---
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"> 

Loss of load hours (h)
===================================

*indexed by: energy, node, test case*

### Description

This indicator is used to analyse the sizing of a system with regard to an energy.  
For each node and each energy in a given system, it indicates the number of hours of 
Loss Of Load (LOL), also called Loss Of Load Expectation (LOLE), when demand 
must be curtailed due to insufficient energy production.  
From a modelling point of view, this corresponds to hours when there exists Loss of Load.

The volume of energy curtailed during these hours is indicated in the KPI [Loss of Load Volume](loss_of_load_volume.md) 
and the associated costs in [Loss of Load Cost](loss_of_load_cost.md).

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

  The usual threshold for determining whether a system is undersized in terms of production is 
  around 3 hours. If, for example, a country has 40 hours of Loss of Load for a given energy, 
  it is undersized for that energy. It considers the fact that if the LOL is “too large”, then 
  additional capacities (power plants or batteries) need to be built to ensure adequacy 
  in the system.
</blockquote>



### Calculation

All the equations below are valid for any realization and are therefore implicitly indexed by test case. 

Let be $x_{n, e}$ the value returned by this KPI for a given node $n$ and energy $e$ and $A_{n,e}^{lol}$ the set of loss of 
load assets producing energy $e$ at node $n$.  
We can then express $x_{n, e}$ as :

$$
x_{n, e} = \frac{\sum_t{f_{n, e}(t)}}{N_h}
$$

with:

- $f_{n, e}(t) = \begin{cases} 
\quad 1 \text{ if} \sum\limits_{a \in A_{n,e}^{lol}} p_{a, n, e}(t) \geq 10^{-3}\\
\quad 0 \text{ otherwise} 
\end{cases}$

A threshold of one kw is set to avoid taking into account hours when demand peak shaving is insignificant.


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

### Indexing

- The energy index of this KPI refers to the produced energy of Loss of load assets
- The node index of this KPI refers to the node consuming the energy produced by Loss of load assets
- The test case index corresponds the test case of the realization variables and parameters are taken from

</div>