Sky Diffuse Shading

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Summary

Sky diffuse shading accounts for the reduction in sky diffuse irradiance caused by neighboring array rows blocking part of the . Unlike beam shading, which depends on sun position, sky diffuse shading losses are determined primarily by array geometry (, tilt angle). For fixed-tilt systems, these losses remain relatively constant throughout the day; for tracking systems, they vary with tracker rotation angle. This model uses a 2D representation of the PV array, analyzing geometry in the plane perpendicular to the row axis.

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Inputs

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Outputs

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Detailed Description

A tilted module in an array can only “see” part of the sky hemisphere—the rest is blocked by the adjacent row in front. The sky diffuse shading factor quantifies this reduction by comparing the visible sky area to what an isolated module would see. This calculation is purely geometric—IAM effects on sky diffuse irradiance are handled separately in the IAM model.

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Step 1: Calculate Blocking Angle

The blocking angle $\psi$ represents the elevation angle from the observation point (center of the module) to the top of the adjacent row in front. For arrays on sloped terrain with cross-axis slope $\beta_c$: $$\psi = \text{atan}\left( \frac{\ell_m \sin(\beta_m) + 2p \tan(\beta_c)}{2p - \ell_m \cos(\beta_m)} \right)$$ For flat terrain ($\beta_c = 0$), this reduces to: $$\psi = \text{atan}\left( \frac{\ell_m \sin(\beta_m)}{2p - \ell_m \cos(\beta_m)} \right)$$ The blocking angle is clamped to non-negative values: $\psi = \max(\psi, 0)$. The cross-axis slope modifies the effective blocking:

• Uphill slope ($\beta_c > 0$, front row higher): increases $\psi$, more blocking
• Downhill slope ($\beta_c < 0$, front row lower): decreases $\psi$, less blocking

Backward diffuse shading (from the row behind when $-\beta_c > \beta_m$ on downhill slopes) is not currently implemented.

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Step 2: Calculate Sky View Factor

The sky view factor with blocking is: $$F_{sky} = \frac{1 + \cos(\beta_m + \psi)}{2}$$ This is the standard isotropic sky view factor formula, where $F_{sky} = 1$ for a horizontal surface with no blocking ($\beta_m = \psi = 0$).

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Step 3: Calculate Shading Factor

The shading factor is the ratio of actual sky view to the baseline (infinite spacing, where $\psi = 0$): $$U_{shd,D} = \frac{F_{sky}}{F_{sky,\infty}} = \frac{1 + \cos(\beta_m + \psi)}{1 + \cos(\beta_m)}$$ where $F_{sky,\infty} = \frac{1 + \cos(\beta_m)}{2}$ is the baseline sky view factor for the tilted module with no row-to-row blocking. Note that $U_{shd,D}$ represents the fraction of sky diffuse irradiance that reaches the module, not the shading loss. A value of 1.0 means no shading (all diffuse reaches the module), while 0.95 indicates a 5% diffuse shading loss.