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Summary

The Sandia model is an empirical temperature model developed at Sandia National Laboratories (King et al., 2004) based on outdoor measurements. Unlike the Heat Balance model, it calculates back-of-module surface temperature first using an empirical exponential relationship for thermal losses with conductive and convective contributions, then derives cell temperature from it.

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Inputs

NameSymbolUnitsDescription
Effective Front POA IrradianceGPOA,front,effG_{POA,front,eff}W/m²Front-side POA irradiance after optical corrections, before DC system losses (from irradiance calculation)
Ambient Air TemperatureTaT_a°CAmbient air temperature
Wind Speedvwv_wm/sWind velocity
Conductive Coefficientaa—Empirical conductive thermal loss coefficient
Convective Coefficientbbs/mEmpirical convective thermal loss coefficient
Cell-to-Module Temp DifferenceΔTc−m\Delta T_{c-m}°CTemperature difference between cell and module surface
Reference IrradianceGrefG_{ref}W/m²Reference irradiance (typically 1000 W/m²)

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Outputs

NameSymbolUnitsDescription
Cell TemperatureTcT_c°COperating temperature of PV cells
Surface TemperatureTmT_m°CBack-of-module surface temperature

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Detailed Description

The Sandia model calculates back-of-module surface temperature using an empirical exponential relationship for thermal losses with conductive and convective contributions: Tm=GPOA,front,eff⋅ea+b⋅vw+TaT_m = G_{POA,front,eff} \cdot e^{a + b \cdot v_w} + T_a where:
  • TaT_a is the ambient air temperature in °C (from weather data)
  • GPOA,front,effG_{POA,front,eff} is the front-side after optical corrections, in W/m² (from irradiance calculation)
  • aa is the empirical conductive coefficient (from DC field definition)
  • bb is the empirical convective coefficient in s/m (from DC field definition)
  • vwv_w is the wind speed in m/s (from weather data)
The exponential term ea+b⋅vwe^{a + b \cdot v_w} represents the thermal resistance between the module and the environment. Both aa and bb are negative, so higher wind speeds reduce the exponential and thus lower module temperature. These coefficients depend on mounting configuration and module construction and are empirically determined.

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Reference Coefficients

The following reference coefficients were empirically derived by Sandia National Laboratories for open-rack mounting (King et al., 2004). These are guidelines only—users can set aa, bb, and ΔTc−m\Delta T_{c-m} freely in the DC field definition.
Module TypeaabbΔTc−m\Delta T_{c-m} (°C)
Glass/cell/glass−3.47−0.05943
Glass/cell/polymer−3.56−0.07503

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Cell Temperature

Cell temperature is derived from surface temperature by adding an irradiance-proportional offset: Tc=Tm+GPOA,front,effGref⋅ΔTc−mT_c = T_m + \frac{G_{POA,front,eff}}{G_{ref}} \cdot \Delta T_{c-m} where:
  • GrefG_{ref} is the reference irradiance in W/m² (typically 1000 W/m²)
  • ΔTc−m\Delta T_{c-m} is the cell-to-module temperature difference at the reference irradiance, in °C (from DC field definition)

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References

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