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Chapter 16Solar TE Converter Applications

Anke Weidenkaff, Matthias Trottmann, Petr Tome, Clemens Suter,Aldo Steinfeld and Angelika Veziridis

Abstract Thermoelectricity does not only serve to protably recover waste heatfrom many technical processes but also to exploit renewable energy resources forpower generation. Conversion of concentrated solar radiation for decentralized elec-tricity supply is a very promising application eld for thermoelectric (TE) devices.However, experimental and theoretical studies with high-temperature resistant ther-moelectric oxide modules (TOMs) reveal that 60 % of the incident solar radiation islost due to reradiation and only 20 % is available for electricity conversion. Calcula-tions with a heat transfer model show that this loss can be substantially reduced from

60 % to only 4 % by using a solar cavity receiver instead of directly irradiated TEmodules. The fraction of actually usable solar power can thereby be increased from20 to 70 %. Despite the improved exploitation of solar radiation, solar-to-electricity

A. Weidenkaff (B ) M. Trottmann A. VeziridisEmpa. Swiss Federal Laboratories for Materials Science and Technology Solid State Chemistryand Catalysis, Ueberlandstrasse 129, CH-8600 Duebendorf, Switzerlande-mail: [email protected]

M. Trottmann

e-mail: [email protected]. Veziridise-mail: [email protected]

P. TomeVienna University of Technology Institute of Solid State Physics, Wiedner Hauptstrasse 8-10,A 1040 Wien, Austriae-mail: [email protected]

C. SuterAFC Air Flow Consulting AG, Weinbergstrasse 72, CH-8006 Zuerich, Switzerlande-mail: [email protected]

A. SteinfeldETH. Swiss Federal Institute of Technology Zurich Institute of Energy Technology,Sonneggstrasse 3, CH-8092 Zuerich, Switzerlande-mail: [email protected]

K. Koumoto and T. Mori (eds.), Thermoelectric Nanomaterials , Springer Series 365in Materials Science 182, DOI: 10.1007/978-3-642-37537-8_16, Springer-Verlag Berlin Heidelberg 2013


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366 A. Weidenkaff et al.

efciency of TOM converters continues to be low due to the still low Figure of MeritZT of oxide materials. This disadvantage may in part be compensated by highertemperature differences resulting in higher conversion efciencies. However, due tothe temperature dependence of TE properties the use of a single material at a largetemperature difference is not ideal. Preferably, a stack of different materials, eachoperating in its most efcient temperature range, should be applied. Calculationswith the heat transfer model show that with a solar cavity-receiver packed with dual-stage cascaded modules containingin addition to Bi-Tea TE oxide available atpresent (ZT = 0.36) a solar-to-electricity efciency of 7.4 % can be achieved. Withfuture advanced oxide materials (ZT = 1.7) an efciency of even 20.8% seems tobe realistic.

16.1 Introduction

In 2008, the world net electricity generation was 19.1PWh and the InternationalEnergy Outlook 2011 predicts an increase by 84% to 35.2PWh by 2035. From1990 to 2008, the growth in net electricity generation was higher than the growthin total energy consumption (3.0% per year and 1.8 % per year, respectively). Theworld demand for electricity is predicted to increases by 2.3 % per year from 2008 to2035, which exceeds the expected growth in total energy consumption of 1.4 % per

year. Although the 20082009 global economic recession slowed the rate of growthin electricity use in 2008 and resulted in negligible change in 2009, worldwideelectricity demand increased again by an estimated 5.4 % in 2010 [ 1].

Fossil fuelsmainly coal and natural gasare expected to remain dominant,but owing to increasing prices and government policies their share will drop from68% in 2008 to 55% in 2035. At the same time, the contribution of renewablesused to generate power is forecast to increase from 19% in 2008 to almost 33% by2035, which means renewables could catch up with coal. This applies particularlyto hydropower and wind, but also to geothermal and solar energy [ 1].

Solar energy is the worlds primary source of energy and theoretically it wouldonly take 2% of Saharas land area to cover the worlds electricity demand. Solarenergy is virtually unlimited, freely available and has no impacts on the ecology.However, itsdrawbacks arehigh dilution, intermittency and unequal distribution overthe earth [ 2]. In 2010, the main use of solar energy to produce power is photovoltaics(PV) and concentrating solar power (CSP).

