High temperature solar thermoelectric generator – Indoor characterization method and modeling

Energy 84 (2015) 485e492

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High temperature solar thermoelectric generator e Indoor characterization method and modeling A. Pereira a, *, T. Caroff b, G. Lorin c, T. Baffie b, K. Romanjek b, S. Vesin b, K. Kusiaku c, H. Duchemin b, V. Salvador b, N. Miloud-Ali b, L. Aixala b, J. Simon b a b c

CEA-Grenoble/DRT/LITEN/DTNM/LFVC, 17 rue des Martyrs, 38054 Grenoble, France CEA-Grenoble/DRT/LITEN/DTNM/LTE, 17 rue des Martyrs, 38054 Grenoble, France CEA-Grenoble/DRT/LITEN/DTNM/LRME, 17 rue des Martyrs, 38054 Grenoble, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 July 2014 Received in revised form 27 February 2015 Accepted 3 March 2015 Available online 7 April 2015

This paper presents an experimental study of a STEG (solar thermoelectric generator) working at high concentration ratio (>100) and high temperature (
450  C). An indoor characterization set-up based on Si80Ge20 thermoelectric material coupled with a selective absorber and a solar concentrating simulator was developed. The goal was to validate a physical model allowing to predict performances of such thermoelectric material for much higher temperatures. Predictive efficiencies were thus extrapolated for a working temperature beyond 800  C. The critical issue deals with the best system dimensioning taking into account the concentrator size, and the efficiency versus the TEG (thermoelectric generator) size. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Solar thermoelectric generator Predictive physical modeling Thermoelectric cascaded device

1. Introduction As in all renewable energy production area, the commercial success of a STEG (solar thermoelectric generator) system is inexorably leaded to a technico-economical compromise. Nowadays, the LCOE (levelized cost of energy) must be as lower as possible to ensure competitiveness with others solar energy recovery systems: PV (photovoltaic), CPV (concentrated photovoltaic), CSP (concentrated solar power) … [1e3]. It is also necessary to develop a robust and reliable technology to reach an attractive performance/cost/ durability ratio. This ratio is obviously linked to the thermoelectric material efficiency and cost, and also to the solar concentration factor. In this context, several recent theoretical assessments showed that thermoelectric materials quantity in STEGs could be reduced without degrading the system efficiency. Thus, the device cost could be lowered. .As an example, a Bi2Te3-based STEG can be optimized for rooftop power generation. Peak efficiency is predicted to be 5% at the standard spectrum AM1.5G, with a thermoelectric material cost below 0.05$/W [4]. Other theoretical studies

* Corresponding author. Tel.: þ33 (0) 438782977; fax: þ33 (0) 438785046. E-mail address: [email protected] (A. Pereira). http://dx.doi.org/10.1016/j.energy.2015.03.053 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

showed that, using thermoelectric materials and solar selective absorbers taken from the state of the art, cascaded STEG yield could exceed 10% [5]. This efficiency obviously depends on both optical performances of the concentrator and of the solar selective absorber, but also on the thermoelectric materials' figure-of-merit (ZT). In vacuum and in the low temperature range (150e250  C), STEGs with Bi2Te3-based materials can reach around 5% efficiency with small optical concentration [6]. An experimental study on STEG with solar concentration of 6  suns and thermoelectric module reported only 0.15% efficiency [7]. Under 66  suns concentration, Amatya and Ram reported a system efficiency of 3% using commercial Bi2Te3-based thermoelectric generators [8]. The most recent experimental work on STEG technology showed promising results for those types of applications [9]. The efficiency was at best 4.6% which was enabled by the use of high-performance nanostructured thermoelectric Bi2Te3-based materials and spectrally-selective solar absorbers in an evacuated environment. All previous experimental works deal with low concentration (<66) and low working temperature system (<550 K). Our work proposes to explore higher solar concentration (>100) experiments on Si80Ge20-based thermoelectric generators which have a high figure-of-merit (ZT) between 700 and 900  C. A modeling of such a system is proposed and predictive efficiencies computations are performed for higher working temperatures.

