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Power limit segment

The PowerLimitSegment enforces directional capacity limits on connection flow. It can also apply a time-slice constraint that prevents simultaneous full-capacity flow in both directions.

Model formulation

Parameters

Parameter Description Default
\(P^{\max}_{s \rightarrow t}\) Maximum power from source to target (kW) Unlimited
\(P^{\max}_{t \rightarrow s}\) Maximum power from target to source (kW) Unlimited
fixed Enforce equality instead of inequality False

Parameters can be scalars or per-period arrays. Scalar values are broadcast across all periods.

Decision variables

Variable Domain Description
\(P_{s \rightarrow t}\) \(\mathbb{R}_{\geq 0}\) Power flow from source to target
\(P_{t \rightarrow s}\) \(\mathbb{R}_{\geq 0}\) Power flow from target to source

Constraints

Directional limits

When power limits are configured:

\[ 0 \leq P_{s \rightarrow t}(t) \leq P_{s \rightarrow t}^{\max}(t) \quad \forall t \]
\[ 0 \leq P_{t \rightarrow s}(t) \leq P_{t \rightarrow s}^{\max}(t) \quad \forall t \]

If fixed=True, these become equality constraints.

Shadow prices: The segments.power_limit.source_target and segments.power_limit.target_source outputs provide the marginal value of relaxing these constraints.

Time-slice coupling

When both power limits are set, the segment adds a time-slice constraint:

\[ \frac{P_{s \rightarrow t}(t)}{P_{s \rightarrow t}^{\max}(t)} + \frac{P_{t \rightarrow s}(t)}{P_{t \rightarrow s}^{\max}(t)} \leq 1 \quad \forall t \]

This models physical limitations of bidirectional devices (for example, inverters that cannot simultaneously charge and discharge at full rate).

Shadow price: The segments.power_limit.time_slice output reports the marginal value of the coupling constraint.

Physical interpretation

Directional limits model hard capacity constraints such as cable ratings or inverter limits. Time-slice coupling models shared hardware constraints that prohibit full flow in both directions at once.

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