Concentrating solar power (CSP) systems focus large amounts of sunlight bymeans of mirrors and lenses to generate temperatures between 400 and 1 , 000 C.This thermal energy is then converted into electricity usually by using steam turbines.However, mechanical converter systems such as gas turbines, rankine cycles, etc.,are working only in a very specic temperature window and are always restrainedat the high T level due to materials limitations. Naturally, part of the exergy of solarconcentration systems or combustion ames is left unexploited. Thermoelectric con-verters (TEC) applying thermoelectric oxide materials offer the unique possibility


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16 Solar TE Converter Applications 367

to use exergy fractions of solar power plants above and below these temperaturelimits, especially at T > 600 C. In the future, TECs will offer a new and attrac-tive alternative for decentralized power generation in addition to well-establishedsystems.

Different systems to convert solar radiation by thermoelectric (TE) modules havebeen tested. A TE module using a at-panel spectrally selective absorber, which isalso a thermal concentrator, was developed, achieving a peak efciency of 4.6%[3]. A parabolic trough concentrator combined with TE modules and placed in thereceiver tube was investigated. The thermal efciency of the concentrator/receiversystem was found to be < 40 % [ 4]. A thermodynamic analysis of a parabolic dishcombined with a Bi-Te module predicted a solar-to-electricity efciency of 2.81%at a temperature of 280 C [5]. The design of a solar cavity-receiver for supply-ing high-temperature heat to a thermionic/thermoelectric system was proposed and

temperature distributions were measured on a prototype made of graphite [ 6].The development of novel high temperature-resistant ( > 900 K) well performing

TE materials has given a fresh impetus to the thermoelectric conversion of highlyconcentrated solar radiation [ 7]. The theoretical solar-to-electricity efciency of Si-Ge alloys operated at a temperature of 1,000K is 12%, revealing the advantageof high temperatures applications [8]. The direct conversion of highly concentratedsolar radiation was experimentally demonstrated by directly irradiated TE modulesoperated at 900 K on the hot side and achieving solar-to-electricity efciencies < 1 %[9, 10].

16.2 Thermoelectric Oxide Modules

Commercial thermoelectric devices are based on Bi 2Te 3 because this materialexhibits a relatively high Figure of Merit [ 11 , 12]. Disadvantages, however, aretheir limited chemical stability at high temperatures in air and their toxicity. There-fore, complex metal oxide ceramics are promising alternative materials for high

temperature applications as they are inert in air at high temperatures, non-toxic, andcost-efcient [ 1317]. Among these oxides, Na xCo 2O4 is especially interesting asit shows a high Figure of Merit ZT 0.8 at T = 800K [18, 19]. However, theproduction of single crystals with dened and stable stoichiometry is difcult.

In contrast, perovskite-type materials can be easily synthesized with controllablecomposition and TE properties. They inherently show a variety of characteristicswhich are interesting for many energy conversion processes [ 2023]. Due to theirvery exible structure their physical-chemical properties can be ne-tuned by intro-ducing suitable cations and anions. But besides that, also the compound morphologybecomes important. This requires the development of appropriate synthesis proce-dures. Chimie douce (soft chemistry) precursor reactions allow the production of high surface area, nanostructured, highly reactive phases not obtainable with con-ventional solid state synthesis routes.


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Direct conversion of solar heat into electrical energy is studied using perovskite-type thermoelectric oxide modules (TOM). As proof-of-principle, p-typeLa 1.98 Sr0.02CuO 4 [24] and n-type CaMn 0.98 Nb 0.02 O3 [25] are used to build a series of four-legTOMs with leg lengths of 4, 5 or 10 mm. The materials are prepared by decomposi-tion of complex precursors containing a premix of the cations on a molecular level[2628]. The main advantage of this synthesis method compared to the conventionalsolid state reaction method, is the homogeneity and purity of the product. Phaseformation occurs at relatively low temperatures (T < 700 C) because no diffusionprocesses are necessary. Thus, sintering processes can be avoided and porous highsurface area products can be formed. The p- and n-type powders are pressed into disc-shaped pellets with a diameter of 20 mm using a hydrostatic press (up to 200 kPa)and sintered for 16 h at 1,373 and 1,523 K, respectively.

