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Congestion rent (€)
======

*indexed by: asset, node, technology, test_case*

<div style="text-align: justify">

### Description

The KPI computes the congestion rent of each transmission assets, i.e., the benefit made when transferring energy from 
a node to another. This indicator is calculated as the subtraction of transmission revenues and transmission costs and
is therefore computed with the same formulas as [asset surplus](asset_surplus.md) KPI.

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

  This indicator is called congestion rent, because at time steps when a line is not saturated, marginal costs in the 
  two extremities of the line converge and transmission revenue from transferring energy from a node to another is 0. 
  Transmission revenues therefore only occur when line is congested and marginal prices for the energy it carries 
  differs between the 2 nodes to which it is connected.

</blockquote>

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

  Since the result is given for each transmission, and that transmissions are 
  directional (e.g. transmission N1−>N2 is different from transmission N2−>N1), 
  one must sum the results given for each direction in order to have the total 
  congestion rent associated to a transmission between two nodes. 

</blockquote>

### Calculation

Let be $x_{a, n}$ the congestion rent of transmission $a$ at node $n$.
We can then express $x_{a, n}$ as:

$$
x_{a, n} = as_{a, n} = ac_{a, n} - ac_{a, n}
$$

With :

- $as_{a, n}$ : the asset surplus of transmission $a$ at node $n$
- $ar_{a, n}$ : the asset revenues of transmission $a$ at node $n$
- $ac_{a, n}$ : the asset costs of transmission $a$ at node $n$

For more detailed explanations on how [asset surplus](asset_surplus.md), [asset revenues](asset_revenues.md) and [asset costs](asset_costs.md) are computed 
please consider looking at associated documentation pages.

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

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