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Node Modeling

Virtual balance nodes that enforce power conservation (Kirchhoff's law).

Model Formulation

Decision Variables

None - nodes only enforce constraints.

Constraints

Power Balance

At each node and time step:

\[ \sum_{c \in \mathcal{C}_{\text{in}}} P_c(t) = \sum_{c \in \mathcal{C}_{\text{out}}} P_c(t) \]

Where:

  • \(\mathcal{C}_{\text{in}}\): Inbound connections to node
  • \(\mathcal{C}_{\text{out}}\): Outbound connections from node
  • \(P_c(t)\): Power on connection \(c\)

Physical Interpretation

Virtual node: Not a physical device, represents electrical junction.

Kirchhoff's law: Current in equals current out (applied to power).

No storage: Energy cannot accumulate at a node (unlike battery).

Use Cases

Single net (simple):

graph LR
    Grid-->Net
    Solar-->Net
    Battery<-->Net
    Net-->Load

Central hub where all elements connect.

Dual node (AC/DC):

graph LR
    Solar-->DC[DC Node]
    Battery<-->DC
    DC<-->|Inverter|AC[AC Node]
    Grid<-->AC
    AC-->Load

Separate buses with inverter connection between them.

Configuration Impact

Topology Complexity Use When
Single node Simple Standard residential
Multiple nodes Complex Hybrid inverters, multi-building

Well-formed network: All elements must connect to at least one node, directly or indirectly.