Energy Scavenging for Energy Ef?ciency in Networks and Applications
Kyoung Joon Kim, Francesco Cottone, Suresh Goyal, and Jeff Punch
Telecommunication networks will play a huge part in enabling ecosustainability of human activity; one of the ?rst steps towards this is to dramatically increase network energy ef?ciency. In this paper we present two novel approaches for energy scavenging in networks. One involves thermal energy scavenging for improving wireless base station energy ef?ciency, and the other involves mechanical energy scavenging for powering sensors in sensor networks, for machine-to-machine (M2M) communications, and for smart grid applications. Power ampli?er (PA) transistors in base stations waste 30 percent of the total energy used in a wireless access network (WAN) as heat to the environment. We propose a thermoelectric energy recovery module (TERM) to recover electricity from the waste heat of PA transistors. A fully coupled thermoelectric (TE) model, combining thermoelectricity and heat transfer physics, is developed to explore the power generation performance and ef?ciency as well as the thermal performance of the TERM. The TE model is comprehensively used to determine optimized pellet geometries for power generation and ef?ciency as a function of PA transistor heat dissipation, heat sink performance, and load resistance. Maximum power generation and ef?ciency for various parametric conditions are also explored. Untapped kinetic energy is almost everywhere in the form of vibrations. This energy can be converted into electrical energy by means of transducers to power wireless sensors and mobile electronics in the range of microwatts to a few milliwatts. However, many problems limit the ef?ciency of current harvesting generators: narrow bandwidth, low power density, micro-electro-mechanical system (MEMS) scaling, and inconsistency of vibrating sources. We explore energy scavenger designs based on multiple-mass systems to increase harvesting ef?ciency. A theoretical and experimental study of two degrees-of-freedom (2-DOF) vibration-powered generators is presented. Both electromagnetic and piezoelectric conversion methods are modeled by using a general approach. Experimental results for the multi-resonant system are in agreement with the analytical predictions and demonstrate signi?cantly better performance in terms of maximum power density per total mass and a wider bandwidth compared to single DOF (1-DOF) generators. ? 2010 Alcatel-Lucent.
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Bell Labs Technical Journal 15(2), 7–30 (2010) ? 2010 Alcatel-Lucent. Published by Wiley Periodicals, Inc. Published online in Wiley Online Library (wileyonlinelibrary.com) ? DOI: 10.1002/bltj.20438
Panel 1. Abbreviations, Acronyms, and Terms BS—Base station CPU—Central processing unit DOF—Degree-of-freedom ICP—Integrated circuit piezoelectric IEEE—Institute of Electrical and Electronics Engineers LDV—Laser doppler vibrometer M2M—Machine-to-machine MEMS—Micro-electro-mechanical system PA—Power ampli?er TE—Thermoelectric TEG—Thermoelectric generator TERM—Thermoelectric energy recovery module VEH—Vibration energy harvester WAN—Wireless access network WSN—Wireless sensor network
Introduction
Energy ef?cient telecommunication networks are expected to play a key role in maintaining a sustainable human society [3]. Innovative energy scavenging techniques may improve the energy efficiency of telecommunication networks. In this paper, we examine two novel energy scavenging techniques. One is a thermal energy scavenging technique to improve the ef?ciencies of base stations (BSs) in wireless access networks (WANs). The other is a mechanical energy scavenging technique for powering sensors in sensor networks, for machine-to-machine (M2M) communications, and for smart grid applications. BSs may consume up to 70 percent of the total energy of a WAN. Hence, energy ef?cient BSs may considerably reduce the operating cost of the WAN and enable the development of eco-sustainable WANs. However, contemporary power amplifiers (PAs) considerably deteriorate the energy ef?ciency of BSs [6]. PA transistors waste nearly 30 percent of the total WAN energy by dissipating the heat to the environment. Effective energy recovery techniques from the waste heat of PA transistors will improve energy ef?ciencies of PAs, BSs, and ultimately WANs. Since the 1960s, many researchers have explored the use of thermoelectric generators (TEGs) to convert heat energy into useful electricity. Researchers have developed thermoelectric generating systems containing TEGs and active heating systems producing heat by consuming fossil fuels or radioisotopes. Such thermoelectric generating systems have been used for the protection of corrosion in metal structures, for powering data gathering equipment, for powering telecommunication equipment in remote terrestrial areas, for space applications, and for medical applications as such as nuclear-powered thermoelectric batteries for cardiac pacemakers [23]. Despite the many historical applications of TEGs for producing electricity using active heat generating systems, research interest in the energy recovery performances of TEGs from waste heat has dramatically increased since the 1990s. Recently reported research includes silicon germanium (SiGe)-based TEGs applied to gasoline engine vehicles [11], bismuth telluride based-TEGs applied to diesel engines [7], thermoelectric power generation systems applied to recover the electricity from municipal waste heat [12], a thermoelectric power generator using solar heating [15], and the thermoelectric recovery of electricity from central processing unit (CPU) waste heat [24, 25, 27]. The improvement of conversion (power generation) ef?ciency of TEGs is a critical factor to make TEGs more attractive for recovering energy from waste heat. Hence, recent studies have focused on the development of novel thermoelectric materials with better ?gures of merit (zT), e.g., a PbSeTe/PbTe quantum dot superlattice structure [8], a p-type Bi2Te3/Sb2Te3 superlattice device [26], an AgPbmSbTe2 m material [10], and a silicon nanowires structure [2, 9]. However, due to the practical dif?culties in scaling and manufacturing, advanced material and novel structure based TEGs are not yet used in real applications. Hence, practical
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and realistic approaches are needed to improve generation ef?ciency. Pellet geometries are expected to considerably affect ef?ciencies of TEGs, and thus the optimization of pellet geometries can be an effective approach to improve ef?ciency [13], as presented in our preliminary result. However, thermal conditions in actual PAs and base stations will affect transistors’ thermal performance as well as the energy recovery performance of TEGs. For application in such thermal conditions, the TEG needs to be integrated with supportive thermal units, and thus a thermoelectric energy recovery module (TERM) is required. Advanced modelling techniques and careful analyses are needed to design TERMs with optimized pellet geometries. These analytical approaches will provide a fundamental basis for energy recovery from the waste heat of PA transistors. In the work on a thermal energy scavenging technique, we investigate the ef?ciency and the performance of the TERM under various thermal and electrical conditions, and develop a fully coupled thermoelectric (TE) model. The TE model combines thermoelectric theory with heat transfer physics. The TE model facilitates the optimization of pellet geometries— pellet height, pellet cross sectional area, and number of thermocouples—for the power generation and the generation ef?ciency of the TERM at various heat dissipation levels of a PA transistor for various heat sink performances and load resistances. The TE model predicts maximum power generation and efficiencies associated with optimized pellet geometries for various parametric conditions. The conversion of dispersed energy in the ambient for powering small electronic devices has generated increased interest in recent years. Among other renewable forms, kinetic energy in the form of mechanical vibrations is deemed to be one of the most attractive for its power density, versatility, and abundance [17, 18]. This type of energy source is present in many things, such as buildings, vibrating machinery, motorized transport, ocean waves, and the human body. Thanks to the recent progress of ultra-low power electronics and wireless protocols (such as IEEE 802.11, IEEE 802.15.4, and ZigBee), wireless sensor networks (WSNs) are well-suited to the power-generating
capability of current harvesting generators that range from 10 microwatts to 300 microwatts per cubic centimeter [19, 21]. Regardless of the conversion mechanism, contemporary vibration energy harvesters (VEHs) are mostly based on single-resonance, single degree-offreedom (1-DOF) oscillators which have the inherent limitation of only providing the maximum energy at their natural frequency. If the vibrating source shifts by a few hertz from resonance, the ef?ciency degrades by 70 to 90 percent. Moreover, as the dimensions shrink below a few millimeters, the resonance goes over the kilohertz region. As a consequence, microelectro-mechanical systems (MEMS)-size harvesters are very inef?cient in the real world, where the most vibrational sources are located around 10 Hz to 100 Hz with variable intensity and bandwidth [14, 22]. Therefore, it is necessary to design a vibration energy harvester capable of adapting to variable frequency sources in order to collect the maximum amount of energy. A multiple vibrating mode solution has been reported by Feng and Hung [5] while others based on nonlinear mechanical behavior have been proposed by Erturk, Hoffmann, and Inman [4] and Marinkovic and Koser [16]. However, these works have achieved only minimal gains in terms of the overall power density and bandwidth. A better analytical approach and more effective concepts in this direction are therefore necessary to realize functional microscale harvesters. In the work on a mechanical energy scavenging technique, we present a general analytical model of a two degrees-of-freedom (2-DOF) VEH suitable for both piezoelectric and electromagnetic conversion techniques. Through this approach, we are able to speculate on the optimal parameters of the harvesters. An electromagnetic prototype is implemented to compare the performance of the 2-DOF versus the 1-DOF common configuration with equivalent total mass. The experimental results reveal enhanced ef?ciency of the 2-DOF system, in close agreement with analytical predictions.
