Bus.md

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.

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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.

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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
)

!!! tip "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.

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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][flixopt.elements.Bus], [BusModel][flixopt.elements.BusModel]