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Summary

Metastability models performance variations in thin-film PV modules caused by reversible changes in material properties based on recent operating history. PlantPredict calculates a metastability scale factor using polynomial regression on 7-day lagged moving averages of cell temperature and POA irradiance, plus a 6-hour lagged moving average of POA irradiance. The scale factor adjusts both voltage and current at maximum power point through separate scalars. The model uses 12 coefficients (C0C_0 through C11C_{11}) determined empirically for specific module technologies.

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Inputs

NameSymbolUnitsDescription
Metastability CoefficientsC0,C1,...,C11C_0, C_1, ..., C_{11}variousPolynomial regression coefficients
7-Day Lagged Avg Cell TempTc,7d‾\overline{T_{c,7d}}°CAverage cell temperature over prior 7 days
7-Day Lagged Avg POA IrrG7d‾\overline{G_{7d}}kW/m²Average POA irradiance over prior 7 days
6-Hour Lagged Avg POA IrrG6h‾\overline{G_{6h}}kW/m²Average POA irradiance over prior 6 hours
Metastability Voltage Scale FactorfV,metaf_{V,meta}—Voltage allocation factor
Max Power VoltageVmpV_{mp}VVoltage at maximum power (before metastability)
Max Power CurrentImpI_{mp}ACurrent at maximum power (before metastability)

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Outputs

NameSymbolUnitsDescription
Metastability Scale Factorfmetaf_{meta}—Power scale factor
Voltage ScalarVscalarV_{scalar}—Voltage adjustment multiplier
Current ScalarIscalarI_{scalar}—Current adjustment multiplier
Adjusted VoltageVmp,adjV_{mp,adj}VVoltage after metastability
Adjusted CurrentImp,adjI_{mp,adj}ACurrent after metastability
Adjusted PowerPmp,adjP_{mp,adj}WPower after metastability

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Detailed Description

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Metastability Scale Factor Calculation

fmeta=C0+C1Tc,7d‾+C3(Tc,7d‾−C2)2+C4G7d‾f_{meta} = C_0 + C_1 \overline{T_{c,7d}} + C_3 (\overline{T_{c,7d}} - C_2)^2 + C_4 \overline{G_{7d}} +C6(G7d‾−C5)2+C7(G7d‾−C5)3+C8(Tc,7d‾−C2)3+ C_6 (\overline{G_{7d}} - C_5)^2 + C_7 (\overline{G_{7d}} - C_5)^3 + C_8 (\overline{T_{c,7d}} - C_2)^3 +C9G6h‾+C11(G6h‾−C10)2+ C_9 \overline{G_{6h}} + C_{11} (\overline{G_{6h}} - C_{10})^2

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Lagged Moving Average Calculations

7-Day Lagged Average (168 hours): Only includes timesteps where irradiance ≥0.1\geq 0.1 kW/m² Tc,7d‾=1n∑i=t−168htTc,iwhere Gi≥0.1\overline{T_{c,7d}} = \frac{1}{n} \sum_{i=t-168h}^{t} T_{c,i} \quad \text{where } G_i \geq 0.1 G7d‾=1n∑i=t−168htGiwhere Gi≥0.1\overline{G_{7d}} = \frac{1}{n} \sum_{i=t-168h}^{t} G_i \quad \text{where } G_i \geq 0.1 6-Hour Rolling Average: Includes all timesteps: G6h‾=1n∑i=t−6htGi\overline{G_{6h}} = \frac{1}{n} \sum_{i=t-6h}^{t} G_i

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Voltage and Current Adjustment

Voltage scalar: Vscalar=1−(1−fmeta)fV,metaV_{scalar} = 1 - (1 - f_{meta}) f_{V,meta} Current scalar: Iscalar=fmetaVscalarI_{scalar} = \frac{f_{meta}}{V_{scalar}} Adjusted values: Vmp,adj=Vmp×VscalarV_{mp,adj} = V_{mp} \times V_{scalar} Imp,adj=Imp×IscalarI_{mp,adj} = I_{mp} \times I_{scalar} Pmp,adj=Vmp,adj×Imp,adjP_{mp,adj} = V_{mp,adj} \times I_{mp,adj}

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References

  • King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.