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Connection Modeling

Connections model power flow paths between elements with optional limits.

Model Formulation

Decision Variables

For each time step \(t\):

  • \(P_c(t)\): Power flow on connection (kW)

Parameters

  • \(P_{\min}\): Minimum power (kW) - from min_power config (can be negative for bidirectional)
  • \(P_{\max}\): Maximum power (kW) - from max_power config
  • Source entity: Where power flows from
  • Target entity: Where power flows to

Constraints

Power Limits

\[ P_{\min} \leq P_c(t) \leq P_{\max} \quad \forall t \]

Direction Convention

  • Positive flow: Source → Target (forward direction)
  • Negative flow: Target → Source (reverse direction, if \(P_{\min} < 0\))

Power Balance Integration

Connection power participates in node balance:

  • At source node: Connection is outflow
  • At target node: Connection is inflow

Physical Interpretation

Unidirectional (\(P_{\min} = 0\)):

  • Solar → Node (generation only)
  • Node → Load (consumption only)

Bidirectional (\(P_{\min} < 0\)):

  • Grid ↔ Node (import/export)
  • Battery ↔ Node (charge/discharge)
  • Inverter between AC/DC nets

Power limits:

  • Wire capacity
  • Inverter rating
  • Circuit breaker limits

Configuration Impact

Parameter Impact
\(P_{\max}\) only Unidirectional with limit
\(P_{\min} < 0, P_{\max} > 0\) Bidirectional (for example, inverter link)
No limits Unlimited (for example, direct grid tie)

Inverter modeling: Connection with ±max_power between DC and AC nodes.