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Nomenclature

Parameter, symbol, units k thermal conductivity, W/m$K S average Seebeck coefficient, V/K Pinc incident optical power, W hOpt optical efficiency, % Rin internal electrical resistance, mU s electrical conductivity, S/m ZT thermoelectric figure-of-merit, d.u. RAbs optical reflection, % aAbs absorption of selective solar absorber, % εAbs emissivity of selective solar absorber, % AM1.5 solar irradiance, W/m2/nm BB black body emission, W/m2/nm PSun solar radiation, W TOpt optical transmission, % THot hot side temperature, K TCold cold side temperature, K V open circuit voltage, V

2. Thermoelectric generators and solar absorber characteristics The TEG (thermoelectric generators) employed in this study were based on two pairs of Si80Ge20 legs (Phosphorus doped for nType and Boron doped p-Type) sandwiched between two copper/ AlN substrates (Fig. 1a). The upper-one is the solar absorber substrate (hot face of the generator) and the downer-one is the heat sink (cold face of the generator). N-type and p-type legs were electrically connected with copper electrodes fixed onto the substrates. Before assembling, every parameter of the thermoelectric figure-of-merit ZT ¼ sS2T/k is measured separately. Electrical conductivity s (S/m) of samples was measured by a four-point direct current switching technique and Seebeck coefficient S (V/K) was measured by a static direct current method based on the slope of the voltage versus temperature-difference curves (ZEM-3, Ulvac GmbH, Ismaning, Germany; samples were parallelepipeds of 5*5*10 mm, working atmosphere was helium, overall measurement errors were ±2.5% and ±1.5% for electrical conductivity and Seebeck coefficient, respectively). The measurement was done from room temperature up to 700  C. Thermal diffusivity was measured using the laser-flash method (LFA 457 MicroFlash®, Netzsch€tebau GmbH, Charbonnie res les Bains, France; samples were Gera squares of 10*10 mm with a thickness of 1 mm, in an Argon working atmosphere). Specific heat was determined using differential €tebau scanning calorimetry (DSC; 404 F1 Pegasus, Netzsch-Gera res les Bains, France; samples are cylinders GmbH, Charbonnie having a diameter of 5.2 mm and a thickness of 1 mm, in an Argon working atmosphere). We then calculated the thermal conductivity k (W/m$K) as the product of thermal diffusivity, specific heat and mass density of the samples (Fig. 1b e the overall measurement error is ±3.3%) [10]. With an electrical conductivity s ¼ 4.34  104S/ m at 700  C and s ¼ 5.32  104S/m at 500  C, the figure-of-merit ZT was respectively 0.65 and 0.52. The geometry proposed in Fig. 1a was dimensioned and optimized to reach a hot side temperature of 700  C for an incident optical power of Pinc ¼ 65 W, regarding the thermal resistivity of Si80Ge20 and the expected experimental conditions (in vacuum, with a solar selective absorber). This optical power is the one

ATEG HTEG PTh PElec PAbs

hTEG hSys

Loss DPTh TAmb εSiGe εAlN h

r Cp Mod PTh TMod Mod PElec LLens εSOA εBB

area of thermoelectric legs, m2 height of thermoelectric legs, m converted thermal power, W generated electrical power, W absorbed power, W thermoelectric generator efficiency, % system efficiency, % intrinsic thermal losses, % ambient temperature, K emissivity of SiGe, % emissivity of AlN, % heat exchange coefficient, W/(m2$K) density, kg/m3 heat capacity, J/(kg$K) simulated thermal power, W simulated temperature, K simulated electric power, W lens length, m state of the art emissivity, % black body emissivity, %

delivered by a 320  320 mm2 Fresnel lens-type concentrator with an optical efficiency of hOpt ¼ 83% for a DNI (Direct Normal Irradiance) of 850 W/m2. This first dimensioning was done in order to perform upcoming outdoor experiments using this Fresnel lens. In

Fig. 1. (a) Thermoelectric generator dimensions and (b) electrical characteristics of the Si80Ge20 n-Type and p-Type thermoelectric legs.

