Solar Thermoelectric Power Conversion

24 Solar Thermoelectric Power Conversion

Daniel Kraemer Massachusetts Institute of Technology

Kenneth McEnaney Massachusetts Institute of Technology

Zhifeng Ren Boston College

Gang Chen Massachusetts Institute of Technology

24.1 Concept of Solar Thermoelectric Power Conversion ................24-1 24.2 Historical Review ............................................................................24-2 24.3 Optimization of STEGs .................................................................24-4 24.4 Simulations and Experiments of STEGs .....................................24-9 24.5 STEG Performance and System Integration ............................24-12 24.6 Potential for Improvement ..........................................................24-13 Acknowledgments .................................................................................... 24-14 References.................................................................................................. 24-14

24.1 concept of Solar thermoelectric Power conversion A solar thermoelectric generator (STEG) consists of thermoelectric (TE) devices sandwiched between a solar absorber and a heat sink as schematically shown in Figure 24.1. The solar absorber converts the sunlight into heat and concentrates it onto one side of the thermoelectric generator (TEG). The heat is then transported through the TEG and partially converted into electrical power by the TEG. The excess heat at the cold junction of the TEG is removed by a heat sink in order to maintain an appreciable temperature difference across the TEG.

Sunlight Sunlight capture Heat input

TEG

Electrical power

Heat rejected Heat sink

FIGURE 24.1

Schematic of an STEG.

24-1 © 2012 by Taylor & Francis Group, LLC

24-2

Modules, Systems, and Applications in Thermoelectrics

Despite some past studies, STEGs have not received wide attention because the efficiencies of STEGs reported so far have been limited to less than 1% for systems without optical concentration and less than ~4% with optical concentration. However, our recent modeling and experimental studies suggest that much higher efficiencies can be achieved in STEGs, and that solar-to-electrical power conversion based on the TE effect is economically feasible. In this chapter, we will first give a review of past experimental and modeling studies on STEGs, followed by a summary of some modeling and experimental results we have done.

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24.2 Historical Review The efficient and cost-effective conversion of the solar radiation, which strikes our planet at a tremendous rate, is a challenging and complex task for science and engineering. So far, photovoltaic and concentrated solar thermal-to-electrical power conversion technologies are considered to be the most promising approaches. The concept of solar TE power conversion has not drawn much attention as a renewable power conversion approach due to the low efficiencies and/or bulky and costly designs that have been reported over the past century. Recent work showed very promising experimental results for a terrestrial STEG design1 that potentially enables low-cost manufacturing and an efficiency of 4.6% under AM1.5G conditions with no optical concentration, and larger than 5% efficiency with only small optical concentration. The history of the solar application of TE generators started more than 120 years ago with the first patents by Weston2,3 which claimed as new inventions the combination of a thermopile with a mirror or lens to focus solar radiation onto the hot junctions, and a storage battery to accumulate the electric energy. The first experimental work, published in 1922, reported an efficiency of 0.008% for an STEG consisting of 105 copper–constantan thermocouples.4 Three decades later Telkes published the first detailed experimental work on STEGs.5 She investigated STEGs with flat-plate solar absorbers in air. In order to reduce air convection losses several glass panes were used to cover the STEG cells. She tested different TE materials and different cooling mechanisms to remove the excess heat on the cold side. In addition, she performed STEG experiments with an optical concentrator that could achieve up to 50 times the incident solar radiation. However, the measured efficiencies of 0.63% at 1 Sun and 3.35% at 50 Suns were too low to be applied on a large scale despite the advantages of reliability and low maintenance. Her conclusion was that this technology would only be useful in tropical regions with high insolation where fuel resources are often absent or not yet developed, and electrical power generation facilities are nonexistent. In the 1960s, the concept of solar TE generation was investigated for space applications where power density (per mass) is the most important design parameter.6–9 The use of Bi2Te3-based STEGs as the power source for near-earth orbit missions was discussed6,7 and it turned out to be a promising application due to higher power density (per mass) and power-to-cost ratio than for photovoltaic cells at that time. STEGs have also been considered for space probe missions close to the sun8,9 due to their resistance to high radiation intensity and their ability to withstand high temperatures by using high-temperature TE materials including PbTe and Si1–xGex. In 2003, Scherrer et al. theoretically investigated the use of skutterudite-based STEGs for deep-space probe missions as well.10 Later efforts on terrestrial solar TE power conversion focused on concentrated STEGs.11–14 The idea is to increase the incident radiation flux onto the solar absorber by means of an optical concentrator system which is similar to those used in solar thermal-to-electrical power conversion technologies. The systems can become structurally and capital-cost intensive15 which makes them mostly applicable as large-scale power generation units and unfeasible for residential and commercial rooftops. Nevertheless, the concentrated solar intensity enables shrinking the size of the STEG cell which will reduce external heat losses. Additionally, by using high-temperature-resistant materials or even segmented TE legs or cascaded TEGs,16 a larger temperature difference across the TE legs can be utilized which will lead to a higher device efficiency if materials are available. These two factors will ultimately contribute to a higher efficiency of those types of terrestrial STEGs.17 However, to put it into perspective, state-of-the-art solar

