Notations
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For all KPIS equations the following notations are used:

##### Realization notations

- T : the set of timesteps of the realization
- $E$ : The set of modelled energies in the realization (including CO2 and CO2 captured)
- $N_h$ : the number of timesteps per hour
- $N$ : the set of nodes of the realization
- $N_a$ : the set of nodes to which asset $a$ is connected (producing or consuming at least one energy at this node)
- $N_{a, e}^p$ : the set of nodes to which asset $a$ produces energy $e$
- $N_{a, e}^c$ : the set of nodes to which asset $a$ consumes energy $e$
- $A$ : the set of assets of the realization
- $A_n$ : the set of assets connected to node $n$
- $A_{e, n}^p$ : the set of assets producing energy $e$ at node $n$
- $A_{e, n}^c$ : the set of assets consuming energy $e$ at node $n$

##### Variables

- $p_{a, e, n}(t)$ : the output flow of energy $e$ produced by an asset $a$ at the node $n$ during timestep $t$
- $c_{a, e, n}(t)$ : the incoming flow of energy $e$ consumed by an asset $a$ at the node $n$ during timestep $t$

##### Parameters

**Static**

- $p\_max_a$: the maximal theorical energy output of an asset $a$
- $p\_max_a^{IN}$: the maximal theorical energy consumption of an asset $a$

**Temporal**

- $av_a(t)$ : the production availability of an asset, defined as a percentage of its $p\_max_a$.
- $av_a^{IN}(t)$ : the consumption availability of an asset, defined as a percentage of its $p\_max_a^{IN}$.
- $p^{*}_a(t)$ : the maximal available power output of an asset $a$, most often referring to its $p\_max_a$ attribute multiplied by its availability $av_a$ timeseries.
- $p^{*, IN}_a(t)$ : the maximal available power input of an asset $a$, most often referring to its $p\_max_a^{IN}$ attribute multiplied by its availability $av_a^{IN}$ timeseries.