Mathematical Models in WaterModels
Notation for Sets
A water distribution network is represented by a directed graph $\mathcal{G} := (\mathcal{N}, \mathcal{L})$, where $\mathcal{N}$ is the set of nodes and $\mathcal{L}$ is the set of arcs (conventionally "links," e.g., pipes and valves). Temporal evolution of the network is represented by a set $\mathcal{K}$, denoting the set of all time steps considered. In summary, the following sets are commonly used when defining a WaterModels problem formulation:
| Notation | WaterModels Translation | Description |
|---|---|---|
| $\mathcal{N}$ | wm.ref[:nw][n][:node] | nodes (to which nodal-type components are attached) |
| $\mathcal{K}$ | nw_ids(wm) | time indices (multinetwork indices labeled by n) |
| $\mathcal{D}$ | wm.ref[:nw][n][:demand] | demands |
| $\mathcal{R}$ | wm.ref[:nw][n][:reservoir] | reservoirs |
| $\mathcal{T}$ | wm.ref[:nw][n][:tank] | tanks |
| $\mathcal{A} \subset \mathcal{L}$ | wm.ref[:nw][n][:pipe] | pipes |
| $\mathcal{P} \subset \mathcal{L}$ | wm.ref[:nw][n][:pump] | pumps |
| $\mathcal{W} \subset \mathcal{L}$ | wm.ref[:nw][n][:regulator] | regulators |
| $\mathcal{S} \subset \mathcal{L}$ | wm.ref[:nw][n][:short_pipe] | short pipes |
| $\mathcal{V} \subset \mathcal{L}$ | wm.ref[:nw][n][:valve] | valves |