© 2012 by Taylor & Francis Group, LLC


Solar Thermoelectric Power Conversion

24-3

thermal-to-electrical power conversion technologies that use conventional power blocks (steam turbine and generator) have adiabatic turbine efficiencies between 70% and 80%, and it will take a significant improvement in TE properties (current TE materials enable an adiabatic TE efficiency of approximately 20%) to replace that power block. This is especially true due to the fact that the power block contributes only about 15% of the total cost of a solar thermal power plant,15 so the cost savings from potentially cheaper TE systems would be small compared to the total cost of the solar energy harvesting system. Nevertheless, Dent and Cobble11 built a prototype STEG comprising a sun-tracking heliostat which directed the incident sunlight onto a parabolic mirror which then focused the sunlight onto an STEG. With PbTe as the high-temperature TE material, Dent et al.’s system reached a hot-side temperature of 510°C and a maximum temperature difference of 420°C across the TE device, resulting in a maximum STEG efficiency of 6.3% excluding the optical concentrator losses. No details on the optical concentration were given. Surprisingly, their experimental results were 30% higher than their theoretical prediction. In 1998 Omer and Infield12 also investigated concentrated STEGs using an infrared lamp with an optical concentrator achieving an incident flux of 20 kW/m2, corresponding to 20 Suns. Experiments were performed with a commercial thermoelectric cooler (TEC) module and an efficiency of 0.9% was reported. Their modeling efforts were based on averaged material properties, however they used a creative way to account for the Thompson heat by calculating it as the product of the current, Thompson coefficient, and the temperature across the module and then adding one half of it to the hot junction and the other half to the cold junction. External heat losses were also included. Their theoretical study discussed the influence of electrical and thermal contact resistances on the optimal length of the TE elements. One of their main conclusions was that TEG modules should be optimized for optimum power and not for highest efficiency, which was supported by their modeling results. However, this is questionable because the STEG design should be optimized for a constant incident solar radiation flux (in their case 20 kW/m2) which leads to the conclusion that the operational point of maximum power output also corresponds to the point of maximum efficiency of the device. In early 2010, Amatya and Ram13 reported an experimental investigation of the concept of STEGs for micropower applications using a commercial TE module combined with a parabolic mirror and a Fresnel lens. They measured an efficiency of 3% at 66 kW/m2 excluding the optical losses of the concentrator. A cost analysis predicted an electricity price of 0.35 $/kWh if the system would be installed in Nepal. The latest work on concentrated STEGs was reported by Li et al.,14 who investigated theoretically the effect of the optical concentration and of the cold-side cooling method on the system efficiency and the hot-side temperature for a specific device geometry (size of heat collector, TE elements, and number of TE couples). They performed simulations with Bi2Te3, skutterudite and LAST (lead–antimony–silver–tellurium) alloy-based TE materials using temperature-dependent properties reported in literature. Their simulated concentrated STEG system could reach efficiencies of 9.8% (Bi2Te3), 13.5% (skutterudite), and 14.1% (LAST) accounting for an optical efficiency of 85%, a solar absorptance of 0.9 and an infrared emittance of the solar absorber of 0.08, and neglecting all other heat losses in the system. They concluded that the conversion efficiency increases with increasing optical concentration and the maximum optical concentration should be selected according to the maximum hot-side temperature permitted by the chosen TE material. Goldsmid et al.18 in 1980 and a more recent work by Vatcharasathien et al.19 compared two lowtemperature STEG systems of which one was a flat-panel design and the other a concentrated STEG system with low optical concentration. Both used commercial Bi2Te3-based TEC/TEG modules for their experimental setups. Goldsmid used a semi-parabolic and Vatcharasathien a 2D compound parabolic concentrator (CPC) for the experiments with optical concentration. The efficiencies reported for both types of STEGs were lower than 1%. Despite the improvements of the properties of TE materials over the last two decades,20–24 the TE device efficiency is still relatively low which means that most of the heat is rejected at the cold junction of the device and could potentially be used for space heating or domestic hot water. This was proposed with promising results by recent publications.1,25 Depending on the fluid temperature at the cold junction, the electrical efficiency of flat-panel STEG cells varied between 4.6% (20°C) and 3.3% (60°C) under one Sun



