Spectral Effect

The effect of the deviation of the actual incident light spectrum from the "AM1.5" spectrum assumed under STC on the power output of PV modules is evaluated using the spectral correction model produced by First Solar [14].

The model is described in Spectral Effect and is a function of absolute air mass \(\mathit{AM}_\text{a} \left( t \right)\) and precipitable water \(P_\text{wat} \left( t \right)\) at time \(t\). The result is a Spectral Shift \(M \left( j, t \right)\) for each submodule, where the technology of each submodule (mono-Si, poly-Si, CdTe, etc.) has been taken into account in evaluating \(M \left(j, t \right)\). If only one technology is used across the Plant, \(M\) will be independent of \(j\). This is used to adjust the irradiance incident on the modules as described below.

If all time steps in the input data have either \(P_{\text{wat}}\) or relative humidity (\(RH\)):

  • If there is a precipitable water value it uses that.

  • Else, it uses the relative humidity (\(RH\)) value to estimate precipitable water, see Precipitable Water.

  • If there are neither, it assumes \(P_{\text{wat}}\) = 2.5 cm.

If these are not present in all records, the default value \(P_{\text{wat}} = 2.5 \text{cm} \) is used in the spectral model.

The average irradiance on submodule \(j\) after the spectral shift is applied is denoted \(G_{\text{spectral}}\).

$$G_{\text{spectral}} \left( j,t \right) = M \left( j, t \right) G_{\text{iam}} \left( j, t \right)$$

At time \(t\), the Effective Irradiance for the Plant will be:

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

The annual spectral effect can be calculated by averaging \(G_{\text{plant,spectral}} \left( t \right)\) and \(G_{\text{plant,iam}} \left( t \right)\) over the year (or any other period of interest) and comparing the results:

$$\Delta_{spectral,year} = \left( \frac{\sum_{\text{year}}{G_{plant,spectral} \left( t \right)}} {\sum_{\text{year}}{G_{plant,iam} \left( t \right)}} - 1 \right) 100\%$$

If an annually-representative result is desired and the input time series is not annually representative (i.e. not a TMY file), the result will need de-seasoning.