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this configuration, the internal electrical resistance of the generator (including legs, brazed joints, copper electrodes and connection wires resistances) was measured around Rin ¼ 47 mU at room temperature. A TiAlN/SiO2-based selective solar absorber was deposited by RF magnetron sputtering on the upper face of the generator (Hot face). Reflection measurements (RAbs) performed with a Perkin Elmer Lambda 950 UVeVisible spectrophotometer and a Bruker Vertex 70 V FTIR (Fourier transform infrared) spectrophotometer enable solar power aAbs calculation (1) and radiative losses εAbs (2) for a given working temperature. Both instruments were respectively calibrated with and a Spectralon® sample. The overall measurements error was ±1%. In equation (1), AM1.5(l) is the solar irradiance, and in equation (2) BB(l) represents the black body emission for a given temperature (3). The optical stack was optimized in order to obtain good optical performances: aAbs ¼ 90% and εAbs ¼ 30% at 500  C. This selective solar absorber permits to reach high temperatures on the generator hot face thanks to the concentrated solar simulator developed in this study.

Z AM1:5 ðlÞ$½1  RAbs ðlÞdl Z AM1:5 ðlÞdl

aAbs ¼

(1)

Z εAbs ¼

BBðlÞ ¼

½1  RAbs ðlÞ$BBðlÞdl Z BBðlÞdl A$l5

ExpðB=lTÞ1 B ¼ 0:014 m$K

With A ¼ 3:74  106 W$m2

(2)

and

(3) 3. Indoor experimental set-up The solar simulator consists of three xenon lamps mounted with AM1.5 spectral filter (Air mass 1.5, ASTM G-173). The flux is spatially cut through a diaphragm facing the vacuum cell in which the TEG is placed (Fig. 2a). At best, it delivers a solar radiation PSun of 37 W on a 21 mm-diameter spot which is equal to the hot area of the TEG. This optical power was measured with a Newport Calorimeter calibrated by the NIST. The cold side of the generator is fixed to an aluminum heat sink directly connected to the vacuum cell (Fig. 2a). The low pressure inside the cell (maintained at 102mbar during the test) prevents thermal losses induced by air convection. The silica window which encloses the thermoelectric generator inside the vacuum cell has an average optical transmission around TOpt ¼ 91% from 350 to 2000 nm, which gives at best an incident optical power of PInc ¼ 33 W. The hot and cold faces temperatures of the TEG are monitored with TK thermocouples. These elements are carefully positioned out of the incident optical flux in order to ensure an accurate measurement of the real TEG gradient temperature.

(Fig. 3a). Fig. 3b reports the internal resistance Rin(T) and voltage V(T) measurements as a function of the hot side temperature, the cold one remaining fixed at 25  C. The thermal power converted by the TEG is the ratio between temperature gradient (DT) and thermal resistance (RTh) of the thermoelectric legs. The thermal resistance is given in Equation (4), where ATEG and HTEG are respectively the area and height of the Si80Ge20-based thermoelectric legs, k(T) is the average thermal conductivity of n-Type and p-Type materials (Fig. 1b) and N the number of legs. The temperature gradient is the ratio between open circuit voltage V(T) and the product of the average Seebeck coefficient S(T) and the number of legs N (5). The thermal power converted by the TEG is then given in equation (6).

4. Thermal and electrical characterization of the STEG

RTh ðTÞ ¼

Using the experimental set-up described in the previous section, the hot and cold side temperatures of the TEG and the associated electrical power generated have been measured for different incident optical power PInc (from 6 to 33 W). The maximum hot side temperature THot reached was up to 450  C for a cold one TCold remained around 25  C for any incident optical power

Fig. 2. (a) STEG characterization experimental set-up e (b) Thermoelectric generator encloses in the vacuum cell with thermocouples on the hot and cold faces.

