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Curtailment (MWh)
=================

*indexed by: asset, data type, energy, node, technology, test case*

### Description

This indicator is used to analyse the volumes of **electricity** that is curtailed in the power system. This KPI enables
to understand if the power system offers sufficient flexibility to capture renewables and how sensitivities on the system
enable to capture renewables. 


Three categories of curtailment are computed in this KPI (corresponding to the *data type* index) : 

- *Well curtailment* : the power consumption of wells as wells are specific assets that usually consume energy at a low cost (for instance at 0,01€/MWh) 
to ensure that the system achieves supply-demand balance constraints at any time step
- *Curtailed renewable production* : the difference between the possible variable RES production and the actual variable
RES production. Variable RES assets are the ones with the tag VARIABLE_RENEWABLE in the asset library.
- *Curtailed hydro production* : the non-utilization of bounded supply for hydro assets (Hydro fleets and Pumped storage fleets) 

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

  Curtailment is only computed for the power system. If you want to see the volumes of energy consumed by well assets 
  for the other energies of the system, please see the KPI [Consumption](consumption.md) or [Supply-demand balance](sdb.md).
</blockquote>


### Calculation

All the equations below are valid for any realization and are 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:

$$
x_{a, e, n} = well_{a, e, n} + vRES_{a, e, n} + hydro_{a, e, n}
$$

with:

- $well_{a, e, n}$ : the *Well curtailment*
- $vRES_{a, e, n}$ : the *Curtailed renewable production*
- $hydro_{a, e, n}$ : the *Curtailed hydro production*

#### Well curtailment

Well curtailment is the power consumption of well assets as wells are specific assets that usually consume 
energy at a low cost (for instance at 0,01€/MWh) to ensure that the system achieves supply-demand balance constraints
at any time step. 

With $A_{n,electricity}^{well}$ the set of well assets consuming energy $electricity$ at node $n$, 
we can then express $well_{a, e, n}$ as :

$$
well_{a, e, n} = 
\begin{cases}
    \frac{1}{N_h} * \sum_{t} {c_{a, e, n}(t)} & \text{if } a \in A_{n, electricity}^{well} \\
    0 & \text{otherwise.}
\end{cases}
$$

#### Curtailed renewable production

Curtailed renewable production is the difference between the possible variable RES production and the actual variable
RES production, per node, per technology. Variable RES assets are the ones with the tag VARIABLE_RENEWABLE in the asset library.

With $A_{n, electricity}^{RES}$ the set of variable RES assets consuming energy $electricity$ at node $n$, 
we can then express $vRES_{a, e, n}$ as :

$$
vRES_{a, e, n} = 
\begin{cases}
    \frac{1}{N_h} * \sum_{t} {p^{*}_a(t) - p_{a, e, n}(t)} & \text{if } a \in A_{n, electricity}^{vRES} \\
    0 & \text{otherwise.}
\end{cases}
$$

#### Curtailed hydro production

Curtailed hydro production is the non-utilization of bounded supply for hydro assets (Hydro fleets and Pumped storage fleets)
as these assets can decide whether they use their water bounded supplies or not. From a modelling point of view, if an 
asset decide to not use its water supply, it should be counted as curtailment of hydro production.

With $A_{n,electricity}^{hydro}$ the set of Hydro fleet and Pumped storage fleet assets producing energy $electricity$ at node $n$, 
we can then express $hydro_{a, e, n}$ as :

$$
hydro_{a, e, n} = 
\begin{cases}
    \frac{1}{N_h} * \sum_{t} {expected_a(t) - realized_a(t)} & \text{if } a \in A_{n, electricity}^{hydro} \\
    0 & \text{otherwise.}
\end{cases}
$$

with:

- $expected_a$ : the expected bounded supply of asset $a$, which refers to the input data
- $realized_a$ : the realized bounded supply of asset $a$, which refers to the results of the optimization

*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 electricity for all this KPI
- The node index of this KPI refers to the node in where the curtailment occurs
- 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

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