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SHGC is a specific metric for window performance, but it is not something that EnergyPlus ever uses directly during a simulation. EnergyPlus will report out a value for center-of-glass SHGC based on the window description, but that is for a special case used for standard reporting with direct normal incidence and fixed thermal boundary conditions. As you say, a real time SHGC, were such a report available, would vary over time with incidence angle as well as the thermal conditions surrounding the window. EnergyPlus already does take this into account.

There is a section in the Engineering Reference called Calculation of Angular Properties that describes how angle of incidence is handled for window performance.

The WindowMaterial:SimpleGlazingSystem has an SHGC input, but it is used by a model that then constructs a more detailed representation of the window, with a different angular model (see table Normalized Transmittance Correlations for Angular Performance), and it would also have a time-varying "SHGC."