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Transmission usage (%)
======

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

### Description

This KPI displays the capacity factor for transmission assets by considering its effective energy consumption versus
its installed capacity.

The transmission usage of a transmission asset is then the ratio of energy flowing through the transmission over its capacity.
For more details on capacity factor, please refer to the KPI [Capacity factor](capacity_factor.md) 


.. warning::
  This KPI is designed to look solely at asset-by-asset results. Aggregations need to be handled with a careful attention as the sum and the average of the transmission usage are not dynamically computed. For instance, the average of the transmission usage of assets of the same technology is the mean of the asset-by-asset value, which is different from the mean of the transmission usage of these assets weighted depending on their installed capacities.

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

  For transmission assets with the flow-based behaviour, this KPI does not return any transmission usage as transmission usages cannot be defined for these assets. 
</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 transmission usage for a given asset $a$, energy $e$ and consumption node $n$. Technology is directly deduced from the asset.
We can then express $x_{a, e, n}$ as:

$$
x_{a, e, n} = \frac{\langle {c}_{a, e, n}(t) \rangle_{t}}{p\_max_a}
$$

<blockquote class="calculation-hint">
  <h4>Calculation hint</h4>

  For transmission with $p\_max_a = 0$, transmission usage will be directly set to zero.
</blockquote>

*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 produced by the asset
- The consumption node index of this KPI refers to the node in which the asset produces
- 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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