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Summary

The Nonlinear Gamma Temperature Dependence model extends the recombination model by using a polynomial relationship for the diode ideality factor temperature scaling instead of a linear relationship. This model is implemented as OneDiodeRecombinationNonLinear in PlantPredict and includes four additional gamma coefficients (aγ,bγ,cγ,dγa_{\gamma}, b_{\gamma}, c_{\gamma}, d_{\gamma}) that define a fourth-order polynomial. The nonlinear model provides improved accuracy for modules with complex temperature-dependent behavior, particularly at temperature extremes.

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Inputs

NameSymbolUnitsDescription
Reference Ideality Factorγref\gamma_{ref}—Diode ideality factor at STC
Reference TemperatureTrefT_{ref}KReference temperature (typically 298.15 K)
Actual TemperatureTactualT_{actual}KOperating cell temperature
Gamma Coefficient Aaγa_{\gamma}1/KLinear coefficient
Gamma Coefficient Bbγb_{\gamma}1/K²Quadratic coefficient
Gamma Coefficient Ccγc_{\gamma}1/K³Cubic coefficient
Gamma Coefficient Ddγd_{\gamma}1/K⁴Quartic coefficient

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Outputs

NameSymbolUnitsDescription
Scaled Ideality Factorγ\gamma—Temperature-scaled diode ideality factor

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Detailed Description

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Temperature Delta

ΔT=Tactual−Tref\Delta T = T_{actual} - T_{ref} where temperatures are in Kelvin.

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Polynomial Gamma Scaling

γ=γref(1+aγΔT+bγΔT2+cγΔT3+dγΔT4)\gamma = \gamma_{ref} (1 + a_{\gamma} \Delta T + b_{\gamma} \Delta T^2 + c_{\gamma} \Delta T^3 + d_{\gamma} \Delta T^4) This fourth-order polynomial allows the ideality factor to vary nonlinearly with temperature, capturing complex physical behavior at temperature extremes.

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Integration with Recombination Model

The scaled gamma is then used in the recombination model calculations:
  1. Calculate alpha: α=q/(kTactualNsγ)\alpha = q/(k T_{actual} N_s \gamma)
  2. Scale saturation current using gamma
  3. Solve circuit equation with recombination term

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Model Selection

Model type determined by PvModel enum value OneDiodeRecombinationNonLinear.

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References

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