This function derives direct normal irradiance (G_B,n) and diffuse horizontal irradiance (G_D) from the global tilted irradiance (G_Ti) using modifications to the DIRINT decomposition model and Perez transposition model. This allows for G_Ti to be input into an energy prediction, largely avoiding decomposition and transposition model errors (with the exception of calculations that require the direct/diffuse components, i.e. shading and IAM).

Inputs

Outputs

 

Algorithm

This model implementation calculates a solution for incidence angles (θ) over and under 90° separately to allow solutions at times when the G_Ti measurement does not include any component of G_D.

1. GTI DIRINT model for θ < 90°

Note that this model uses a modified (tilted) clearness index as described in the Clearness Index section. Unmodified DIRINT equations (see DIRINT Model) are used to calculate G_B,n. G_D can then be calculated using:

Known errors are introduced when using the G_Ti as an input into the GTI DIRINT model (i.e. differences in proportions of diffuse and direct irradiance between global horizontal irradiance and G_Ti and the fact that G_Ti also includes ground reflected radiation). So, after G_D and G_B,n are calculated from the measured G_Ti using the reverse decomposition of GTI DIRINT, the forward transposition using Perez is used to calculate G_Ti as a check. The measured G_Ti and calculated G_Ti can then be compared and used as the iteration criteria in an optimization loop.

In the optimization loop, the initial calculation uses the measured G_Ti to calculate K_t. Subsequent iterations adjust the G_Ti until the K_t provides a G_B,n and G_D value such that a modeled G_Ti matches the measured G_Ti. The G_Ti value is adjusted using:

Where i is the index corresponding to the iteration number, D is the difference between the modeled and measured G_Ti, and C is a coefficient to ensure an iterative solution (1.0 for i <3, 0.5 for 3 ≤ i < 10, 0.25 for 10 ≤ i < 20, and 0.125 for 20 ≤ i < 30). Often, only two iterations are needed. The following illustrates the flow chart for the model when θ < 90°.

2. GTI DIRINT model for θ ≥ 90°

After G_B,n and G_D are calculated for θ < 90°, average early morning and late afternoon K_t‘ values are determined by averaging K_t‘ values for morning and afternoon instances when θ is between 65° and 85°. Besides K_t‘, the solution for G_B,n requires K_t which is rearranged from the original DIRINT equation to solve for K_t instead of K_t‘:

The G_D can then be determined using:

Reference

Marion, B., A model for deriving the direct normal and diffuse horizontal irradiance from the global tilted irradiance.  Solar Energy 122 (2015), pp. 1037-1046.