Energy Harvesting Cycles of Dielectric ElectroActive Polymer Generators Emmanouil Dimopoulos

Department of Energy Technology

Electrical Energy Engineering

Aalborg University

Denmark, Aalborg 9220

Email: em.dimopoulos@gmail.com

Ionut Trintis Department of Energy Technology

Electrical Energy Engineering

Aalborg University

Denmark, Aalborg 9220

Email: itr@et.aau.dk

Stig Munk -Nielsen Department of Energy Technology

Electrical Energy Engineering

Aalborg University

Denmark, Aalborg 9220

Email: smn@et.aau.dk

Abstract-Energy harvesting via Dielectric ElectroActive Poly­mer (DEAP) generators has attracted much of the scientific interest over the past few years, mainly due to the advantages that these smart materials offer against competing technologies , as electromagnetic generators and piezoelectrics. Their higher energy density, superior low-speed performance, light-weighted nature as well as their shapely structure have rendered DEAPs candidate solutions for various actuation and energy harvesting applications. In this paper, a thoroughly analysis of all energy harvesting operational cycles of a DEAP generator, coupled to a non-isolated power electronics converter, is conducted and for the first time experimental results for each one of them are presented.

I. INTRODUCTION

Dielectric ElectroActive Polymers (DEAPs), produced by

Danfoss PolyPower AlS [1], consist of a thin dielectric

elastomer film, i.e. silicone, enclosed by two corrugated,

highly conductive and shapely silver electrodes, which in turn

determine the compliant and the stiff planar directions of the

film. Typically, two elastomer films are combined to form one

DEAP element with one electrode per side as seen in Fig. 1.

(a) (b)

Fig. l. Structure of a (a) single elastomer film (b) typical DEAP element.

Under certain operational conditions a DEAP element is

capable of acting either as an actuator, converting electrical

energy to mechanical, or as a generator, converting mechanical

energy to electrical one.

A. Actuator Mode Upon application of voltage across the electrodes, the film

elongates in the compliant direction, transversely to the inter­

nal E-field, expanding in area and contracting in thickness, due

to the Maxwell stress tensor. The actuation mode of a DEAP

element, assuming an isochoric deformation and a fixed width

material, i.e. w, is visualized in Fig. 2.

f------ 1-(a)

A+dA

+ ++++++++++++++++++++++ I "..:. h+dhI Elastomer film , /

----------------------- '� I f+df I (b)

Fig. 2. Actuator mode of the DEAP element (a) initial state (b) final state.

As the area of the electrodes increases (dAjdt>O) , re­

pelling charges are sparsely distributed, while as the thickness

decreases (dhjdt<O) , attracting charges are equilibrated in

closer proximity, acting in favor of the electrostatic forces,

thus converting electrical energy into mechanical energy.

B. Generator Mode

From an electrical point of view the DEAP element, as it

is illustrated in Fig. 1, is a parallel plate variable condenser,

as its capacitance depends highly on the strain imposed to the

material. Indicatively, for an isotropic material,

C( ) = Er . EO . A(t) t

h(t)

E . A(t)

h(t)

dC

dt

E dA E ' A dh

h'dj----,-;2' dt

(1)

(2)

where E is the permittivity of the elastomer, expressed as

the product of the relative permittivity of the elastomer Er, and the vacuum permittivity EO. Denoted with A and hare

the, strain dependent, area and thickness of the parallel plate

condenser respectively.

Allowing a pre-charged and pre-stretched DEAP element to

contract, as seen in Fig. 3, will inevitably lead to an increment

of its electric potential energy.

978-1-4673-2421-2/12/$31.00 ©2012 IEEE 374

A+dA

I------ f+df-(a) (b)

Fig. 3. Generator mode of the DEAP element (a) initial state (b) final state.

As the area of the electrodes decreases (dAjdt<O) , re­

pelling charges are densely distributed, while as the thickness

increases (dhjdt>O) , attracting charges are remotely equi­

librated, working oppositely to the electrostatic forces, thus

converting mechanical energy into electrical energy.

