Salvage value and the objective function
#2
Thanks for your question, even though I am somewhat confused by it.

I add some quotes from the documentation below that may be of help:

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Investments whose technical lives exceed the model’s horizon receive a SALVAGE value for the unused portion of their technical lives. Salvage applies to several types of costs: investment costs, sunk material costs, as well as decommissioning costs and surveillance costs.
[…]
What are the costs that should trigger a salvage value? The answer is: any costs that are directly or indirectly attached to an investment. These include investment costs and decommissioning costs. Fixed annual costs and variable costs do not require salvage values, since they are paid each year in which they occur, and their computation involves only years within the horizon.
[…]
The principle of salvaging is simple, and is used in other technology models such as MARKAL, etc: a technology with technical life TLIFE, but which has only spent x years within the planning horizon, should trigger a repayment to compensate for the unused portion TLIFE-x of its active life.

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The total salvage value thus corresponds to a credit for the (discounted) costs attributable to unused portion of the technical lives of investments, and as such, it is included in the objective function as a negative term. Only technologies whose life extends beyond EOH are credited with a salvage value.

So we can summarize the inclusion of the salvage values as follows:

  • Objz includes the salvage value, by excluding the portions of the investment-related costs attributable to the unused portions of their technical lives, by crediting back those portions of the costs. And Objz is reported as is, being exactly the value of that variable in the model solution.

  • The reported annualized costs (Cost_*) also implicitly include the salvage value, by excluding the portions of the investment-related costs attributable to the unused portions of their technical lives, because the annualized costs include only costs paid within the model horizon.

  • The reported total annual costs (Reg_ACost) also implicitly include the salvage value, by excluding the portions of the investment-related costs attributable to the unused portions of their technical lives, because the annual costs include only costs paid within the model horizon.

All annual costs are always reported only for the model periods. Any annualized investment payments falling beyond the model horizon are thus excluded, just like they are (in net terms) excluded also from the objective function (by first including them in the investment cost component and then subtracting the salvage values credited back). And so, in essence both cases are including the salvage values, either explicitly (Objz) or implicitly (annual costs).

Concerning Cost_NPV, there one might have chosen to report the salvage values also in a separate component. But also in that case the total sum should of course be equal to Objz, whether the salvage values are reported separately or not. The salvage value is thus included also in Cost_NPV, by excluding the portions of the investment-related costs attributable to the unused portions of their technical lives.

So, to me the reporting looks all very consistent, and that's why I am a bit confused about the question.  Could you elaborate in some more detail what makes you conclude that "the salvage value doesn't seem to be included in the objective function reported."?  Surely, the salvage value is included by crediting it back, and thus excluding the associated costs beyond the EOH from the total value of Objz, as described in the documentation.
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RE: Salvage value and the objective function - by Antti-L - 27-02-2023, 06:54 PM

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