Tilt Effect

The Tilt Effect quantifies the difference between the Global Horizontal Irradiation (\(G_\text{h}\)) at the site and the Global Irradiation incident on each module at its orientation (governed by the chosen tilt and azimuth angles but also potentially varying somewhat across the array, particularly in uneven terrain).

We will denote the direct, diffuse, and reflected components of light incident on the POA as \(G_\text{dir,poa}\) , \(G_\text{dif,poa}\) and \(G_\text{r,poa}\). The global irradiance incident on the POA \(G_\text{poa}\) is then:

$$G_\text{poa} = G_\text{dir,poa} + G_\text{dif,poa} + G_\text{r,poa}$$

\(G_{\text{dir}}\) and \(G_{\text{dif}}\) are transposed to \(G_{\text{dir,poa}}\), \(G_{\text{dif,poa}}\) and \(G_{\text{r,poa}}\) as described in Transposition.

SolarFarmer can model PV Plants situated in uneven terrain, which means that the modules in each rack may have different orientations, and hence \(G_{\text{poa}}\) for each rack will differ. We denote the \(G_\text{poa}\) for submodule \(j\) with orientation \(o_\text{j}\) at date/time \(t\) as \(G_\text{poa} \left(o_\text{j}, t \right)\), and this will have the same value for all submodules mounted on the same rack (ignoring shading effects at this stage).

The average irradiance on the tilted modules (ignoring shading) making up the Plant Array at time \(t\) is:

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

Where \(A \left( j \right)\) is the active area of the submodule \(j\) (which is likely constant for the entire array).

At a given timestamp \(t\), the tilt effect for the entire Plant Array is:

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

\(G_\text{plant,poa}\) and \(G_\text{plant,h}\) can be averaged over any period and the same formula used to derive the Tilt Effect (and any of the other effects discussed in subsequent sections) over that period. For example, monthly average POA, with timestep \(\Delta t\), is the total power divided by the number of timesteps. Annual average is similar.

$$G_\text{poa,month} = \frac{\sum_\text{month}^{N}{G_\text{poa} \left( t \right) \Delta t}} {\sum_\text{month}^{N}{\Delta t}} = \frac{\sum_\text{month}^{N}{G_\text{poa} \left( t \right)}}{N}$$

For the Effects diagram, a long-term average, annually-representative result is required. If the input timeseries is not an exact year of data (like a TMY dataset) and/or has gaps in it, then care must be taken to de-season the result before presenting this as annually representative.

To calculate a de-seasoned annual result as well as monthly results:

  • Calculate the average horizontal and POA irradiances (averaged over the whole array as above) for each of the 12 calendar months;

  • Monthly Tilt Effect values can be calculated from these monthly averages;

  • Create annual average values for these irradiances by taking a weighted average of the monthly averages, weighting by the number of days in each month (use 28.25 days for February);

  • Calculate Annual Tilt Effect from annual averages as above.