Lowest of AC–DC power output for electrostrictive polymers energy harvesting systems

Optical Materials 36 (2014) 80–85

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Lowest of AC–DC power output for electrostrictive polymers energy harvesting systems Mounir Meddad a,b, Adil Eddiai a,c, Abdelowahed Hajjaji d,⇑, Daniel Guyomar a, Saad Belkhiat b, Yahia Boughaleb c, Aida Chérif a,b a

Laboratoire de Génie Electrique et Ferroélectricité (LGEF), INSA LYON, Bat. Gustave Ferrie, 69621 Villeurbanne Cedex, France DAC HR Laboratory, Université Ferhat Abbas, 19000 Sétif, Algeria Département de Physique, Faculté des Sciences, Laboratoire de Physique de la Matière Condensée (LPMC), 24000 El Jadida, Morocco d Ecole Nationale des Sciences Appliquees El Jadida, Université d’el Jadida, EL Jadida, Morocco b c

a r t i c l e

i n f o

Article history: Available online 9 July 2013 Keywords: Electrostrictive polymer Energy harvesting AC–DC converter

a b s t r a c t Advances in technology led to the development of electronic circuits and sensors with extremely low electricity consumption. At the same time, structural health monitoring, technology and intelligent integrated systems created a need for wireless sensors in hard to reach places in aerospace vehicles and large civil engineering structures. Powering sensors with energy harvesters eliminates the need to replace batteries on a regular basis. Scientists have been forced to search for new power source that are able to harvested energy from their surrounding environment (sunlight, temperature gradients etc.). Electrostrictive polymer belonging to the family of electro-active polymers, offer unique properties for the electromechanical transducer technology has been of particular interest over the last few years in order to replace conventional techniques such as those based on piezoelectric or electromagnetic, these materials are highly attractive for their low-density, with large strain capability that can be as high as two orders of magnitude greater than the striction-limited, rigid and fragile electroactive ceramics. Electrostrictive polymers sensors respond to vibration with an ac output signal, one of the most important objectives of the electronic interface is to realize the required AC–DC conversion. The goal of this paper is to design an active, high efficiency power doubler converter for electrostrictive polymers exclusively uses a fraction of the harvested energy to supply its active devices. The simulation results show that it is possible to obtain a maximum efficiency of the AC–DC converter equal to 80%. Premiliminary experimental measurements were performed and the results obtained are in good agreement with simulations. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Energy harvesting devices converting ambient energy into electrical energy have attracted much interest in both the military and commercial sectors. Some systems convert motion, such as that of ocean waves, into electricity to be used by oceanographic monitoring sensors for autonomous operation. Another application is in wearable electronics, where energy harvesting devices can power or recharge cell phones, mobile computers, radio communication equipment, etc. All of these devices must be sufficiently robust to endure long-term exposure to hostile environments and have a broad range of dynamic sensitivity to exploit the entire spectrum of wave motions. Much has been written about the benefits of wireless sensors and the potential of energy harvesting to provide power for the life of these devices. Disposable, long-life batteries will continue to be used in wireless sensor applications but, as the technologies mature, energy harvesting will create some shift ⇑ Corresponding author. Tel.: +212 658390619. E-mail addresses: [email protected], [email protected] (A. Hajjaji). 0925-3467/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optmat.2013.05.008

in battery usage from primary to rechargeable batteries for applications that need higher power over the life of the device. The greatest potential, however, lies in a new class of devices that will be battery-free and thus enable applications that would have been prohibitively expensive due to the maintenance cost of eventual and repeated battery replacement. Energy harvesting can be obtained from different energy sources, such as mechanical vibrations, electromagnetic sources, light, acoustic, air flow, heat, and temperature variations [1–4]. The tremendous advances in polymeric material technology have led to the development of various processing techniques that make possible the production of polymers with tailormade properties (mechanical, electrical). Such materials enable the creation of new designs in a cost-effective fashion with small size and weight. Thanks to their flexibility, processability and high productivity, electrostrictive polymer belonging to the family of electro-active polymers, offer unique properties for the electromechanical transducer technology has been of particular interest over the last few years in order to replace conventional techniques such as those based on piezoelectric or electromagnetic [5–9]. Generally, electroactive polymers have the ability to induce strains that are as