DT ¼

HTEG kðTÞ$N$ATEG

VðTÞ SðTÞ$N

PTh ðTÞ ¼

VðTÞ$kðTÞ$ATEG HTEG $SðTÞ

(4)

(5)

(6)

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Fig. 3. (a) Temperature measurements and thermal power converted by the TEG e (b) Voltage and internal resistance measurements. Fig. 4. (a) Electrical power and TEG efficiency as a function of incident optical power e (b) System efficiency and thermal losses as a function of optical absorbed power.

The converted thermal power behavior (PTh) is not linear because of the decrease of the Si80Ge20 thermal conductivity with the temperature and the increasing radiative losses. As a result, the recorded hot temperature is not linear with the optical power (PInc) received by the TEG. The generated electrical power PElec plotted in Fig. 4a is calculated from the measured internal resistance Rin(T) and voltage V(T) of the TEG, using Equation (7). The TEG efficiency reported in this figure is the ratio between the electrical power and the converted thermal power (8). The system yield is estimated from equation (9) in which the absorbed power is the product of the incident optical power by the absorption coefficient of the selective coating, namely PAbs ¼ Pinc  aAbs.

. PElec ¼ VðTÞ2 4  Rin ðTÞ

(7)

hTEG ¼

PElec PTh

(8)

hSys ¼

PElec PAbs

(9)

Overall, from these measurements, the TEG has a yield conversion hTEG around 3% for a temperature difference between hot and cold surfaces of about 400  C. For the same temperature, the generated electric power is approximately 500 mW. The intrinsic Loss of the device were calculated according to the thermal losses DPTh

PTh/PAbs ratio and plotted in Fig. 4b with the system performance

hSys (9). These losses increase with the absorbed power because of the rise of radiative losses induced when the hot face temperature increases. The system performance achieved hSys ¼ 1.6% for PAbs ¼ 29 W. 5. Thermal behavior modeling of the STEG The thermal behavior of the TEG exposed to a concentrated light flux was modeled based on the finite element method, in order to predict the STEG efficiency for higher working temperatures. The electrical performances were then calculated from an analytical model using the results obtained in the finite element modeling. Fig. 5 shows the finite element modeling of a TEG performed under COMSOL® software. It describes the boundary conditions used via the heat transfer equations (conduction, radiation) and the relationship that simulates the concentrated light flux absorbed by the selective treatment deposited on the upper face of the TEG (PAbs ¼ Pinc  aAbs). The radiative losses involved by the emissivity of the selective absorber (εAbs) are calculated based on the TEG hot surface tem! perature according to Equation (10), where n is the normal vector of the boundary, k the thermal conductivity of the solar absorber, εAbs its emissivity and sSB the StephaneBoltzmann constant.

  ! 4  n $ðkAbs VTÞ ¼ εAbs sSB TAmb  T4

(10)

A. Pereira et al. / Energy 84 (2015) 485e492 Mod PTh ¼ 4  kSiGe  VT  ATEG

Fig. 5. Boundary conditions and model input for the finite element numerical simulation.

The emissivity temperature dependence was calculated from measurements made by spectrophotometry in the 300 nm-20 mm spectral range. This change is estimated analytically from the emission of black body BB(l) and the reflectivity of the treatment RAbs(l) according to Equation (2). Table 1 shows the emissivity of the materials constituting the device and involved in the losses induced by radiation (εSiGe, εAlN). These data were calculated from spectrophotometric measurements using Equation (2). As for the hot surface of the TEG, the radiative losses of legs (Si80Ge20), back face of the hot side and front face of the cold side (AlN) are calculated using Equations (11) and (12).