Modelling of TERM
This section mainly discusses the development of the TE model for the TERM. First, fundamentals of
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qh Th P N
Tc qc RL I—Electrical current N—n-type material P—p-type material qc—Heat flow out, cold side qh—Heat flow in, hot side RL—Load resistance Tc—Temperature, cold side Th—Temperature, hot side I
materials is bismuth telluride (Bi2Te3). Two pellets are connected electrically in series and thermally in parallel, and RL is serially connected with the thermocouple. When a temperature difference occurs across the thermocouple due to heat ?ow through the thermocouple, an electric current is generated in the generation circuit by the Peltier effect. The Peltier effect occurs due to the fact that the amount of electrical energy carried by the charged carriers associated with the flow of the electrical current depends on the material. Further explanations regarding the Peltier effect can be found in the literature [23]. Heat flows qh and qc through a TEG can be expressed by the following equations: qh qc NIaTh NIaTc (Th (Th Tc ) uTEG Tc ) uTEG NI 2 R 2 NI 2 R 2 (1) (2)
Figure 1. Schematic of a thermocouple in generation mode.
thermoelectric power generation are introduced. An illustration and basic theories are used to support the introduction. Second, the physical structure of a TERM is proposed to recover the energy from waste heat of a PA transistor. Third, a fully coupled TE model for the TERM is developed to investigate both thermal performance and power generating performance of the module. The TE model is generated by concatenating thermoelectric physics with heat transfer physics. Basics of Thermoelectric Power Generation The principle of thermoelectric power generation is introduced in this section using an illustration and some basic theories. Figure 1 shows the working principle of a thermoelectric generator. Though we show only a single thermocouple consisting of p-type and n-type materials for the purpose of illustration, typical TEGs often contain hundreds of thermocouples. In Figure 1, qh is the heat ?ow to the hot side of the thermocouple, qc is the heat ?ow out of the thermocouple via the cold side of the thermocouple, Th and Tc are the temperatures of the thermocouple hot and cold sides, I is current, and RL is an electric load resistance of the generation cycle. The thermocouple consists of two dissimilar materials, one of which is electrically positive relative to the other material. One of the most common thermocouple
where N is the number of thermocouples, a is the Seebeck coef?cient, uTEG is the TEG thermal resistance, and R is the electrical resistance of a thermocouple. In equation 1 and equation 2, the first terms, NIaTh and NIaTc, are the energy terms due to the Peltier effect; the second term, (Th Tc) uTEG, is the heat conduction purely due to the temperature difference across pellets (the temperature difference between the hot and the cold sides of the TEG); and the third term, NI 2 R 2, is the Joule heating effect. The further information including the derivations of equation 1 and equation 2 can be found in the literature [23]. I is de?ned as: I Na(Th TC ) NR RL (3)
In equation 3, the numerator is the voltage generated across the TEG, and the denominator is the total electrical resistance of the generation system. The total resistance is evaluated by adding the net electrical resistance of the TEG, i.e., NR to R L. In equation 3, R is de?ned as: R 2rH Ap Rc (4)
where r is the electrical resistivity of the pellet, H is the height of the pellet, A p is the pellet cross sectional
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area, and R c is the electrical contact resistance of a thermocouple. R c is de?ned as: Rc 4R c Ap
r
(5)
where R c r is the electrical contact resistivity of a thermocouple. The thermal resistance of a TEG, uTEG, is de?ned as: uTEG H 2N. kAp (6)
where k is the thermal conductivity of the pellet. The generated power of a TEG associated with RL is de?ned as: PL I 2RL (7)
while the power generation ef?ciency, h, is de?ned as the ratio of PL to qtot as follows: h PL qtot (8)
where qtot is the total heat ?ow from the source. Fully Coupled Thermoelectric Model To recover waste energy from PA transistors, a TERM is proposed. Figure 2 illustrates the physical structure of the TERM. The TERM consists of a heat spreader, a TEG, and a heat sink. Established thermoelectric materials are bismuth telluride (Bi2Te3)-type materials, lead telluride (PbTe), and silicon germanium alloys [23], and research continues to be undertaken in the pursuit of new materials [8, 9, 10, 26]. Figures-of-merit for thermoelectric materials are
strongly temperature dependent. Bi2Te3 has the best ?gure-of-merit up to 250°C. PbTe is an appropriate material for temperatures ranging from 250°C to 500°C. SiGe is operable up to 1000°C, although it has the lowest ?gure-of-merit. Junction temperatures of contemporary PA transistors range from 150°C to 200°C in nominal operating conditions. Hence, Bi2Te3 was chosen as the thermoelectric material for the TERM. Forced air convection techniques are utilized to control the temperatures of all the electrical components, including transistors, in typical PAs. Hence, the proposed module contains a heat sink. The heat sink enables effective heat transfer to the ambient and ultimately reduces the cold side temperature of the TEG to improve power generation performance. To reduce the thermal resistance between the heat source and the TEG, we propose the use of a copper heat spreader. A fully coupled TE model for the TERM was developed to explore both the power generation performance and the thermal performance of the module. The TE model concatenates TE theory with heat transfer theory. Figure 3 shows the schematic of the TE model. In Figure 3, qtot is the total heat ?ow from the source; qh is the heat ?ow to the TEG hot side, denoted by the subscript h; PL is the generated power by the TEG; and qc is the heat ?ow out of the cold side of the TEG, denoted by the subscript c. The subscripts j and a denote junction and the ambient, respectively. ujh and uca are thermal resistances between j and h and between c and a. Figure 3 shows
Heat source Heat spreader TEG Heat sink —Thermal resistance a—Ambient c—Cold h—Hot j—Junction qtot j
jh
h qh
TEG
c qc
ca
a
PL PL—Power generated by the TEG qc—Heat flow from TEG qh—Heat flow to TEG qtot—Total heat flow from the source TEG—Thermoelectric generator
TEG—Thermoelectric generator
Figure 2. Thermoelectric energy recovery module (TERM).
