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## Marginal costs (€/MWh)

*indexed by: energy, node, test case*

### Description

This view shows a time series of the marginal costs for producing each energy at each simulation node.

### Calculation

At a node $n$ the supply demand balance equation for an energy $e$ can be written as:

$$
\forall t \in T \sum_\limits{a \in A^p_{n,e}} p_{a, n, e}(t) = \sum_\limits{a \in A^c_{n,e}} c_{a, e, n}(t)
$$

As long as the optimization problem representing our energy system is linear, this equation has a dual value 
associated that represents the marginal cost of energy $e$. The value returned by this indicator is directly this dual
variable.


.. note::
   To simplify the analysis, CO2 and captured CO2 are included in this indicator. The unit is then €/t instead of €/MWh

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

  For energy CO2, the value returned by this indicator is the opposite of the dual value associated to the CO2 emissions
  consumption balance equation.
</blockquote>

### Indexing 

- The energy index of this KPI refers to the energy which marginal costs is displayed
- The node index of this KPI refers to the node at which an energy marginal costs is displayed
- The test case index corresponds the test case of the realization variables and parameters are taken from