The TE materials are chosen based on best compatibility factors and not on TE

activity. The Figure of Merit ZT of the p-type material is nearly constant (

0.02)at higher temperatures (up to 800K) while the ZT of the n-type material increaseswith increasing temperature up to 0.08. The electrical resistivity of both materialsshows metallic behavior with between 2024m cm and |S| 160 V K1 atT =300 K. The temperature gradient along the TE legs is almost linear and lower inp-type than in n-type legs due to a higher thermal conductivity of the p-type materialabove T =400 K.

Four-leg thermoelectric oxide modules (Fig. 16.1 ) are assembled by connectingthe p- and n-type legs electrically in series and pressing them between two electrically

insulated and thermally conductive Al 2O3 layers (Rubalit

708S, CeramTec GmbH,Plochingen, Germany) with a cross section of 25 25mm 2 and thickness of 0.25mm[9]. The individual components are put together according to the scheme in Fig. 16.2 .

In a rst step, a dual-layer screen printing through a stainless steel stencil isapplied in order to metallize the electric contacts of the TE legs and the Al 2O3plates [ 29]. The rst layer is printed with AuPtPd conductor paste (4597 AuPtPd,DuPont, Wilmington, USA), dried at 423K for 15 min to evaporate the solvents, andannealed at 1,223K for 15 min to induce the diffusion. The second layer is printedwith AgPd conductor paste (DuPont, Wilmington, USA), again dried at 423K for

15 min and annealed at 1,223 K for 15min. In a second step, Ag sheets serving aselectric contacts are placed between the TE legs and the Al 2O3 plates using a locating

Fig. 16.1 Photo of a four-legTOM


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Fig. 16.2 Assembly of afour-leg module [ 30]

mask (Fig. 16.2 ). Finally, the assembled modules are heated at 1,223 K for 1 h in orderto solder the electric contact layers and also to ensure the mechanical resilience of the module [ 30]. Through a long-term measurement (65h) of one selected TOM, theperformance stability at high temperatures was proven.

It can be shown that graphite coating of the hot Al 2O3 absorber plate induceda larger temperature gradient in the TOMs signicantly improving the maximumoutput power and conversion efciency. Thus, TOMs are coated with a homogeneousblack graphite layer on the hot side in order to increase the absorption of solarradiation by improving the emissivity ( ).

16.3 Developing a Heat Transfer Model for TOMs Under SolarIrradiation

These demonstrator TOMs can be used to analyze the direct conversion of high-temperature solar heat under controlled conditions. Therefore, the TOM is arrangedin the focal plane of a High Flux Solar Simulator (HFSS) used as heat source


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Fig. 16.3 High-ux solar simulator at ETH: an elliptical mirror redirects the radiant power of the

enclosed argon arc lamp onto the target ( TOM ) placed in the focal plane; incident solar radiativeuxes are measured by a thermogage ( F )

(Fig. 16.3 ) [31]. A water-cooled high-pressure argon arc lamp, enclosed in a quartztube produces radiation in the visible, infrared and ultraviolet region. The power uxintensity and the temperature can be adjusted by varying the position of the targetalong the axis of the focusing mirrors or by changing the electrical input power at thearc electrodes. The HFSS is able to supply ux intensities exceeding 500W cm 2 andtemperatures higher than 3,000 K. The input heat uxes (014.4W cm 2 ) are mea-sured by a water-cooled Thermogage Circular Foil Heat Flux Transducer TG1000-1 (Vatell Corporation) placed symmetrically to the TOM in the focal plane. TheThermogage has a calibration range between 0179 W cm 2 , a sensor sensitivity of 0.084mVW 1 cm2 and a sensor emissivity of 0.97. The HFSS delivers an intensethermal radiation with the heat transfer characteristics of highly concentrating solarsystems [ 31]. The solar ux concentration is characterized by the mean solar con-centration ratio C dened as

C = Qsolar ( I

A)

(16.1)

where Q solar is the solar power intercepted by a target of area A. The ratio C isoften expressed in units of suns when normalized to an incident normal beaminsolation I = 1 kW/m 2 . The four-leg module was exposed to a maximum meansolar concentration ratio of 300 suns.

