Calculation of INVCOST for technology with negative ILED earlier than the base year
I have been trying to recreate the TIMES OBJINV calculation for processes with lead times.

The process in question has TLIFE=40, ELIFE=30 and ILED=-5.  The model base year is 2010 and the periods are 2010, 2011, 2012, 2013-2017, 2018-2022, further 5-year periods.

I've calculated OBJINV coeffs for 2011 and 2020 vintages.  See the attached workbook for the discount rates and calculation.

For 2020, I can almost recreate the TIMES calculation (I'd be interested to know the cause of the 0.05% error, but am not worrying about it).

For 2011, when the lead time would be prior to the base year, I can't recreate the TIMES calculation.  Do you know what I'm doing incorrectly?

Attached Files
.xlsx   uk-times_objective_function_analysis_iled_question.xlsx (Size: 27.38 KB / Downloads: 4)
Thanks for the interesting question.

Let's focus on the 2011 case which worried you. I can see in your Excel file a row with the following entries:
Cost in UK TIMES 9.07597 <-- calculated here

I assume that this value is what you would also expect TIMES to generate? At least I can see it is the result of your Excel calculation.

I tested with a simple test model and with the parameters you have disclosed, and I got an objective coefficient 9.07597369 for the 2011 investment costs. It looks exactly the same value as in your Excel calculation, and so I can only conclude that I can see no difference to your calculation.

Could you please confirm that this is also the value you expected to see?  If so, could you clarify how you expect me to be able to reproduce the problem you are seeing?
Thanks, Antti.

Looking again, I think I must have made a mistake extracting the 2011 vintage coefficient from the objective equation - I also have the correct number from the model equations and I can't recreate the 8.32 value I extracted previously.  It's very odd as I'm sure I checked that I had the right value.  I'm glad my calculation was correct, but sorry that I wasted your time with the question.

I hope other people will find the workbook useful for understanding how TIMES calculates investment costs for processes with lead times.
pauldodds Wrote:For 2020, I can almost recreate the TIMES calculation (I'd be interested to know the cause of the 0.05% error, but am not worrying about it).

The cause of the 0.05% error is the use of time-dependent general discount rates (G_DRATE).  I think one of the main ideas behind the annualization of the investment costs is that, assuming zero risk premium (no NCAP_DRATE specified) and zero IDC (no NCAP_ILED specified), the lump-sum present value of the investment payments should be equal to the original investment cost (NCAP_COST), when the annual payments are discounted back to the beginning of the commissioning year.

However, your calculation is inconsistent with this equivalence principle.

For some extreme examples, consider buying an electric car in 2012, which has a price £30,000 and ELIFE=10. Assume first that G_DRATE is constant, with the values 1%, 10% and 100%. With all these discount rates, the lump-sum investment cost obtained by discounting the annual investment payments (£3700, £4439, £15015) back to the beginning of the commissioning year is still in all cases exactly £30,000. But now, assume that G_DRATE is 10% in 2012, but then either A) decreases to 1% or B) increases to 100% starting from 2013. Using your calculation method, in the first case A), the lump-sum investment cost would have a value of £42,459, and in case B) it would have a value of only £8,868! So, in case B) the electric car, which is bought in 2012 with the price £30,000, would effectively cost only £8,868, just because of the annualization of the investment cost.  I think such a price reduction would be inconsistent, but perhaps you disagree?

To avoid such artificial alteration in prices when G_DRATE is changing, TIMES currently does not follow your calculation, but discounts the payments back to the commissioning year by the G_DRATE of that year, and therefore in TIMES the lump-sum payment is consistent with NCAP_COST. Would you prefer that your approach is adopted instead?

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