24-4


condition and could be higher with small optical concentrations. Although the potential combination of solar hot water systems and TEGs was recognized before,5 there has been no practical way to achieve the combination economically. A theoretical and experimental work on cogeneration systems was published by Rockendorf et al.26 in 2000. Their solar collector comprised vacuum tubes with water heat pipes. The steam was condensed at the hot side of a TEG module to convert some of the thermal energy into electrical power. The water that heated up at the cold side of the TEG was then stored in a tank for further use. A maximum electrical efficiency of 1.1% for an insolation of approximately 0.9 kW/m2 was reported when the cold-side fluid temperature was maintained at ambient temperature. Increasing the fluid temperature to 63°C reduced the efficiency to 0.65%. In addition to the low efficiency, the TEG also represented an additional thermal resistance in the system which resulted in a drop of the solar collector efficiency by 45% compared to an identical collector without a TEG. Those experimental results and further simulations led the authors to the conclusion that the gain in electrical power did not balance the large loss in thermal energy output. Consequently, the proposed TE collector was concluded to be economically unfeasible. Another interesting concept for STEGs is to incorporate them in a photovoltaic (PV)–TE hybrid system. Luque and Marti27 discussed the limiting efficiency of coupled thermal and photovoltaic converters. They concluded that in practical cases where the solar thermal system is limited by a reasonable hot-side temperature and the PV cell is limited by a reasonable finite number of different band-gap materials the hybrid converter may give significantly higher efficiency than the individual solar converters alone. In 2005, Zhang et al.28 published the first work proposing a PV–TE hybrid system. The authors suggested splitting of the solar spectrum into two distinct parts. The visible part of the spectrum was converted by the solar cell and the IR portion by a TE generator. The authors considered Bi2Te3 as the low-temperature TE material for the TEG but also proposed to use high-temperature materials and large optical concentration to improve the system efficiency. One year later Vorobiev et al.29 discussed two hybrid system designs. In both designs the PV cell was located above the TEG cell. In one system, the cells were thermally insulated from each other. The light that was transmitted by the PV cell was optically concentrated onto the TEG. The second design related to concentrated PV cells, where cell heating due to high incident solar flux can significantly affect the performance of the system. Mounting the PV cell directly on the TEG enabled conversion of not only the radiation transmitted through the PV cell but also the generated heat due to the thermalization of electron–hole pairs to the band gap energy inside the PV cell. The reported simulation results, however, are unrealistic. The assumed TE properties were very optimistic which overestimated the contribution of the TEG to the performance of the hybrid system. Kraemer et al.30 developed an optimization methodology for PV–TE hybrid systems in which the heat generation of the PV cell should be minimized while achieving maximum hybrid system efficiency. The authors discussed different PV(thin film)–TE hybrid cells and came to the conclusion that the largest increase in efficiency compared to initial PV cell efficiency can be achieved for polymer solar cells.

24.3 optimization of SteGs The first step in designing a STEG is to consider how to create a temperature difference across the TEG. The TEG modules commercially available today consist most commonly of a large number of closely packed TE legs. The legs usually have a small cross-sectional area of 1–4 mm2 and a length (L) of about 1–2 mm. The heat flux flowing through a TEG is on the order of qte ≈ k

∆T L

(24.1)

where k is the thermal conductivity of the TE legs. Taking k ~ 1 W/m K and ΔT = 100–500°C, the device heat flux through a thermoelectric leg is 5 × 104–5 × 105 W/m2. This heat flux is 50–500 times larger than AM1.5G solar insolation (1000 W/m2). Clearly, concentration of the solar flux is needed to create a


24-5



reasonable temperature difference across the TEGs, which is required to efficiently convert the heat flux into electricity. Such concentration was mainly achieved by optical means in the past (Figure 24.2a). However, optical concentration systems with a concentration ratio higher than 50 are usually bulky and add considerable cost to a STEG. Another way to concentrate the solar flux to a TEG is via heat conduction, as shown in Figure 24.2b. In this case, solar radiation is absorbed by an absorbing surface deposited on a highly thermally conductive substrate (e.g., copper). The absorbed solar radiation will flow to the TEG via heat conduction. We will call the ratio between the solar absorber area, Aabs, and the total cross-sectional area of the TE elements, ATE , the thermal concentration, Cth (Figure 24.2c). Of course, a combination of optical and thermal concentration can be adapted whenever economically feasible. When large thermal concentration is used, heat loss via radiation and air conduction/convection from the surface of the hot solar absorber can be significant and detrimental to the efficiency of the device. For STEGs with large optical concentration those losses are less important. Based on the assumption of temperature-independent properties, Rowe31 for high optical concentration and Chen32 for large thermal concentration obtained that the efficiency of a STEG can be expressed as   Tabs − Tc  1 + (ZT )m − 1  ε σ(T 4 − Tc4 ) Qcon ηSTEG = ηot ηTEG =  ηopt − e abs −   T C q A C q 1 + (ZT )m + Tc / Tabs  abs opt sol abs opt sol    

(24.2)

where the first factor is the opto-thermal efficiency, ηot, which includes the optical efficiency, ηopt = ηconcτgαs, that accounts for possible optical solar concentration losses, ηconc, the glass transmission losses, τg, and the absorptance, αs, of the solar absorber. The second term of the opto-thermal efficiency corresponds to the radiation losses from the absorber (at temperature Tabs) to the cold side and ambient (at temperature Tc). The effective emissivity εe accounts for radiation losses from both sides of the absorber. The incident radiation flux onto the STEG is the constant incident solar radiation qsol multiplied by the optical concentration Copt. The third term of the opto-thermal efficiency is the loss via air conduction/convection, Qcon. The second factor of the STEG efficiency is the TE generator efficiency, ηTEG, which is here assumed to be the ideal TE efficiency equation.33 It is determined by the Carnot efficiency multiplied by the adiabatic TE efficiency which is a function of (ZT)m, the averaged figure of merit (a)