According to (2) during the relaxation phase the capacitance

decreases. However, neglecting leakage losses, the internal

electrical charge of the element can be considered constant

Q = C(t) . V(t) (3)

and hence the voltage V increases. The electric potential

energy stored inside a variable condenser is a function of the

electric potential difference across its electrodes, along with

its capacitance and it is given by

(4)

Where it becomes apparent that even though the capacitance

decreases, the electric potential energy Ue (t) increases, as it

is a function of the voltage squared.

C. State of the art Initially dielectric elastomers, made by silicone,

polyurethane or acrylic substances, were used as actuators,

converting electrical energy to mechanical energy, mainly

due to their tremendous demonstrated strains (over 300%)

and high energy densities. Indeed in [2], the elastic energy

density of a circular acrylic elastomer was measured equal to

3.4J/g, which is much higher than any other field activated

material as piezoelectrics, i.e. 0.13J/g for advanced single

crystal ceramics, or electromagnets where the energy density

is around 0.04J/g with typically lower material densities [3],

[4].1

During the last decade research over the DEAP ability to

operate as a generator, converting mechanical energy to elec­

trical energy, was also sparked. The high energy density during

generation mode, light-weighted nature, good low-speed per­

formance, as well as the good impedance matching to several

energy sources, are only few of the advantages triggering that

interest. Several energy harvesting infrastructures have been

considered in the literature, highlighting the applicability of the

DEAP technology. In [5], numerous potential applications of

DEAP generators, as well as their advantages over competing

electromagnetic and field activated technologies can be found.

lThe typical density of dielectric elastomer materials is found approxi­mately equal to Ig/cm3, while for steel is close to 8g1cm3.

In 2005 an acrylic heel-strike generator, converting human

motion into electrical energy, characterized by an energy

density of 400mJ/g, reported an energy output of 800mJ/step

[4], [5]. Later, generation of 28t.d, via an acrylic elastomer

without any kind of external mechanical system imposing

stress on the element, was documented in [6].

Employing a typical non-isolated bidirectional buck-boost

power electronics converter to a DEAP generator an energy

production of 26.7mJ/cycle was achieved in [7]. Finally, a

simple self-priming circuit, overcoming the need for a peri­

odical external charge supply, was proposed in [8], generating

4.4mJ/stroke with an energy density equal to 12.6mJ/g.

The optimum way to harvest electric potential energy from

a DEAP generator, during the relaxation phase depicted in

Fig. 3, has itself sparked some research. Until present, three

different operational cycles have been considered; namely the

Constant Charge (cq, the Constant Voltage (CV ) and the

Constant E-field (CE), all of them titled by the variable kept

"constant" during the relaxation phase.

In [9], [10] a theoretical analysis between the three op­

erational cycles, based on idealized models, was conducted,

indicating that the CE is the most energy efficient cycle, with

the CC and CV demonstrating inferior performance. More,

the CC cycle was shown to offer minimization of the leakage

losses. However, it has not yet been possible to validate those

outcomes by experimental measurements.

The aim of this paper is to present and analyze the non­

ideal operational cycles accompanied - for the first time -

by respective experimental results. In Section II, the funda­

mental operational cycle, i.e. CC, of a DEAP generator is

thoroughly presented and all differences among the operational

modes are highlighted. In Section III, the laboratory setup is

demonstrated and in Section IV experimental measurements

are presented and discussed.

