Bus¶

A Bus is where flows meet and must balance — inputs equal outputs at every timestep.

Carriers¶

Buses can optionally be assigned a carrier — a type of energy or material (e.g., electricity, heat, gas). Carriers enable:

Automatic coloring in plots based on energy type
Unit tracking for better result visualization
Semantic grouping of buses by type

# Assign a carrier by name (uses CONFIG.Carriers defaults)
heat_bus = fx.Bus('HeatNetwork', carrier='heat')
elec_bus = fx.Bus('Grid', carrier='electricity')

# Or register custom carriers on the FlowSystem
biogas = fx.Carrier('biogas', color='#228B22', unit='kW', description='Biogas fuel')
flow_system.add_carrier(biogas)
gas_bus = fx.Bus('BiogasNetwork', carrier='biogas')

See Color Management for more on how carriers affect visualization.

Basic: Balance Equation¶

\[ \sum_{in} p(t) = \sum_{out} p(t) \]

heat_bus = fx.Bus(label='heat')
# All flows connected to this bus must balance

If balance can't be achieved → model is infeasible.

With Imbalance Penalty¶

Allow imbalance for debugging or soft constraints:

\[ \sum_{in} p(t) + \phi_{in}(t) = \sum_{out} p(t) + \phi_{out}(t) \]

The slack variables \(\phi\) are penalized: \((\phi_{in} + \phi_{out}) \cdot \Delta t \cdot c_\phi\)

heat_bus = fx.Bus(
    label='heat',
    imbalance_penalty_per_flow_hour=1e5  # High penalty for imbalance
)

Debugging

If you see a virtual_demand or virtual_supply and its non zero in results → your system couldn't meet demand. Check capacities and connections.

Reference¶

Symbol	Type	Description
\(p(t)\)	\(\mathbb{R}_{\geq 0}\)	Flow rate of connected flows
\(\phi_{in}(t)\)	\(\mathbb{R}_{\geq 0}\)	Slack: virtual supply (covers shortages)
\(\phi_{out}(t)\)	\(\mathbb{R}_{\geq 0}\)	Slack: virtual demand (absorbs surplus)
\(c_\phi\)	\(\mathbb{R}_{\geq 0}\)	Penalty factor (`imbalance_penalty_per_flow_hour`)
\(\Delta t\)	\(\mathbb{R}_{> 0}\)	Timestep duration (hours)

Classes: Bus, BusModel