The bottom side of the TOM is cooled by cold water circulating in a Cu block.TOMs are attached to an Al-holder using a thermally conductive paste (DuPont TM )in order to increase the heat transfer from the cold Al 2O3 layer to the Al-holder. TheAl-holder itself is placed on the Cu-cooling unit with a surface area of 50 50 mm 2(Fig. 16.4 a). A series of 0.5mm thick K-type thermocouples is used to measure thetemperature at the hot and cold side of the TOM as well as at the TE legs.

The incident solar radiation is increased stepwise and held constant for35 min. Due to the low thermal inertia and fast temperature response, steady-state


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Fig. 16.4 Schematic illustration of the position of the TOM on the cooling unit and the type-Kthermocouples ( T ); voltage/power output of the module ( V ) is measured at the cold end

conditions are assumed for each time interval. A maximum temperature of 625 Ccan be generated before self-ignition of graphite is induced.

Applying external loads in the range of Rload = 0.1 3.5 to a TOM with leglength l = 4 mm, incident solar radiative uxes of q solar = 1.8, 2.9, 4.1, 5.4, 8.2and 10 W cm 2 resulted in a maximum output power Pmax =0.006 , 0.015 , 0.023 ,0.031, 0.038 and 0.046 W, respectively [32].

The solar-to-power efciency of the TOM is dened as

= pmax

Aabs q solar (16.2)

where P max is the maximal power output and q solar the mean incident solar radiativeux through the absorber surface Aabs . Modules with leg lengths l of 4, 5, and 10 mmprovide maximum power outputs Pmax of 45.6, 51.6 and 42.2mW at q solar of 9.9,9.7, and 5 .7Wcm 1 , respectively (Fig. 16.5 ). Data is plotted up to the maximumsolar ux (i.e. 9.9, 9.7 and 5 .7Wcm 1 , respectively) at which T hot = 625 C and,thus, the stability limit of the graphite coating is reached. The efciency increaseswith increasing q solar as a result of the higher temperature difference across the legs,which in turn corresponds to a higher Carnot limitation [ 33]. In contrast, decreases

with increasing temperature as reradiation losses are proportional to the fourth powerof T . Thus, an optimum q solar , where reaches a maximum, is expected. Themeasurements show that max = 0.065% at q solar = 4Wcm 2 for TOMs withl = 4mm, max = 0.06% at q solar = 8 Wcm 2 for TOMs with l = 5mm, andmax =0.083% at q solar =4Wcm 2 for TOMs with l =10 mm.

It is also found that the contact resistances, which vary in the range of 0 .29 8 W cm 2 ) , where the model predicts a 15 % higher value. This discrep-ancy is attributed to the insufcient cooling of the cold plate at high uxes revealedby a rise of its temperature, which in turn causes a higher absorber plate temperatureand, consequently, higher reradiation losses. Thus, the temperature difference acrossthe legs is shifted to higher temperatures and reduced due to increased reradiation.

The solar-to-electricity efciencies are numerically simulated using Eq. 16.2 withthe maximum output power Pmax calculated with Eq. 16.3 . The data is shown inFig. 16.8 (along with the experimentally determined efciencies from Fig. 16.5 ).

The percentage of Q solar transferred by the different heat transfer modes is shownin Fig. 16.9 for two cases: (1) radiative ux q solar = 6Wcm 2 and leg lengthl =10mm, and 2) q solar =10Wm 2 and l =5 mm. In both cases, the heat lossesby reradiation and free convection from the absorber plate represent more than 70%of Q solar . About 20% of Qsolar is transferred by conduction through the legs, and< 10 % is lost by radiation to the cold plate.

The efciency at a given solar radiative ux also depends on the leg length, theleg width and the distance between the legs. Regarding the leg length, the highestefciency = 0.081% is obtained at q solar = 4Wcm 2 with 7.5mm legs. Atq solar < 3 Wcm 2 the 10mm legs are most efcient, while at q solar > 7 W cm 2the 5mm legs are advantageous. Thus, with increasing solar radiative uxes the


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Fig. 16.7 Simulated and experimental V OC as a function of the solar radiative ux for leg length lof 4, 5, and 10mm

Fig. 16.8 Simulated and experimental efciency as a function of the solar radiative ux for leglength l of 4, 5, and 10 mm (experimental data from Fig. 16.5 )


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Fig. 16.9 Percentage of Q solartransferred by the differentheat transfer modes

optimum leg length decreases. As for the leg width and distance, the calculationssuggest that values as small as possible are most favorable.