II. ENERGY HARV ESTING CYCLES

The analysis of the distinct energy harvesting cycles will

be based upon monitoring the rate of change of numerous

variables characterizing the material behavior, i.e. capacitance

C(t) , voltage V(t) , electric field strength E(t) and the electric

potential energy Ue(t), as functions of the condenser area rate

of change dAj dt. Assuming an isochoric deformation for the

DEAP element,

Volume = A· h where dVolumejdt = 0 = > (5)

A· �� = -h· �� (6)

where Volume denotes the elastomer volume. Equation (2)

can now be simplified by substitution of (6) into

dC c dA - = 2 · _ ·-.

dt h dt (7)

Respectively, the voltage formula can be derived by a

combination of (1), (3) and (6) as follows,

375

V(t) = Q (t) . h(t)

E . A(t)

dV Q dh Q . h dA

dt E . A .

dt - E ' A 2 .

dt dV Q . h dA

dt =

-2· E ' A2 .

dt'

(8)

(9)

(10)

Accordingly, the electric field of a condenser is defined as

the ratio of the voltage across its electrodes over its thickness.

dE

dt

E( ) = V(t)

t h(t)

1 dV V dh

h .

dt - h2 . dt'

(11)

(12)

Substituting (6) and (10) into (12) leads in the simplified

formula

dE V dA --- . -

dt A· h dt (13)

Finally, by multiplication of the electrostatic field energy

density UE formula with the DEAP volume, the desired

relationship for the electric potential energy can be attained,

1 2 Ue = UE . Volume = 2" . E . E . Volume (14)

dUe dE dt = E . E . Volume' dt (15)

d�e = -E ' E . V . �� (16)

Equations (7), (10), (13) and (16) can now be used to

thoroughly unfold all aspects of the non-ideal harvesting

cycles. It is evident that a similar procedure can generate the

respective equations for the capacitance C(t) , voltage V(t) , electric field strength E(t) and electric potential energy Ue(t),

as functions of the condenser thickness rate of change dh/dt, instead of dA/ dt.

A. Constant Charge The fundamental harvesting cycle, corresponding to CC is

presented in Fig. 4 and Fig. 5. It consists of four transitions

commencing and ending fromlto point 1 moving in an ascend­

ing order.

Ue [Jl I Constant Charge Cycle I

Uemax,charge

uemi"di'�:'::" :::::::::�::r_�_: ___ 1�: ___ : .. _:: .. :: .. _:: ... ::: __ � .. . :::-_ .. � .. �_ .. ",, ____ J l l Stretch;ng

3

Ummin Ummin,relax Ummax,stretchUmmax Urn [Jl

Fig. 4. Electrical energy Ue versus mechanical energy Urn during CC cycle.

As previously stated, the CC-CV-CE cycles differ mainly

during the transition from point 3 to point 4, i.e. relaxation

phase. Hence, the description of the fundamental working cy­

cle can provide a solid base for comparison, if all rest distinct

characteristics between the cycles are adequately highlighted.

After n cycles the DEAP element is at point 1. The general

analysis conducted in this paper is based on the conjecture

that a non-isolating power electronics converter is employed

to enable the DEAP generator to operate under the investigated

cycles. Hence, the voltage across the element cannot be

equalized to zero at point l. Yet, total discharge of the element

at the end of each working cycle is applicable, by employing

other topologies incorporating a transformer.

As the voltage is not zero, there is an amount of internal

charge stored inside the element and thus there is a residue of

electrical energy. In addition, as pre-stretching the element en­

hances its maximum strain and electrical breakdown strength

[11], the DEAP is typically pre-stretched during a generation

cycle and thus there is also an amount of mechanical energy

stored inside the element too.

l) Transition 1 -+ 2: An external energy source imposes

mechanical stress on the DEAP element, which operates as an

actuator elongating in the compliant direction. An amount of

the internal electric potential energy is converted to mechanical

energy and thus as seen in Fig. 4 and Fig. 5, both the electrical

energy and the E-field experience a drop, as the mechanical

energy and strain increase. Mathematically, actuation mode

implies dA/dt>O and hence according to (13) the E-field

decreases and so does the electric potential energy (16).