  ! 4  n $ð  kSiGe VTÞ ¼ εSiGe sSB TAmb  T4

(11)

  ! 4  n $ðkAlN VTÞ ¼ εAlN sSB TAmb  T4

(12)

489

(16)

This model was used to numerically evaluate the thermal behavior of TEG subjected to various light flux. To do this, for the boundary conditions and using the absorbed power (PAbs) by TEG as model input data, we calculated the temperature reached by the hot face and the temperature difference between the cold and the hot faces (Fig. 6a). The absorbed power is considered equivalent to the one calculated under experimental conditions to compare the results with experimental measurements. The simulated hot surface temperature appears overestimated compared to the temperature recorded during the tests (about 50  C). To explain this discrepancy, two assumptions can be made. The first would involve an inaccurate measurement of temperature induced by a non-ideal positioning of thermocouples. The second would be a poor estimate of the radiative and heat conduction losses in the model. Nevertheless, the simulated behavior of TEG is generally acceptable compared with experimental data. The thermal power transmitted through the thermoelectric legs was also calculated for the same absorbed power (16). Fig. 6b shows the comparison of simulated values with the values calculated from the experimental data (6). A good agreement can be observed even if the temperature of the hot face is overestimated in the model (Fig. 6a). This seems to point out that some heat losses are

The parameters used for the boundary conditions for heat transfer equation (13) and thermal insulation (14) are listed in Table 1. A heat exchange coefficient h ¼ 6000 W/(m2$K) is applied to maintain the lower surface of the TEG to ambient temperature TAmb (15).

! rCP u $VT ¼ V$ðkVTÞ þ Q

(13)

!  n $ðkVTÞ ¼ 0

(14)

!  n $ðkVTÞ ¼ hðTAmb  TÞ

(15)

The thermal power transmitted through the legs of the TEG is calculated from equation (16) wherein the thermal conductivity of Si80Ge20 is implemented according to the average measured values performed for different temperatures (Table 1).

Table 1 Emissivity, calorific capacity, density and thermal conductivity used in the model.

ε Cp

r k

Cu

AIN

Si80Ge20 (n and p)

385 8700 400

2.104  T þ 0.88 738 3300 150

3.105  T þ 0.77 630 2900 4

J/kg$K kg/m3 W/m$K

Fig. 6. Comparison between measurements and modeling: (a) Temperature difference between the cold and the hot faces and modeling e (b) Thermal power converted by the TEG.

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neglected in the case of the simulation or that the temperature of the hot face is not accurate enough. Nevertheless, the good correlation between the numerical computation of the thermal power and the values calculated from experimental measurements are used to accurately estimate the theoretical performance of TEG. The simulated temperature allows us to calculate the electric power generated by the TEG (17) using the voltage V(TMod) and internal resistance Rin(TMod) variations with the temperature measured during the test (Fig. 3b). Despite the difference between simulated temperature and temperature recorded during testing, we obtained an excellent agreement between the measured electric power and electric power derived from the relation (17) (Fig. 7a). The STEG efficiency is estimated from equation (18) and plotted in Fig. 7b.

. Mod PElec ¼ VðTMod Þ2 4  Rin ðTMod Þ

(17)

. Mod Mod PTh hTEG ¼ PElec

(18)

The model and experimental measurements of electrical power, TEG efficiency and system efficiency are in a good agreement. The model reproduces well the saturation of the system efficiency induced by the increase of radiative losses with the absorbed power PAbs (Fig. 7b). This model is a useful tool to extrapolate achievable performance of the STEG with higher absorbed power. Therefore, it predicts the electrical power generated by such a system for

Fig. 7. Comparison between measurements and modeling: (a) Electrical power and TEG efficiency e (b) System efficiency and thermal losses as a function of optical absorbed power.

