meaning of NCAP in a simple test model

[Enya]

Hi,

I was playing around with a very simple TIMES model to try and understand some basic principles and got confused about the value of NCAP.

I am testing a model with:
- Periods: 2026 (1) ; 2027-2034 (8) ; 2035-2045 (11) ; 2046-2055 (10) ; 2056-2065 (10) - 2066-2075 (10)
- Flat demand of 10 tables
- BY capacity of 10 'TableMakers' that can each produce 1 table per year, with a lifetime of 15 years
- A technically identical technology called 'TableMaker10' is available for investment in the following periods
- Discount factor set to zero

I was now testing in excel what I would have expected the value of NCAP to be, but it does not match the NCAP that is shown in the TIMES results.

Excel calculation for the first three periods:



TIMES results:


Questions:
- I would expect the new capacity installed for the period 20230 to equal 5.33 (as in the excel), but the TIMES NCAP show 2.67 in 2030 which equals the new capacity in 2030 exactly. What doesn NCAP represent exactly?
- I would expect the 2040 new capacity or NCAP to equal 11*0.67 = 7.37 but TIMES NCAP shows 7.64 in 2040. I have no idea where this number could come from...
==> Could you clarify how the NCAP is determined in TIMES? I have not found anything that could explain this in the manual either but perhaps I am looking in the wrong place?

Kind regards and thanks in advance!

[Antti-L]

The available capacities are assumed to be constant within each period, and the demands are measured only at the Milestone year of each period.  Therefore, the model needs to install new capacity sufficient for satisfying the demand in the Milestone year (2.67 according to your Excel table).

The whole purpose of using periods with lengths > 1 is to reduce the size of the model, and that is why there are no capacity/activity variables for each year in each period, but basically only one variable for a representative year, the Milestone year.  Nonetheless, this approximation actually works quite well, because the Milestone year is, by default, always at the middle of each period, and therefore the effects of demand projections are usually pretty well averaged by the Milestone years. In your case, the next Milestone year is 2040 with the demand level 9.33 to be satisfied by new capacity, and so for example, for the year 2034 one can calculate the effective new capacity investment being 5.33 when assuming Milestone years exactly in the middle, just like you assumed to be required at the end of the 2030 period. However, in TIMES, the Milestone years actually cannot always be exactly in the middle, but occur 0.5 years earlier for periods with even number of years, and that typically causes a small overestimation in the required capacity investments, to be on the safe side. As far as I know, the formulation has been primarily designed by Richard Loulou, McGill professor of management science and operations research, and has been reviewed in detail by many ETSAP partners.

You said that you would expect the new capacity to be 5.33 already in 2030, although the demand gap is only 2.67 in 2030. In that case the model would thus be overestimating the costs. Of course, in principle one could formulate the investments in each period in such a way that the total investments into new capacity would satisfy the demand in every year of the period.  Unfortunately, that would not be possible without adding new variables, basically for each year, and so it would refute the whole idea of reducing the model size by using period lengths > 1. By assuming linear evolution of the demand between Milestone years it would be possible without adding new variables, and such an option is in fact available in TIMES, but again, even in that case the demands are measured only at the Milestone years, and the capacity in 2030 would only need to satisfy the demand in 2030.

If you don't like the approximation, but would like to see the new capacity increasing to 5.33 in 2034, you can always use period lengths of 1, and thereby get a capacity trajectory satisfying the year-by-year demand.

[Antti-L]

Additional note: 
I guess I misunderstood the demands; you said that the demand is flat 10. Sorry, I looked at the values in the DEMTABLE row.  Indeed, the "total capacity" is also shown flat 10, which therefore satisfies the demand anyway.  So, what I described was in fact referring to the demand that needs to be satisfied by the cumulative new capacity in each Milestone year, but that would not change the explanations I gave.