In conclusion, the heat transfer analysis of 4-leg TOMs with leg lengthsl =510mm indicates that more than 70 % of the incident solar power is lost due toreradiation and free convection from the absorber, while 20% is conducted throughthe legs and less than 10 % is lost by radiation to the cold plate. Heat conduction isthe predominant mode of heat transfer across the legs. This is supported both by themeasured and the simulated linear temperature proles across the legs. The best leglength l of a 4-leg TOM with leg width a = 4.5 mm is 7.5 mm resulting in an ef-ciency of 0.081% at q solar = 4 W cm 2 . Smaller leg width and distance (namely,width a = 3mm, gap d = 1mm, leg length l = 7.5mm) leads to an efciency = 0.4 %. Thus, smaller dimensions than those actually used here are expected toincrease the efciency of 4-leg TOMs to 0.5%.

16.4 Increasing the Conversion Efciency by Using a SolarCavity-Receiver

The heat transfer analysis of directly irradiated TE modules shows that 60% of the incident solar radiation is lost by reradiation. This reradiation can be signi-cantly reduced by placing the TOMs in a solar cavity-receiver, thus, enhancing theirconversion efciency. A cavity-receiver is a well-insulated enclosure with a smallopening, the aperture, to let radiation in. Because of multiple internal reections, thecavitys apparent absorptance apparent exceeds the inner surface absorptivity and,consequently, increases its ability to absorb incoming irradiation.

Analysis of directly irradiated TOMs in a solar cavity-receiver reveals that theproposed design is advantageous in two respects: (1) the geometrical congurationallows efcient capture of concentrated solar radiation and signicant reduction of reradiation losses; (2) thedirect irradiation of theTOMs enables efcientheat transferto thesite,bypassing thelimitations associated with heat conduction through thewalls


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Fig. 16.10 Design of a solar cavity-receiver packed with 18 TOMs. a Exterior view containing thecavity and the compound parabolic concentrator; b Cross-sectional view of a solar cavity-receiver;c Longitudinal view of a solar cavity-receiver

of an opaque solar absorber (i.e. limitations imposed by the materials with regardsto maximum operating temperature, thermal conductivity, and resistance to thermalshocks).

A sketch of a 1 kW solar cavity-receiver designed for 18 TOMs is shown inFig. 16.10 . The rectangular shape of the solar cavity-receiver contains inlets and out-lets for an encapsulated circulating water cooling system. The rectangular aperturefor the incidence of concentrated solar radiation is at the top of the solar cavity-receiver. Smaller apertures reduce reradiation losses but intercept less sunlight. Con-sequently, the optimum aperture size becomes a compromise between maximizingradiation capture and minimizing radiation losses [ 34]. To some extent, the aperturesize may be reduced with the help of non-imaging secondary concentrators, e.g.a compound parabolic concentrator (CPC) placed at the aperture in tandem with the

primary concentrating system [ 35]. Here, the integral water-cooled CPC enhancesthe radiative ux by a factor of 1.4 and provides a uniform irradiation of the TEmodules. This is crucial to realize equal temperature differences across the modules.Besides the above-mentioned quality of the electrical and thermal contacts, the per-formance and conversion efciency also depend on the packing quality of the TEmodules inside the solar cavity-receiver including the lateral insulation of the TOMarray (18 pcs.). An efcient thermal contact between the TOMs and the cooler of the solar cavity-receiver is provided by a thermal conduction paste (DuPont) and bya special clamping mechanism containing springs and ribbons. The hot side tem-perature is monitored and controlled to avoid the cavity temperature exceeding themelting point of Ag (T

1, 235K) used for the contacts [36].