incident power densities that can be delivered by Fresnel solar concentrators or parabolic mirrors. In addition, the impact of selective treatment performances, the internal resistance of the TEG and the thermal conductivity of Si80Ge20 on overall system performance can be studied. 6. Predictive performances of the STEG Improved optical performance of selective treatment can increase the power density absorbed by the TEG, while limiting the radiative heat loss. At least, its absorption in the solar spectral range (aAbs) must be maximized to ensure a good coupling between the incident solar flux and the device. Ideally, its emissivity at high temperature has to be decreased in order to reduce radiation losses. The model developed in this study was used to quantify the impact of the absorber optical performance on the electric power generated and the system efficiency. For the same absorption coefficient (aAbs ¼ 90%), a comparison was made between the emissivity of a black body (εBB ¼ 90%), our TiAlN/SiO2 treatment (εAbs ¼ 30%) and state of the art value at 500  C (εSOA ¼ 10% [11]) in order to estimate the emissivity reduction influence (Fig. 8a). A comparison of maximum and minimum values (εBB ¼ 90% and εSOA ¼ 10%) shows that a black body treatment requires 25% higher power consumption for generating electric power of about 1 W. At iso-performance, this implies a concentrator with higher dimensions in the case of the black body (about 25% more than for a system using εSOA ¼ 10%). In order to predict the performance that could be achieved in an outdoor environment, we assumed a Fresnel lens concentrator with an optical efficiency of hOpt ¼ 83% for a Direct Normal Irradiance of 850 W/m2. For different size of a squared lens (LLens), the system efficiency is calculated for different absorber performances (εSOA ¼ 10%, εAbs ¼ 30% and εBB ¼ 90%) as a function of the incident power delivered by the concentrator (Fig. 8b). Whatever the absorber emissivity, the maximum of efficiency is reached for a 320  320 mm2 lens which provides around 65 W incident power on the TEG (e.g. Pinc ¼ PSun$L2Lens$TOpt$hOpt). This power value is the one expected from the optimization of the TEG dimension using the thermal resistivity of Si80Ge20. From Fig. 8a, this incident power leads to 59 W absorbed by the TEG which induces a temperature difference of about 550  C from hot to cold side. Above 550  C, radiative losses become major, inducing this way a slight decrease of the system efficiency. In this configuration, the concentration ratio is 170. The maximum efficiency reached is 1.8% for the lowest emissivity (εSOA ¼ 10%). From Fig. 8b, one can observe a plateau between 75 and 95 W of incident power. For the same lens size (e.g. 320  320 mm2), we can conclude that the system efficiency will be stable (1.8%) for DNI between 800 and 1000 W/m2. In this last part, we carried out numerical simulations in order to determine the power generated per square meter on the ground depending on different thermoelectric materials and regarding their operating temperature. In these simulations, the thermoelectric materials considered were Bi2Te3 (for low-temperature range 20e250  C), n-Mg2SiGe0.4 and p-MnSi1.75 (for mediumtemperature range 250e500  C) and Si80Ge20 (for hightemperature range 500e900  C). The properties of Bi2Te3 were taken from industrially produced materials (best ZT ¼ 1 at 80  C). Those of Mg2SiGe0.4/MnSi1.75 and Si80Ge20 were taken from literature [12]. As in previous simulations, the temperature of the absorber is determined for DNI ¼ 850 W/m2, for given absorption and emissivity (aAbs ¼ 90%, εSOA ¼ 10%) and using a concentrator with optical efficiency of 83%. For the three types of selected materials, Fig. 9a shows the electric power density generated by one square meter of solar concentrator on the ground, depending on the hot side temperature. These simulations were done with a

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Fig. 8. (a) Predictive performances for STEG using different absorbers (εSOA ¼ 10%, εAbs ¼ 30% and εBB ¼ 90%) as a function of (a) absorbed power and (b) incident power.

