Spectral Shift Adjustment

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Summary

The Spectral Shift Adjustment accounts for variations in module performance due to changes in the solar spectrum. PlantPredict implements five spectral correction approaches: None, Monthly Override, Spectral 1 (technology-specific models), Spectral 2 (multi-parameter), and Spectral 3.0 (experimental). The spectral shift factor $M$ is a multiplier applied to effective irradiance after IAM corrections. The factor depends on atmospheric conditions (air mass, precipitable water) and module technology (Sandia, First Solar POR/QED, or generic multi-parameter).

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Inputs

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Outputs

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Detailed Description

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Model Selection

PlantPredict selects the spectral model based on configuration:

1. If UseSpectral30 = true: Spectral 3.0 model
2. If SpectralShiftModel = None: $M = 1$
3. If SpectralShiftModel = MonthlyOverride: Monthly user-specified values
4. If SpectralShiftModel = Spectral_1: Technology-specific models
5. If SpectralShiftModel = Spectral_2: Multi-parameter model

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Model 1: None

No spectral correction: $$M = 1$$

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Model 2: Monthly Override

User-specified monthly spectral shift factors: $$M = M_{\text{month}}$$ where $M_{\text{month}}$ is retrieved from monthly factors table for the current month.

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Model 3: Spectral 1 (Technology-Specific Models)

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Sandia Polynomial Model

For modules with Sandia spectral response: $$M = \sum_{i=0}^{n} a_i (AM')^i$$ where $[a_0, a_1, ..., a_n]$ are Sandia A-factors and $AM'$ is pressure-corrected air mass.

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First Solar POR Model

For First Solar POR modules (water vapor dependent): $$M = 0.6318 + 0.1341 \cdot e^{0.9757 (W + 0.05)^{0.0788}}$$ where $W$ is precipitable water (cm). If $W < -900$: $M = 1$ (failsafe).

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First Solar QED Model

For First Solar QED modules (water vapor dependent): $$M = 1.266 - 0.0913 \cdot e^{1.1987 (W + 0.5)^{-0.21}}$$ where $W$ is precipitable water (cm). If $W < -900$: $M = 1$ (failsafe).

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Model 4: Spectral 2 (Multi-Parameter Model)

Six-parameter model accounting for air mass and precipitable water: $$M = b_0 + b_1 AM' + b_2 W + b_3 \sqrt{AM'} + b_4 \sqrt{W} + b_5 \frac{AM'}{\sqrt{W}}$$ where:

• $[b_0, b_1, b_2, b_3, b_4, b_5]$ are module-specific Spectral2 coefficients
• $AM'$ is pressure-corrected air mass
• $W$ is precipitable water (cm)

Limits applied:

• If $W < 0.1$: $W = 0.1$
• If $AM' > 10$: $AM' = 10$

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Model 5: Spectral 3.0 (Experimental)

Seven-parameter model including clear sky index (temporary implementation for First Solar): $$M = b_0 \cdot K_c + b_1 \cdot W + b_2 \cdot \sqrt{W} + b_3 \cdot AM' + b_4 \cdot \sqrt{AM'} + b_5 \cdot \frac{AM'}{\sqrt{W}} + b_6$$ where:

• $K_c = GHI / GHI_{clear}$ is clear sky index
• $[b_0, b_1, b_2, b_3, b_4, b_5, b_6]$ are Spectral30 coefficients
• $AM'$ is pressure-corrected air mass
• $W$ is precipitable water (cm)

Clear sky index limits:

• If $K_c$ is NaN: $K_c = 0$
• If $K_c > 2$: $K_c = 2$

Limits applied:

• If $W < 0$: $\sqrt{W} = 0$
• If $AM' < 0$: $\sqrt{AM'} = 0$
• If $W = 0$ or $AM' = 0$: $AM' / \sqrt{W} = 0$

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Precipitable Water Calculation

If precipitable water is not directly available, it is calculated from relative humidity or dewpoint.

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From Relative Humidity (Gueymard 1994)

$$h = 0.1 \cdot \left( 0.4976 + 1.5265 \frac{T_K}{273.15} + e^{13.6897 \frac{T_K}{273.15} - 14.9188 (\frac{T_K}{273.15})^3} \right)$$ $$\rho_v = \frac{216.7 \cdot RH}{100 \cdot T_K} \cdot e^{22.33 - \frac{4914}{T_K} - 10.922 (\frac{100}{T_K})^2 - 0.39015 \frac{T_K}{100}}$$ $$W = h \cdot \rho_v$$ where $T_K = T + 273.15$ (temperature in Kelvin), $RH$ is relative humidity (%), and $W$ is in cm.

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From Dewpoint (August-Roche-Magnus)

Version 10 and Earlier: $$e_s(T_d) = 6.11 \cdot e^{\frac{17.1 T_d}{234.2 + T_d}}$$ $$e_s(T) = 6.11 \cdot e^{\frac{17.1 T}{234.2 + T}}$$ $$RH = 100 \cdot \frac{e_s(T_d)}{e_s(T)}$$ Version 11 and Later (AEKR Coefficients): $$e_s(T_d) = 6.1094 \cdot e^{\frac{17.625 T_d}{243.04 + T_d}}$$ $$e_s(T) = 6.1094 \cdot e^{\frac{17.625 T}{243.04 + T}}$$ $$RH = 100 \cdot \frac{e_s(T_d)}{e_s(T)}$$ Then calculate $W$ from $RH$ using the Gueymard method above.

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Application to Irradiance

Spectral shift factor applied after IAM: $$E_{beam,spectral} = E_{beam,IAM} \times M$$ $$E_{sky,spectral} = E_{sky,IAM} \times M$$ $$E_{ground,spectral} = E_{ground,IAM} \times M$$

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References

• Gueymard, C. (1994). Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States. Solar Energy, 53(1), 57-71.
• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.
• Marion, B., MacAlpine, S., Deline, C., et al. (2017). A practical irradiance model for bifacial PV modules. 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), 1537-1542.
• pvlib-python Documentation. Atmosphere Module: gueymard94_pw. https://pvlib-python.readthedocs.io/