> ## Documentation Index
> Fetch the complete documentation index at: https://docs.plantpredict.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Sandia Model

export const POAIrradiance = () => <Tooltip tip="Solar irradiance on the tilted module surface (beam + diffuse + reflected); drives PV power generation.">
    POA irradiance
  </Tooltip>;

## 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](/models/poa-irradiance/overview)) |
| **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)                                                                                                    |

***

## 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 |

***

## 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 <POAIrradiance /> after optical corrections, in W/m² (from [irradiance calculation](/models/poa-irradiance/overview))
* $a$ 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)

***

## References

* King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). *Photovoltaic array performance model.* SAND2004-3535, Sandia National Laboratories. DOI: [10.2172/919131](https://doi.org/10.2172/919131)