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Loss of load cost (€)
========================

*indexed by: node, energy, test case*

### Description

This indicator is used to estimate the costs associated with system undersizing with regard to an energy.  
For each node and each energy in a given system, it indicates the total costs associated to Loss Of Load (LOL) over the considered period. This corresponds to the cost of not satisfying demand over the considered period : that associated costs to all the energy that is not served. From a modelling point of view, this amounts to give a cost to a 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 volume of energy curtailed during these hours in [Loss of Load Volume](loss_of_load_volume.md).

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

  In classic models, this cost is directly indexed on the value of Loss of Load (VoLL), which is the amount customers would be willing to pay in order to avoid a disruption in their electricity service.  
</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 :

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

with:

- $c_a$ the Loss Of Load price for the asset $a$

### 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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