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Energy storage capacities (MWh)
======

*indexed by: asset, energy, node, technology and test case*

### Description

This KPI displays the energy storage capacity of every energy storage asset. 
The way in which this capacity is calculated depends on the definition of the storage, i.e. the behaviour of the storage asset.
In fact the storage capacity can be defined either directly in MWH or with a discharge time (if the asset has the behaviour “DISCHARGE_TIMES”).

Finally, for an asset of a pathway study, this KPI returns the installed capacity for each period of the pathway.

For co2 and co2 captured producing assets, the equivalent result is available in the KPI [CO2 captured storage capacities](co2_captured_storage_capacities.md).

<blockquote class="custom-hint">
  <h4>Modelling hint</h4>

  The discharge time corresponds exactly to the time needed to empty the storage (no efficiency consideration) and not to "produce" as much energy as the size of the storage.
</blockquote>

### Calculation

The equation below is valid for any realization and is therefore implicitly indexed by test case. 

Let be $x_{a, e, n}$ the installed capacity returned by the KPI for a given asset $a$, energy $e$ and node $n$. Technology is directly deduced from the asset.
The calculation of this energy storage capacity differs according to the behaviour of the asset. 

If the asset **has the behaviour “DISCHARGE_TIMES”**, the energy storage capacity is computed as follows:
$$
x_{a, e, n} =  p\_max_a . \Delta_a
$$
with $p\_max_a$ the installed capacity of the storage asset, as computed in the KPI [Installed capacities](installed_capacities.md) and $\Delta_a$ the discharge time of asset $a$.
    
If the asset **does not have the behaviour “DISCHARGE_TIMES”**, the energy storage capacity is a direct input parameter of the asset, which is the storage capacity parameter of asset $a$, $s\_max_a$ 
$$
x_{a, e, n} =  s\_max_a
$$

*Global variables and parameters notations definitions can be consulted [here](../notations.md).*

### Indexing

- The asset index refers to the name of the asset 
- The energy index is the energy stored by the asset
- The node index of this KPI refers to the node in which the asset consumes
- The technology index refers to the technology type of the asset
- The test case index corresponds the test case of the realization variables and parameters are taken from


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