(b)

Sunlight Optical concentrator system

Sunlight Solar absorber

Heat flow

Heat rejected

Solar absorber TEG Heat rejected Heat sink

Pelectric

TEG Pelectric

(c) Cross-sectional area of TE elements, ATE Cth =

Heat sink

Aabs ATE

Absorber area, Aabs

FIGURE 24.2 (a) Conceptual STEG design with large optical concentration, (b) conceptual STEG design with large thermal concentration, (c) graphical explanation of thermal concentration Cth, which is the ratio between the absorber area Aabs and the total cross-sectional area of the TE elements ATE.


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 Aabs − An − Ap Aabs  Tabs − Tc Qcon = kair  +  (Tabs − Tc ) ≈ 2kair L L L 1  

(24.3)

(a)

(b) 10 Incident solar radiation Optical concentrator Solar absorber p

n

Enclosure

100

ηTEG

8

80

ηot

6

60

4 2 0

40

ηSTEG

20

Tc = 25°C 50

100

150

200

250

Opto-thermal efficiency (%)

where L1, the separation between the absorber and glass enclosure is assumed to be equal to the separation between the absorber and the cold side, which is set equal to the TE leg length L. For the case of large thermal concentration the presence of the TE legs can be neglected and with that the cross-sectional areas of the TE legs, An and Ap, do not need to be subtracted from the absorber area. Using typical values for the temperature difference, leg lengths and the thermal conductivity of air, kair, it turns out that the conduction and convection losses can easily exceed the radiation losses. Hence, to achieve reasonable efficiency at a low optical concentration ratio, vacuum operation is favored. Fortunately, existing technology in evacuated tubes for solar–thermal steam plants and solar hot-water systems has proven that vacuum operations are realistic and economically feasible.34 To achieve high opto-thermal efficiency, the absorber should have high absorptance in the wavelength spectrum of the incident solar radiation but a low emittance for the spectrum of a blackbody at the operational temperature. This spectral behavior is characteristic for wavelength-selective solar absorbers widely used in solar thermal applications. These state-of-the-art solar absorbers have a large absorptance in the solar spectrum (2–2.5 μm) between 4% and 8% depending on the operational temperature (100–250°C). With increasing temperature the IR emittance will continue to increase due to temperature-dependent emissivity and the temperature-dependent shift of the blackbody spectrum to shorter wavelengths resulting in a larger overlap with the region of high absorptance/emittance.35,36 We note that in Equation 24.1, the opto-thermal efficiency decreases while the TEG efficiency increases with increasing absorber temperature, Tabs. Hence, an optimal hot-side temperature exists that maximizes the STEG efficiency which corresponds to a specific thermal concentration. The larger the thermal concentration the higher is the absorber temperature. Figure 24.3b shows the variations of the three efficiencies for a set of given conditions. Using the introduced model based on temperature-independent (ZT)m, this optimal absorber temperature is given by

STEG/TEG efficiency (%)


for the thermocouple. Important to realize for the STEG optimization is that the maximum power point of a STEG also corresponds to the operation point of maximum STEG efficiency due to the incident solar radiation being a fixed heat input. This is different for other TEG applications such as waste heat recovery with, for example, a fixed hot-side temperature and a variable heat input. In this case, the TEG has different maximum efficiency and maximum power conditions. For a TEG housed inside an enclosure with narrow gaps (Figure 24.3a), we can express the conduction losses as

0

Absorber temperature (°C)

FIGURE 24.3 (a) Concept of a unicouple STEG cell with large thermal and small optical concentration mounted inside a narrow-gap glass enclosure, (b) graphical explanation of STEG optimization: black solid line is the TE generator (TEG) efficiency, gray dashed line is the opto-thermal efficiency, black dash-dotted line is the STEG efficiency.


24-7


4 1 + (ZT )m  1 + (ZT )m + Tc /Tabs  ηoptCoptqsol − ε eσ(Tabs − Tc4 ) = 4 4 ε s σTabs Tc 1 + (ZT )m / (Tabs − Tc ) + 1/2  1 + (ZT )m + 1  

(

)

(24.4)

 An   kp + kn Ap  T 1 + ZT + (T − T ) / 2 c m h c Cth L = 3 A 4 ε σ T T n s h m 1+ Ap

(24.5)

