When running an annual simulation using the weather file which beam and diffused solar radiation values are actually used?

Looking at the Engineering reference there is an explanation of using different models for the design day solar calculation. However, during an annual simulation, which values are used for I_b, I_h, and I_g values for the equation 5.67 in Engineering Reference? I have put the link to the equation here. https://bigladdersoftware.com/epx/doc... Does EnergyPlus run a model used in the design day calculation? or use the radiation data from the weather file? Like "Direct Normal Radiation", "Diffuse Horizontal Radiation"..?

Id be grateful if you could clarify.

Correct, there are different models to apply to design day solar calculations. However, these are separate from the Solar Gains equation you shared for the annual simulation. The annual simulation uses solar radiation parameters set as weather data from the EPW (EnergyPlus weather) file, and you can read the EPW data dictionary to understand what weather variables are defined. It appears that the variables you asked about are:

I_b, beam (direct) radiation - Direct Normal Radiation
I_h, horizontal radiation - Global Horizontal Radiation
I_g, ground-reflected diffuse radiation - there's not a direct EPW variable for this, but you could multiply the Diffuse Horizontal Radiation by the Albedo

For more information, there is a (very) thorough Unmet Hours post with diagrams on this topic and another Unmet Hours post describing the design day solar calculations as well.