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I will try and address your two questions below:
> I understand that PASTI refers to capacity invested in the past. If a construction period (ILED) has been set, do we need to subtract the construction period from the real construction year when setting the PASTI YEAR?
NCAP_PASTI(r,v,p) is indeed meant for defining past investments into capacity, in terms of the amount of capacity installed. Originally, it was even restricted only to capacities installed before the model horizon, but that restriction has been relaxed. So, NCAP_PASTI can be used also for defining capacities installed within the model horizon. The index v of the attribute refers to the capacity vintage. The full set of capacity vintage years in a TIMES model is the union of the set of all years that have NCAP_PASTI defined and the set of Milestone years t. When NCAP_ILED(r,v,p) > 0 has also been defined, the commissioning year of any capacity vintage v will always be B(v)+NCAP_ILED(r,v,p), where B(v) is the beginning year of period v. The beginning years B(t) of all periods t, where t is a Milestone year, is the first year in that period, but for all other vintage years v, B(v) = v, i.e. the beginning year of v is the year v itself.
For example, if you have defined NCAP_PASTI(r,'2011',p) = 1 and NCAP_ILED(r,'2011',p)=4, and the year 2011 does not coincide with any Milestone year, the commissioning year will be B(2011)+4 = 2015. However, if 2011 coincides with a Milestone year, then the commissioning year may occur also before 2015, depending on what the beginning year B(2011) is. So, if the model has a Milestone year 2011 such that B(2011) = 2010, the commissioning year would be 2014.
However, note that you can also use negative NCAP_ILEDs, and then the commissioning year will be B(v) itself (and the construction period is then [B(v)−NCAP_ILED(r,v,p),..., B(v)−1]). So, if you would like to define NCAP_PASTI directly for the commissioning years, you can do that by using negative NCAP_ILEDs.
> What is the function of Vintage? If Vintage is set to ‘No’, will it still be updated if INVCOST or EFF is set to every Milestone Year?
For vintaged processes, any efficiencies, emission factors, flow shares etc. are vintage-specific, meaning that the values of those parameters will by default remain unchanged throughout the lifetime of each vintage. You can, however, also shape them according to age, for example such that efficiencies would be deteriorating by age. If Vintage is set to ‘No’, none of those flow-related attributes are vintage-specific, but are Milestone-year-specific. Investment costs, on the other hand, are always vintage specific, regardless of the Vintage option.