Figure 24.4 summarizes the losses affecting the STEG performance that have been discussed so far. This figure is obtained with a detailed model of STEG cells, which includes a more accurate heat transfer model, electrical contact resistances and temperature-dependent properties of the TE materials and the solar absorber.25 The model is briefly described in the next section. If nonconcentrated sunlight strikes an STEG cell which uses a black absorber and is exposed to air at standard conditions the performance is very poor (solid line). The maximum efficiency hardly reaches 0.5%. An enhancement in the STEG cell performance is expected when the cell is mounted inside an evacuated enclosure due to the elimination of air conduction/convection losses (dash-dotted line). However, the radiation losses from the black absorber still limit the maximum efficiency to approximately 1.5%. Replacing the black absorber by a spectral solar absorber boosts the performance significantly to between 4% and 5% for an effective ZT of 1 (dashed line). If the TE material has an effective ZT of 0.8 the maximum STEG efficiency will not exceed 4% (dotted line). As discussed, the alternative to thermal concentration of the heat flux is optical concentration of the radiation flux to create the necessary temperature difference across the TEG. Then the absorber losses are minimized due to the small absorber size. Therefore, with high enough optical concentration it is possible to achieve similar or even better performance with an STEG cell exposed to atmospheric air and using a black absorber 8 Black absorber, in air, ZT = 1, Copt = 50

7 STEG cell efficiency (%)


It is interesting to note that the optimal absorber temperature is independent of the TEG geometry. The thermal concentration and leg length obeys the following relation:

6

Selective absorber, in vacuum, ZT = 1

5

Selective absorber, in vacuum, ZT = 0.8

4 3 2 Black absorber, in air, ZT = 1.0

1 0

1

Black absorber, in vacuum, ZT = 1.0

10 100 Thermal concentration Cth

1000

FIGURE 24.4 Simulation results for different STEG designs: solid line—STEG without optical concentration, in air, with black absorber and effective ZT of 1; dash-dotted line—STEG without optical concentration, in vacuum, with black absorber and effective ZT of 1; dotted line—STEG without optical concentration in vacuum with stateof-the-art wavelength-selective solar absorber and effective ZT of 0.8; dashed line—STEG without optical concentration, in vacuum, with wavelength-selective solar absorber and effective ZT of 1; solid line with open squares—STEG with 50× optical concentration, in air, with black absorber and effective ZT of 1.



24-8


(solid line with open squares) than in vacuum with large thermal concentration and a sophisticated spectral solar absorber. However, the feasibility of this type of STEG still has to be proven due to additional optical concentration losses (mirror/lens losses, tracking losses, diffuse-light losses) which are not included in the STEG cell efficiency. An important conclusion from this figure is that the STEG design with large thermal concentration can only meet its potential when the solar absorber losses are minimized. Kraemer et al. investigated in detail the constraints on the optimal STEG design due to external irreversibilities such as electrical contact resistances, geometry-dependent radiation losses and temperature nonuniformity of the solar absorber.25 The effect on the geometric optimization parameter Cth L (product of thermal concentration and TE leg length) is also discussed. The minimum TE element length can be limited by the electrical contact resistance. The smaller the TE element, the larger is the relative electrical contact resistance and the performance loss. However, this loss in performance is less than 2% (rel.) for an electrical contact resistance of 5 × 10−7 Ω cm2 for an element as short as 0.3 mm. Thus with reasonably low electrical contact resistance the STEG performance as well as the geometrical optimization parameter stays unaffected and the minimal element length is mainly limited by manufacturing processes. The geometry-dependent radiation losses have a larger effect on the STEG cell performance. This limits the maximum element length and suggests using the shortest TE elements possible. For a simple flat-plate design, longer TE elements result in a larger gap between the solar absorber and the cold side; this increases the radiation losses from the back side of the absorber and from the sidewalls of the TE elements to the blackbody surroundings. For example, changing the element length from approximately 0.8 to 4 mm decreases the STEG cell efficiency from approximately 5.35% to 5%. Another concern with large thermal concentration is the temperature drop within the absorber from its outer edge to the TE elements. The temperature drop is due to the radial conduction resistance and large radial heat flux of large absorbers. If the temperature nonuniformity in the solar absorber is large, then most of the absorber will have a higher temperature than its junction with the TE elements. A higher temperature results in more radiation losses than if the absorber temperature were uniformly at the TE hot-junction temperature. This causes a decrease of the opto-thermal efficiency. We can use a simple annular fin model37 including the incident radiation as a constant heat source along the fin in order to estimate this temperature nonuniformity. This fin model approximates the absorber as a copper disc with thermal conductivity of 380 W/(mK), thickness t = 0.2 mm, and radius Rabs and the TE elements as a cylindrical base with radius r TE at a fixed temperature (Figure 24.5a). A solution based on Bessel functions is available to approximate the temperature gradient within the absorber depending on the STEG design geometry. The simulation results shown in Figure 24.5b–d, however, are obtained from a numerical solution based on a radial finite difference scheme. In all three cases, the thermal concentration is varied. Figure 24.5b shows the simulation results for changing solar absorber size while maintaining a constant TE element cross-sectional area. In Figure 24.5c, the solar absorber size is kept constant and the cross-sectional area of the TE elements is varied. The temperature drop within the absorber is significantly larger if the absorber size is increased compared to if the crosssectional area of the TE elements is decreased. This is because the heat flux conducted radially is proportional to the square of the absorber radius, but the increase of the radial conduction resistance scales with ln(Rabs/r TE).37 Figure 24.5d shows simulation results using a significantly larger cross-sectional area of the TE elements which can be thought of as a TEG module with a large number of closely packed thermocouples. The simulations show that with an equivalent radius of 4.8 mm (20 thermocouples with equivalent radius of 1.08 mm) the temperature drop within the absorber becomes very large in order to drive the large heat flux. In addition to the temperature gradient away from the TEG module, there will be a significant nonuniformity of the temperature over the TEG module if due to cost-considerations the copper substrate thickness, t, is chosen to be 0.2 mm.25 This suggests that conventional TEG modules are not suitable for solar applications with no/low optical concentration and large thermal concentration. The best performance will be achieved for STEG cells which individually consist of a solar absorber mounted to a small TE unicouple as shown in Figure 24.6. These unicouple STEG cells can be electrically connected in series to a larger STEG cell array in order to increase the voltage and power output.


