Contraint on primary energy

[LucasD]

Dear forum,

I have been trying to implement a UC to constrain the share of low-carbon primary energy over time in TIAM-FR (a global model). I defined Commodity Sets to represent low-carbon primary energy with
- PRIBIO including bioenergies,
- PRIRNW including intermittent renewables, nuclear and hydro
- PRICCS including fossil fuel commodites that are used in processes equipped with carbon capture thus capturing fossil carbon CPT*N (PSet_CO = CPT*N)
- PRIFOS including all primary fossil fuel commodities

With this UC, I want to force the model to ensure a global minimum low-carbon share of primary energy over time (L_t) such that

Code:

$$ Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_flo(PRICCS,PSet_CO = CPT*N) > L_t \cdot (Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_COMCON(PRIFOS)$$
$$ (1-L_t) \cdot (Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW)) + Var_flo(PRICCS,PSet_CO = CPT*N) - L_t \cdot Var_COMCON(PRIFOS) > 0$$

 I attach the formulation of the UC in a screenshot. In rows 15 to 18, I set UC_IRE on commodities that can be traded as the constraint should not include the flows of commodities traded. The constraint is only applied as of 2030 and the model starts in 2018.

I have two issues with this contraint:
1) dummy imports for the base year while the constraint is only effective in 2030 onwards (UC_RHST~0=5)
2) the constraint is satisfied unless the UC_IRE (row 15-18) are activated

Do you have an idea on how to fix these issues? I made sure the Browser was reading the constraint properly.

Thanks,
Lucas

[Antti-L]

>1) dummy imports for the base year while the constraint is only effective in 2030 onwards (UC_RHST~0=5)

Dummy imports for what?  If you mean dummy imports for this constraint in the Base year, I think that should not be possible (because as you say, it is only effective 2030 onwards).

> 2) the constraint is satisfied unless the UC_IRE (row 15-18) are activated

Do you mean the constraint is not satisfied if UC_IRE (row 15-18) are activated?  And if so, what do you mean by that: do you mean that there are then dummy imports for the constraint, or that you made that conclusion in some other way?  Anyway, I think the UC_IRE coefficients are not consistent for your purpose.

[LucasD]

>1) dummy imports for the base year while the constraint is only effective in 2030 onwards (UC_RHST~0=5)

Dummy imports for what?  If you mean dummy imports for this constraint in the Base year, I think that should not be possible (because as you say, it is only effective 2030 onwards).

> 2) the constraint is satisfied unless the UC_IRE (row 15-18) are activated

Do you mean the constraint is not satisfied if UC_IRE (row 15-18) are activated?  And if so, what do you mean by that: do you mean that there are then dummy imports for the constraint, or that you made that conclusion in some other way?  Anyway, I think the UC_IRE coefficients are not consistent for your purpose.

>1) the dummy imports qre not for the constraint but for commodities related to the constraint e.g. solar and other renewables

>2) I do mean that the constraint is not satisfied when UC_IRE are activated. By that, I mean that the minimum low-carbon share of primary energy is ensured if trades are accounted for (i.e. UC_IRE are deactivated). I can observe that in the results. But when I activate rows 15-18, the constraint is still satisfied if I include Var_Fin and Var_Fout of TU processes in my results table. Which makes me think, as you said, that the UC_IRE coefficients are not consistent for my purpose. So how can I ensure a minimum low-carbon share of primary that does not include the consumption of commodities trhough TU processes in the formulation of my constraint?

[LucasD]

Hello Antti, do you have any ideas on how I can ensure that trades are not included in my constraint? It seems UC_IRE is not the right solution...

Thank you,
Lucas

[Antti-L]

> Hello Antti, do you have any ideas on how I can ensure that trades are not included in my constraint? It seems UC_IRE is not the right solution...

Hmm... not sure why you say so ("UC_IRE is not the right solution")?  But then again, I don't know your mathematical formulation:  I could not see any indication of the trades being handled in your formulation:

$$ Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_flo(PRICCS,PSet_CO = CPT*N) > L_t \cdot (Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_COMCON(PRIFOS)$$
$$ (1-L_t) \cdot (Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW)) + Var_flo(PRICCS,PSet_CO = CPT*N) - L_t \cdot Var_COMCON(PRIFOS) > 0$$

I would suggest to handle the exclusion of the trade flows first explicitly in your mathematical formulation.  Then it should be straightforward to translate it into a user constraint.

[LucasD]

Well, UC_IRE does not seem to be the right solution since my constraint is not satisfied looking at the results, i.e. when I look a the low-carbon share of primary energy with Var_Fin of PRIBIO,PRIRNW, and PRIFOS. In this Var_Fin table are also included the TU_ processes trading PRIFOS and PRIBIO. The constraint is satisfied when TU_ processes are included in this table but not if I filter them. Earlier in this post, you also said that "UC_IRE coefficients are not consistent for your purpose."

Anyway, here is the mathematical formulation reviewed:

$$ Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_flo(PRICCS,PSet_CO = CPT*N) - Var_IRE(PRIBIO) - Var_IRE(PRIFOS) > L_t \cdot (Var_COMCON(PRIBIO) + Var_COMCON(PRIRNW) + Var_COMCON(PRIFOS) $$

Perhaps my problem is that I'm not looking at the right attributes in the Results tab, but I can't figure out what is my mistake.

[Antti-L]

Well, I don't think that is sufficiently unambiguous, because in the model, the trade flow variables (Var_IRE(r,v,t,p,com,ts,ie)) have the IE index as well.  What does your Var_IRE(PRIBIO) and Var_IRE(PRIFOS) represent, i.e. how should they be written out in terms of the trade flows?

But ok, I guess they must be either (imports−exports), (exports−imports) or (imports+exports) or just (exports)?
I any case, after clarifying that, you will be able to see what the correct UC_IRE coefficients are for your constraint.