Total costs (€/year)#

indexed by: asset, cost type, node, pathway, technology, test case

Description#

This KPI refers to the total costs of the system, i.e., the total costs of operating the system (the costs directly linked to the operation of each asset present in the system) as defined in the KPI System costs, to which are added investment costs and fixed operating costs. This KPI enables to compute and analyse the distribution of the annual payments of operation costs and annuities for each of the period of the pathway.

These costs are annualized and distributed over the lifetime of the assets they are attached to. Investment and repowering costs include the premium, which captures the cost of financing an asset and the financial risk associated, and the ratio avoiding side effects if the lifetime of the asset expires after the end of the pathway horizon.

Modelling hint

The actualization is not considered in this KPI (even if costs are actualized in the objective function). This means that a pathway step in 2040 gives its results in the currency used for its creation. If you used €2020 for your CAPEX and FOC the result displayed by this KPI will also be in €2020. Please also note that the cost is given per period. This means that for a ten-year duration period, you have to multiply the displayed cost by 10 to get the total cost over the period.

Costs shared between nodes

Additionally, as an asset could produce or consume energy at several nodes. For practicality purposes and to share costs between those nodes, the total cost of an asset is equally divided between the nodes for which the asset is linked. Then, for instance, a transmission between the nodes A and B will see its asset costs equally shared between A and B.

Calculation#

Global#

All the equations below are valid for any realization and are therefore implicitly indexed by test case. The same remark applies to technology as this index is directly linked to the asset. The formulas are valid when directly considering pathway and period, so that the equations are implicitly indexed by period and pathway.

Let be $x_{a, n}$ the value returned by this KPI for a given asset $a$ and node $n$.

We can then express $x_{a, n}$ as :

\[x_{a, n} = s_{a, n} + f_{a, n} + i_{a, n}\]

With:

$s_{a, n}$ the system costs for a given asset $a$ and node $n$ such as computed by the System costs KPI
$f_{a, n}$ the fixed operating costs for a given asset $a$ split over the nodes to which $a$ is linked
$i_{a, n}$ the investment costs for a given asset $a$ split over the nodes to which $a$ is linked

Note

Fixed operating costs and investment costs only depend on assets parametrization and therefore are not indexed by node. It is after computing these costs per asset that they are spread equally between nodes to which assets are linked and that an additional node index is added.

Fixed operating costs#

Fixed operating costs are the results of the simple multiplication of asset production capacity and associated unitary fixed operation costs.

\[f_{a, n} = \frac{1}{N_a} \cdot \bar{p}_a \cdot foc_{a}\]

With:

$\bar{p}_a$ : the maximal energy production capacity of asset $a$ such as returned by Installed capacities KPI.
$foc_a$ : the fixed operating costs parameter for a given asset $a$

Warning

For transmission assets $\bar{p}_a$ refers to the maximal energy consumption capacity as long as CAPEX parameter refers to the costs of expending this capacity and not the production one.

Investment costs#

Investment costs calculation differ whether the asset capacity is optimized or not.

\[\begin{split}i_{a, n} = \frac{1}{N_a} \cdot \begin{cases} \quad uAIC_a + ASC_a & \text{if the asset is never optimized throughout the pathway}\\ \quad oAIC_a + oARC_a + oDC_a + ASC_a & \text{otherwise}\\ \end{cases}\end{split}\]

Where:

$uAIC_a$ the annualized investment costs for a given asset $a$ (unoptimized assets only)
$oAIC_a$ the annualized investment costs for a given asset $a$ (optimized assets only)
$oARC_a$ the annualized repowering costs for a given asset $a$ (optimized assets only)
$oDC_a$ the decommissioning costs for a given asset $a$ (optimized assets only)
$ASC_a$ the annualized storage costs for a given asset $a$ (all type of assets)

Annualized investment costs#

The calculation of annualized investment costs for a given asset $a$ and node $n$ depends on the considered period $p$. The overnight investment cost is firstly annualized into annuities with the following formula:

\[AnIC_a = \frac{1}{N_a} \frac{overnight\_investment\_cost_a}{\sum_{i \in [0, D_a[} q_a^i}\]

With:

$AnIC_a$ the annualized investment capacity cost (without cost of financing, in €/MW) of asset $a$
$q_a = \frac{1}{1 + R^a}$
$R_a$ the asset discount rate, including global discount rate and the risk of financing asset
$D_a$ the lifetime of asset $a$
$overnight\_investment\_cost_a$ : the overnight investment capacity cost parameter (without cost of financing, in €/MW) of asset $a$

Then, this annualized investment capacity cost is used to compute the global value of annualized investment costs as follows:

$uAIC_a = AnIC_a \cdot \bar{p}_a$
$oAIC_a = AnIC_a \cdot (add_a - repow_a)$

With:

$add_a$ the added capacity of a given asset $a$
$repow_a$ the repowered capacity of a given asset $a$

Then, for optimized assets only, the value is distributed over the asset lifetime. For instance, let’s consider an optimized asset with a lifetime $D = 20$ without repowering:

Year	$add_a $	$oAIC_a$	Annualized investment cost
2020	25	$a_{2020} = AnIC_a \cdot 25$	$a_{2020}$
2030	100	$a_{2030} = AnIC_a \cdot 100$	$a_{2020} + a_{2030}$
2040	1000	$a_{2040} = AnIC_a \cdot 1000$	$a_{2030} + a_{2040}$

Annualized repowering costs#

The calculation of the annualized repowering costs for a given asset $a$ and node $n$ rely on the same principle as the annualized investment costs: 1. Computation of the annuities 2. Distribution of the annuities over the asset lifetime