24-9

Solar Thermoelectric Power Conversion Constant incident solar radiation

(a)

T Tbase

800

190

r

450

185

t

180

Rabs

(c) 184

1300 800 450 250

183

Cth = 100

182

0

(d) 300

5 10 15 Radial position on absorber (mm)

20

800

260

180

40

1300

280 450 250

200

Rabs = 17.03 mm

rTE = 1.08 mm


220

0

250

240

181 180

100

Temperature (°C)

rTE

Temperature (°C)


Cth = 1300

195

Temperature (°C)

Th,TE

(b) 200

Cth = 100 0

rTE = 4.8 mm


200

FIGURE 24.5 (a) model geometry of STEG for radial fin analysis: Tbase is the fixed base temperature of the radial fin which is set equal to the hot-junction temperature of Th,TE (180°C) of the TE element, r TE is the equivalent TE element radius r TE = (ATE/π)(1/2) and Rabs is the equivalent radius Rabs = (Aabs/π)(1/2) of the solar absorber. Graphs are simulation results (numerical solution based on radial finite difference scheme) of the radial fin for different thermal concentrations Cth with (b) fixed r TE = 1.08 mm and changing Rabs, (c) fixed Rabs = 17.03 mm and changing r TE , and (d) fixed r TE = 4.8 mm and changing Rabs.

It can be concluded that in order to minimize TE material costs, the length of the TE element should be reduced. However, to keep the optimal Cth L for maximum unicouple STEG cell performance the thermal concentration must be increased by reducing the cross-sectional area of the TE elements and not by increasing the absorber size in order to prevent detrimental performance losses from a large radial temperature nonuniformity.

24.4 Simulations and experiments of SteGs A detailed model has been developed for STEG designs as schematically shown in Figure 24.6.25 This model can be used to simulate and optimize the performance of STEG cells based on large thermal concentration with no/small optical concentration (Figure 24.6a) and small thermal concentration with large optical concentration (Figure 24.6b). The model takes into account temperature-dependent properties of the TE materials and the spectral solar absorber, electrical contact resistances, geometrydependent heat losses, and the nonuniform temperature of the solar absorber. The losses are schematically summarized in Figure 24.7a and b. In order to account for the effect of the temperature-dependent TE material properties, the electrical contact resistances, and the heat losses from the sidewalls of the TE elements on the STEG cell performance, the TE elements are discretized and solved numerically with the iterative technique38,39 as shown in Figure 24.7c. Besides the properties of the solar absorber and TE materials, the geometry-dependent radiation losses, the temperature distribution within the solar absorber, and the electrical contact resistance,


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(a)

(b)

Sunlight

Sunlight Optical concentrator system

qin Frequency selective surface

TE elements

Heat flow

qin

TE elements


TE leg

p

Cu plates (electrodes and radiation shield) ITE

n

Cu substrate

p

n

Solder contacts

Cu plates (electrodes and radiation shield)

Unicouple Solder contacts TEG VTE

Solar absorber

VTE

ITE

Load

Load

FIGURE 24.6 Detailed schematic of a unicouple STEG cell with (a) large thermal concentration and (b) large optical concentration.

(a)

(c)

qin

Eb,ss

T

0

Solar absorber QTE,h

Heat flow Eb1

J S = iS –

Eb2

x

k DT T dx

x + dx

TE element S(T), k(T), ρ(T)

Eb3 QTE,c

L Electrical contact resistance (b)

T

(iST)x qr

Th,TE R

μ i –e x

–k

dx

dE/dx (iST)x+dx

μ i –e x+dx

dT dx x

–k

dT dx x+dx

FIGURE 24.7 Graphical illustration of external losses from (a) thermal radiation and electrical contact resistance and (b) temperature nonuniformity in absorber, (c) discretization of TE elements and energy balance over one increment with Js as the local entropy flux, S the Seebeck coefficient, k the thermal conductivity, ρ the electrical conductivity, T the local temperature, (–e) the electron charge, i the current density, and µ as the local electrochemical potential (Fermi level).


