Spectrum splitting metrics and effect of filter characteristics on photovoltaic system performance

Juan M. Russo; Deming Zhang; Michael Gordon; Shelby Vorndran; Yuechen Wu; Raymond K. Kostuk

doi:10.1364/OE.22.00A528

Optics Express
Vol. 22,
Issue S2,
pp. A528-A541
(2014)
•https://doi.org/10.1364/OE.22.00A528

Spectrum splitting metrics and effect of filter characteristics on photovoltaic system performance

Juan M. Russo, Deming Zhang, Michael Gordon, Shelby Vorndran, Yuechen Wu, and Raymond K. Kostuk

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Juan M. Russo, Deming Zhang, Michael Gordon, Shelby Vorndran, Yuechen Wu, and Raymond K. Kostuk, "Spectrum splitting metrics and effect of filter characteristics on photovoltaic system performance," Opt. Express 22, A528-A541 (2014)

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Abstract

During the past few years there has been a significant interest in spectrum splitting systems to increase the overall efficiency of photovoltaic solar energy systems. However, methods for comparing the performance of spectrum splitting systems and the effects of optical spectral filter design on system performance are not well developed. This paper addresses these two areas. The system conversion efficiency is examined in detail and the role of optical spectral filters with respect to the efficiency is developed. A new metric termed the Improvement over Best Bandgap is defined which expresses the efficiency gain of the spectrum splitting system with respect to a similar system that contains the highest constituent single bandgap photovoltaic cell. This parameter indicates the benefit of using the more complex spectrum splitting system with respect to a single bandgap photovoltaic system. Metrics are also provided to assess the performance of experimental spectral filters in different spectrum splitting configurations. The paper concludes by using the methodology to evaluate spectrum splitting systems with different filter configurations and indicates the overall efficiency improvement that is possible with ideal and experimental designs.

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Fig. 1 Ideal PV cell SCE spectral response with bandgap wavelengths corresponding to four different material systems. The AM1.5 solar reference spectrum is also shown.

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Fig. 2 SCE for InGaP₂-Emcore [9,10], GaAs-Alta [9] (maximum SCE at λ = 0.86μm) and Si-PERL [11] (maximum SCE at λ = 1.11μm). An ideal filter for the GaAs-Alta PV cell in a SSS will have a shortwave cutoff of λ_S = 0.64μm and long wave cutoff of λ_L = 0.877μm.

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Fig. 3 Band pass spectrum splitting configurations. (a) Band pass filter transmittance and reflectance operation. (b) Cascaded configuration. The width of the input beam is DA however the size of the system must be larger to accommodate non-axial PV cells.

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Fig. 4 Spatial band separation. (a) Transmission diffraction filter showing single diffraction order and zero^th order beams. Spatial band separation using: (b) transmission diffractive filters, (c) reflection diffractive filters with total internal reflection.

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Fig. 5 Dispersive spectrum splitting. (a) A single dispersive filter projects the complete spectrum along a distance corresponding to the entrance aperture on the receiver (PV cell) plane. Wavelength separation only occurs at the edge of the aperture. b) Focusing power is combined with the dispersive element to separate spectral components along the receiver plane that can then be collected by PV cells with different spectral responsivities.

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Fig. 6 Diagram of the aperture overlap function for (left) no focusing, (right) 4X focusing. With increased focusing the shape of the aperture overlap function changes from triangular to rectangular.

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Fig. 7 (Top) SCE of each PV cell is shown with the ideal filter performance transmittance overlaid. (Bottom) The converted spectral power is shown color coded according to the PV cell used for conversion. The single junction efficiency η_k, filtered efficiency η*_k and bandgap wavelength λ_BG are indicated on the graph. The ideal maximum achievable performance with these 4-PV cells is 51.89%.

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Fig. 8 Reported data for InGaP₂-Emcore [9,10], GaAs-Alta [9], Si-PERL [11], and GaSb [14,16] PV cells from the literature is used instead of ideal for the analysis with ideal filters. The total η_SSS = 41.65% with an IoBB = 47.78%.