Figure 3. Schematic of a fully-coupled thermoelectric model.
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that the TE model embeds a power generation cycle in a thermal network. Figure 3 explains the physics behind the model that heat flow from the source conducts to the TEG, a certain amount of the heat is converted into the useful power, and the rest of the heat is dissipated to the ambient. In the TE model, qtot can be expressed as: qtot (Tj Th) ujh (9)
where Tj is the junction temperature. Heat ?ow from the TEG cold side to the ambient, qca, can be expressed as: qca (Tc Ta) uca (10)
where Ta is ambient temperature. Assuming that the heat loss from the source to the ambient is negligible compared to the heat conducting through the heat spreader to the TEG hot side, qtot can be considered to be equal to qh. Thus, by combining equation 1 and equation 9, the following equation can be obtained: qtot NIaTh (Th Tc) uTEG NI 2R 2 (Tj Th) ujh (11)
The heat out of the TEG cold side eventually dissipates to the ambient: i.e., qc qca. Incorporating equation 2 with equation 10 results in the following equation: qc NIaTc (Th Tc) uTEG NI 2R 2 (Tc Ta) uca (12)
Considering the energy balance in a TEG, one can see that the power can be also obtained by subtracting qc from qh. Solving equations 3 through equation 8, and equation 11 through equation 12 simultaneously, thermal and power generating performances and generation ef?ciencies are determined.
Analysis of TERM
The TE model (equations 3–8 and 11–12) is ?rst used to explore the performance of the TERM under baseline conditions, and then the TE model is used to optimize pellet geometries. Consequently, the TE model predicts the performance of the TERM associated with optimized pellet geometries. Consistent material properties, ambient temperature, and heat
source size are used for the analyses with both baseline and optimized conditions. Typical material properties of Bi2Te3 are used: a Seebeck coefficient of 4 10 4 V/K, an electrical resistivity of 1 10 5 m, and a thermal conductivity of 1.5 W/mK. An electrical contact resistivity of 1 10 9 m2 is used. The average air temperature in the enclosures for high power electronic equipment can reach up to 35°C, and thus this value is used for the ambient temperature. A heat source size of 10 mm 10 mm is selected. For the baseline conditions, a pellet height of 1 mm, 250 thermocouples, and the pellet cross sectional area of 1 mm2 are used. For the baseline condition, the TERM contains a Cu heat spreader having the size of 50 mm 50 mm 5 mm, with a 0.1 mm thick solder layer between the transistor and the heat spreader, and a 0.3 mm thick adhesive layer in the interface between the heat spreader and the TEG. ujh is estimated to be 0.3 K/W by adding the thermal resistances through the solder layer, the heat spreader, and the adhesive layer. For the optimized conditions (i.e., the analysis with the optimized pellet geometries), it should be noted that the footprint of the TEG and the heat spreader size should vary with optimized pellet geometries associated with various thermal boundary conditions. The TEG footprint area is assumed to be twice the total cross sectional area of pellets. The heat spreader size is assumed to be identical to the TEG footprint. Heat spreaders are assumed to have square shapes as the baseline conditions. Solder and adhesive layers are assumed to be 0.1 mm and 0.3 mm thick, respectively, similar to the baseline conditions. ujh is estimated to have an almost consistent value varying from 0.25 K/W to 0.32 K/W despite various heat spreader widths ranging from 50 mm to 350 mm and a consistent thickness of 5 mm. Hence, ujh is assumed to be 0.3 K/W for all the cases. Various uca (0.1, 0.5, 1 K/W) are used to assess the in?uence of the heat sink on the result. All the parameters for the analysis are provided in Table I. Performances With Baseline Conditions Equations 1 through 3 and equation 7 show that Th, Tc , and PL depend on RL. Equation 12 shows that uca
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Table I.
Parameter values for baseline condition. Value 4 1 10 10
4 5
Parameter a r k H N AP Rc ujh Ta
TEG—Thermoelectric generator
Description Seebeck coef?cient Electrical resistivity Thermal conductivity Pellet height Number of thermocouples Pellet cross sectional area
(V/K) ( -m)
1.5 (W/mK) 1 (mm) 250 1 (mm2) 1 10
9
( -m )
2
Electrical contact resistivity Thermal resistance between junction and TEG hot side Ambient temperature
0.3 (K/W) 35 (°C)
may considerably affect Th Tc. To explore the effects of RL and uca on both the thermal and power generating performances of the TERM, the solutions were obtained associated with RL of 6 and uca of 0.5 K/W, RL of 100 and uca of 0.5 K/W, and RL of 6 and uca of 0.1 K/W at various values of qtot ranging up to 100 W . 6 represents a load-matched condition; the electrical resistance of the TEG is matched with the load resistance. The predicted results are shown in Figure 4. Figure 4a and Figure 4b clearly show the considerable in?uence of RL on Tj and PL. For example, associated with qtot of 100W, PL is reduced from 3.4W to 1.4W as RL increases from 6 to 100 . This is mainly due to the well-known fact that the load-matched condition creates higher power than any other case [23]. It should be noted that Tj increases as RL increases from 6 to 100 , e.g., 204°C to 240°C with qtot of 100W. Associated with 100W, less power is generated and consequently more heat conducts to the TEG than in the case with 6 . In this case, the greater the heat conduction, the higher the junction temperature. Figure 4a and Figure 4c show the positive effect of the reduction of uca on both thermal and power generating performances; e.g., Tj is reduced from 204°C to 168°C by 18 percent, and PL increased from 3.4W to 3.6W by 6 percent with qtot of 100W. As uca decreases, Th Tc increases. The increase of Th Tc is induced by
the bigger decrease of Tc than the decrease of Th. The increase of Th Tc explains the better performance associated with a smaller uca. The evaluated Tj shows an almost linear increase with the increase of qtot while the calculated PL shows a quadratic increase with the increase of qtot. The result implies that Th Tc may almost linearly increase with the increase of qtot. Performances With Optimized Pellet Geometries The TE model is utilized to optimize pellet geometries: i.e., pellet height, H; number of thermocouples, N; and pellet cross sectional area, AP. Optimized pellet geometries are obtained using N ranging from 25 to 2500 and H ranging from 0.01 mm to 10 mm at values of qtot ranging from 20 W to 100 W, associated with various thermal and electrical conditions. The thermal conditions, i.e., qca of 0.1 K/W, 0.5 K/W, and 1 K/W, are used, and the electrical conditions, i.e., RL of 5 and 100 , are used. Consequently, the TE model predicts maximum power generation, Pmax, and generation ef?ciencies, hmax, associated with the optimized pellet geometries. The junction temperatures, Tj, of PA transistors range from 150°C to 200°C when the transistors operate at nominal conditions of WAN equipment. In this study, the arithmetic mean value, i.e., 175°C, is used for all the cases. The analysis uses the same material properties of Bi2Te3, Rc r, qjh, Ta as the previous section; Table I shows all the parameters.
