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Summary

The Heat Balance model calculates cell temperature from heat generation and dissipation using conductive and convective heat transfer coefficients. This physics-based approach models the energy balance between absorbed solar radiation and heat loss to the environment.

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Inputs

NameSymbolUnitsDescription
Ambient Air TemperatureTaT_a°CDry-bulb air temperature
Wind Speedvwv_wm/sWind velocity
Effective POA IrradianceGeffG_{eff}W/m²Effective irradiance after all optical losses
Module STC EfficiencyηSTC\eta_{STC}—Module efficiency at standard test conditions
Heat Absorption CoefficientαT\alpha_T—Heat absorption coefficient
Conductive CoefficientUcU_cW/m²·KConductive heat transfer coefficient
Convective CoefficientUvU_vW/m²·K per m/sConvective heat transfer coefficient
Cell-to-Module Temp DiffΔTc−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°CModule surface (back-of-module) temperature

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Detailed Description

The Heat Balance model calculates cell temperature from heat generation and dissipation: Tc=Ta+αT⋅Geff⋅(1−ηSTC)Uc+Uv⋅vwT_c = T_a + \frac{\alpha_T \cdot G_{eff} \cdot (1 - \eta_{STC})}{U_c + U_v \cdot v_w} where:
  • TaT_a is ambient air temperature (°C)
  • αT\alpha_T is heat absorption coefficient (from module definition, typically 0.9)
  • GeffG_{eff} is effective POA irradiance (W/m²)
  • ηSTC\eta_{STC} is module efficiency at STC (from module definition)
  • UcU_c is conductive heat transfer coefficient (W/m²·K)
  • UvU_v is convective heat transfer coefficient (W/m²·K per m/s)
  • vwv_w is wind speed (m/s)
The thermal behavior is characterized by a thermal loss factor designated here by UU, which can be split into a constant component UcU_c and a factor proportional to the wind velocity UvU_v. These factors depend on the mounting mode of the modules (sheds, roofing, facade, etc.).

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Module Surface Temperature

Tm=Tc−GeffGref⋅ΔTc−mT_m = T_c - \frac{G_{eff}}{G_{ref}} \cdot \Delta T_{c-m} where:
  • GrefG_{ref} is reference irradiance (typically 1000 W/m²)
  • ΔTc−m\Delta T_{c-m} is cell-to-module temperature difference (°C)

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References

  • Faiman, D. (2008). Assessing the outdoor operating temperature of photovoltaic modules. Progress in Photovoltaics: Research and Applications, 16(4), 307–315.