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high as two orders of magnitude greater than the movements possible with rigid and fragile electroactive ceramics. Electroactive polymers materials have higher response speeds, lower densities and improved resilience when compared to shape memory alloys. Limiting factors to electroactive polymers are low actuation forces, mechanical energy density and lack of robustness. However, there have been reported successful applications in catheter steering elements, miniature manipulators, dust-wipers, miniature robotic arms and grippers. More recently research has been focused on electroactive polymer for energy harvesting [10–13], but none of them include discussion of AC–DC conversion, which is an important part of Energy harvesting. The objective of this paper was to develop a new prototype based on electrostrictive polymer for increasing the conversion AC–DC power. Electrostrictive polymers sensors respond to vibration with an ac output signal, it is necessary to convert this ac voltage to a dc voltage to power some electronic devices. Such the rectifier was realized with tow diode, the use of the new prototype increases the power converted 80% compared with the conventional structure thereby offset the power consumed by the rectifier circuit. The first part of this paper concerns the classical approach for harvesting energy with AC–DC rectifier, and the second part focuses on new prototype for increasing the power conversion. The performance of this configuration powering a resistive load and AC–DC conversion has also been analyzed. It was found that such a process rendered it possible to increase the converted power by 80%. 2. Principle Electrostriction is defined as a fourth rank tensor property and the basis of the electromechanical coupling mechanism in all insulators. The advantages that electrostrictors have over other actuator materials include low hysteresis of the strain-field response, no remnant strain, reduced aging and creep effects, a high response speed, and substantial strains at realizable electric fields [14–16]. Magnitudes of electrostrictive effects depend largely upon the type of material. From a practical point of view, electrostrictive stresses can either be seen as a benefit for electromechanical devices, when high strain materials are required or as a drawback in microelectronics and high voltage devices where the mechanical stresses and strains can lead to breakdowns in insulator materials. Electrostriction is defined as the quadratic coupling between strain and electric field, or between strain and polarization. Because the polymer was not piezoelectric, it was necessary to induce polarization with dc bias to obtain a pseudo–piezoelectric [17,18]. Tow configuration were compared in this study and are illustrated in Fig. 1. Is presented in (a) the conventional configuration with a rectifier circuit (c). An electrical load is connected to the output of the converter to calculate the power rectified. Consequently, when the polymer was excited both electrically and mechanically, the power harvested on the load depends on the current harvested. The key part of the proposed approach (b) was a metal form on which the polymer film was attached; consequently the cycle mechanical excitation will result in two cycles of deformation of the polymer with a frequency of 2fm. The main advantage of this configuration was its simplicity for increasing the conversion abilities of electrostrictive materials through a rectifier circuit. 3. Modeling This section aims at exposing a theoretical of the maximum output power that can obtained using the proposed configuration then, from the analytical power expression, the change in operating frequency between the two configurations that only takes into

account intrinsic parameter is derived. Electrostrictive is generally defined as a quadratic coupling between the polarization and the electric field, the strain Sij and electric flux density Dm are expressed as independent variables of the electric field intensity Em and stress Tij by the constitutive relation as [19]:

8 < Sij ¼ M ijkl Ek El þ sEijkl T kl

ð1Þ

: D ¼ eT E þ 2M E T i ijkl l kl ijkl k

where sEijkl is the elastic compliance, Mijkl is the electric field-related electrostriction coefficient, and eTijkl is the linear dielectric permittivity. An isotropic electrostrictive polymer film contracts along the thickness direction and expand along the film direction when electric field is applied across the thickness. Assuming a linear relationship between electric field and polarization P = (e – e0)E, with e the dielectric constant, it can be shown that the linearized constitutive equations for a electrostrictive film can be written as using the Vogt notation [12]:

(

S1 ¼ M 31 E23 þ sE11 T 1

ð2Þ

D3 ¼ eT33 E3 þ 2M31 E3 T 1 From the following equation:

 T1 ¼

S1  M 31 E23 sE11

 ) D3 ¼ E3



eT33 þ

2M 31 ðS1  M 31 E23 Þ sE11

 ð3Þ

Assuming uniform strain and electric field over the sample allows expressing the microscopic equation of the current:

I¼

Z

@D3 dA @t

A

ð4Þ

where A corresponds the area of the electrostrictive polymers. The induced current from the polymer can be related to the strain and electric field by:

#  Z "  2M @S1 E @E3 T 2M 31  31 @t 3 2 I¼ e33 þ E S1  3M31 E3 þ dA @t s11 sE11 A

ð5Þ

Here M31 is the apparent electrostrictive coefficient used to describe the experimental dependence of the current response of the material on the applied strain and electric field. In fact, when an electric field is applied to any material, it determine the charge displacement that leads to the field induced strain. The phenomenon is called ‘‘piezoelectricity’’. If the strain depends quadratically on the electric field, then tow phenomena ‘‘electrostriction’’ and ‘‘electrostatic’’ (Maxwell effect). 3 With @E and @S@t1 are times derivates from electrical field and @t strain. Assuming that the electric field features a dc bias and an component (E3 = Edc + Eac) the current expression turns to:

""

I¼A

eT33 2

# #   M231 2M31 S1 @Eac 2M31 @S1 2 ð E þE Þ þ þ ð E þE Þ ac ac dc dc @t @t sE11 sE11 sE11

ð6Þ The ac component of the electric field is generated by the load such as:

Eac ¼ 

RI e

ð7Þ

With e is the thickness of the sample. Therefore, the current expression turns to: " " # #  2    R 6M2 RI 2M31 S1 @I 2M31 RI @S1 I ¼ A  eT33  E 31 Edc þ þ þ E  dc e e @t e @t s11 sE11 sE11 ð8Þ

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Fig. 1. Diagram of the prototype circuit, (a) classical approach, (b) proposed approach, (c) diagram of the AC–DC conversion.

The modelling in the first step was realized as displays the 3 analysis of the short-circuit current in this cause @E ¼ 0, the short@t circuit current can be given by:

ICC ¼ 2M 31 YEdc

Z A

@S1 dA @t

ð9Þ

From Eq. (9) various solutions exist to improve the energy harvesting. One can for instance, increase the area of polymer, the bias electric field, or the strain, but also the frequency. Assuming the uniform strain, the relation between the displacement and the strain S1 in the polymer can be expressed by S1 ¼ DL0L.

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Fig. 2. Diagram of mechanical system configuration.

For the second configuration S1 can be determined by the parameters of the length sample film L0 and X which represents vertical displacement of the beam at the connection point From Eq. (9) it is clear that the current generated in the first configuration depending on fm by against in the second configuration with stretch for a single cycle of mechanical excitation, current generated depends on 2fm. The power harvested by the polymer can be expressed by:

Pharv ested / RI2CC

ð10Þ

The DC power consumed by the load is expressed by [20] in the form:

Pharv ested

dc

¼

16Rf

2

aEdc Sm  C p V d 2

1 þ ð4fC p Þ

2 ð13Þ

The choice of storage capacity, an important parameter in the design and performance of electrostrictive polymer generator.

where R is the electric load. It is clear that increasing the frequency leads to an increase in the power harvested (see Fig. 2). 4. Modelling of the ac conversion This first part is detailed in the work; we will apply this method on the proposed structure to improve our harvested system [9]. The expression of the voltage across resistor is expressed as:

V~ ¼

Cb aEdc R jx~S1 C b þ C p 1 þ jRC b C p x jx~S1 C þC p

ð11Þ

b

Power harvesting in the resistor R is equal to:

Pharv ested

ac

¼

~ V~   C b 2 V ¼ 2R Cb þ Cp

1þ



a2 R

2

RC b C p x C b þC p

x2 E2dc S2m J x~S1

2

ð12Þ

Fig. 4. Harvested power as a function of the load resistor in AC and DC regime for a deformation of 0.5% and a given electric field of 7 V/lm using the proposed structure.

Fig. 3. Equivalent circuit for charging a capacitor.