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250 200 Tj(°C) 150 100 50 0 0 20 (a) RLof 6 40 60 qtot(W) and
caof
8 7 6 PL(W) Tj(°C) 5 4 3 2 1 80 0.5 K/W 0 100
250 200 150 100 50 0 0 20 40 60 qtot(W) and
ca of
8 7 6 4 3 2 1 0 80 0.5 K/W 100 PL(W) 5
(b) RLof 100 8 7 6 4 PL(W) 5 3 2 1 0
250 200 Tj(°C) 150 100 50 0 0 20 (c) RLof 6 PL—Generated power qtot—Total heat flow from the source RL—Load resistance Tj—Junction temperature 40 60 qtot(W) and
ca of
80 0.1 K/W
100
Figure 4. Thermal and power generating performances of the energy scavenging module versus various heat ?ows from the source, qtot .
Results with Uca of 0.1 K/W. Figure 5 presents the predicted results associated with a uca of 0.1 K/W. Figure 5a and Figure 5b show that Hopt is 10 mm for all values of qtot and RL. It is again instructive to note that the values of H for the calculation range from 0.01 mm to 10 mm. This interesting result is mainly due to the fact that maximum temperature difference across pellets occurs at the maximum height in the parametric range. The effect of the temperature difference across the pellets is seen to be a dominant in?uence on the power generation. Figure 5a and Figure 5b show that both Nopt and APopt associated with both values of RL increase as qtot
increases from 20 W to 100 W. It is obvious that Tj increases with the increase of qtot. To maintain Tj consistently, i.e., 175°C for increasing qtot, the thermal resistance across the TEG, uTEG, should be reduced with the increase of qtot. The product of 2N and AP determines the effective pellet area of the TEG, Ae. In order to reduce uTEG,A e, should be increased. Hence, the predicted results in Figure 5a and Figure 5b show that both Nopt and APopt increase with the increase of qtot. Figure 5c shows that hmax decreases with the increase of qtot , e.g., 5.8 percent at 20 W and 4.5 percent at 100W. As previously noted, to consistently
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APopt(mm2), Hopt(mm)
200 150 Nopt 100 50 0 0
Nopt APopt Hopt
800 Nopt 600 400 200 0 0
15 10 5 0 120
APopt Hopt
15 10 5 0 120
20
40
60 80 qtot(W)
100
20
40
60 80 qtot(W)
100
(a) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 5 . 7 6
max(%) max
(b) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 100 .
5 4 3 2 1 0 0 20 40 60 qtot(W) (c) Maximum power generations and generation efficiencies versus various heat flows from the source at RL of 5 and RL 100 . 80 100 120 Pmax 5 100 5 100
efficiency resistance between c and a APopt—Optimized pellet cross sectional area Hopt—Optimized pellet height Nopt—Optimized number of thermocouples
ca—Thermal
max—Generation
Pmax(W),
Pmax—Maximum power generation qtot—Total heat flow from the source RL—Load resistance TE—Thermoelectric
Figure 5. TE model results with a Uca of 0.1K/W.
maintain Tj for increasing qtot, uTEG should be reduced. The decrease of uTEG results in a decreasing temperature difference across the TEG, Th Tc. The decrease of Th Tc can explain the decrease of hmax with the increase of qtot. Pmax increases from 1.2W to 4.5W as qtot increases from 20W to 100W despite the decrease of hmax. The increase of Pmax is more in?uenced by the increase in qtot than by the effect of decreasing hmax. The result suggests that the value of Nopt APopt for each RL is reasonably invariant. Both hmax and Pmax are functions of Nopt, APopt, and Hopt, and it should be
noted again that Hopt was found to be 10mm for all the cases. The reasonably invariant value of Nopt APopt for each RL can explain that the values of hmax with two values of RL that are very similar to each other. The reasonably invariant value of Nopt APopt can also explain the similarity in the behavior of Pmax and hmax. for RL. Results With Uca of 0.5 K/W. Figure 6 presents the results associated with a uca of 0.5 K/W. The predicted Hopt is seen to be 10 mm, and the result again supports that a dominant parameter affecting hmax and Pmax is
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APopt(mm2), Hopt(mm) 15
250
20
1000 Nopt
20
300 250
20
1600 APopt(mm2), Hopt(mm) Nopt 1200 Nopt 800 400 0 0 20 40 60 qtot(W) 80 100 120 APopt Hopt
20 15 10 5 0
15
200 Nopt 150 100 50 0 0 20 40 60 qtot(W) 80 Nopt APopt Hopt 100
5 0 120 10
(a) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 5 . 6
max(%)
(b) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 100 .
5 4 3 2 1 0 0 20 40
max
Pmax(W),
Pmax 5 100 5 100 60 qtot(W) 80 100 120
(c) Maximum power generations and generation efficiencies versus various heat flows from the source at RL of 5 and RL of 100 . efficiency resistance between c and a APopt—Optimized pellet cross sectional area Hopt—Optimized pellet height Nopt—Optimized number of thermocouples
ca—Thermal max—Generation
Pmax—Maximum power generation qtot—Total heat flow from the source RL—Load resistance TE—Thermoelectric
Figure 6. TE model results with a
ca
of 0.5 K/W.
Th Tc. Similar to the previous case, Figure 6a, 6b, and 6c show that the values of Nopt and A Popt increase, the value of hmax decreases from 5.4 percent to 2.7 percent, and the value of Pmax increases from 1.1 W to 2.7 W as the value of qtot increases from 20 W to 100 W. Figure 6c shows that the values of hmax associated with two values of RL are very similar to each other. This parametric behavior can be explained by the physical reasons already stated for the previous case.
Results With Uca of 1 K/W. Figure 7 presents the results associated with a uca of 1 K/W. Similar to the previous results, Hopt was found to be 10 mm. The result shows again that Th Tc is a dominant parameter affecting hmax and Pmax. Similar to the previous cases, Figures 7a, 7b, and 7c show that the values of Nopt and APopt increase, and the value of hmax decreases from 5 percent to 0.4 percent, as the value of qtot increases from 20W to 100W. Pmax shows a parabolic profile with qtot increasing from 1 W to 1.7 W but
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APopt(mm2), Hopt(mm)
800 Nopt 600 Nopt 400 200 0 0 20 40 60 qtot(W) 80 100 APopt Hopt
40 APopt(mm2), Hopt(mm) 30 20 10 0 120
3000 2500 2000 Nopt 1500 1000 Nopt APopt Hopt
40 30 20 10 APopt(mm2), Hopt(mm) 17
500 0 0 20 40 60 qtot(W) (b) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 100 . 80 100 0 120
(a) Optimized number of thermocouples, pellet cross sectional area, and pellet height versus various heat flows from the source at RL of 5 . 6
max(%)
5 4
max
Pmax(W),
3 2 1 0 0 20 40 60 qtot(W) 80 Pmax
5 100 5 100
100
120
(c) Maximum power generations and generation efficiencies versus various heat flows from the source at RL of 5 and RL of 100 . efficiency resistance between c and a APopt—Optimized pellet cross sectional area Hopt—Optimized pellet height Nopt—Optimized number of thermocouples
ca—Thermal max—Generation
Pmax—Maximum power generation qtot—Total heat flow from the source RL—Load resistance TE—Thermoelectric
Figure 7. TE model results with a
ca
of 1K/W.
eventually decreasing to 0.4 W. Figure 7c shows that the values of hmax associated with two values of RL are very similar to each other. Physical reasons already detailed in the results with 0.1K/W can explain the parametric behavior observed here.
