A question of Cost_Salv

[xiao.li8@mcgill.ca]

Hi,


I encountered a mismatch when manually calculating the salvage cost, which differs from the salvage cost reported in the TIMES outputs.
For example, consider the case of compressed air energy storage (CAES):

• The technology lifetime is 60 years, and the model horizon ends in 2050.
  


• An investment in 2021 (representing 2021–2022) should still retain salvage value beyond 2050. By my calculation, its salvage should be:
  

         5.94*(2021+60-2050)/60*2*(1/(1.05)^(2050-2021))≈1.49
     [where 5.94 is the annualized investment cost, the factor (2021+60−2050)/60 adjusts for the unused life after 2050, the multiplier 2 accounts for the two years represented by 2021, and the 1.05 term applies the 5% discount rate.]

• Similarly, for 2025 the salvage comes out to around 11…
  

However, when I sum these values across all milestone years, the result is much larger (~220) than the reported salvage cost of 31.20 in the TIMES output.


Why does this discrepancy occur? Because I want to allocate those Salv to different periods.






Process Attribute - 2021 2025 2030 2035 2040 2045 2050
ESTCAESS101_24h Cost_Inv 5.943572433 12.85068651 14.21155223 14.21155223 14.41924721 14.59241133 14.93538698
ESTCAESS101_24h Cost_Salv 31.20915649


Best,
Xiao

[Antti-L]

> By my calculation, its salvage should be: 5.94*(2021+60-2050)/60*2*(1/(1.05)^(2050-2021))≈1.49
    [where 5.94 is the annualized investment cost, the factor (2021+60−2050)/60 adjusts for the unused life after 2050, the multiplier 2 accounts for the two years represented by 2021, and the 1.05 term applies the 5% discount rate.]

I am not able to see where you got this expression. The documentation (Part II) gives the correct formulas for calculating the salvage values, see below. Can you explain how you derived your expression from the formulas given in the documentation? Note also that the reported salvage values are discounted to the discounting base year (G_DYEAR), just like in the objective, while the formulas in the documentation give the values calculated at EOH+1, which are then discounted back to G_DYEAR in the objective function.
     
The reported salvage values (which are reported by each vintage) thus correctly reflect those discounted salvage values, consistent with the documentation.

Could you also explain why you would "want to allocate those Salv to different periods"?

[xiao.li8@mcgill.ca]

> By my calculation, its salvage should be: 5.94*(2021+60-2050)/60*2*(1/(1.05)^(2050-2021))≈1.49
    [where 5.94 is the annualized investment cost, the factor (2021+60−2050)/60 adjusts for the unused life after 2050, the multiplier 2 accounts for the two years represented by 2021, and the 1.05 term applies the 5% discount rate.]

I am not able to see where you got this expression. The documentation (Part II) gives the correct formulas for calculating the salvage values, see below. Can you explain how you derived your expression from the formulas given in the documentation? Note also that the reported salvage values are discounted to the discounting base year (G_DYEAR), just like in the objective, while the formulas in the documentation give the values calculated at EOH+1, which are then discounted back to G_DYEAR in the objective function.
 
The reported salvage values (which are reported by each vintage) thus correctly reflect those discounted salvage values, consistent with the documentation.

Could you also explain why you would "want to allocate those Salv to different periods"?

Hi Antti,

I want to know the net-cost for each period after the deduction of leftover value.

Best,
Xiao

[Antti-L]

Hmm... but the reported annual costs already represent the net costs (after deducting the salvage value). If you would allocate the salvage value to different periods and deduct such values from the total annual costs, you would be deducting the salvage values twice, wouldn't you?

[xiao.li8@mcgill.ca]

Hmm... but the reported annual costs already represent the net costs (after deducting the salvage value). If you would allocate the salvage value to different periods and deduct such values from the total annual costs, you would be deducting the salvage values twice, wouldn't you?

Hi Antti,

Maybe I was confused. Do you mean Cost_Inv reports the investment cost after deducting the salvage value?

Best,
Xiao

[Antti-L]

> Do you mean Cost_Inv reports the investment cost after deducting the salvage value?

Yes, it does. It reports the investment cost after deducting the salvage value, in terms of annualized costs over the lifetime falling within the horizon.

[xiao.li8@mcgill.ca]

> Do you mean Cost_Inv reports the investment cost after deducting the salvage value?

Yes, it does. It reports the investment cost after deducting the salvage value, in terms of annualized costs over the lifetime falling within the horizon.

Hmmm.. Thank you for saving my potential time... I was confused.......