Flows

A flow represents energy transfer on a bus. Each flow \(f\) has a non-negative rate variable \(P_{f,t}\) bounded by an optional nominal capacity \(\bar{\mathrm{P}}_f\).

Bounds

When Flow.size is set, the rate is bounded by relative minimum and maximum profiles:

\[ \bar{\mathrm{P}}_f \cdot \underline{\mathrm{p}}_{f,t} \leq P_{f,t} \leq \bar{\mathrm{P}}_f \cdot \bar{\mathrm{p}}_{f,t} \quad \forall \, f, t \]

By default \(\underline{\mathrm{p}}_{f,t} = 0\) and \(\bar{\mathrm{p}}_{f,t} = 1\), so the bounds simplify to \(0 \leq P_{f,t} \leq \bar{\mathrm{P}}_f\). With no capacity (\(\bar{\mathrm{P}}_f = \infty\)) the flow is just \(P_{f,t} \geq 0\).

Fixed Profile

When Flow.fixed_relative_profile (\(\pi_{f,t}\)) is set, the rate is pinned to a profile scaled by the capacity:

\[ P_{f,t} = \bar{\mathrm{P}}_f \cdot \pi_{f,t} \quad \forall \, f, t \]

Implemented by setting both bounds equal to the profile value.

Effect Contributions

Each flow contributes to tracked effects (cost, emissions, …). Per-timestep:

\[ \mathrm{c}_{f,k,t} \cdot P_{f,t} \cdot \Delta t_t \]

\(\mathrm{c}_{f,k,t}\) is the per-flow-hour coefficient (Flow.effects_per_flow_hour). Units cancel: e.g. €/MWh × MW × h = €. Contributions feed into the effect tracking equations.

See also

• Sizing — when Flow.size is a Sizing object instead of a fixed value.
• Status — when Flow.status is set, the flow becomes semi-continuous \(\{0\} \cup [\underline{\mathrm{P}}, \bar{\mathrm{P}}]\).
• Carrier Balance — Multi-Node — when Flow.node targets a specific node.

Parameters

Symbol	Description	API
\(P_{f,t}\)	Flow rate variable	flow--rate[flow, time]
\(\bar{\mathrm{P}}_f\)	Nominal capacity	Flow.size
\(\underline{\mathrm{p}}_{f,t}\)	Relative lower bound	Flow.relative_minimum
\(\bar{\mathrm{p}}_{f,t}\)	Relative upper bound	Flow.relative_maximum
\(\pi_{f,t}\)	Fixed relative profile	Flow.fixed_relative_profile
\(\mathrm{c}_{f,k,t}\)	Effect coefficient per flow-hour	Flow.effects_per_flow_hour
\(\Delta t_t\)	Timestep duration (h)	dt

See Notation for the full symbol table and Indexing Convention for how indices broadcast.