Summary of Results
In this work, the advanced modelling and analyses techniques provide a ?rst-order theoretical basis to develop a novel TERM. The predicted results show
that hmax and Pmax considerably decrease with the increase of uca from 0.1 K/W to 1 K/W; e.g., hmax decreases from 5.8 percent to 5 percent and Pmax decreases from 1.2W to 1W at a qtot of 20W. The decrease of hmax and Pmax can be explained by the decrease in Th Tc induced by the increase of the net thermal resistance of the module. The results showed that the TERM may recover PA transistor power up to nearly 6 percent when Tj, qtot, and Ta are 175°C, 20W, and 35°C, respectively. This result implies that the TERM may improve the ef?ciency of
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a PA up to nearly 4 percent when PA ef?ciency is 30 percent. Consequently, the TERM may improve BS ef?ciency by nearly 3 percent and WAN ef?ciency by 2 percent. The expected improvements in energy ef?ciencies of PAs and BSs provide solid evidence that the TERM can be a cost-effective energy recovery solution in WAN equipment. It is important to note that the parametric results shown in Figure 5, Figure 6, and Figure 7 reveal that the TEG footprint increases by up to a factor of 50 relative to the baseline case with the increase of the source heat ?ow. In an actual application, the heat sink footprint may also be expected to increase correspondingly to match the increase in the TEG footprint. Since the heat sink thermal resistance may be a strong function of its footprint, this may result in a decrease in the value of uca.. The particular behavior that is observed will thus depend on how strongly uca is dependent on the heat sink footprint. In the analysis presented in this paper, we have considered a ?rst-order analysis for all important physical effects, such that uca is assumed to be constant as the source heat ?ow and TEG footprint increase. We consider this to be a realistic limiting case for analyzing the optimized pellet geometries and the associated TERM performance. A more detailed analysis examining higher-order effects, such as, for example, the dependence of the heat sink thermal resistance on the footprint, was considered to be beyond the scope of this work.
Conversion element m2 VL k2 d2 z2
m1
k1
d1
z1
? d—Friction k—Elasticity m—Mass VL—Voltage load ?—Acceleration z—Displacement
Figure 8. Model of coupled double degree-of-freedom vibration energy harvester.
both 1-DOF and 2-DOF con?gurations of an electromagnetic prototype. The analytical power function, in conjunction with experimental results, is used to compare the con?gurations. Description of the Model Figure 8 shows a schematic design of a doublemass VEH, which comprises a vibration energy converter arranged above a single-mass oscillator. In this general model, the second stage can be either a piezoelectric or an electromagnetic converter as illustrated in Figure 9. The overall system is basically modelled as a 2-DOF spring-mass damper oscillator. Two inertial masses m1 and m2 are connected in series by means of springs with stiffness k1 and k2 to the housing of the device. An acceleration y applied to ¨ the base causes the masses to move with a relative displacement of z1 and z2. In case of electromagnetic conversion, the movement of a permanent magnet, embedded within the second mass m2, induces an electrical current i into the adjacent coil, which in turn is transferred into the resistive load RL, whereas, in the case of piezoelectric conversion, the inertial
Theoretical Analysis of VEH
To date, multiple DOF motion-driven generators have not been adequately investigated as a valid alternative to the commonly used single DOF harvesters. Signi?cant improvements in terms of higher bandwidth and power density can be achieved using multiple-mass con?gurations, though they come at the cost of slightly larger space requirements for mass displacement. The aim of this work is to compare the performance of spring-mass damper 2-DOF and 1-DOF generators with equivalent total inertial mass excited by random or sinusoidal vibration. A general theory for the operation of electromagnetic and piezoelectric VEHs is presented in the following section. This approach effectively describes
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i
RL
i
RL
B Mass
Piezoelectric element Coil k Moving magnet z Mass
z
k ? (b) Piezoelectric
? (a) Electromagnetic B—Magnetic field i—Electrical current k—Elasticity
Vibrations
RL—Load resistance ?—Acceleration z—Displacement
Figure 9. Models of single degree-of-freedom electromagnetic and piezoelectric vibration energy harvesters.
force produces a stress upon a piezoelectric bar (or cantilever beam) so that an electric ?eld is generated due to dielectric coupling h33 along the vertical direction (or transversal h31). By neglecting the gravitational force and the internal resistance of the converter, the governing equations for a 1-DOF vibration-driven generator [20] can be rewritten in a general form valid for both the conversion mechanisms: mz . e VL
.. . aVL dz kz . vcVL dc vc z
my
..
(13)
The ?rst equation describes the dynamics of the inertial mass, while the second equation accounts for the conversion of its movement into electrical energy. VL is the resultant voltage across the resistive load and d accounts for the mechanical damping. Table II describes the electromechanical parameters. The parameters
a, d, vc, respectively, represent the electrical restoring force coef?cient, electromechanical conversion factor, and the cutoff frequency of the equivalent highpass circuit of the converter. They are functions of the electrical design parameters, depending on the transduction method as listed in Table II. The magnetic ?eld B across the coil of length l and self-inductance Le de?nes the electromagnetic generator, and the piezoelectric transducer is de?ned by the voltage over displacement ratio h33 and inherent capacitance C0. By using this general approach, the differential equations for the 2-DOF oscillating system can be written in the following way:
.. . m1z1 (d1 d2 )z1 (k1 k2 )z1 d2 z2 k2 z2 m1 y . . .. .. d2z2 k2z2 d2z1 k2z1 aVL m2 y ? m2 z2 . . VL vcVL dc vc z2 . .
(14)
Table II.
