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Design and global optimization of high-efficiency thermophotovoltaic systems

Peter Bermel, Michael Ghebrebrhan, Walker Chan, Yi Xiang Yeng, Mohammad Araghchini, Rafif Hamam, Christopher H. Marton, Klavs F. Jensen, Marin Soljačić, John D. Joannopoulos, Steven G. Johnson, and Ivan Celanovic

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Abstract

Despite their great promise, small experimental thermophotovoltaic (TPV) systems at 1000 K generally exhibit extremely low power conversion efficiencies (approximately 1%), due to heat losses such as thermal emission of undesirable mid-wavelength infrared radiation. Photonic crystals (PhC) have the potential to strongly suppress such losses. However, PhC-based designs present a set of non-convex optimization problems requiring efficient objective function evaluation and global optimization algorithms. Both are applied to two example systems: improved micro-TPV generators and solar thermal TPV systems. Micro-TPV reactors experience up to a 27-fold increase in their efficiency and power output; solar thermal TPV systems see an even greater 45-fold increase in their efficiency (exceeding the Shockley–Quiesser limit for a single-junction photovoltaic cell).

© 2010 Optical Society of America

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Figures (16)
Fig. 1
Fig. 1 Approaches to TPV conversion of heat to electricity. The traditional design is depicted in (a), and a novel approach based on manipulation of the photonic density of states is depicted in (b). The anticipated increase in efficiency associated with the latter approach can exceed 100%.

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Fig. 12
Fig. 12 Optimized emittance spectra of semiconductor selective absorbers depicted in Fig. 10, as a function of angle. Note that optimized designs with one or more front coating layers see fairly constant performance up to angles of ±60°.

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Fig. 2
Fig. 2 Design of the μTPV generator. Hydrocarbon fuel flows from a storage tank to the interior of the selective emitter and back out. The heated selective emitter then radiatively couples to the nearby TPV module to generate electricity (adapted from Ref. 31).

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Fig. 3
Fig. 3 Three 1D structures examined as selective emitters in this work: (a) a polished Si wafer (b) a polished Si wafer with a 4-bilayer 1D PhC, and (c) a polished Si wafer with a metal layer (tungsten or platinum) and a 4-bilayer 1D PhC. Their optimized emittance spectra are shown in Fig. 4; the resulting efficiency, power (per unit area), and overall figure of merit for each structure is listed in Table 2.

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Fig. 4
Fig. 4 Spectral emittance of four structures at 1000 K: a polished Si wafer (Fig. 3(a)), a polished Si wafer with a 4-bilayer 1D PhC (Fig. 3(b)), a polished Si wafer with tungsten and a 4-bilayer 1D PhC (Fig. 3(c)), and a platinum wafer with a 3-bilayer 1D PhC (similar to Fig. 3(c)). The efficiency, power, and overall figure of merit for each structure is listed in Table 2.

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Fig. 6
Fig. 6 (a) Side view of the tungsten 2D PhC selective emitter, consisting of partially open cylindrical cavities supporting multiple resonant modes with a low-frequency cutoff, arranged in a 2D square array. (b) The structure depicted in (a) plus a rugate filter (depicted here with 6 distinct materials and 6 periods of periodicity p) on top, separated by an air gap.

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Fig. 7
Fig. 7 Emissivity spectrum of three tungsten structures: two experimentally measured (flat and a 2D PhC) and one computer-optimized (a 2D PhC with larger a and r).

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Fig. 8
Fig. 8 Spectral emittance for combined tungsten 2D PhC and rugate filter. Emitted photons with wavelengths λ < 2.23 μm (depicted in blue) are capable of being absorbed by the InGaAsSb TPV device.

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Fig. 9
Fig. 9 Diagram of a solar TPV system. Sunlight is collected via optical concentrators and sent to a selectively absorbing surface. That structure is thermally coupled to a selective emitter, which in conjunction with a filter, thermally emits photons with energies matched to the semiconductor bandgap of the TPV cell receiving them.

