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Performance analysis of experimentally viable photonic crystal enhanced thermophotovoltaic systems

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Abstract

One of the keys towards high efficiency thermophotovoltaic (TPV) energy conversion systems lies in spectral control. Here, we present detailed performance predictions of realistic TPV systems incorporating experimentally demonstrated advanced spectral control components. Compared to the blackbody emitter, the optimized two-dimensional (2D) tantalum (Ta) photonic crystal (PhC) selective emitter enables up to 100% improvement in system efficiency. When combined with the well characterized cold side tandem filter and the latest InGaAs TPV cells, a TPV energy conversion system with radiant heat-to-electricity efficiency of 25% and power density of 0.68 W cm−2 is achievable today even at a relatively low temperature of 1320 K. The efficiency could be increased to ∼ 40% (the theoretical 0.62 eV single bandgap TPV thermodynamic limit at 1320 K is 55%) as future implementation of more optimized TPV cells approach their theoretical thermodynamic limit.

© 2013 Optical Society of America

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Figures (7)

Fig. 1
Fig. 1 (a) Conventional thermophotovoltaic (TPV) energy conversion system without spectral control. (b) TPV system with 2D photonic crystal (PhC) selective emitter and cold side filter. Spectral control enables performance enhancement of up to 400% over the conventional TPV system.
Fig. 2
Fig. 2 Simulated high temperature (T = 1478 K) normal spectral emittance of flat Ta and 2D Ta PhCs optimized for GaSb (Design I: r = 0.43 μm, d = 8.00 μm, a = 0.95 μm), InGaAs (Design II: r = 0.51 μm, d = 8.00 μm, a = 1.11 μm), and InGaAsSb (Design III: r = 0.57 μm, d = 8.00 μm, a = 1.23 μm). As can be seen, the cutoff is easily shifted by modifying the dimensions of the PhC.
Fig. 3
Fig. 3 Measured normal incidence transmittance of tandem filters optimized for 0.5 eV and 0.6 eV TPV cells. The tandem filters consist of dielectric stacks of antimony selenide (Sb2Se3) and yttrium fluoride (YF3), terminated with a 1 μm thick heavily doped indium phosphide arsenide (InPAs) layer as the plasma filter. The tandem filters are sourced from Rugate Technologies, Inc.
Fig. 4
Fig. 4 Relevant optical properties for optimized components in an InGaAsSb TPV system. The normal incidence emittance ε and hemispherical emittance εH of the optimized 2D Ta PhC emitter, and 45° reflectance Rθ=45° of the 0.53 eV tandem filter is shown to match the external quantum efficiency (EQE) of InGaAsSb. An ideal cutoff emitter is included in the analysis to elucidate the effect of non-ideal spectral emittance of the optimized 2D Ta PhC.
Fig. 5
Fig. 5 (a) Radiant heat-to-electricity ηTPV for various emitters with or without an optimized tandem filter in combination with InGaAsSb TPV cell at fixed view factor F = 0.99 (10 cm × 10 cm flat plate geometry with separation s = 500 μm). An optimum temperature T exist for each combination. Due to considerable emission below the bandgap of the In-GaAsSb TPV cell for the emitters considered, significant improvement is seen with the use of the tandem filter. (b) Overall spectral efficiency when TPV cavity effects are included, ηCav–Spec. When F = 0.99, use of a selective emitter is not critical if an optimized tandem filter is present. (c) TPV cell efficiency ηCell. For T > 1200 K, degradation of ηCell is seen due to larger series resistance losses from high carrier injection.
Fig. 6
Fig. 6 With T fixed at the optimum, the most efficient combination depends on the experimentally achievable F. For F > 0.97 (10 cm × 10 cm flat plate geometry with separation s < 1.7 mm), the use of the optimized tandem filter allows the greybody to slightly outperform the optimized 2D Ta PhC selective emitter. In contrast, it is important to restrict below bandgap emission via selective emitters in TPV systems with smaller view factors.
Fig. 7
Fig. 7 ηTPV for an InGaAsSb TPV system including an ideal cutoff emitter with varying below bandgap hemispherical emittance εlw with or without a 0.53 eV optimized tandem filter at a fixed temperature T of 1250 K. (a) F = 0.99. To outperform the greybody - optimized tandem filter combination, εlw must be smaller than 0.03, to a point where addition of the tandem filter is detrimental given the larger reduction in power density for a small improvement in ηTPV. (b) F = 0.97. To outperform the greybody - optimized tandem filter combination, εlw must be smaller than 0.08. As F is reduced, both aspects of spectral control become important.