Electromechanical parameters. Electromagnetic Bl/RL Bl RL/Le Piezoelectric h33C0 aRL 1/RLC0 Description Electrical restoring force factor Conversion coef?cient Characteristic cut-off frequency
Parameter a dc vc
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The ?rst two equations model the dynamics of the inertial masses, while the third equation accounts for the mechanical-to-electrical energy conversion of the second mass. In order to calculate the analytical formula of the electrical power delivered to the load, we can proceed by deriving the transfer function of the output voltage for each system. Transfer Functions By transforming the motion equation 13 and equation 14 into the Laplace domain, with s as the Laplace variable, and considering the forced solution, Y(s), Z1(s), Z2(s), and V(s) are, respectively, the acceleration, the displacements of the masses, and the output voltage. Thus, the governing equations for the single-mass generator are: a ms2 ds k dc vc s s a Z ba b vc V a mY b 0 (15)
Z1
Y 3 . (s vc ) (m1m2s det B (d2m2 vc (d2m1 d2m1 m1m2vc )s2 m1adcvc )s (m1k2 m2k2
(19) vc (m1k2 m2k2 )
d2m2)
Z2
Y (m m s2 det B 1 2 m1k2 m2k1
(d1m2 m2k2 ) (d1m2
d2m1
d2m2 )s (20)
V
Ydvc s (m m s2 det B . (s vc ) 1 2 m1k2 m2k1 m2k2 )
d2 m1 d2m2 )s (21)
The transfer functions between displacement, voltage, and input acceleration (with its minus sign included) are therefore de?ned as follows: HZ1Y(s) Z1(s) ; Y(s) HZ2Y (s) Z2 (s) ; Y(s) HVY(s) V (s) Y(s) (22) with the Laplace variable s jv. Let us now calculate the electrical power dissipated by the load RL when .. the excitation is harmonic y Y0 e jvt of frequency v, for the 1-DOF generator: P1DOF (v) e Pe(v) ? Y( jv) ? 2 ? V(jv) ? 2 2RL P1DOF (v) e ? HVY( jv) ? 2 ? Y(jv) ? 2 2RL
The left-side matrix, which we call A, represents the generalized impedance of the oscillating system. This equation can be easily solved by means of linear algebraic methods, so that the displacement and output voltage solutions are given by: mY Z (s vc ) det A mY . (s vc ) 3 2 ms (mvc d)s (k adc vc d2 vc )s kvc (16) V mY dvs det A c c ms3 (mvc
mY . dc vc s 2 d)s (k adc vc
dvc )s
kvc (17)
2 Y0 ` 2RL (vc
mdc vc jv 2 jv)( mv jvd
2
k)
adv c jv
`
while for the double-mass transducer we get: (d2s k2 ) 0 Z1 m1s2 (d1 d2)s k1 k2 (d2s k2) m2s2 d2 s k2 a ? °Z2? ° 0 dc vc s s vc V m1Y (18) ° m2Y ? 0 The generalized impedance is now a 3 3 matrix, which we call B. The solution of such a system in the Laplace domain is give by the following expressions: while for the double-stage system we get: P2DOF (v) e dc vc jv[ m2m1v2 (m2d1 m2d2 )jv k1m2 k2m1 ∞ 5 2RL (a5 jv a4v2 a3 jv3 a2v2 Y2 0
(23)
2 m1d2 k2m2 ] ∞ a1 jv a0 )
(24) with the following coef?cients:
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a5 a4 a3
m1m2 m1m2vc k1m2 d2m2 k2m2 d2m1 k2m1 d2m1 d1m2 d1d2 d2m2 ) m1k2 m1adc vc m2k2 m2k1 )
vc(d1m2 a2 d1k2 d2k1
vc (d1d2 d2 ) k2d1 )
adcvc(d1 a1 a0 k1k2 k1k2vc
vc (k1d2
adcvc (k1
k2 ) (25)
By using this theoretical approach, we are interested in comparing the output power of the conventional 1-DOF over a 2-DOF vibration energy harvester of equivalent total inertial mass m m1 m2 for different mass ratios m1/m2. In particular, this model allows us to establish if the double-coupled mass arrangement presents an ef?ciency gain with respect to the single-mass configuration when driven by random or harmonic vibrations. We are now able to predict the optimal design characteristics in order to maximize the electrical power for a given excitation. Finally, the same theoretical approach described here can be applied to derive the solutions of the electromechanical variables when the transduction occurs through the first mass or through both masses. To do this, it is sufficient to add the electrical restoring force term aV and its coupled equation for each mass that introduces a mechanical-to-electrical energy conversion into the system of equation 14.
Experimental Investigation of VEH
To the aim of a dynamic comparative test of multiplemass versus conventional single-mass systems, an electromagnetic transducer was implemented to be con?gurable in both single- and double-mass arrangements. Though it is not well optimized to achieve practical power, the different combinations of the inertial masses and springs change not only the mechanical vibration response, but also the voltage across the resistive load in good qualitative agreement with the theoretical model above mentioned. The physical properties of the prototype and the experimental rig are described in the coming sections along with the results.
Model Characteristics and Experimental Setup Figure 10 shows the layout of the electromagnetic VEH prototype and experimental setup. Table III summarizes the measured and derived electromechanical characteristics of the generator. The tests were performed by varying the mass ratio m1/m2 and investigating various options for electromechanical coupling by positioning the magnet/coil ?rst on the top mass and then on the bottom mass. For the comparison, the 1-DOF system con?guration was realized by setting a single moving mass m m1 m2 with an embedded magnet linked to the base of the cylinder by a spring of effective stiffness k. The basic support consists of a polycarbonate cylinder of size 20 mm 55 mm and 0.5 mm of thickness. The position of the coil was adjusted along the vertical axis in order to test various con?gurations and to maximize the ?ux linkage variation. Meanwhile, the total inertial mass and other electromagnetic characteristics were kept equivalent for both the single- and double-mass systems. A 12 mm 3 mm disk-shaped neodymium magnet (NdFeB) was attached alternatively to the ?rst mass and to the second mass. The effective radial magnetic ?eld B was measured with a gauss-meter probe (Hirst) and ranged in the interval 0.01–0.1 Tesla from the outer (rout 15mm) to the inner (rin 12mm) radius of the coil. The air-core solenoid was made of several turns of copper wire with measured self-inductance of 160 mH. The damping coefficients and the springs’ stiffnesses were derived experimentally and through ?tting analysis with the theoretical model. The velocity of the top mass was measured by means of a laser doppler vibrometer (LDV), while the input acceleration was monitored with a PCB Piezotronics single axis Integrated Circuit Piezoelectric (ICP*) accelerometer attached to an Agilent Technologies 35639A spectrum analyzer. The dynamic signal analyzer drove the electromagnetic shaker through a charge ampli?er to generate the random vibrations. The frequency response was averaged over a de?nite period of time and stored on the internal hard disk drive of the analyzer. Performance Comparison As the theoretical model suggests, two special cases for the double-mass arrangement are considered here:
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Coil Magnet Harmonic steel spring
Moving magnet mass m2 Coaxial coil Mass m1 Spring
Laser doppler vibrometer RL
Accelerometer
Prototype
Load (e.g., wireless sensor node)
VL
LDV
Spectrum analyzer
Accelerometer
?Shaker
Noise generator and charge amplifier
DOF—Degree-of-freedom LDV—Laser doppler vibrometer m—Mass RL—Load resistance VEH—Vibration energy harvester VL—Voltage load
Shaker
Experimental setup
Figure 10. Layout of the 2-DOF VEH prototype and experimental setup.
?
Case 1. Magnet placed on the top mass, m2, with m1 m2. ? Case 2. Magnet placed on the bottom mass, m1, with m1 m2. Due to the geometric constraints, the actual masses investigated are: m1 15.24 gr and m2 3.49 gr for case 1; m1 4.09 gr and m2 15.24 gr for case 2. The frequency response of the two systems was analyzed under random Gaussian noise vibration of acceleration range s 1 – 3 m/s2 (0.2–0.3g), which is typical of most vibration sources: e.g., vibrating machinery, transportation, households, and bridges [22]. The power
spectrum of the voltage drop across the resistive load was averaged over a time interval of 100 seconds. The ef?ciency of vibration energy harvesting systems is often intended as the power density per unit of volume or base area of the generator over the acceleration level [1, 14]. As for linear systems, the power is proportional to the acceleration squared, and, bearing in mind that both con?gurations have the same area, we prefer to compare the power density per unit of acceleration squared de?ned as P (1 s2 ) . ? Vrms ? 2 RL. The theoretical ?tting is calculated by using the voltage transfer function
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Table III.