E [V/ml I Constant Charge Cycle I Ebrk ____ oo •••••••••••••• ___________ ••••••••••• _____________ •••• 0 ••••••• ______ _

Emax --------------------�

Emax,charge Discharging

l r--___ -' Stretching

A[ml

Fig. 5. E-field versus strain during CC cycle.

As the DEAP element is electrically isolated and has

relatively low leakage losses, the amount of electrical energy

converted into mechanical one can be calculated by equating

the charges of points 1 and 2, i.e. Q l = Q 2 ,

1 2 C1 6.El--+2

= 2" . C1 . VI . (C2 -

1) ( l7)

where it becomes apparent that this undesired energy con­

version can be limited if VI is set to zero.

2) Transition 2 -+ 3: Equation (7) indicates that the capac­

itance of the DEAP generator increased during the previous

transition. Therefore, a power electronics converter is now

376

coupled to the element in order to boost its voltage to a higher

level, i.e. V3, increasing its electric potential energy, as well

as its E-field strength.

As now the DEAP element stores electrical charge it be­

haves again as an actuator. Put differently, during the boosting

phase the elastomer area increases, while its thickness de­

creases, similarly to the transition between points 1 and 2.

If the element is free to expand on its own "will" an increase

in both the capacitance, as well as, the stored mechanical

energy is anticipated. More precisely, when point 3 is reached,

point of maximum strain Amax , the DEAP capacitance and

mechanical energy attain their maximum value.

3) Transition 3 ---+ 4: Now the DEAP element is let free

to relax, releasing part of its mechanical energy. In the CC

cycle there is no interaction between the DEAP element and

the power electronics converter during the relaxation phase

and thus in this transition the internal charge of the element

remains constant.

As the material contracts, its area decreases (dAjdt<O) leading to a decrement in the capacitance value (7) but to an

increment in the voltage across the element electrodes (10). In

addition, according to (13) and (16) the E-field strength and

electric potential energy increase. In other words, during the

relaxation phase part of the mechanical energy initially stored

in the system is being converted to electrical energy, which

reaches its maximum value at point 4. Equating charges as

during transition from point 1 to point 2, straightforwardly

leads to

1 2 C3 6.E3--+4 = - . C3· V3 . (- - 1) (18)

2 C4

from where it is inferred that the amount of the harvested

electrical energy depends strongly on the level that the DEAP

voltage was boosted to, during transition among points 2

and 3. It also depends on the capacitance variation of the

DEAP generator during the relaxation phase. However, both

the voltage and the field strength at point 3, must be limited

well below the breakdown limits, as they both increase during

the transition from point 3 to point 4. Following a similar

procedure as previously and assuming that the increasing

voltage reaches its breakdown value, i.e. V4 = Vbrk. can lead

to

C4 C4 V3 =

C3 . Vbrk where

C3 < 1 (19)

indicating the boosting phase limitation of the CC cycle.

4) Transition 4 ---+ 1: In this last transition the DEAP

element is re-coupled to the power electronics converter which

now bucks the voltage across the element down to VI , harvest­

ing the electric potential energy stored inside it.

As electrical charge is now drawn out of the DEAP, it

behaves again as a generator. Put differently, during the

bucking phase the elastomer area decreases, while its thickness

increases, similarly to the transition between points 3 and 4.

Once again, if the element is free to expand on its own "will"

a decrease in both the capacitance (7), as well as in the stored

mechanical energy is anticipated. More precisely, when point 1

is reached, point of minimum strain, i.e. Amin, the mechanical

energy and DEAP capacitance attain their minimum values.

B. Constant Voltage In the CV cycle, during the relaxation phase, the voltage

across the DEAP element is controlled inside a pre-defined

hysteresis band [Vmin, Vmax ] as illustrated in Fig. 6.