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Fig. 9 SCE analysis of the SSS system in [17] using GaAs-Alta and Si-PERL. At left, the system with an ideal filter and at right with experimental holographic filter data.

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Fig. 10 Grating-lens dispersive SSS using a transmission holographic grating. Although the experimental system uses a broadband grating, dominated by in-band losses (non-optimized grating).

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Equations (17)

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η_{k}^{} = \frac{P_{O U T - P V}}{P_{I N - o p t i c a l}} = \frac{J_{S C} \cdot V_{O C} \cdot F F}{P_{I N - o p t i c a l}}

P_{I N - o p t i c a l} = \int E_{I N} (λ) \cdot d λ

J_{S C} = \int E_{A M 1.5} (λ) \cdot S R (λ) \cdot d λ = \frac{q}{h c} \int λ \cdot E_{A M 1.5} (λ) \cdot E Q E (λ) \cdot d λ,

\begin{array}{l} η_{k}^{} = \frac{1}{P_{A M 1.5}} \int E_{A M 1.5} (λ) \cdot S R (λ) \cdot V_{O C} \cdot F F \cdot d λ \\ = \frac{1}{P_{A M 1.5}} \int E_{A M 1.5} (λ) \cdot S C E (λ) \cdot d λ, \end{array}

η_{k}^{*} = \frac{1}{P_{A M 1.5}} \int T (λ) \cdot E_{A M 1.5} (λ) \cdot S C E_{k} (λ) \cdot d λ

η_{S S S} = \sum_{1}^{K} η_{k}^{*}

η_{S S S} \neq η_{P V} \cdot η_{_{}}^{o e},

I o B B = \frac{η_{S S S}}{M A X [η_{1}, η_{2} \dots η_{2}]} - 1

O = \frac{I o B B}{I o B B_{I d e a l}}

O_{f i l t e r l o s s} = 1 - O

\begin{array}{l} η_{S S S} = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [\begin{array}{l} S C E_{1} (λ) + \\ T_{1} (λ) \cdot S C E_{2} (λ) + \\ T_{1} (λ) \cdot T_{2} (λ) \cdot S C E_{3} (λ) \dots \end{array}] \cdot d λ \\ = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [S C E_{1} (λ) + \sum_{k = 1}^{K} (S C E_{k + 1} (λ) \cdot \prod_{i = 1}^{k} T_{i} (λ))] \cdot d λ \end{array}

T_{i} (λ) = (1 - S C E_{i} (λ)) \cdot u (λ - λ_{B G_{i}})

η_{S S S} = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [\begin{array}{l} S C E_{1} (λ) \cdot R_{1} (λ) + \\ \sum_{j = 2}^{K - 1} (S C E_{j} (λ) \cdot R_{j} (λ) \cdot \prod_{i = 1}^{j - 1} T_{i} (λ)) + \\ S C E_{K} (λ) \cdot \prod_{i = 1}^{M} T_{i} (λ) \end{array}] \cdot d λ

T_{i} (λ) = 1 - R_{i} (λ) .

η_{S S S} = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [\begin{array}{l} S C E_{1} (λ) \cdot [T_{1} (λ) + (1 - T_{2} (λ))] + \\ S C E_{2} (λ) \cdot [T_{2} (λ) + (1 - T_{1} (λ))] \end{array}] \cdot d λ

D_{F} = \frac{d θ}{d λ} .

\begin{array}{l} η_{S S S} = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [\begin{array}{l} S C E_{1} (λ) \cdot τ_{1} (λ) \cdot T (λ) + \\ S C E_{2} (λ) \cdot τ_{2} (λ) \cdot T (λ) + \dots \end{array}] \cdot d λ \\ = \frac{1}{P_{A M 1.5}} \cdot \int E_{A M 1.5} (λ) \cdot [\sum_{k = 1}^{K} S C E_{k} \cdot τ_{k} (λ) \cdot T (λ)] \cdot d λ \end{array}

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Equations (17)

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