Characteristics of the electromagnetic prototype. Value 6 (mm) 3 (mm) 0.01–0.1 (Tesla) 12 (m) 12 (mm) 15 (mm) 5 (mm) 160 (mH) 2.7 (ohm) 100.2 (ohm) Description Magnet radius Magnet height Magnetic ?eld range seen by the coil Total length of the coil wire Coil inner radius Coil outer radius Coil height Self-inductance of the coil Coil internal resistance Optimal load resistance Total inertial mass Measured effective elastic constant Friction factors derived as ?tting parameters
Parameter rm hm B
l
rin rout h Le Re RL m K d d2 m1 k1 m2 k2 0.2;
18.7 (gr) 98.19 (N/m) (N s/m)
0.1; d1 0.015
(equation 22) squared, and the average power is given by integrating over the frequency domain and normalizing by the resistive load. Discussion of the Results Figure 11 and Figure 12 show the power density comparison over the frequency domain between the 1-DOF and 2-DOF con?gurations for cases 1 and 2, respectively. Table IV summarizes the prototype characteristics relative to the resonance values. The discrepancy between experimental and theoretical total power for the 2-DOF system is 12 percent for case 1 and 33 percent for case 2. On the other hand, by considering the resonant modes, we find an agreement of 6 percent for frequency values and 11 percent for their corresponding power peak. In case 2, however, relative discrepancies are 5 percent and 32 percent, respectively. With regard to the total power gain of the 2-DOF over the 1-DOF con?guration, we notice a substantial theoretical underestimation, particularly for case 2. This is due to experimental factors not considered by the linear
theory: the actual magnetic ?eld in proximity of the coils, air friction (the plunger-like design of the prototype masses), and nonlinear behavior of the real springs. The conversion coef?cient dc was derived as a fitting parameter in the analytical curve because of the difficulty of estimation for the actual nonuniform magnetic field. The electromagnetic coupling results in a relatively weak value of dc 0.12. This is attributed to the small average magnetic ?eld which is estimated to be B 0.02 Tesla (the coilmagnet gap is too large: ri rm 6 mm) and the short length of the coil wire l 12 m. Moreover, the mechanical damping is relatively high—d 0.05–0.1Ns—due to air friction. In spite of these simpli?cations, the theoretical curves are in good agreement with experimental ones for the better part of the frequency domain. In case 1, where the mechanical-to-electrical conversion occurs with the top mass m2, we observe as expected two resonances at 11 Hz and 31 Hz, the ?rst of which coincides with that of the single-mass arrangement. The relative enhancement of the power density
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10
3
10 Power density (mW/(m2/s4))
4
Theory 1-DOF Theory 2-DOF Exp 1-DOF Exp 2-DOF
10
5
m1/m2 4.37 electromechanical conversion by mass m2
10
6
10
7
10
8
100
101 Frequency (Hz)
102
DOF—Degree-of-freedom Exp—Experiment m—Mass VEH—Vibration energy harvester
Figure 11. Case 1: power density comparison of the 2-DOF versus 1-DOF electromagnetic VEH under random Gaussian vibration noise of amplitude Srms 2.37m/s2.
harvested by the 2-DOF generator in comparison with the 1-DOF generator, under the same excitation, results in P2DOF P1DOF . 100 204 percent. Considering the bandwidth, the 2-DOF system demonstrates greater ef?ciency both below and above the main natural mode for at least 20 Hz. In case 2, the conversion still occurs by means of the smaller mass, the bottom one, m1. The two measured resonances are 9 Hz and 36 Hz. In the interval 10 Hz to 35 Hz, the 1-DOF generator presents a much better efficiency, whereas outside this range, the 2-DOF seems the best choice. Hence, the latter con?guration could bene?t from multi-resonant vibration sources with energy located primarily at low and high frequencies. Even in this case, under the same
wideband excitation, the relative gain results are P2DOF P1DOF . 100 198 percent.
Application Hypothesis of VEH
The main purpose of this study is to compare the efficiencies of 2-DOF and 1-DOF configurations of VEH. For this reason, the testing prototype was not optimized to achieve high power capability. The overall maximum power density is around 0.16 mW/cm3@9Hz (case 2) under random acceleration of 2.37 m/s2, which is relatively poor compared to commercially available devices. For example, the Perpetuum PMG17 is capable of 7.35 mW/cm3@100Hz excited by just 0.25 m/s2 of acceleration [19, 20]. However, the approach proposed here can be applied
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10
2
10
3
Theory 1-DOF Theory 2-DOF Exp 1-DOF Exp 2-DOF
Power density (mW/(m2/s4))
10
4
m1/m2 0.27 electromechanical conversion by mass m1
5
10
10
6
10
7
10
8
100
101 Frequency (Hz)
102
DOF—Degree-of-freedom Exp—Experiment m—Mass VEH—Vibration energy harvester
Figure 12. Case 2: power density comparison of the 2-DOF versus 1-DOF electromagnetic VEH under random Gaussian vibration noise of amplitude Srms 2.65m/s2.
to a range of transduction techniques like magnetostrictive, piezoelectric, and electrostatic. In principle, this could be implemented by “breaking” the total inertial mass into multiple masses linked to each other by spring elements. For given acceleration level, the superior 2-DOF configuration would enhance the power density by a factor of 2x at the cost of slightly larger space requirements for the displacement of the masses. For example, under only 0.025 grms of a vibration source tuned at 60 Hz (e.g., a vibrating pump or truck provides random vibrations of 0.05 grms to 0.2 grms), Perpetuum’s singleresonant PMG17 vibration energy harvester is capable of providing 2 mW to continuously supply the Texas Instruments' CC2420 radio frequency (RF) transceiver
and MSP430* 16- bit ultra-low-power microcontroller [19]. At this low level of vibration, such a wireless node is capable of sampling 2 kilobytes of data over 100 line-of-sight meters every 60 seconds via the IEEE 802.15.4 protocol. In principle, the more efficient multi-resonant method discussed here could be applied to this existing technology or to other similar ones. In this way, the transmittable packets could be doubled or the delay time halved.
Conclusion
In this paper, two novel energy-scavenging techniques have been proposed. One is a thermal energy scavenging technique utilizing the system-level optimization technique of TEG pellet geometries to
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Table IV. Power response of the electromagnetic prototype. Theory Frequency (Hz) Case 1 1-DOF Resource peak Total PS area (mWm 2s3) 2-DOF Resource peak 1 Resource peak 2 Total PS area (mWm 2s3) Total gain P 2DOF /P 1DOF (%) Case 2 1-DOF Resource peak Total PS area (mWm 2s3) 2-DOF Resource peak 1 Resource peak 2 Total PS area (mWm 2s3) Total gain P 2DOF /P 1DOF (%)
Accel—Acceleration DOF—Degree-of-freedom PS—Power spectrum
Experiment Power/accel (mW/m2/s4)
2
Frequency (Hz)
Power/accel2 (mW/m2/s4)
11.74 1.58 10
3
0.36
10
3
11 1.43 10
3
0.32
10
3
11.74 29.75 2.29 10
3
0.77 2.45
10 10
3 5
11 31 2.62 10
3
0.63 3.57
10 10
3 5
186.15
204.81
10.98 1.68 10
3
11.3
10
4
11 1.89 10
3
3.78
10
4
8.62 36.86 1.89 10
3
6.52 1.13
10 10
3 3
9 36 2.79 10
3
2.00 0.37
10 10
3 3
112.18
198.41
recover the energy from the waste heat of PA transistors. The other is a mechanical energy scavenging technique that exploits a novel multi-resonant vibration energy harvesting approach based on a springlinked mass chain. In the work for the thermal energy scavenging technique, a fully coupled TE model has been developed integrating TE physics with heat transfer physics. The TE model has been used to optimize pellet geometries such as pellet height, number of thermocouples, and pellet cross sectional area to maximize power generation and ef?ciencies under various thermal and electrical conditions; heat dissipations of a PA transistor, heat sink performances, and load resistances. The TE model has determined the maximum
26 Bell Labs Technical Journal DOI: 10.1002/bltj
power generations and ef?ciencies associated with the optimized pellet geometries. Optimized pellet height was found to be 10 mm for the chosen parametric range. The results suggest that the temperature difference across pellets is a dominant parameter affecting power generation and efficiencies. Maximum generation ef?ciencies associated with optimized pellet geometries are seen to be independent of load resistances. The study showed that optimized pellet geometries could enable the TERM to have generation ef?ciency up to 5.8 percent given a source heat ?ow of 20 W, a thermal resistance between the cold side of the TEG and the ambient of 0.1 K/W, and an ambient temperature of 35°C. These results show that the TERM may recover the waste heat from a PA transistor.