24-11


5

4 3

1

(sim)

kWm–2

(exp) 1 1.5 kWm–2 (sim)

2 1 0 100

kWm–2

1.5 kWm–2 (exp) 150

350 200 250 300 Thermal concentration

400

4 Cth = 299 (sim)

3

Cth = 299 (exp)

2

Cth = 168 (sim)

1 0 0.2

Cth = 168 (exp) 1.4 1.8 0.6 1.0 Incident solar radiation flux (kWm–2)

STEG efficiency (%)

(c) 7 6 5 4

1 kWm–2 (sim)

3

1 kWm–2 (exp) 1.5 kWm–2 (sim)

2 1 0

1.5 kWm–2 (exp) 0

10 20 30 40 50 Cold-side temperature (°C)

60

FIGURE 24.8 Experimental results with simulations result showing (a) the optimization of the thermal concentration (b) the effect of the incident solar radiation, and (c) the effect of the cold-side temperature.

the optimal geometrical optimization parameter C th L is dependent on the solar intensity striking the solar absorber and on the cold-junction temperature. Consequently, the STEG cells should be optimized for best performance over the course of a day or even the year for the specific location where the system will be installed. Figures 24.8 and 24.9 show simulation and experimental results of the most recent publications on STEGs.1,25 The optimal C th L decreases with increasing cold-junction

STEG cold-junction heat rejection (W)


STEG efficiency (%)

(b) 6

5

STEG efficiency (%)

(a) 6

800

100

50

25

15 W/K

750 700 650

5%

4%

0%

1% 3%

2%

600 550

2%

500 450

3.0 A

10

1% 30

40 50 60 70 80 STEG cold-junction temperature (°C)

0% 90

2.5 A 2.0 A 1.5 A 1.0 A 0.5 A 0.0 A

100

FIGURE 24.9 STEG operation diagram for Cth L = 0.4 m and heat sink (fluid) temperature of 25°C showing the cold-junction heat rejection for an STEG area of 1 m2 as a function of the cold-junction temperature and the STEG cell current. Red dashed lines are contour lines of constant STEG efficiencies. Black solid lines are lines of constant cell currents. Gray dash-dotted lines are lines of constant cold-side thermal conductance.


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CthL = 0.20 m

6

CthL = 0.30 m CthL = 0.40 m

5 4 3

CthL = 0.70 m

2 1 0 0

CthL = 1.30 m 0.5 1 1.5 2 2.5 Solar intensity (kW/m2)

3

(b) 6 STEG efficiency (%)

STEG efficiency (%)

(a) 7

5 4

Tc = 25°C Tc = 50°C Tc = 75°C Tc = 100°C

3 2 1 0 0.2

0.4

0.6

0.8

1

1.2

CthL (m)

FIGURE 24.10 Simulation results showing the effect of (a) the solar intensity and of (b) the cold-junction temperature on the STEG cell efficiency and the geometrical optimization parameter Cth L.

temperature and solar intensity (Figure 24.10a and b). Kraemer et al. 25 also showed that if the STEG efficiency is averaged over the course of a day, it becomes a weaker function of C th L which means that in the case of a cogeneration system the C th L can be varied in favor of the thermal efficiency of the overall system efficiency without significantly affecting the daily electrical performance. The integration of an STEG in a cogeneration system will be discussed in more detail in Section 24.5. Guided by the detailed model briefly described above experiments were performed1 and some results are summarized in Figure 24.8. Figure 24.8a shows the experimental optimization of the thermal concentration for a given TE element length, L, and two different incident solar fluxes. Higher solar intensity results in a smaller optimal thermal concentration and in a higher STEG efficiency. As predicted by the model, an STEG cell with fixed geometry shows a dependence on changes of the incident solar flux and cold-junction temperature (Figure 24.8b and c). A peak in STEG efficiency can be observed at a specific solar intensity. At fluxes larger than this solar intensity, the flux through the TEG increases which results in a higher absorber temperature. The higher temperature increases the radiation heat losses from the solar absorber, causing a decrease in the opto-thermal efficiency that is larger than the increase in TEG efficiency, resulting in lower STEG cell efficiency. A higher cold-junction temperature results in a lower STEG efficiency for three reasons. An increasing cold-junction temperature drives up the absorber temperature, which results in larger radiation losses from the solar absorber. This not only results in a lower absorber efficiency but also reduces the temperature difference between the hot- and the cold-junction which reduces the device efficiency. In addition, for TE materials such as Bi 2Te3 the temperature-dependent figure of merit decreases for temperatures higher than ~100°C. Consequently, the higher the STEG operation temperature (Tabs > 100°C) the lower is the effective figure of merit, (ZT)m, resulting in a lower adiabatic TE efficiency.

