bimorph construction employs a symmetrical arrangement of the
piezoelectric material around the neutral axis creating strain as
also shown in Figure 3.
In this paper we compare two experimental methods of
measuring efficiency for resonant piezoelectric cantilever energy
harvesters and present experimental results for typical energy
harvesting devices.
2. Energy Harvester System
4. Anatomy of a Piezoelectric Harvester
Figure 2. Harvested power as a function of amplitude and frequency
In some cases such as generating power from human motion,
or from vehicle traffic, the energy is not strictly wasted and
extracting more power will increase the power consumed by
the source. In these situations efficiency becomes an important
metric. In many cases the energy source is not a simple vibration
and harvesting from impulse motion is of interest e.g. for
powering pacemakers [5] and for frequency conversion where
a low frequency source can be used to impulsively excite a high
frequency oscillating harvester. In these cases performance is
directly related to the efficiency.
Figure 7. Variation of phase angle between base force and displacement (103 kΩ load)
(1)
5. Experimental Setup
Such performance measurements can be used to map out
the characteristics of the system and compared to models to
implement optimisation strategies to maximise performance [2,3].
However, they don’t provide direct information on the energy
transfer and losses within the system. An important parameter in
this respect is efficiency, defined as the ratio of energy or power
OUT to energy or power IN to the energy harvester.
Vibration harvesting systems are not limited to the Carnot
efficiency as is the case for a heat engine such as a thermoelectric
harvester. Piezoelectric harvester efficiency can, in theory,
approach 100%. A small harvester attached to a large inertia
vibration source doesn’t significantly load the vibrating system
and the energy drawn from the system is small. However, overall
system performance can be boosted by improving efficiency,
particularly when other design constraints such as the vibrating
volume are taken into account [4].
Input mechanical energy was evaluated from the displacement
at the first maximum after the initial impulse and the spring
constant according to Eq.1. The electrical energy was obtained by
integration of the power dissipated in the resistor over the period
from the deflection maximum to the end of the decay (Eq.2). The
efficiency was obtained as the ratio of the two energies (Eq.3).
(2)
Figure 8. Power in and power out as a function of frequency (103 kΩ load).
(3)
Results are shown for varying load resistance in Figure 6.
Figure 7 shows that as resonance is reached, a phase angle
of approximately 35° is observed between the force and the
displacement. The power out to power in are shown in figure 8.
Both show a peak at the resonant frequency of 26.4 Hz with a
peak output power of approximately 16 µW for an input power
of 660 µW. This equates to an efficiency at resonance of 2.4%, in
good agreement with the results from the impulse experiment
7. Conclusions
Efficiency is an important parameter in the characterisation of
vibration energy harvesting systems, both in terms of the loading
of the source of the energy and in device optimisation and
minimisation of losses in energy transfer across system boundaries.
Figure 4. Experimental Setup.
The experimental setup is shown in Figure 4. A vibration motor
provided mechanical excitation to the energy harvester. The
transmitted force was measured using a Dytran 1053V1 dynamic
force transducer with a Kistler 5114 coupler. The root and tip
displacements were measured using two MEL laser triangulation
sensors. The piezoelectric cantilever was a commercial ceramic
bimorph fitted with a 1 g tip mass. Electrical output was
recorded using a National NIPXI4461 (1MΩ) in parallel with a
programmable resistance load.
Figure 6. Efficiency obtained from impulse response as a function of load
resistance.
Because the decaying oscillation occurs at the resonant
frequency of the cantilever, it is expected that a similar efficiency
would be achieved in continuous resonant operation, but
there is no experimental confirmation of this. We therefore
measured efficiency under continuous sinusoidal vibration by
also measuring the force input. The input mechanical power,
Two methods of measuring efficiency are compared showing that
measurements from an impulse excited decaying oscillation are
comparable to those obtained from direct measurement under
sinusoidal vibration. The impulse excitation method is simpler to
implement, so these results validate the interpretation of impulse
efficiency measurements for continuous excitation.
There are a number of sources of error that limit the accuracy of the
technique. These include accurate measurement of the stiffness,
distributed mass loading, extraneous contributions to phase of the
transmitted force and non-linear effects.
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