Ue [J] I Constant Voltage Cycle I

Vm .. Uema �� ••••••••••••••••••••••••••••••••••••• n •••••••••••••• II.······

Uem .. ,<h"" ••••••••••••••••••••••••••••••• �::�,'n�" .. ,.:.::::: .�::" ':'3 Vmm

uemin.dis�::jn ::::::::::�f�. __ .+ ___ .. ___ ... __ ... __ ... ___ .. __

: : Stretching

! l

iCha,g;ng

12 1 Ummax.stretch Ummax Um [J]

Fig, 6, Electrical energy Ue versus mechanical energy Um during CY cycle.

Specifically, during transition from point 2 to point 3, the

DEAP element is charged up close to the electric field strength

breakdown value as depicted in Fig. 7. Point 3 is now in a

higher electric potential energy level than the respective point

in the CC cycle. Subsequently, the element is let free to relax

and thus its voltage increases. When Vmax is reached the buck

function of the converter is triggered, harvesting energy from

the DEAP by discharging it to the voltage level of Vmin. Then

the voltage of element is let free to increase again until the

next buck triggering instance. Finally, when the end of the

relaxation phase is sensed, the voltage of the DEAP is bucked

down to VI .

E [Vim] I Constant Voltage Cycle I

'-!; ���:;����T�=' :r Discharging

1 r------..I ;::.'2 Stretching

Charging

Fig, 7. E-field versus strain during CY cycle,

A[m]

As the element relaxes, contracting in area and expanding

in thickness, its E-field (13) and electric potential energy (16) tend to increase, as in the case of the CC cycle. However,

when the buck operation is triggered and the element is

discharged both the E-field and the Ue decrease. A deformation

of the element similar to the one previously described in the

transition from point 4 to point 1 is anticipated, as the element

377

behaves as a generator when charge is withdrawn from it.

Thus, every discharging instance during the relaxation phase

will slightly reduce the mechanical energy stored inside the

element.

C. Constant E-field

In the CE cycle, during the relaxation phase, the internal

E-field strength of the DEAP generator is controlled inside

a pre-defined hysteresis band [Emin, Emax L as illustrated in

Fig. 8.

U. [J] I Constant E-field Cycle I Relaxing Uemax ------····--···----·r.···.· ...... --- Emax

Ue 4 · m ... <h"" ................ OJJ+-i"",: ........ --"'''-- -''''<---'''"- �j 3" Emm

I,charging Uemin,discharge -••••• -••• - �-t::'j::��="""'_...J Uemio ...... ·-.... ·t ...... r .. ·s;

;�·t�hi

�� ........ - i 2/

Ummin Ummin,relax Ummax.stretch Ummax Urn [J]

Fig. 8. Electrical energy Ue versus mechanical energy Urn during CE cycle.

The operating principle is similar to the CV cycle as during

transition from point 2 to point 3 the DEAP element is charged

up close to the electric field strength breakdown value as

illustrated in Fig. 9. When the element relaxes its E-field

increases until it reaches Emax . Then, the buck function of

the converter is triggered, harvesting energy from the DEAP

by discharging it until the E-field equals Emin. The element

relaxes again until the next bucking instance. Once the end of

the relaxation phase is sensed the voltage of the element is

bucked down to VI , similarly to both CC and CV cycles.

E [Vim]

Ebrk Em ..

Emax,charge, Emin

Fig. 9.

I Constant E-field Cycle I

1 r--___ --J

A[m]

E-field versus strain during CE cycle.

The fundamental difference between CE and CV harvesting

cycles, is that during the relaxation phase of the foremost

one the electric potential energy of the DEAP element is

not decreasing, as in the case of the latter one. Instead, it

follows the exact variation of the E-field strength as dictated

by equation (16) and illustrated in Fig. 8.

In addition, Fig. 5 indicates that during the CC cycle the

maximum value of the electrical field strength Emax is reached

at the end of the relaxation phase. Oppositely, Fig. 7 illustrates

that, in the case of CV cycle, the respective maximum value

Emax is reached at the first bucking instance during the

relaxation phase. Fig. 9 on the other hand, referring to the

CE cycle, shows that the Emax value of the hysteresis band

corresponds to the maximum value of the electric field strength

during the entire cycle.