24.5 SteG Performance and System integration In solar TE systems, approximately 50–80% of the intercepted solar heat is released at the cold junction of the device. This waste heat must be removed in order to maintain the cold junction at a given temperature for highest STEG performance. One way to remove this excess heat is first to spread it out on the cold side using a metallic heat spreader, and then to transfer the heat to the environment via natural convection, similar to what is done for the heat management of PV cells. In certain applications such as cogeneration, this waste heat is actually the input to a secondary system, such as a domestic hot-water loop. Small deviations from the peak TEG operating point can have large (positive




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or negative) effects on the quantity of heat delivered to the heat sink. As a result, an STEG cogeneration system can be designed to favor the production of either electrical power or waste heat, depending on the demands of the application. This can be accomplished by choosing the appropriate geometric parameter CthL (Figure 24.10b). If it is desired to optimize the system for maximum electrical power then there is one specific optimal CthL for a specific cold-junction temperature and incident solar flux as discussed in previous sections. Conversely, choosing a smaller CthL results in more heat transported to the hot water loop because the absorber stays at a lower temperature and thus the system radiation losses are smaller. Fortunately, as mentioned in the previous section, in the case of a daily total STEG electrical energy output is a weaker function of CthL, so it is possible to deviate from the optimal CthL for maximum electrical performance with only a negligible affect on the daily electrical performance. For a system with fixed C th L, it is even possible to adjust the balance between electrical power and waste heat solely by adjusting the electrical current of the circuit. As an example, we consider a system of C th L = 0.4 m. Because the waste heat and cold-junction temperature are both affected by the current, it is useful to plot the waste heat per 1 m 2 absorber area as a function of cold-junction temperature at various currents (Figure 24.9). Superimposed on this figure (dashed lines) are contour lines representing the corresponding STEG efficiency. This STEG operation diagram can be used to determine the conditions where the STEG can operate, because the performance of any heat sink can be characterized by the relationship between the heat sink temperature and the rejected heat. As an example, if the cold-junction heat removal is managed by a fluid passing over the cold junction, the constant of proportionality between the transferred heat and the temperature difference between the fluid and the cold junction is the thermal conductance, Uth = A × h in units W/K. In Figure 24.9, dash-dotted lines of constant Uth are plotted in gray assuming a fluid temperature of 25°C. Changing the electrical current allows the system to operate at different points along this characteristic Uth curve, which affects the cold-junction temperature, the amount of rejected heat, and the amount of electrical power generated. For example, if it is desirable to generate more waste heat in the morning and more electricity in the afternoon, it is possible to run the system in an “overdrive” mode (with super-optimal current) in the morning, and then run the system at optimal current in the afternoon. Interestingly to notice is that there will always be two operational current points with same STEG efficiency but with different cold-junction heat rejection rates if the STEG is operated at off-optimal conditions. For example, for a heat sink with thermal conductance of 25 W/K the line of constant Uth intersects the 4% efficiency contour line twice. One intersection corresponds to a cell current of 1 A and the other one to approximately 1.75 A. At higher cell current more heat is transported through the TE unicouple by the energy carriers and rejected at the cold junction. This will drop the temperature of the solar absorber but also increase the cold-junction temperature in order to support the larger heat flux.

24.6 Potential for improvement There are some ways to improve the STEG cell efficiency, including improving the TE materials; increasing the absorber’s solar absorptance; decreasing the absorber’s IR emittance; changing the STEG geometry; developing selectively transmitting glass; or increasing the optical concentration. Figure 24.11 shows the predicted performance boost for various improvements such as the reduction of the effective emittance of the solar absorber (Figure 24.11a). If optical concentration is used, the operational absorber temperature of the STEG cell will be limited by the temperature stability of the TE materials. In the case of Bi2Te3 materials the operational absorber temperature is limited to below 250°C. Figure 24.11b shows that a further increase of the optical concentration from 3 to 10 will not lead to a significant increase of efficiency if the temperature limit of the solar absorber is set to 220°C. However, if segmented TE elements or cascaded TEGs with different materials are used higher optical concentration is beneficial (Figure 24.11c).


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STEG efficiency (%)

10

(c)

0

STEG efficiency (%)


STEG efficiency (%)

(a) 10 9 8 7 6 5 4 3 2 1 (b) 0 12

ε = 0.03 Copt = 1

ε = 0.07 ε = 0.12

8 6

Copt = 1

4

Th = 220°C

2

ε = 0.03

Copt = 3 Copt = 10

14 12 10 8 6

Copt = 1

4

Copt = 3

2 0

ε = 0.06 0.5

Copt = 10

1.0 1.5 Effective figure of merit (ZT)M

2.0

FIGURE 24.11 Simulation of the performance of an STEG in vacuum as a function of the effective figure of merit (ZT)M showing results (a) for an STEG without optical concentration with different solar absorber emittance, (b) for different optical concentrations Copt with constant solar absorber emissivity of ε = 0.03, limited absorber temperature to Th = 220°C, and (c) for different optical concentrations Copt with constant solar absorber emissivity of ε = 0.06 and no limits on the absorber temperature.

Acknowledgments We would like to thank Drs. Bed Poudel, J. Christopher Caylor, and Matteo Chiesa for helpful discussions. This material is partially based upon work supported as part of the “Solid State Solar-Thermal Energy Conversion Center (S3TEC),” an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number: DE-SC0001299/ DE-FG02-09ER46577 (D.K, K.M, G.C., and Z.F.R.), and by MIT-Masdar program (D.K. and G.C.).

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