Constraints
We define the following methods to provide a compositional approach toward defining linking constraints used in coupled power-water models. Such methods should always be defined over AbstractPowerWaterModel.
PowerWaterModels.constraint_fixed_load — MethodConstraint for modeling a fixed load (i.e., not connected to a pump). Since the base power formulation uses a variable, $0 \leq z_{it} \leq 1$, to model the proportion of maximum load served at load $i \in \mathcal{L}$, time index $t \in \mathcal{T}$, a value of one indicates the full load being served, as expected for non-pump loads. That is, these constraints are
\[z_{it} = 1, \, \forall i \in \mathcal{L}^{\prime}, \, \forall t \in \mathcal{T},\]
where $\mathcal{L}^{\prime}$ is the set of loads not connected to a pump.
PowerWaterModels.constraint_pump_load — MethodConstraint for modeling a variable load (i.e., connected to a pump). Since the base power formulation uses a variable, $0 \leq z_{it} \leq 1$, to model the proportion of maximum load served at load $i \in \mathcal{L}$, time index $t \in \mathcal{T}$, a value of one indicates the maximum load is being served (denoted as $pd$). Any other value will represent some proportion of this maximum. Linking pump power to load is thus modeled via
\[P_{jt} = z_{it} \sum_{c \in \mathcal{C}} pd_{ict}, \, \forall (i, j) \in \mathcal{D}, \, \forall t \in \mathcal{T},\]
where $\mathcal{D}$ is the set of interdependencies, linking loads, $i \in \mathcal{L}$, to pumps, $j \in \mathcal{P}$. Here, $P_{j}$ is a variable that represents pump power and $\mathcal{C}$ is the set of conductors, i.e., power is bounded by $\sum_{c \in \mathcal{C}} pd_{ict}$.