Far Shading / Horizon Effect

The Far Shading (or Horizon) effect quantifies the amount of irradiance lost due to shading by objects included in the horizon line supplied to the modelling software. The distinction between Far- and Near Shading is that Far Shading is assumed to affect the entire PV plant simultaneously, whereas the effects of Near Shading are examined on a module-by-module basis and give rise to more complex electrical effects owing to their uneven spread.

For each timestep, it is established whether the solar height is lower than the height of the horizon. First, a rough check is carried out at the beginning and end of the period that is represented by the timestep, to determine whether the sun crossed the horizon. Where the sun's azimuth falls between the defined horizon points, a linear interpolation between the horizon points on either side of the sun's azimuth is first made, and the sun's height at its specific azimuth compared to the height of the linear interpolation at the same azimuth.

If the sun is below the horizon for the entire period that the timestep represents, the in-plane beam/direct irradiance at that time step is assumed to be zero for all modules. If the sun crosses the horizon line within the period that the timestep represents, the proportion of time that the sun is above the horizon is determined by using higher resolution time steps within that period. The in-plane beam irradiance is then scaled accordingly.

Diffuse and reflected irradiances are not changed by far shading, so:

$$G_\text{dif,poa,far} \left( o_{j}, t \right) = G_\text{dif,poa} \left( o_{j}, t \right)$$

$$G_\text{r,poa,far} \left( o_{j}, t \right) = G_\text{r,poa} \left( o_{j}, t \right)$$

Note that we are ignoring any diffuse shading that the horizon might be causing -- this will likely only be at all significant where there a large, relatively distant object such as a mountain forms part of the horizon. This is an area that could be improved in future to take the horizon's effect on diffuse irradiance into account.

The beam irradiance depends on the sun's position relative to the horizon. If the sun is above the horizon for the entire period that is represented by time \(t\):

$$G_\text{dir,poa,far} \left( o_{j}, t \right) = G_\text{dir,poa} \left( o_{j}, t \right)$$

If the sun is below the horizon for the entire period that is represented by \(t\):

$$G_\text{dir,poa,far} \left( o_{j}, t \right) = 0$$

If the sun crosses the horizon in the period, \(t\), the irradiance is scaled according to the proportion of time that the sun is above the horizon (\(t_\text{above horizon}\)) compared to when it rose or set at sea-level (\(t_\text{sea level rise set}\)):

$$G_\text{dir,poa,far} \left( o_{j}, t \right) = G_\text{dir,poa} \left( o_{j}, t \right) \left( \frac{t_\text{above horizon}}{t_\text{sea level rise set}} \right)$$

Denoting the far-shaded global POA irradiance timeseries for submodule \(j\) with orientation \(o_\text{j}\) at time \(t\) as \(G_\text{poa,far} \left( o_{j}, t \right)\),

$$G_\text{poa,far} \left( o_{j}, t \right) = G_\text{dir,poa,far} \left( o_{j}, t \right) + G_\text{dif,poa,far} \left( o_{j}, t \right) + G_\text{r,poa,far} \left( o_{j}, t \right)$$

The average irradiance on the Plant Array at time \(t\) considering the Far Shading effect is:

$$G_\text{plant,far} \left( t \right) = \frac{\sum_{j = 1}^{N_\text{submodules}}{G_\text{poa,far} \left( o_{j}, t \right) A \left( j \right)}} {\sum_{j = 1}^{N_\text{submodules}}{A \left( j \right)}}$$

At a given timestamp \(t\), the Far Shading Effect for a PV array is:

$$\Delta_\text{far} \left( t \right) = \left( \frac{G_\text{plant,far} \left( t \right)}{G_\text{plant,poa} \left( t \right)} - 1 \right) 100\%$$

Average the power over any period and apply the same formula to obtain the Far Shading Effect for that period, taking care to de-season annual results as described in Tilt Effect for the Tilt Effect.