We then have

\[AnRC_a = \frac{1}{N_a} \frac{repowering\_cost_a}{\sum_{i \in [0, D_a[} q_a}\]

With:

$AnRC_a$ the annualized repowering capacity cost (without cost of financing, in €/MW) for a given asset $a$ and node $n$
$repowering\_cost_a$ the repowering overnight capacity cost parameter (without cost of financing, in €/MW) of asset $a$

Then, this annualized repowering capacity cost is used to compute the global value of annualized repowering costs as follows:

\[oARC_a = AnRC_a \cdot repow_a\]

The value is finally distributed over the asset lifetime. For instance, let’s consider an optimized asset with a lifetime $D = 20$ with repowering:

Year	$repow_{a, n}$	$oARC_{a, n}$	Annualized repowering cost
2020	25	$r_{2020} = AnIC_a \cdot 25$	$r_{2020}$
2030	100	$r_{2030} = AnIC_a \cdot 100$	$r_{2020} + r_{2030}$
2040	1000	$r_{2040} = AnIC_a \cdot 1000$	$r_{2030} + r_{2040}$

Annualized storage costs#

The calculation of annualized storage costs depends on the behavior of the given asset $a$ :

\[\begin{split}ASC_a = \frac{1}{N_a} \cdot \begin{cases} \quad oASC_a & \text{if the asset $a$ has both optim_pathway and discharge_times behaviours active}\\ \quad uASC_a & \text{otherwise}\\ \end{cases}\end{split}\]

With:

$oASC_a$ the annualized storage costs for the given asset $a$ (optimized assets with discharge times behavior only)
$uASC_a$ the annualized storage costs for the given asset $a$ (other storage assets)

The calculation of the $oASC_a$ rely on the same principle as the annualized investment costs: 1. Computation of the annuities 2. Distribution of the annuities over the asset lifetime

The overnight storage investment cost is firstly annualized into annuities with the following formula:

\[AnSC_a = \frac{overnight\_storage\_cost_a}{\sum_{i \in [0, D_a[} q_a}\]

With:

$AnSC_a$ the annualized storage capacity cost (without cost of financing, in €/MW) for a given asset $a$
$overnight\_storage\_cost_a$ the storage overnight capacity cost (without cost of financing, in €/MW) of asset $a$

Then, this annualized storage capacity cost is used to compute the global value of annualized investment costs as follows:

$oASC_a = AnSC_a \cdot add_a \cdot discharge\_times_a$
$uASC_a = AnSC_a \cdot storage\_capacity_a$

Energy storage capacities

Then, for optimized assets with discharge times only, the value is distributed over the asset lifetime. For instance, let’s consider an optimized asset with discharge time and a lifetime $D = 20$:

Year	$add_a$	$Dis_a$	$oASC_{a, n}$	Annualized storage cost
2020	25	2	$s_{2020} = AnSC_a \cdot 25 \cdot 2$	$s_{2020}$
2030	100	3	$s_{2030} = AnSC_a \cdot 100 \cdot 3$	$s_{2020} + s_{2030}$
2040	1000	4	$s_{2040} = AnSC_a \cdot 1000 \cdot 4$	$s_{2030} + s_{2040}$

Decommissioning costs#

For decommissioning costs, no annualisation is needed as we consider that the uninstallation of an asset is immediate. Then, no distribution over the asset lifetime is needed. However, to be consistent with the other costs displayed in this indicator, the decommissioning costs need to be divided by the duration of the period. Then the decommissioning costs of the given asset $a$ and node $n$ is computed as follows:

\[oDC_a = \frac{decommissioning\_cost_a \cdot (less_a - repow_a)}{d}\]

With:

$decommissioning\_cost_a$ the decommissioning overnight capacity cost (without cost of financing, in €/MW) of asset $a$
$less_a$ the capacity decommissioned for a given asset $a$
$d$ the duration of the considered period

Indexing#

The cost type index of this KPI refers to the type of cost. Additionally, to the ones added directly in the KPI System costs the following ones are added: Fixed operating costs, Annualized investment costs, Annualized investment storage costs, Annualized repowering costs, Annualized decommissioning costs, Unoptimized annualized investment costs and Unoptimized annualized investment storage costs.
The remarks regarding the share of costs between energies and the distribution between nodes for straddling assets as defined in the KPI System costs are still valid for this indicator.
The test case index corresponds to the test case from which realization variables and parameters are taken from.

Year	\(add_a\)	\(Dis_a\)	\(oASC_{a, n}\)	Annualized storage cost
2020	25	2	\(s_{2020} = AnSC_a \cdot 25 \cdot 2\)	\(s_{2020}\)
2030	100	3	\(s_{2030} = AnSC_a \cdot 100 \cdot 3\)	\(s_{2020} + s_{2030}\)
2040	1000	4	\(s_{2040} = AnSC_a \cdot 1000 \cdot 4\)	\(s_{2030} + s_{2040}\)

Year	$add_a $	\(oAIC_a\)	Annualized investment cost
2020	25	\(a_{2020} = AnIC_a \cdot 25\)	\(a_{2020}\)
2030	100	\(a_{2030} = AnIC_a \cdot 100\)	\(a_{2020} + a_{2030}\)
2040	1000	\(a_{2040} = AnIC_a \cdot 1000\)	\(a_{2030} + a_{2040}\)

Year	\(repow_{a, n}\)	\(oARC_{a, n}\)	Annualized repowering cost
2020	25	\(r_{2020} = AnIC_a \cdot 25\)	\(r_{2020}\)
2030	100	\(r_{2030} = AnIC_a \cdot 100\)	\(r_{2020} + r_{2030}\)
2040	1000	\(r_{2040} = AnIC_a \cdot 1000\)	\(r_{2030} + r_{2040}\)