III. EXPERIMENTAL SETUP

The experimental setup illustrated in Fig. 10, is a mechan­

ical test rig, consisting of an induction motor, coupled to the

DEAP element via a circular disc. The induction machine

is controlled by means of speed and so the DEAP element

position is controlled. Imposing stress on the DEAP generator,

by rotating the motor with constant speed, leads to a sinusoidal

variation of its capacitance value.

The DEAP element deforms linearly and uniaxially towards

a single direction, implying that the deformation described in

Section II, associated with the charging and discharging phases

can not be visualized by this setup. Put differently, the element

is not allowed to expand or to contract on its own "will" and

hence the deformation applicable during transitions from point

2 to point 3 and from point 4 to point 1 can not be reflected

in the experimental measurements.

Fig. 10. Laboratory setup in Aalborg University. Denmark.

An auxiliary, electrically isolated, DEAP element is also

installed back-to-back with the main elastomer, in order to

provide real-time deformation data. Those data are in turn used

by the Power Take Off (PTa) unit, seen in the top of the rig in

Fig. 10, to estimate the real-time values of the DEAP strain and

thickness. More specifically, the capacitance of the auxiliary

element is monitored and its derivative is computed. A sign

change in the derivative indicates maximum/minimum stretch

positions.

In addition, as the voltage across the DEAP element is also

monitored, an estimation of the electric field strength value

can be attained, if homogeneity is assumed. Finally, the PTa

unit consists of one boost and one buck converter, which are

triggered based on the data acquired by the auxiliary DEAP

element.

378

IV. EXPERIMENTAL MEASUREMENTS

Operating the laboratory setup presented in Section III,

graphs, illustrating the DEAP voltage and E-field strength as

functions of the applied strain, can be composed for all distinct

harvesting cycles. Table I presents the operating conditions of

the conducted experiments.

TABLE I OPERATING CONDITIONS

Cycle Hysteresis Band

Const. Charge Const. Voltage

Const. E-field

800V 1200V

1200V

350V 500V

500V

V E [1100, 1200]V

E E [12, 13]V/um

For all three harvesting cycles it was decided to discharge

the element to a rather high VI voltage level, in order to

appreciate the conversion of electrical energy to mechanical

one during the stretching period. Additionally, and for the

sake of the conducted analysis' validity, a common maximum

stretch of 32.5% was set among all energy harvesting cycles.

Figs. 11 and 12 depict the measurements acquired during

several CC cycles.

1200 tOOO

� 800 Q) � 600 (5 >

400

" "

Constant Charge Cycle Voltage versus Strain

4;---� :: --------- 3 I-I ---------------" " " '" ,I "

lL�.-.,... \1 �--�..,.----���-�� ..... __ ..,.1l.2 2005 10 15 20 25 30 35

Strain [%1

Fig. 11. CC cycle Voltage versus Strain measurements.

As expected, and in accordance with Figs. 4 and 5, during

the stretching phase the DEAP voltage and E-field strength

decreased, from 350V-4V/um to approximately 250V-2.5V/um

respectively. Further, the strict limitation bonded with the

charging phase became apparent.

Constant Charge Cycle E-field versus Strain 14,---�----�----�----�----�--- -,

ElO � "0 8 Q; "j' 6 w

4

10 15 20 25 Strain [%1

30

Fig. 12. CC cycle E-tield versus Strain measurements.

35

Undoubtedly, even if the V3 voltage was only set equal to

800V (E3 approximately equal to 9V/um), still at point 4 it

reached its maximum, i.e. 1200V (E3 exceeding 12V/um),

indicating that use of (19) is of paramount importance prior

to any CC cycle operation.