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M. Meddad et al. / Optical Materials 36 (2014) 80–85

Table 1 Gives the values of the polymer parameters used for a frequency of 6 Hz. Type

Permitivity

Pu 1%C

Young’s modulus (MPa)

11

Area A (cm2) 

34

1.6 4

Thickness e (lm)

Capacity blocked (lF)

Field Edc (V/lm)

52

0.4

5

Fig. 3 shows a simplified diagram of a storage circuit with a bridge rectifier.From this circuit:

8 > <

VðtÞ ¼ Iq Rd 1  e

> :

V 1 ðtÞ ¼ hV 1 i





t Rd C a

! 0 6 t 6 td

ð14Þ

hV 1 i Represents the average value of the voltage across the capacitor accumulate td, represents the conduction time for the two diodes. Rd represents the dielectric losses. The energy transfer occurs between the locked and the capacity storage capacity only when VðtÞ ¼ V 1 ðtÞ þ 2V dd . So (14) can be written as:



2V dd þ hV 1 i ¼ VðtÞ ¼ Iq Rd 1  e

Iq ¼ C a



t Rd C a

!

dðV 1 þ 2V dd Þ 1 dV 1 1 þ ðV 1 þ 2V dd Þ þ C d þ V1 dt Rd R1 dt

Fig. 5. Power harvested according to the load and the storage capacity.

ð15Þ

ð16Þ

In the Laplace domain Eq. (16) becomes:

  Iq 1 1 2V dd V1 þ ¼ ðC a þ C d ÞðpV 1  hV 1 iÞ þ þ Rd R1 p pRd

ð17Þ

If we set

Ce ¼ Ca þ Cd ¼

CbCp Rd þ C d et Re ¼ Cb þ Cp R1

Found the following equation:

V1 ¼

Iq Ce

Fig. 6. Harvested power according to the storage capacity.

dd  2V þ phV 1 i Rd C e  p p þ Re1C e

ð18Þ

This relationship is in the time domain: ta

V 1 ðtÞ ¼ V 1 ðaÞeR1 Cd

a6t6b

with

V 1 ðaÞ ¼



Iq Re  2V dd

 at d  atd Re  1  eRe Ce þ hV 1 ieRe Ce Rd

ð19Þ

Now we calculate the energy transferred to the load 1 W1 ¼ R1

"Z  #  2 Z T a 2 atd  atd ta Re  R1 C d R C R C e e e e þ hV 1 ie Iq Re  2V dd dt þ V 1 ðaÞe dt 1e Rd td a ð20Þ

transfer to the boot are almost the same for different loads which support relatively low voltages. The variation of the power harvested in accordance with the storage capacity is shown in Fig. 6. In all cases the maximum energy in the load reaches its maximum when the capacitor C1 is less than some pF. Beyond this value the ability to accumulate power is always constant. However, a small storage capacity C does not store a lot of energy and have little effect at the constant time, by cons for large values of C yield decreases and the power delivered to the load is minimum. With a mean value of the storage capacity of the order of a few nF one corresponds to function optimally and in accordance with the results described in Fig. 5

thus  2      ðatd Þ 2ðatd Þ 1 Re Re C e Iq Re  2V dd ða  td Þ  2Re C e 1  e Re Ce þ 1  e Re Ce R1 Rd 2       ðat Þ 2ðatd Þ d 2 Re Re C e 1  e Re C e þ hV 1 i Iq Re  2V dd Re C e 1  e Re Ce  ð21Þ R1 Rd 2

W1 ¼

Fig. 4 shows the harvested e power with AC regime and after conversion, according to the load resistor and a constant electric field of 7 V/lm and strain 0.5% at 3 Hz respectively (see Table 1). The graphical representation of the generated power and storage capacity according to the load resistance has allowed us to follow soon now, the impact of parameter C (storage capacity) on the power gendered. It is note that the characteristics of the energy

5. Conclusions This article proposes an application approach for increasing the conversion abilities of electrostrictive polymers with the use of an electronic circuit with a storage circuit. Based on a mechanism of doubling frequency of the polymer displacement through a proposed mechanical structure, we can also obtain a higher dynamic current. This effect renders possible a significant increase in terms of converted power; it was found that the maximum output power could reach 0.03 lW, which is 80% more than in classical techniques. This value demonstrated the excellent potential of this technique for energy harvesting. The structure proposed in this

M. Meddad et al. / Optical Materials 36 (2014) 80–85

paper thus represents a good tool for estimating the potential materials for energy harvesting.

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