Compound Annual growt rate constraint under stochastic mode

[Mahmoud]

Dear all, 

I am facing some trouble understanding one of my results: 
I have a dynamic constraint on the annual growth rate of power plants capacities (CAGR= 1%). The constraint I am imposing is of type t, t+1 ( var_cap(t) * growth(t) >= var_cap(t+1) -1). please see the attached file for more detail on the constraint. 

Furthermore, I am running the stochastic version of TIMES with two stages. The second stage starts at 2040 and has 2 SOWs. The only thing that is different between SOW1 et SOW2 is that NCAP_COST(year in 2037-2052) of CCUS techs is lower under SOW2. 

My problem: the growth rate of power capacities in all the regions of my model between 2035 and 2040 appears to be way higher than the imposed constraint. I don't know if this is related to the fact that I am defining SOWs. If it's the case, could you provide any help regarding the way one should modify dynamic constraints under the stochastic version of TIMES?

[Mahmoud]

And here's the weird result I get: installed power capacity in France  
Also I attached and excel file of slack variables values (user_con) and the shadow price (user_confxm) of the constraint of installed capacity annual growth rate. Except for 2010, user_con is always at -1 which is the seed value of my dynamic constranint. Altough, the shadow prices of year 2040 and 2050 (second stage of the model) are higher in sow 2 (in which we assume lower prices for CCU and in which we have higher installed power capacity). I also checked the dummy imports. there are none for this consraint.

[Antti-L]

Thanks very much for reporting about this issue.

I checked the GAMS implementation, and the issue turned out to be a caused by a very old bug under the stochastic mode, but concerning only dynamic constraints of type (t,t+1). The RHS bound is in this case taken from period t, which may not have the SOWs that t+1 does. In your case, the issue arises with the constraints t=2035, which are defined for both SOW, because the constraints involve also t+1=2040. The RHS bound is defined correctly for SOW=1 because t=2035 includes that SOW=1, but the RHS bound is not defined for SOW=2, because t=2035 does not include SOW=2.  This oversight will be fixed in the next version of TIMES.

The issue does not appear if using (t,t–1) constraints, which can therefore be used as a workaround. As far as I can see, any (t,t+1) constraint can be expressed as a (t,t–1) constraint (for example, I have myself practically always been using (t,t–1) constraints).

[Mahmoud]

Thank you Antti for you reply. I am looking forward to installing the next version of TIMES  
Just a last quick question: Is the way I am imposing the t,t-1 formulation of the dynamic constraint right (please see attached file)

Best Regards, 
Mahmoud

[Antti-L]

You must then put GROWTH on the RHS, so change the UC_ATTR column header to UC_ATTR~RHS.

[canismajoris]

Thank you Antti. I've just tested it myself and it worked just fine.
Have a great day

[Antti-L]

The new TIMES v4.5.3 (just released), should fix the problem with (t,t+1) dynamic constraints under multi-stage stochastic.

[Mahmoud]

Thank you very much Antti for the update!