Respective measurements for CV cycles are illustrated in

Figs. 13 and 14. Similarly to the CC cycles, during the

stretching period an amount of the internal electric potential

energy is being converted to mechanical energy. However now,

at point 3, the voltage was boosted to 1200V rather than 800V,

due to the fundamental advantage of the CV cycle, which

allows the voltage swings across the DEAP generator to be

effectively controlled.

Indeed, as the DEAP element was relaxing, its voltage was

sustained inside the pre-defined hysteresis band, by triggering

the buck converter five times. As predicted by Fig. 7 a

decrement in the E-field strength during transition from point

3 to point 4 can be visualized in Fig. 14.

Constant Voltage Cycle Voltage versus Strain 1400,---�----�----�----�----�--_

1200 � 1000 Q) F 800 g 600

400

10 15 20 25 Strain 1%1

30 35

Fig. 13. CV cycle Voltage versus Strain measurements.

In addition and in contrast with what was depicted in Fig.

12, during the CV cycle experiments the maximum field

strength was reached at the first bucking instance; during

the relaxation phase. Undeniably, after reaching Emax , i.e.

13.5V/um, for the first time, at approximately 30% strain,

the E-field strength remained lower during the rest of the

periodical cycling.

Constant Voltage Cycle E-field versus Strain 14,---�----�----�----��,-��--,

4 �.-. ... '\-_ ..... ,;'i� ... ____ �1,;------_� �7---\'�,\3 12 IJ 10 'AI \

I' \ \\ '[ 10 � 8 Qj "j' 6 w

4

�I \ II

�L" . \\ ,( 1 12

��--�10�--�15,---�2�0----�2�5----�3�0 --�35 Strain 1%1

Fig. 14. CV cycle E-tield versus Strain measurements.

Figs. 15 and 16 depict the corresponding experimental

measurements for the CE cycles. Similarly, to the CC and CV

cases, a reduction in the electric potential energy during the

transition between points 1 and 2 can be seen. According to

the CV experiments during the charging phase the voltage was

boosted to 1200V. The PTO unit, estimated the E-field strength

by dividing the sensed DEAP voltage with the evaluated

thickness of the elastomer, as it was computed by the data

provided by the auxiliary DEAP element.

379

Hence, the E-field could be sustained in the pre-defined

hysteresis band by triggering the buck converter five times.

As discussed during Section II, the maximum E-field strength

corresponds to the Emax as it was pre-set in Table I.

Constant E-field Cycle Voltage versus Strain 1400�--�----�--��--��--�----�

1200

� 1000 Q) 0> 800 .l!! � 600

400

2oo5 L----1io�--�IL

5----2�0�--�2L

5----3�0�--�35

Strain [%]

Fig. IS. CE cycle Voltage versus Strain measurements.

In Figs. 11-16 the slope of the increasing/decreasing voltage

and E-field strength, during the charging /discharging phases,

comes sometimes in direct contradiction with the expectations

formed based on the analysis of Section II.

While mapping the mechanical limitations of the experi­

mental setup it was mentioned that neither the actuator mode

during the charging phase nor the generator mode during

the discharging phase, would be visible in the experimental

data presented in this paper, due to the limited degrees of

freedom of the DEAP generator, as their were imposed by the

mechanical test rig itself.

However, the visualized slopes in Figs. 11-16 cannot be

justified only by the mechanical system limitations. Rather

than assuming that the DEAP is in generator mode, instead of

actuator and vice versa, this contradiction should be considered

as an effect imposed by the interplay of the mechanical system

limitations with the respective limitations of the electrical

system.

Constant E-field Cycle E-field versus Strain 14,---�----�----�----�----�----, 12

EIO -2 ;. 8 Qi

X 6 4

25L---�10�---1�5�--�2�0----�2�5----3�0�--�35 Strain [%]

Fig. 16. CE cycle E-field versus Strain measurements.

Indeed, in Figs 15 and 16 for example, the boost con­

verter was switched at a rather low frequency, i.e. 4kHz,

and therefore the charging phase was not concluded prior

to the relaxation phase commencement. Oppositely, the buck

converter was switched at a higher frequency, i.e. 20kHz,

and so the element was successfully discharged before the

beginning of the stretching phase.

