Sandia Model

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.

Inputs

Name	Symbol	Units	Description
Effective Front POA Irradiance	$G_{POA,front,eff}$	W/m²	Front-side POA irradiance after optical corrections, before DC system losses (from irradiance calculation)
Ambient Air Temperature	$T_a$	°C	Ambient air temperature
Wind Speed	$v_w$	m/s	Wind velocity
Conductive Coefficient	$a$	—	Empirical conductive thermal loss coefficient
Convective Coefficient	$b$	s/m	Empirical convective thermal loss coefficient
Cell-to-Module Temperature Difference	$\Delta T_{c-m}$	°C	Temperature difference between cell and module surface
Reference Irradiance	$G_{ref}$	W/m²	Reference irradiance (typically 1000 W/m²)

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Outputs

Name	Symbol	Units	Description
Cell Temperature	$T_c$	°C	Operating temperature of PV cells
Module Surface Temperature	$T_m$	°C	Back-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:

$$T_m = G_{POA,front,eff} \cdot e^{a + b \cdot v_w} + T_a$$

where:

• $T_a$ is the ambient air temperature in °C (from weather data)
• $G_{POA,front,eff}$ is the front-side after optical corrections, in W/m² (from irradiance calculation)
• $a$ is the empirical conductive coefficient (from DC field definition)
• $b$ is the empirical convective coefficient in s/m (from DC field definition)
• $v_w$ is the wind speed in m/s (from weather data)

The exponential term $e^{a + b \cdot v_w}$ represents the thermal resistance between the module and the environment. Both $a$ and $b$ 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.

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 $a$, $b$, and $\Delta T_{c-m}$ freely in the DC field definition.

Module Type	$a$	$b$	$\Delta T_{c-m}$ (°C)
Glass/cell/glass	−3.47	−0.0594	3
Glass/cell/polymer	−3.56	−0.0750	3

Cell Temperature

Cell temperature is derived from surface temperature by adding an irradiance-proportional offset:

$$T_c = T_m + \frac{G_{POA,front,eff}}{G_{ref}} \cdot \Delta T_{c-m}$$

where:

• $G_{ref}$ is the reference irradiance in W/m² (typically 1000 W/m²)
• $\Delta T_{c-m}$ 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. DOI: 10.2172/919131