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Summary

The Heat Balance model is an extended form of the Faiman (2008) model that calculates cell temperature from the energy balance between absorbed solar radiation and heat loss to the environment. It uses experimentally determined conductive and convective heat transfer coefficients to characterize thermal dissipation, and accounts for the fractions of irradiance converted to electricity (via module efficiency at ) and reflected off the surface of the module (via the absorption coefficient).

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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
Absorption CoefficientαT\alpha_T—Fraction of incident irradiance absorbed by the module
Module STC EfficiencyηSTC\eta_{STC}—Module efficiency at standard test conditions
Conductive Coefficientucu_cW/m²·KConductive heat transfer coefficient
Convective Coefficientuvu_vW/m²·K per m/sConvective heat transfer 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 Heat Balance model calculates cell temperature from heat generation and dissipation: Tc=Ta+αT⋅GPOA,front,eff⋅(1−ηSTC)uc+uv⋅vwT_c = T_a + \frac{\alpha_T \cdot G_{POA,front,eff} \cdot (1 - \eta_{STC})}{u_c + u_v \cdot v_w} where:
  • TaT_a is the ambient air temperature in °C (from weather data)
  • αT\alpha_T is the absorption coefficient (from module definition, fraction of irradiance not reflected or transmitted, typically 0.9)
  • GPOA,front,effG_{POA,front,eff} is the front-side after optical corrections, before DC losses, in W/m² (from irradiance calculation)
  • ηSTC\eta_{STC} is the module efficiency at STC (from module definition)
  • ucu_c is the conductive heat transfer coefficient in W/m²·K (from DC field definition)
  • uvu_v is the convective heat transfer coefficient in W/m²·K per m/s (from DC field definition)
  • vwv_w is the wind speed in m/s (from weather data)
The thermal behavior is characterized by a thermal loss factor u=uc+uv⋅vwu = u_c + u_v \cdot v_w, split into a constant conductive component ucu_c and a wind-proportional convective component uvu_v. These coefficients depend on many factors (e.g., mounting configuration, module technology, local climate) and are in practice experimentally determined. In alignment with PVsyst, uvu_v default value is zero, effectively eliminating the convective contribution and reducing the model to a constant thermal loss factor. Users should input a non-zero value if they want wind velocity to affect cell temperature.

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Module Surface Temperature

Tm=Tc−GPOA,front,effGref⋅ΔTc−mT_m = T_c - \frac{G_{POA,front,eff}}{G_{ref}} \cdot \Delta T_{c-m} where:
  • GrefG_{ref} is the reference irradiance in W/m² (from module definition, 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

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