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Summary

The angle of incidence is the angle between incoming solar rays and the normal (perpendicular) to the module surface. Accurate calculation of the angle of incidence is essential for determining direct beam irradiance on the plane of array and applying incidence angle modifiers.

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Inputs

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Outputs

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Detailed Description

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Vector Formulation

The angle of incidence is calculated using the dot product of the solar position vector and the surface normal vector. Solar position unit vector: s⃗=[sin⁡(θz)sin⁡(γs)cos⁡(θz)sin⁡(θz)cos⁡(γs)]\vec{s} = \begin{bmatrix} \sin(\theta_z) \sin(\gamma_s) \\ \cos(\theta_z) \\ \sin(\theta_z) \cos(\gamma_s) \end{bmatrix} Surface normal unit vector: n⃗=[sin⁡(βm)sin⁡(γm)cos⁡(βm)sin⁡(βm)cos⁡(γm)]\vec{n} = \begin{bmatrix} \sin(\beta_m) \sin(\gamma_m) \\ \cos(\beta_m) \\ \sin(\beta_m) \cos(\gamma_m) \end{bmatrix} Angle of incidence: cos⁡(θAOI)=s⃗⋅n⃗\cos(\theta_{AOI}) = \vec{s} \cdot \vec{n} θAOI=arccos⁡(sin⁡(βm)sin⁡(θz)cos⁡(γs−γm)+cos⁡(βm)cos⁡(θz))\theta_{AOI} = \arccos\left( \sin(\beta_m) \sin(\theta_z) \cos(\gamma_s - \gamma_m) + \cos(\beta_m) \cos(\theta_z) \right)

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References

  • Iqbal, M. (1983). An Introduction to Solar Radiation. Academic Press, p. 23.