Interpreting the marginals of a UC (User_conFXM)

[Wiesmeth]

Hi,

this question is probably geared more towards TIMES in general but maybe someone can offer some insights.
My problem is as follows:

• I implemented a Constraint (UC_FLO) for total emissions over multiple regions (UC_RHST), with a value given for each period (2040, 2045, 2050)
  


• the model horizon reaches from 2000 to 2050 with a 5 year timestep
  

Now I'm trying to interpret the UC shadow price as the GHG-price for this specific year. This is what I can see in Veda_BE (User_conFXM):
2040: -2.96 2045: -3.10 2050: -2.39

I was able to find this in the Reference Manual:
PAR_UCSM (uc_n,r,t,s) User_conFXM Marginal cost of fixed bound user constraint Marginal of user constraint (uc_n) by region ®, period (t) and timeslice (s). The marginals are undiscounted, if the constraint is defined by region and period. The marginals of cumulative and multiregion user constraints are thus not undiscounted, due to ambiguity. 

So this means the results in BE would be discounted, so to get the undiscounted numbers I multiply by the discountfactor of each period. With 10% discountrate, the factors should be 2040: 45.3, 2045: 72.9 and 2050: 117.4

Multiplication with the results from BE yields the following "cost":
2040: -134 2045: -226 2050: -280

So far so good but it made me wonder why I get such high mitigation cost and I tried to implement some dummy GHG-Sink which takes up those emissions for a certain cost.
Yet the sink wasn't active in 2050, when I set cost of let's say 279€/unit - it only became active at exactly 1/5 of the cost (period length!?) which means 280/5 --> 56€/unit.

Now to my actual question:
Does this mean that the shadow price of the UC is five times (number of years within a period) the discounted marginal abatement cost?
Why is the period length being taken into account for the shadow price and where in the TIMES documentation could I find a description of this behaviour?

Thanks,
Michael

[Antti-L]

You have understood it correctly:  You can undiscount the User_conFXM values by yourself, if the discount rates are equal in all regions.

But I suspect that you have applied incorrect un-discounting factors. The correct period-wise NPV factors are given by the reporting attribute Time_NPV, which you should have in VEDA-BE (note that it is reported for each region, so be sure not to collapse it over regions). You should divide the User_conFXM values by these values.

Indeed the period lengths affect Time_NPV, in the same way as they affect the impact of a unit change of a variable in the Objective. The raw dual values (marginal) of the constraint give the impact of one unit increase in the constraint slack on the objective. And this impact will mean a one-unit change of basic variables that represent all years in the period, not just one year, and that has to be taken into account in the undiscounting.

[Wiesmeth]

You have understood it correctly:  You can undiscount the User_conFXM values by yourself, if the discount rates are equal in all regions.

But I suspect that you have applied incorrect un-discounting factors. The correct period-wise NPV factors are given by the reporting attribute Time_NPV, which you should have in VEDA-BE (note that it is reported for each region, so be sure not to collapse it over regions). You should divide the User_conFXM values by these values.

Indeed the period lengths affect Time_NPV, in the same way as they affect the impact of a unit change of a variable in the Objective. The raw dual values (marginal) of the constraint give the impact of one unit increase in the constraint slack on the objective. And this impact will mean a one-unit change of basic variables that represent all years in the period, not just one year, and that has to be taken into account in the undiscounting.

Thank you for your swift response and confirmation.
The TIME_NPV values really helped understanding this!