VAR_NcapM interpretation

[Mahmoud]

Dear all 

I have a very basic question about the interpretation of VAR_NcapM. 
From doc part 2: "Undiscounted reduced costs of investment variable (VAR_NCAP) of process (p); only reported, when the capacity variable is at its lower or upper bound [...] the undiscounted reduced costs can be interpreted as the necessary decrease / increase in the investment cost coefficient, such that the investment variable will leave its lower (upper) bound."

I have defined a power plant for which the costs are in the 'invcost" attached file. The same power plant doesn't deploy in my scenario. What I am struggling to understand is why the reduced costs of the investment variable (second attached file) higher than the investment costs I have specified. I am having a hard time figuring out what could push the reduced cost higher than the investment cost.

Thank you for your help

Mahmoud

[Antti-L]

You are quite right, that is the correct interpretation.

The raw dual values (reduced costs) of the (non-basic) VAR_NCAP variables are simply undiscounted, by dividing it by the objective coefficient for VAR_NCAP corresponding to a unit investment cost (NCAP_COST=1).  Therefore, the resulting undiscounted VAR_NcapM reported gives the impact of a unit change in VAR_NCAP on the objective, in terms of an investment cost having the same impact.

Parameters directly affecting the dual values through the objective coefficients for VAR_NCAP include the following:

  ● Investment cost, NCAP_COST(r,v,p)
  ● Investment taxes and subsidies, NCAP_ITAX & NCAP_ISUB
  ● Fixed O&M cost, NCAP_FOM(r,v,p)
  ● Fixed taxes and subsidies, NCAP_FTAX & NCAP_FSUB
  ● Decommissioning costs, NCAP_DCOST(r,v,p)
  ● Commissioning lead time, NCAP_ILED(r,v,p)
  ● Economic life, NCAP_ELIFE(r,v,p)
  ● Technology-specific discount rate, NCAP_DRATE(r,v,p) (if different from G_DRATE)

Parameters / constraints that may indirectly affect the dual value (reduced cost) for VAR_NCAP include the following:

  ● Any lower bounds on process availability
  ● Growth constraints on capacity
  ● Any other user constraints involving the process capacity

However, in your case, it seems that the only parameters of the process are NCAP_COST and NCAP_DRATE, and so it remains unclear how the dual values are deduced by the solver. But anyway, TIMES simply divides those dual values by the unit objective coefficient of NCAP_COST, giving the impact of a unit change in VAR_NCAP on the objective, in terms of an investment cost that would have an equivalent impact on the objective.

[Mahmoud]

Thank you for the detailed explanation, Antti.

NCAP_COST and NCAP_DRATE are not the only parameters of the technology. I filtered out the other params for the screenshot.