As thoroughly explained all energy harvesting cycles are

based on the precise, real-time monitoring of the strain state

of the DEAP element. In addition, the CV and CE cycles

need to monitor the voltage and E-field progression during

the relaxation time respectively.

Seen from the DEAP energy harvesting point of view the CE

cycle has been theoretically shown to offer higher energy gains

in comparison with the CV and CC cycles [9], [10]. Further, as

the primary DEAP state control, common in all cycles, is based

on continuously monitoring the E-field strength value, safely

discharging the generator right before the E-field reaches the

breakdown value, the CE cycle utilizes the primary control

system more effectively.

Seen from the power electronics point of view however, the

CV cycle offers the advantage of directly configurable DEAP

voltage swings, thus simplifying the selection of the power

electronics converter switches. An advantage, which can be

indirectly associated with the CE cycle as well.

V. CONCLUSION

A short introduction in the DEAP technology has been

achieved. In addition, all energy harvesting cycles considered

so far, i.e Constant Charge, Constant Voltage and Constant E­

field, have been thoroughly analyzed accompanied by respec­

tive formulas, indicating the state of several DEAP parameters

during each cycle. Finally, experiments on all cycles have

been presented and discussed, confirming the validity of the

conducted analysis. Expectations around this new promising

energy harvesting field are quite high and additional research

over its applicability in practical applications must be con­

ducted in the forthcoming years.

ACKNOWLEDG MENT

The authors acknowledge the contribution and support of

Danfoss PolyPower AlS. Thanks to Carsten Karup Nielsen

for debugging and repairing the PTa units.

REFERENCES

[1] Danfoss PolyPower A/S website, www.polypower.com [2] R. Pelrine, R. Kornbluh, Q. Pei, J. Joseph, "High-Speed Electrically

Actuated Elastomers with Strain Greater Than 100%", Science 287 (5454), pp. 836-839, 2000.

[3] S. Park and T. Shrout, "Ultrahigh Strain and Piezoelectric Behavior in Relaxor Based Ferroelectric Single Crystals", 1. Applied Physics 82, pp. 1804-1811, 1997.

[4] R. Pelrine, R. Kornbluh, J. Eckerle, P. Jeuck, S. Oh, Q. Pei, S. Stanford, "Dielectric elastomers: generator mode fundamentals and applications", Smart Structures and Materials 2001: ElectroActive Polymer Actuators and Devices, ed. Y. Bar-Cohen, Proc. SPIE 4329, pp. 148-156, 2001.

[5] H. PrahJad, R. Kombluh, R. Pelrine, S. Stanford, 1. Eckerle, S. Oh "Poly­mer Power: Dielectric Elastomets and Their Applications in Distributed Actuation and Power Generation", Proc. ISSS, 28-30 July, 2005.

[6] C. Jean-Mistral, S. Basrour, J. J. Chaillout and A.Bonvilain, "A Complete Study of ElectroActive Polymers for Energy Scavenging: Modelling and experiments", DTIP 25-27 April 2007.

[7] D. Jens, S. Munk-Nielsen, R. 0. Nielsen, "Energy harvesting with di­electro active polymers", PEMD 2010.

[8] T. McKay, B. O'Brien, E. Calius, I. Anderson, "Realizing the potential of dielectric elastomer generators", EAPAD 2011.

[9] C. Graf, J. Maas, D. Schapeler "Optimized energy harvesting based on electro active polymers", ICSD, 4-9 July 2010.

380

[10] B. Czech, R.Y Kessel, P. Bauer, "Energy harvesting using dielectric elastomers", EPE-PEMC, 2010.

[11] G. Kofod, "The static actuation of dielectric elastomer actuators: how does pre-stretch improve actuation?", 1. Phys. D: Appl. Phys. 41, 2008

381