Question on UC_ATTR

[charlene.barnet]

Hi, 

I am trying to constrain to capacity growth of electricity producing power plants (gas power plants and wind farms) so that the models smoothly increase capacities instead of concentrating investment on a specific period. 

To do so, I tried to use the UC_ATTR attribute, however my constraint does not seem to work properly (runs always end being qualified "infeasible"). I consulted the documentation to construct this constraint. Is it properly formulated or is there any problem (see attachment) ? 

Thank you very much for your help 

Charlène

[Antti-L]

Yes, you seem to have a confusion about the growth coefficients.  You are using the dynamic type (t, t−1), activated by specifying GROWTH under UC_ATTR~RHS, which is fine as such, but you seem to be overlooking that important fact by yourself.  The coefficients are always treated as growth coefficients only on the side where GROWTH is specified, and thus on the RHS in this case.

For example, your equation for the maximum growth rate of wind capacities (first row of "Capacities_ELCWIND_Growth…") can be read as follows:

   1.5 × VAR_CAP(t, Elcwind)  ≤  1 × VAR_CAP(t−1, Elcwind) − 0.25

On the LHS, you see the coefficient 1.5 for VAR_CAP, which you have defined in the UC_CAP column.  On the RHS, the coefficient for VAR_CAP is 1, as defined in the UC_CAP~RHS column (growth coefficient=1, rendering as 1).  And finally, the RHS constant is −0.25, as defined in the UC_RHSRTS column.  I think these are pretty easily readable from your specification.  Anyway, to better see what this constraint does, we can divide both sides by 1.5 and get:

  VAR_CAP(t, Elcwind)  ≤  0.6666667 × VAR_CAP(t−1,Elcwind) − 0.16666667

You should see that the constraint is requiring the capacity of wind to be decreasing by over 33% between the successive periods t−1 and t.  Obviously, this cannot be what you intended, but can be expected to cause infeasibilities.  To solve the issue, just define the growth coefficients on the RHS side, and probably you also meant the RHS constant to have a positive sign…?

[Antti-L]

Note also that the growth coefficients represent annual growth multipliers. Therefore, if you would use the 1.5 coefficient as a growth coefficient (by putting it on the RHS side), the maximum growth in wind capacity over a ten years' time would be 1.5^10 − 1 = 56.67 = 5667%.  I am not sure if that is what you meant, but I would consider it a very mild constraint on the capacity growth, allowing perhaps unrealistically high growth until 2050.

[charlene.barnet]

Note also that the growth coefficients represent annual growth multipliers. Therefore, if you would use the 1.5 coefficient as a growth coefficient (by putting it on the RHS side), the maximum growth in wind capacity over a ten years' time would be 1.5^10 − 1 = 56.67 = 5667%.  I am not sure if that is what you meant, but I would consider it a very mild constraint on the capacity growth, allowing perhaps unrealistically high growth until 2050.

Thank you very much for your help ! There was indeed a big confusion on my side ! Now, the constraint seems to be working perfectly fine. The 1.5 coefficient was just a test, because I wanted to check if the problem was coming from the constraint being too strong. 

Attached the corrected form of the constraint, if it can be of any help to others. 

Thank you again, i wish you a nice week. 

Charlène

[charlene.barnet]

Note also that the growth coefficients represent annual growth multipliers. Therefore, if you would use the 1.5 coefficient as a growth coefficient (by putting it on the RHS side), the maximum growth in wind capacity over a ten years' time would be 1.5^10 − 1 = 56.67 = 5667%.  I am not sure if that is what you meant, but I would consider it a very mild constraint on the capacity growth, allowing perhaps unrealistically high growth until 2050.

Thank you very much for your help ! There was indeed a big confusion on my side ! Now, the constraint seems to be working perfectly fine. The 1.5 coefficient was just a test, because I wanted to check if the problem was coming from the constraint being too strong. 

Attached the corrected form of the constraint, if it can be of any help to others. 

Thank you again, i wish you a nice week. 

Charlène