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The peak radiative ux is varied between 128 and 657 suns. All electric wires areconnected at a pin board allowing the connection to be switched from parallel (mea-surement of individual TOMs) to serial connection circuit (collective measurementof series-connected TOMs). TOMs are measured individually and series-connectedat different radiation intensities with regard to the temperature distribution in thecavity, open-circuit voltage, maximum output power at different external loads andthe conversion efciency. Open-circuit voltage V OC , maximum output power Pmaxand the efciency increase monotonically with C . V OC and Pmax of each TOM aremeasured individually showing the highest V OC and Pmax for TOMs located at thebottom of the cavity. The maximum generated voltage of series-connected TOMsis V OC = 7.7V at T max = 885 K. The total resistance increases with increasingheat ux mainly due to an increase in contact resistance Rcont and in the materialresistance of the TE legs arising from its metallic nature. A maximum output power

of Pmax 1.42 W and a solar-to-electricity conversion efciency of 0.13 % areachieved. Compared to the efciency of a directly irradiated TOM (which was only0.06 % at a mean solar radiative ux of 8 W cm 2 [9, 32]), this is an improvementof

62 %. Thus, the cavity-receiver conguration was able to increase the efciencyby a factor of 2.16.

The open-circuit voltage data measured as a function of the mean solar concen-tration ratio over the aperture is used to validate a heat transfer model formulated toanalyze the thermal energy partition [ 37].

The model domain is shown in Fig. 16.11 . The cavity contains N modules with M

p/n-type leg pairs. The previous heat transfer analysis of single modules revealed 1Dtemperature proles in the p/n-type legs and negligible radiation exchange betweenthe hot and cold plate [ 32]. Thus, the considered heat transfer modes are 3D radiativeand 2D convective exchange within the cavity, 1D conduction through the legs of the modules, and 2D convective heat loss out of the cavity. Further, it is assumedthat (1) the graphite-coated Al 2O3 plates are opaque, gray and diffuse [ 38] andhave uniform temperature; (2) the gas phase is radiatively non-participating, withrefractive index equal unity; (3) radiative heat transfer between hot/cold plates andp/n-type legs is neglected. Only open-circuit voltages are simulated.

The distribution of incoming radiation within the cavity is approximated to beuniformly 50, 26 and 24 % of the incident radiation on the bottom, lower and upperTOMs, respectively. 15% of the incoming radiation is lost through the spacingbetween the modules. At low radiative uxes V OC is slightly underestimated whichis attributed to the incorrect assumption of a linear temperature dependence of thematerial properties. In contrast, a slight overestimation is observed at high radiativeuxes due to insufcient cooling of the cold plate resulting in a decrease of the tem-perature difference and, consequently, a decrease of V OC . The same phenomenoncould be observed for single TOMs with similar p/n-type leg dimensions [32].

Thecorresponding percentages of thesolar power input transferred by thedifferentheat transfer modes are shown in Fig. 16.12 . 71 % of Q solar is conducted through thep/n-type legs and converted to power. 23 % of Q solar is lost by conduction throughthe cavity and CPC walls, including losses to water-cooled surfaces. Only 4 and2 % of Q solar is lost by reradiation and convection through the aperture, respectively.


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Fig. 16.11 Illustration of the model domain: cross-section of a rectangular ( box ) cavity-receiverwith a windowless rectangular aperture for the incidence of concentrated solar radiation. The cavitycontains an array of N modules with M p/n-type leg pairs. A 2D ( trough ) CPC is incorporated atthe aperture to augment the solar ux concentration

The comparison with single TOM measurements without cavity [ 32] indicates that

the cavity effect reduces reradiation losses from 60 to 4 % of Qsolar , while the usefulheat conduction through the p/n-type legs increases from 20 to 71 % of Qsolar .According to Eq. 16.4 (with T = (Th + Tc) /2), future improved thermoelectric

oxide modules with ZT =1 will have a theoretical efciency of theo 15.8% whenoperated at T h =900 K and T c =300 K [ 39]):

theo = T h T c

T h = 1 + Z T 1

Z 1 + Z T +T c / T h(16.4)

Assuming that 71% of Qsolar is conducted through the p/n-type legs the actualefciency might exceed 11.2%. Potential applications include solar dishes up to50kW for decentralized power generation and hybrid concepts of TE converterscombined with heat engines to recover spilled solar radiation.