Predicted results also suggest that the TERM may improve efficiencies of PAs, BSs, and eventually WANs by nearly 4 percent, 3 percent, and 2 percent, respectively, and can form part of an effective energy recovery solution for WAN equipment. The TE model includes the important ?rst-order physical effects necessary for the prediction of the optimized pellet geometries and the associated TERM performance. However, the TE model doesn’t consider other higher-order physical effects, such as, for example, the dependence of heat sink thermal resistance to the heat sink footprint, the effect of the thermal interface resistances, and the manufacturability of the TEG geometries. A more detailed TE model would help to quantify whether these higher-order physical effects have a strong in?uence on the optimized pellet geometries and TERM performance. In the work on the mechanical energy scavenging technique, we developed a novel multi-resonant vibration energy harvesting approach based on springlinked mass chains. To realize this new technique, we devised a general analytical model for both piezoelectric and electromagnetic conversion. An ef?ciency comparison between 2-DOF and 1-DOF harvesting systems was carried out using an electromagnetic prototype. Two special cases were investigated for the mass ratio m1/m2. Under random noise excitation, the experimental 2-DOF con?guration demonstrated an improvement of a factor 2x in terms of power density and a wider frequency response with respect to the 1-DOF configuration, in good agreement with the theoretical predictions. Consequently, the data load capabilities of a vibration-driven wireless sensor node can be doubled or the delay time between transmissions halved. In this paper, we explored two energy harvesting techniques: one thermoelectric, the other mechanical. In both cases, we presented work that advances the utility of such energy scavenging techniques. As greater awareness is placed on the energy ef?ciency of telecommunication networks, inevitably, a greater focus will be placed on improving the energy efficiency of networking equipment either directly or indirectly. In the case of direct improvement, the results of the thermoelectric energy scavenger are eminently applicable. In the case of indirect improve-
ment, lateral thought may be needed and may take the form of placing telecom equipment into sleep modes or by powering-off equipment altogether. Methods will have to be developed that can revive equipment from such operational modes. The VEH scavenger techniques presented here are now eminently applicable, since we now require self-powered sensors to help bring the slumbering equipment back into operation. Acknowledgements The authors wish to thank IDA Ireland for supporting the development of the thermal energy scavenging technique and Enterprise Ireland for supporting the investigation of the mechanical energy scavenging technique under the Proof-of-Concept project PC/07/042. The involvement of Jeff Punch is supported by Science Foundation Ireland under grant 03/CE3/I405. *Trademarks
ICP and PCB are registered trademarks of PCB Group, Inc. MSP430 is a trademark of Texas Instruments.
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(Manuscript approved April 2010)
KYOUNG JOON KIM is a member of technical staff at Alcatel-Lucent Bell Labs in Blanchardstown, Ireland. His current research focus is on the development of an energy recovery technique from the waste heat of electronic components. He received a B.S. degree from Chung-Ang University in Seoul, Korea; an M.S. degree
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DOI: 10.1002/bltj
from the University of Minnesota at Minneapolis/ St. Paul; and a Ph.D. degree from the University of Maryland, College Park. All the degrees were received in mechanical engineering. Prior to joining Bell Labs, Dr. Kim was a senior research engineer at Amkor Technology and worked on the development of advanced thermal packaging techniques for microelectronics. Earlier, he worked as a postdoctoral fellow in mechanical engineering at the University of Illinois on the development of a thermal mapping technique for nanotopography and investigated thermo-optical behaviors of polymer Bragg gratings during his doctoral studies. He has authored or coauthored 11 technical papers. FRANCESCO COTTONE is research fellow at Stokes Institute at the University of Limerick, Ireland. He is currently working on novel vibration energy harvesting generators for wireless sensor networks in collaboration with Alcatel-Lucent Bell Labs. He received M.S. and Ph.D. degrees in physics, respectively, from the University of Camerino and from the University of Perugia, Italy. Dr. Cottone was formerly a member of Istituto Nazionale di Fisica Nucleare (INFN), Italy. He worked for the VIRGO project for gravitational wave detection at the European Gravitational Observatory (EGO). His research experience included work on the quantum Hall effect, low thermal noise materials, eddy current noise effects, and nonlinear stochastic dynamic systems prior to his current focus on harvesting vibration energy through nonlinear piezoelectric and electromagnetic generators. He has published more than 30 journal papers and workshop proceedings and participated at international conferences. SURESH GOYAL is a distinguished member of technical staff at Alcatel-Lucent Bell Labs Research in Murray Hill, New Jersey, and an adjunct professor at the University of Limerick, in Limerick, Ireland, where his research focus is on mechanics and energy harvesting. He is currently leading strategy development for Bell Labs’ green research efforts and coordinating its research in ecosustainability. He obtained his Ph.D. from Cornell University, Ithaca, New York; an M.S. from the University of Iowa, in Iowa City; and a B.Tech. from the Indian Institute of Technology, Kharagpur, India, all in mechanical engineering. Dr. Goyal is a founding member of Bell Labs Ireland, and the Center for Telecommunications Value-Chain-Driven Research
(CTVR), where he led the Test and Reliability research group and co-led strategy development for ?ve years. He has previously held positions in optical networking research and wireless packaging research, leading a broad research group focused on reducing the manufacturing cost of network equipment. He also served as adjunct professor at Carnegie-Mellon University, in Pittsburgh, Pennsylvania. Dr. Goyal is a fellow of the ASME and has more than 70 peerreviewed publications, nine patents, three Best Paper awards, and several internal Bell Labs awards. JEFF PUNCH is a senior research fellow at the Stokes Institute, University of Limerick, Ireland. He collaborates with the Institute’s partners and clients on a range of research programs and is currently leading the Thermals and Reliability Strand at the CTVR Telecommunications Research Centre, an SFI-funded multi-university research program in collaboration with Bell Laboratories. He has a range of research interests in the analysis of micro-scale mechanical engineering phenomena within the electronics application area— with particular emphasis on thermal and energy management, and reliability physics. He has a strong track record in governmental and industrial research programs. He has authored or co-authored over 80 refereed publications, holds ?ve patents, and has presented more than 50 invited talks worldwide on aspects of the thermal management and reliability of electronic systems. ◆
DOI: 10.1002/bltj
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