cold side temperature and an ambient temperature respectively of TCold ¼ 50  C and TAmb ¼ 20  C. The generated power density ranges between 25 and 45 W/m2 (e.g. yield material from 5 to 9%). The main conclusions are the following: first, the hot face temperature must exceed 700  C with Si80Ge20 to outperform the Bi2Te3 at 250  C. Second, this temperature must exceed 800  C to outperform the Mg2SiGe0.4/MnSi1.75 at 500  C. The system performance may be increased by using cascaded TEG devices with suitable materials adapted for each temperature range along the thermal gradient. A comparison of the performance of thermoelectric modules cascaded made of different materials (Bi2Te3, Mg2SiGe0.4/MnSi1.75 and Si80Ge20) is presented in Fig. 9b. The evolution of the electric power density of STEG based on the maximum operating temperature of different materials is plotted for the best absorber performances (aAbs ¼ 90%, εSOA ¼ 10%). The power densities are determined as a function of the cold face temperature for hot face temperatures of Si80Ge20 (THot ¼ 700  C), Mg2SiGe0.4/MnSi1.75 (THot ¼ 500  C) and Bi2Te3 (THot ¼ 200  C) and a cold temperature around 50  C (ambient temperature was still TAmb ¼ 20  C) (Fig. 9). The performances of such cascaded TEG can be determined by summing the powers obtained on the Fig. 9b with respective cold side (see red points (in web version)). Taking into account the internal electrical resistance of the generator (including legs, brazed joints, copper electrodes and connection wires resistances), these calculations let us expect a power density of 68 W/m2 and an 8% system yield with this cascaded architecture. An attractive application will be the integration of Solar

Fig. 9. Predictive performances for STEG (a) using different thermoelectric materials as a function of the hot side temperature (b) using cascaded devices with suitable materials for each temperature range Bi2Te3, Mg2SiGe0.4/MnSi1.75 and Si80Ge20.

ThermoElectric Generator into thermal solar systems for energy cogeneration. In such systems the electric power could be adapted all along the day to produce either electricity or hot water [4]. Hybrid thermal solar thermoelectric systems could reach 52.6% efficiency at solar concentrations of 100 suns and temperature of 776 K [13].

7. Conclusion In this paper, high solar concentration experiments were performed on SiGe-based thermoelectric generators. A modeling of such a system was proposed and predictive efficiencies computations were performed for higher working temperature. Experimentally, a temperature difference between hot and cold surfaces of around DT ¼ 400  C was achieved for an absorbed optical power of PAbs ¼ 29 W, which induced a generated electric power of 500 mW. In this configuration, the system efficiency was hSys ¼ 1.6% and the thermoelectric yield was hTEG ¼ 3%. A thermal-optical model based on finite element method was developed. The results of these simulations were in a good agreement with the experimental measurements. In order to predict the STEG efficiency for higher working temperatures, this model was used for greater incident optical power (e.g. for higher

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concentration ratio) using the absorber emissivity compared to a degraded and an upgraded absorber emissivity (respectively εSOA ¼ 10%, εAbs ¼ 30% and εBB ¼ 90%). These calculations underlined that whatever the absorber emissivity, the maximum of efficiency is reached for 64 W incident power, which was in a good agreement with the first dimensioning of the TEG. We found that the maximum efficiency was 1.8% for the lowest emissivity (εSOA ¼ 10%). These performances will be confirmed later with outdoor experiments performed with a 320  320 mm2 Fresnel lens, which will be reported in a next paper. In a last part, we modeled the power generated per square meter on the ground depending on different thermoelectric materials (Bi2Te3, Mg2SiGe0.4/MnSi1.75 and Si80Ge20) and regarding their operating temperature. TEG cascaded devices were also studied. The best performances would be achieved with a Si80Ge20/ Mg2SiGe0.4/MnSi1.75/Bi2Te3 cascaded module which should deliver around 68 W/m2 with an 8% system yield. These simulations will be confirmed in the next paper using the experiments performed outdoor with a Fresnel lens.

Acknowledgements This work has been financially supported by Hotblock OnBoard S.A.S. (http://www.hotblock.fr). The authors would like to grate€l and Mr. fully acknowledge Mr. Thompson Mike, Mr. Dufourcq Joe Yannick Yvin for their significant contribution.

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