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Fig. 16.12 Percentage of different heat transfer modes: conduction through the p/n-type legs,reradiation and convective losses through the aperture, and conduction losses through the cavityand CPC walls. Q solar =710 W and C =620 suns

16.5 Potential of Solar TE Devices

The heat transfer analysis of a 1 kW th solar cavity-receiver has shown that reradiationlossesare reduced to4 % of the incoming solar radiation compared to60% for directlyirradiated 4-leg modules. The results reveal the high potential and the signicantadvantage of the cavity design. However, the measured maximum solar-to-electricityefciency does not get beyond 0.13 % due to the low Figure of Merit ZT of the usedoxide materials (

0.05). An approach towards a higher overall Figure of Merit is to

use cascaded modules at large temperature differences [ 40]. The heat transfer modelof the 1 kW th solar cavity-receiver can be adjusted to evaluate the characteristics of a cubic 50 kW th solar cavity-receiver packed with cascaded modules. Furthermore,the effect of module efciency and cavity temperature on the receiver efciency canbe assessed.

Due to the temperature dependence of TE properties the use of a single materialat a large temperature difference is not ideal [40]. Preferably, a stack of differentmaterials, each operating in its most efcient temperature range, should be applied.Figure 16.13 illustrates the general construction of such a cascade module. The mod-ule consisting of K sandwiched, thermally series-connected module units (stages)

Fig. 16.13 Illustration of acascade module consisting of K stages andoperated betweenthe temperatures T K+1 and T 1


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is operated between temperatures T K+1 and T 1 [39]. Each stage k is composed of different TE materials.

A two-stage design ( K = 2) represents the simplest form of a cascaded TEmodule. Based on a theoretical combination of a Bi-Te alloy on the cold side anda perovskite-type compound on the hot side of the module, the solar-to-electricityefciency of a 50 kW th solar cavity-receiver as a function of cavity dimensions,aperture width, maximum temperature and TE leg length can be analyzed. TheBi-Te alloy has a Figure of Merit ZT of 1. For the perovskite materials used onthe hot side a ZT value of either 0.36 or 1.7 was assumed depending on the appliedmaximum temperature (900 or 1,200 K). With reference to standard Bi-Te modules[41], each stage contains M = 2,822 TE legs (1,411 p/n-type leg pairs), each leghaving a cross-section of A leg =1.05 1.05mm 2 .

The adjusted heat transfer model is used to optimize the cavity-receiver geom-

etry to a certain extent (height H = 3090cm and width X = 4080cm) and toinvestigate the effect of module efciency and the hot plate temperatures ( T h,max =9001200 K) on the solar-to-electricity efciency and the total leg length.

A good trade-off between the efciency solar and the required number of modules N is achieved for X =60cm and H =50 cm where the model predicts solar =7.3and 11.1% at T h,max = 900 and 1,200 K, respectively, with N = 156 modules.A maximum reradiation loss of 6.7% at T h,max = 1, 200 K is identied which iscomparable to the 1 kW th solar cavity-receiver (4 %). Based on the optimum cavityparameters ( H =50cm, X =60cm, N =156), the receiver efciency as a functionof the Seebeck coefcients ( S high = 90196 V/K) and the maximum temperatureT h,max =9001,200 K, is assessed. With the intermediate calculation of the moduleefciency mod,dual the model predicts a solar-to-electricity efciency of the cavity-receiver ranging from solar = 7.4 % ( Pmax = 3.7kW at mod,dual = 11 .7 %) atT h,max =900K to solar =20 .8 % (Pmax = 10.4kW at mod,dual =26%) at T h,max =1, 200 K. At the same time, however, the TE legs (ltotal =lBi-Te +lPerovskite ) have tobe elongated from ltotal = 7mm at T h,max = 900K to ltotal = 21.7mm at T h,max =1, 200 K, in order to compensate the increasing Peltier heat ux at higher maximumtemperatures on the hot side.

In conclusion, the 50kW th cavity-receiver packed with presently available ther-moelectric materials (low-temperature Bi-Te with ZT = 1 and high-temperatureperovskite-type oxide with ZT =0.36, mod,dual = 11 .7%) already reaches an ef-ciency of solar =7.4 %. In the future, new more efcient high-temperature materi-als (with a predicted ZT =1.7) might improve the solar conversion efciency up to20.8 % rendering them competitive to other solar conversion devices.

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