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Loss of load volume (MWh)
========================

*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 volume of Loss Of Load (LOL). This corresponds to the volume of energy (including reserves) over the considered period that is not served, i.e., the volume of a given energy demand that is curtailed due to a lack of production. From a modelling point of view, this corresponds to the volume delivered by Loss Of Load assets.

The number of Loss Of Load hours for each node and energy is indicated in the KPI [Loss of Load hours](loss_of_load_hours.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 is not given in terms of Loss Of Load volume 
  but rather in terms of Loss Of Load hours (cf [Loss of Load hours](loss_of_load_hours.md)). This is because the focus is on a lack of peak capacity rather than a 
  lack of peak production.
</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 :

$$
x_{n, e} = \frac{\sum\limits_{t, a \in A_{n,e}^{lol}} p_{a, n, e}(t)}{N_h}
$$

*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

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