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Experimental FeatureThe Metastability model is an experimental feature currently available only to the PlantPredict team for internal testing.

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Summary

The Metastability model accounts for performance variations caused by reversible changes in material properties based on recent operating history. It computes a power scale factor from lagged moving averages of cell temperature and POA irradiance. The scale factor is split into voltage and current scalars that adjust the maximum power point output from the single-diode model. The model uses 12 coefficients (C0C_0 through C11C_{11}).

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Inputs

NameSymbolUnitsDescription
Metastability CoefficientsC0,C1,...,C11C_0, C_1, ..., C_{11}variousModel coefficients
Metastability Voltage Scale FactorfV,metaf_{V,meta}—Voltage allocation factor
Max Power VoltageVmpV_{mp}VVoltage at maximum power point
Max Power CurrentImpI_{mp}ACurrent at maximum power point
Cell TemperatureTcT_c°CCell temperature at each timestep
Effective POA IrradianceGeffG_{eff}kW/m²Total effective POA irradiance (front + rear, after IAM, spectral, soiling, and shading corrections) at each timestep

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Outputs

NameSymbolUnitsDescription
Adjusted VoltageVmp,adjV_{mp,adj}VVoltage after metastability adjustment
Adjusted CurrentImp,adjI_{mp,adj}ACurrent after metastability adjustment
Adjusted PowerPmp,adjP_{mp,adj}WPower after metastability adjustment

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Detailed Description

The metastability correction proceeds in three steps: (1) compute lagged moving averages of cell temperature and POA irradiance that characterize recent operating history, (2) evaluate a polynomial scale factor from those averages, and (3) split the scale factor into voltage and current adjustments applied to the maximum power point.

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Lagged Moving Averages

The model uses two look-back windows. The 7-day (168-hour) window captures the thermal and irradiance history that drives slow defect-state transitions, while the 6-hour window captures shorter-term irradiance conditions. 7-day lagged average (168 hours): Only timesteps where Geff≥0.1G_{eff} \geq 0.1 kW/m² are included, filtering out nighttime and very low-light periods. The averages are divided by the count nn of qualifying timesteps: Tc,7d‾=1n∑i=t−168htTc,iwhere Geff,i≥0.1\overline{T_{c,7d}} = \frac{1}{n} \sum_{i=t-168h}^{t} T_{c,i} \quad \text{where } G_{eff,i} \geq 0.1 G7d‾=1n∑i=t−168htGeff,iwhere Geff,i≥0.1\overline{G_{7d}} = \frac{1}{n} \sum_{i=t-168h}^{t} G_{eff,i} \quad \text{where } G_{eff,i} \geq 0.1 6-hour lagged average: All timesteps are included, and the average is divided by the total number of timesteps in the window: G6h‾=1n∑i=t−6htGeff,i\overline{G_{6h}} = \frac{1}{n} \sum_{i=t-6h}^{t} G_{eff,i}

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Scale Factor

The lagged averages feed a polynomial with 12 empirical coefficients (C0C_0 through C11C_{11}). The polynomial includes linear, quadratic, and cubic terms in Tc,7d‾\overline{T_{c,7d}} and G7d‾\overline{G_{7d}}, plus linear and quadratic terms in G6h‾\overline{G_{6h}}: fmeta=C0+C1Tc,7d‾+C3(Tc,7d‾−C2)2+C8(Tc,7d‾−C2)3+C4G7d‾f_{meta} = C_0 + C_1 \overline{T_{c,7d}} + C_3 (\overline{T_{c,7d}} - C_2)^2 + C_8 (\overline{T_{c,7d}} - C_2)^3 + C_4 \overline{G_{7d}} +C6(G7d‾−C5)2+C7(G7d‾−C5)3+C9G6h‾+C11(G6h‾−C10)2+ C_6 (\overline{G_{7d}} - C_5)^2 + C_7 (\overline{G_{7d}} - C_5)^3 + C_9 \overline{G_{6h}} + C_{11} (\overline{G_{6h}} - C_{10})^2

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Voltage and Current Adjustment

The scale factor fmetaf_{meta} is split into a voltage scalar and a current scalar using the user-defined voltage allocation factor fV,metaf_{V,meta}, which controls what fraction of the power change is attributed to voltage versus current: Vscalar=1−(1−fmeta)⋅fV,metaV_{scalar} = 1 - (1 - f_{meta}) \cdot f_{V,meta} Iscalar=fmetaVscalarI_{scalar} = \frac{f_{meta}}{V_{scalar}} These scalars are then applied to the maximum power point voltage and current from the single-diode model: 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}