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I have a question regarding the bounding of an activity by its capacity (EQ_CAPACT).

First, at p.160 of the part II documentation of the TIMES model, it says that within one period, the activity is assumed constant.

However, by looking at the different types of investment cases in detail, it seems, resulting from a new investment within that period, the available capacity differs for the different years within that period.

An example for investment case 1.a at p.143 of part II of the TIMES documentation, one can see that the available capacity in the first year of the period is equal to 3 'blocks', for the second and third year of the period, it is 4 'blocks' and in the final year of the period, it is again 3 'blocks'.

Also, because investments made in a specific period can result in available capacity at (the end of) the previous period or during the beginning of one of the following period(s), it is clear that the available capacity within a given period differs for different years within 1 period.

So my question finally is: there seems to be a discrepancy between a constant activity within one period (p.160) and an activity bounded by an available capacity (which varies for different years within that period), or am I wrong?

The only explanation that I can think of is that TIMES only produces one EQ_CAPACT for each period (possibly for every TS within the representative year M(t) of that period though), but this would result in errors (as in some years of that period, the constant activity exceeds the available capacity, or on the other hand, that the activity in some years would be bounded by a too low capacity).

Thanks in advance for helping me clearing this out!

Kris

You are right, in the standard formulation of TIMES, there are some discrepancies between the detailed accounting of the investment and fixed costs in the objective function and the assumed constant activities and average available capacities within each period. However, you can eliminate these discrepancies by using the switch \$SET OBLONG YES (when using the standard objective formulation), or by using one of the alternative objective formulations (e.g. \$SET OBJ MOD, \$SET OBJ LIN).

Even though the designers of TIMES were highly qualified scholars and from prestigious universities, such as KU Leuven and McGill, there are indeed some discrepancies in the assumptions on the capacity evolution in standard TIMES. However, these discrepancies are not between the assumed activities and available capacities within periods, but between the detailed accounting of the investment and fixed costs in the objective function and the assumed more simplified evolution of the activities and capacities within each period, when period lengths are longer than one year.

The main motivation behind defining periods longer than one year is to avoid the model size increasing too much when long model horizons are analyzed. And that is also why TIMES always produces only one EQ_CAPACT for each period and every TS within the representative year M(t) of that period. In the standard formulation of TIMES, both the activities and capacities are assumed to be constant within each period, representing the average activity and the average available capacity in the period. This is clearly indicated already in Part I of the documentation, in Section 4.4.3 Use of capacity (Part I), where the available capacity in period t is referred to as CAP(r,v,t,p). The concept of the average available capacity is further explained in Part II of the documentation, Section 4.10 VAR_NCAP(r,v,p). The internal parameter COEF_CPT(r,v,t,p) defines the fraction of capacity built in period v being available in period t, and is explained in Section 5.3.6 Equation: EQ(l)_CAPACT.

There is also an alternative formulation available in TIMES, which assumes a linear evolution of activities and capacities between milestone years. That is another way of achieving the desired simplification of the model when using period lengths longer than 1 year.

Notwithstanding, in the objective function the evolution of capacities is always considered on a detailed year-to-year basis. Since many years now, the ETSAP community has been well aware of the small discrepancies between the objective function and the more simplified "physical" assumptions in the model. I will not try presenting any formal treatment of these discrepancies here, but their impacts can be easily analyzed and illustrated by simple test models. For the specific case mentioned (investment Case 1.a), see the illustrative analysis in the following note:

In summary, to some extent such discrepancies exist in the standard formulation of TIMES, but their impacts are usually quite small, typically at most a few per-cent of the marginal costs. Moreover, in order to eliminate the impacts of the discrepancies, you can use the switch \$SET OBLONG YES (for the standard objective formulation), or one of the alternative objective formulations (e.g. \$SET OBJ LIN, \$SET OBJ MOD). I would recommend using some of these options when concerned.
As I'm focusing mainly on the use of the available capacity, discrepancies between the investment cost and fixed costs in the objective function and the assumed simplified evolution of capacity does not really concern me. However, what is essential for me to know is whether TIMES dispatches the simplified available capacity or the capacity for which costs are accounted, and know I know.

Thank you Antti!

Very good.  I was not sure of the main concern.

Anyway, if you want to analyze capacity dispatching on a year-to-year basis with TIMES, you simply need to use 1-year periods for those parts of the model horizon. As I am sure you know, you can use variable period lengths in TIMES in a flexible way for such purposes.