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Role of spectral non-idealities in the design of solar thermophotovoltaics

Andrej Lenert, Youngsuk Nam, David M. Bierman, and Evelyn N. Wang

Open Access Open Access

Abstract

To bridge the gap between theoretically predicted and experimentally demonstrated efficiencies of solar thermophotovoltaics (STPVs), we consider the impact of spectral non-idealities on the efficiency and the optimal design of STPVs over a range of PV bandgaps (0.45-0.80 eV) and optical concentrations (1-3,000x). On the emitter side, we show that suppressing or recycling sub-bandgap radiation is critical. On the absorber side, the relative importance of high solar absorptance versus low thermal emittance depends on the energy balance. Both results are well-described using dimensionless parameters weighting the relative power density above and below the cutoff wavelength. This framework can be used as a guide for materials selection and targeted spectral engineering in STPVs.

© 2014 Optical Society of America

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Figures (13)
Fig. 1
Fig. 1 Generalized spectral non-idealities: deviations from unity emittance at wavelengths below the cutoff (δh ) and from zero emittance above the cutoff (δl ) on both the absorber (a) and the emitter (e) side. The following spectral fluxes are shown for reference: AM 1.5D with 40x concentration (gray) and blackbody emission at 1300 K (light red).

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Fig. 2
Fig. 2 Schematic of a planar STPV device and its components. The window and the absorber are grouped together as “absorber-side”. The emitter and the filter are grouped together as “emitter-side”. The model accounts for parasitic losses from the inactive area and the mechanical supports.

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Fig. 3
Fig. 3 Optimized STPV efficiency in the presence of (a) 0.10 and (b) 0.01 non-idealities (δ). Design space covers a range of bandgaps and optical concentrations. Each operating point corresponds to a specific absorber-side cutoff [Fig. 4], absorber-emitter temperature [Fig. 5], and emitter-to-absorber area ratio [Fig. 6]. Arrow points to region where the STPV efficiency exceeds the PV efficiency (same cell as in STPV) as delineated by the dash-dot line.

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Fig. 4
Fig. 4 Optimal absorber-side cutoff wavelength (λc ) for an STPV with (a) 0.10 and (b) 0.01 non-idealities. Dash-dot line [see Fig. 3] delineates the region where STPV efficiency exceeds the PV efficiency. (c) and (d) λc plotted as energy (Ec ) relative to the PV bandgap energy (Eg ), corresponding to (a) and (b) respectively. Thick black contours represent the median cutoff wavelength for each cluster from Appendix A with the corresponding 10/90 percentile of each cluster [see Fig. 13] shown with thin contours. Note: the emitter-side cutoff is set to the bandgap energy.

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Fig. 5
Fig. 5 Optimal temperature of the absorber-emitter for an STPV with (a) 0.10 non-idealities, compared to an STPV with (b) 0.01 non-idealities. Dash-dot line [see Fig. 3] delineates the region where STPV efficiency exceeds the PV efficiency. Thin contours represent the 10/90 percentile of each λc cluster [see Fig. 4].

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Fig. 6
Fig. 6 Geometrical optimization of the size of emitter with respect to the absorber (AR): (a) Emitter is smaller than the absorber (AR<1), (b) Emitter is larger than the absorber (AR>1).

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Fig. 7
Fig. 7 Optimal absorber-emitter geometry (emitter-to-absorber size, AR) for an STPV with (a) 0.10 non-idealities, compared to an STPV with (b) 0.01 non-idealities. Dash-dot line [see Fig. 3] delineates the region where STPV efficiency exceeds the PV efficiency. Thin contours represent the 10/90 percentile of each λc cluster [see Fig. 4].

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Fig. 8
Fig. 8 The impact of independently increasing the emitter-side emittance below λg (blue) as compared to decreasing the emittance above λg (red), schematically shown in (a), on the STPV efficiency (b). δ = 0.10 is the baseline case.

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Fig. 9
Fig. 9 Emitter-side weighting parameter We for an STPV with (a) 0.10 compared to (b) 0.01 non-idealities.

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Fig. 10
Fig. 10 The impact of independently increasing the absorber-side solar absorptance (blue) as compared to decreasing the thermal emittance (red), schematically shown in (a), on the STPV efficiency (b). The baseline case has uniform spectral non-idealities (δ = 0.10).

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Fig. 11
Fig. 11 Absorber-side weighting parameter for an STPV with (c) 0.10 compared to (d) 0.01 non-idealities. Thin contours represent the 10/90 percentile of each λc cluster [see Fig. 4].

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Fig. 12
Fig. 12 Optimization of the absorber-side cutoff wavelength. Net spectral flux (a) integrated up to a wavelength of interest (b). Optimal cutoff wavelength shown.

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Fig. 13
Fig. 13 Grouping of absorber-side cut-off wavelengths. Histogram of optimal cutoff wavelengths corresponding to Fig. 3 for (a) 0.10 and (b) 0.01 non-ideality cases. (c) AM 1.5D spectral flux (gray) with the median cutoff wavelength (solid black) for each cluster and its corresponding 10/90 percentile (dashed lines).

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Equations (13)

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σ ( T a e 4 − T a m b 4 ) ( ε ¯ a A a + ε ¯ e A e + ε ¯ n a e f f | A e − A a | ) + Q p a r a s i t i c = α ¯ a A a c G s
ε ¯ n a e f f = [ 1 δ l + 1 ( 1 − 0.96 ) − 1 ] − 1
p u = ∫ 0 λ g ε λ e b λ λ λ g d λ
e b λ = 2 π h c 2 λ 5 ( e h c / λ k b T − 1 )
v = V o c V g = k b T P V E g ln ( f ∫ 0 λ g R λ , e d λ ∫ 0 λ g R λ , P V d λ )
m = z m 2 ( 1 + z m − e − z m ) ( z m + ln ( 1 + z m ) )
z m + ln ( 1 + z m ) = q V o c k b T P V
W e = e λ > λ g e λ < λ g
W a = σ ( T a e 4 − T a m b 4 ) c G s
W a = σ ( T a e 4 − T a m b 4 ) c G s = α ¯ a b s ε ¯ a b s + ε ¯ e m i t ⋅ A R + p a r a s i t i c
∫ 0 λ ( H λ ' − Q λ ' ) d λ '
C 1 ( ∫ 0 λ H λ ' − Q λ ' d λ ' ) + C 2
C 1 = 1 − δ l a − δ h a C 2 = δ l a [ c G s − σ ( T a e 4 − T a m b 4 ) ]
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