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Fig. 10
Fig. 10 Three related semiconductor selective absorbers (a) germanium wafer on a silver substrate (b) previous with a single front coating layer (c) germanium on silver with a single dielectric back coating and three front coating layers in front.

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Fig. 13
Fig. 13 Optimized emittance spectra of the semiconductor selective absorbers depicted in Fig. 10, with silicon substituted for germanium, designed for operation under concentrated AM1.5 sunlight at 1000 K and C = 100.

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Fig. 11
Fig. 11 Optimized emittance spectra of the semiconductor selective absorbers depicted in Fig. 10, designed for operation in unconcentrated AM1.5 sunlight at 400 K.

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Fig. 14
Fig. 14 Optimized emittance spectra for emitters at 2360 K (left) and 1300 K (right). The corresponding efficiencies are 54.2% and 44.7%, respectively.

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Fig. 15
Fig. 15 Optimized emittance spectra for emitters at 2360 K (left) and 1000 K (right). The corresponding efficiencies are 66.3% and 44.0%, respectively.

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Fig. 5
Fig. 5 (Inset) Chirped rugate filter index as a function of position (using 6 materials) and (Main image) its emittance as a function of wavelength. Emitted photons with wavelengths λ < 2.23 μm (depicted in blue) are capable of being absorbed by the InGaAsSb TPV device.

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Fig. 16
Fig. 16 Model of the dispersion of the imaginary part of the refractive index for both T = 300 K, along with a comparison to experiment [25], and projected values for T = 1000 K.

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Tables (6)

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Table 1 Experimental measurements of the TPV micro-combustor system depicted in Fig. 2, with one TPV cell of area 0.5 cm2, when fueled by butane and oxygen, as a function of butane flow rate (note that all measurements yielded an open-circuit voltage Voc = 247 mV per cell). Note that Isc is the short circuit current of the cell, and FF is the fill factor, defined as the ratio of the maximum power output to the product of Isc and Voc

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Table 2 Predicted efficiency, power generation, and overall product figure of merit values for multiple μTPV emitter designs at 1000 K (view factor F = 0.4)

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Table 3 Selective absorber data for operation under unconcentrated light at 400 K

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Table 4 Selective absorber data for operation under 100x concentrated light at 1000 K

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Table 5 Selective emitter optimization results. Symbols are defined in the text; those with dimensions of length are quoted in nm, those with units of energy are quoted in eV, and those with dimensions of temperature are quoted in K. Note that different FOM values are not necessarily comparable

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Table 6 Selective absorber optimization results. Symbols are defined in the text; those with dimensions of length are quoted in nm and those with dimensions of temperature are quoted in K

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Equations (5)

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J ( V )   =   ∫ 0 ∞ d λ   [ 2 q c λ 4   ɛ ( λ ) EQE ( λ ) exp   ( h c / λ k T )   −   1 ]   −   [ q ( n 2   +   1 ) E g 2 k T d 4 π 2 h ¯ 3   c 2 e − E g / m k T d   +   J nr ]   ( e q V / m k T d   −   1 ) ,
η t   =   α ¯   −   ɛ ¯ σ T 4 C I
ɛ ¯   =   ∫ 0 ∞ d λ   ɛ ( λ ) / { λ 5   [ exp   ( h c / λ k T )   −   1 ] } ∫ 0 ∞ d λ / { λ 5   [ exp   ( h c / λ k T )   −   1 ] } .
E g   ( T )   =   E g   ( 0 )   −   α T 2 T   +   β ,
k ( ω )   =   { k o   exp   [ ( h ¯ ω   −   E f ) / E o ] , h ¯ ω   <   E f k o   exp   [ ( h ¯ ω   −   E f ) / α E o ] , E f   ≤   h ¯ ω   <   E f   +   2 α E o k 1   exp   [ β ( h ¯ ω   −   E g − 2 α E o ] , E f   +   2 α E o   ≤   h ¯ ω   <   E x k 2 h ¯ ω   −   E x , h ¯ ω   ≥   E x ,
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