Tables (1)

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Table 1 Predicted ηTPV,max for three different TPV cells utilizing experimentally realizable spectral control components at fixed F = 0.99. Optimum temperature indicated in brackets is determined for each TPV system combination using fabricated and characterized TPV cells (GaSb [45], InGaAs [3], and InGaAsSb [45]). Results indicate that current state of the art fabricated TPV cells are ∼ 50% as efficient as their thermodynamically ideal counterparts. It is also interesting to note that spectral control via the optimized 2D Ta PhC and tandem filter enables TPV cells with larger bandgaps (GaSb) to perform as well as TPV cells with smaller bandgaps (InGaAsSb). However, the use of smaller bandgap TPV cells would result in lower optimum temperatures.

Equations (16)

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i BB ( λ , t ) = 2 h c 2 λ 5 [ exp ( h c λ k T ) 1 ]
P em = 0 d λ 0 π 2 d θ 1 0 2 π d ϕ 1 A 1 d A 1 [ i BB ( λ , T ) ε ( λ , θ 1 , ϕ 1 ) cos θ 1 sin θ 1 ]
d Q d A 1 d A 2 = i BB ( λ , T ) ε ( λ , θ 1 , ϕ 1 ) d A 1 d F 2
d F 2 = cos θ 1 cos θ 2 s 2 d A 2
d F l = cos θ 1 cos θ l s l 2 d A l
P re = p = 1 d λ d F 2 p + 1 d A 1 [ i BB ( λ ) R 2 p R 1 p 1 ( 1 R 1 ) ε ( λ , θ 2 p + 1 , ϕ 2 p + 1 ) ]
P re = p = 1 d λ d A 2 p + 1 d A 1 [ i BB ( λ ) R 2 p R 1 p 1 ( 1 R 1 ) ε ( λ , θ 2 p + 1 , ϕ 2 p + 1 ) cos 2 θ 2 p + 1 s 2 p + 1 2 ]
P cell = p = 1 0 λ g d λ d A 2 p d A 1 [ i BB ( R 1 R 2 ) p 1 ( 1 R 2 ) ε ( λ , θ 2 p , ϕ 2 p ) cos 2 θ 2 p s 2 p 2 ]
I sc = 2 q c p = 1 IQE ( λ ) d λ λ 4 [ exp ( h c λ k T ) 1 ] d A 2 p d A 1 [ ( R 1 R 2 ) p 1 ( 1 R 2 ) ε ( λ , θ 2 p , ϕ 2 p ) cos 2 θ 2 p s 2 p 2 ]
I = I sc I o exp [ q ( V + I R s ) m k T c ] V + I R s R sh
η TPV = P elec , max P em P re
η Cav Spec = P cell P em P re
η Cell = P elec , max P cell
ε H ( λ ) = 1 π 0 π 2 d θ 1 0 2 π d ϕ 1 [ ε ( λ , θ 1 , ϕ 1 ) cos θ 1 sin θ 1 ]
FOM = x η TPV + ( 1 + x ) J elec , max PhC J elec , max BB
I o = A 2 q ( n 2 + 1 ) E g 2 k T c 4 π 2 h ¯ 3 c 2 exp ( E g / k T c )
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