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A Bus is a simple nodal balance between its incoming and outgoing flow rates.

$$ \label{eq:bus_balance} \sum_{f_\text{in} \in \mathcal{F}_\text{in}} p_{f_\text{in}}(\text{t}_i) = \sum_{f_\text{out} \in \mathcal{F}_\text{out}} p_{f_\text{out}}(\text{t}_i) $$

Optionally, a Bus can have a excess_penalty_per_flow_hour parameter, which allows to penaltize the balance for missing or excess flow-rates. This is usefull as it handles a possible ifeasiblity gently.

This changes the balance to

$$ \label{eq:bus_balance-excess} \sum_{f_\text{in} \in \mathcal{F}_\text{in}} p_{f_ \text{in}}(\text{t}_i) + \phi_\text{in}(\text{t}_i) = \sum_{f_\text{out} \in \mathcal{F}_\text{out}} p_{f_\text{out}}(\text{t}_i) + \phi_\text{out}(\text{t}_i) $$

The penalty term is defined as

$$ \label{eq:bus_penalty} s_{b \rightarrow \Phi}(\text{t}_i) = \text a_{b \rightarrow \Phi}(\text{t}_i) \cdot \Delta \text{t}_i \cdot [ \phi_\text{in}(\text{t}_i) + \phi_\text{out}(\text{t}_i) ] $$

With:

  • $\mathcal{F}\text{in}$ and $\mathcal{F}\text{out}$ being the set of all incoming and outgoing flows
  • $p_{f_\text{in}}(\text{t}i)$ and $p{f_\text{out}}(\text{t}i)$ being the flow-rate at time $\text{t}i$ for flow $f\text{in}$ and $f\text{out}$, respectively
  • $\phi_\text{in}(\text{t}i)$ and $\phi\text{out}(\text{t}_i)$ being the missing or excess flow-rate at time $\text{t}_i$, respectively
  • $\text{t}_i$ being the time step
  • $s_{b \rightarrow \Phi}(\text{t}_i)$ being the penalty term
  • $\text a_{b \rightarrow \Phi}(\text{t}_i)$ being the penalty coefficient (excess_penalty_per_flow_hour)

Implementation

Python Class: [Bus][flixopt.elements.Bus]

See the API documentation for implementation details and usage examples.

See Also