Thanks for your clarifications.

> Hopefully that makes sense and my interpretation is indeed correct!

Well yes and no. Yes, under some simplified conditions/assumptions, but no, not quite in general. Let me try and explain:

The objective function formulation has been designed by highly qualified experts (such as Richard Loulou, McGill professor of management science and Dr. Denise Van Regemorter, KU Leuven), and, as you should see from the documentation (Part II), the objective function has been very carefully formulated with a high level of detail e.g. in the various different investment cases and their streams of annual payments. Each of those streams consists of ELIFE yearly payments and is equivalent (in terms of present value) to a single payment of the lump-sum investment cost assumed to occur at year k. Note also that these streams of payments include all individual years, and not just the milestone years or the model.

In the objective function, the annual investment payments INVCOST(y) correspond to the sum of the yearly payments of over all streams having a payment at year y. These values INVCOST(t) (for y=t) would indeed be equal to the annual investment cost, Cost_Inv(t) reported for each period t, if we would use the default annual cost reporting. However, with the default annual cost reporting one would not be able to reproduce the objective function from the annual costs, for several reasons:

• The values INVCOST(y), where y=t, refer to the sum of payments in the individual year y only; the payments in other years of period t (the period with milestone year t) may be different, due to the complex investment cost accounting.

• In the objective function the annualized investment payments of each stream are spread over ELIFE years, which may be different from the full technical life TLIFE. And because of that, the annualized payments might all occur within the model horizon, even though the technical life would extend beyond end-of-horizon (EOH). Therefore, with the default annual cost reporting the (implicit) salvage values would not be correctly credited for any technology having ELIFE # TLIFE and TLIFE extending beyond EOH.

Therefore, because the default annual cost reporting would not be consistent with the objective function when discounted and summed together, the option of using levelized annual cost reporting has been introduced (enabled with $SET ANNCOST LEV). And when that is used, the reported annual costs are, of course, no longer equal to the INVCOST(y) values used in the objective function. In the levelized annual cost reporting, all investment costs are assumed to be spread over TLIFE (not ELIFE), and when that extends beyond EOH, the portion of the investment costs not being salvaged is levelized over those years of the lifetime that fall within the active model horizon (the calculation for the salvage value portion is described in detail the Documentation). In this way we can get annual costs that are consistent with the objective function, and which can be used for reproducing the objective function. The same levelizing approach is used for all costs that may have a salvage value (investment, decommissioning, and surveillance costs)

Note also that the user can also request more accelerated functional depreciation in the value of the capacity, by defining NCAP_FDR(r,y,p) (representing additional annual depreciation in the value), such that the salvage value will then be smaller than it is according to the default salvage value accounting (based on the discounted portion of TLIFE falling beyond EOH).

Nonetheless, under very simplified assumptions where ELIFE = TLIFE for all investments, and all investments would have only a single stream of payments (to eliminate any additional complexities caused by the cases with multiple streams), and there are no decommissioning or surveillance costs nor NCAP_ILED, your expression SALVAGE(z) = sum{y | y ≥ EOH+1 } ( DISC(y,z) × INVCOST(y) ) would indeed be correct (where INVCOST(y) refers to the annual investment cost terms employed in the objective function).

I hope the above might clarify most of your remaining doubts?

> Hopefully that makes sense and my interpretation is indeed correct!

Well yes and no. Yes, under some simplified conditions/assumptions, but no, not quite in general. Let me try and explain:

The objective function formulation has been designed by highly qualified experts (such as Richard Loulou, McGill professor of management science and Dr. Denise Van Regemorter, KU Leuven), and, as you should see from the documentation (Part II), the objective function has been very carefully formulated with a high level of detail e.g. in the various different investment cases and their streams of annual payments. Each of those streams consists of ELIFE yearly payments and is equivalent (in terms of present value) to a single payment of the lump-sum investment cost assumed to occur at year k. Note also that these streams of payments include all individual years, and not just the milestone years or the model.

In the objective function, the annual investment payments INVCOST(y) correspond to the sum of the yearly payments of over all streams having a payment at year y. These values INVCOST(t) (for y=t) would indeed be equal to the annual investment cost, Cost_Inv(t) reported for each period t, if we would use the default annual cost reporting. However, with the default annual cost reporting one would not be able to reproduce the objective function from the annual costs, for several reasons:

• The values INVCOST(y), where y=t, refer to the sum of payments in the individual year y only; the payments in other years of period t (the period with milestone year t) may be different, due to the complex investment cost accounting.

• In the objective function the annualized investment payments of each stream are spread over ELIFE years, which may be different from the full technical life TLIFE. And because of that, the annualized payments might all occur within the model horizon, even though the technical life would extend beyond end-of-horizon (EOH). Therefore, with the default annual cost reporting the (implicit) salvage values would not be correctly credited for any technology having ELIFE # TLIFE and TLIFE extending beyond EOH.

Therefore, because the default annual cost reporting would not be consistent with the objective function when discounted and summed together, the option of using levelized annual cost reporting has been introduced (enabled with $SET ANNCOST LEV). And when that is used, the reported annual costs are, of course, no longer equal to the INVCOST(y) values used in the objective function. In the levelized annual cost reporting, all investment costs are assumed to be spread over TLIFE (not ELIFE), and when that extends beyond EOH, the portion of the investment costs not being salvaged is levelized over those years of the lifetime that fall within the active model horizon (the calculation for the salvage value portion is described in detail the Documentation). In this way we can get annual costs that are consistent with the objective function, and which can be used for reproducing the objective function. The same levelizing approach is used for all costs that may have a salvage value (investment, decommissioning, and surveillance costs)

Note also that the user can also request more accelerated functional depreciation in the value of the capacity, by defining NCAP_FDR(r,y,p) (representing additional annual depreciation in the value), such that the salvage value will then be smaller than it is according to the default salvage value accounting (based on the discounted portion of TLIFE falling beyond EOH).

Nonetheless, under very simplified assumptions where ELIFE = TLIFE for all investments, and all investments would have only a single stream of payments (to eliminate any additional complexities caused by the cases with multiple streams), and there are no decommissioning or surveillance costs nor NCAP_ILED, your expression SALVAGE(z) = sum{y | y ≥ EOH+1 } ( DISC(y,z) × INVCOST(y) ) would indeed be correct (where INVCOST(y) refers to the annual investment cost terms employed in the objective function).

I hope the above might clarify most of your remaining doubts?