---
jupytext:
  text_representation:
    extension: .md
    format_name: myst
    format_version: 0.13
    jupytext_version: 1.10.3
kernelspec:
  display_name: Python 3
  language: python
  name: python3
---

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

Congestion hours (h)
======

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

### Description

The KPI computes the number of hours of congestion a transmission asset faces during the optimization.

The number of congestion hours corresponds to the number of hours during which an interconnection is saturated with respect to its available capacity. 


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

  This KPI enables to understand if the established interconnections are undersized (high number of hours for a given asset). 
  Investing in the interconnection can help decreasing the congestion rent in the considered energy system.
</blockquote>

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

  For transmission assets with the flow-based behaviour, this KPI does not return any number of congestion hours as congestion 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 value returned by the KPI for a given asset $a$, energy $e$ and node $n$. Technology is directly deduced from the asset.
We can then express $x_{a, e, n}$ as:

$$
x_{a, e, n} = \frac{1}{N_h} * \sum_{t} \mathbb{1}_{\text{c}_{a, e, n}(t)}
$$

Where:

$$
\mathbb{1}_{\text{c}_{a, e, n}(t)} =
\begin{cases}
    1 & \text{if } p_{a, e, n}(t) > 99.99 \% * p^{*}_a(t) \\
    0 & \text{otherwise.}
\end{cases}
$$

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

  An interconnection is considered saturated when its production reaches 99.99% of its available production capacity. 
  The choice of 99.99% instead of 100% as a criterion for congestion hours is made for numerical purposes.
</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 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

</div>