Switch

Switch represents an ideal \(N\)-phase EMT switch between two buses. Series current \(\mathbf{i}_{12}\) is directed from terminal 1 to terminal 2. The required Boolean input open operates all phases: true is open and false is closed. The switch contains no energy storage; switching transients arise from the connected EMT network.

Block Diagram

Figure 1: Switch model

Model Parameters

Symbol	Units	JSON	Description	Note
\(N\)	[-]	N	Number of phases	Required, positive integer

Parameter Validation

\[N \in \mathbb{Z}_{>0}\]

Model Derived Parameters

None.

Model Ports

Symbol	Port	Type	Units	Description	Note
\(\mathbf{v}_1\)	v1	Input	[V]	Terminal 1 bus voltage	\(\mathbf{v}_1 \in \mathbb{R}^N\)
\(\mathbf{v}_2\)	v2	Input	[V]	Terminal 2 bus voltage	\(\mathbf{v}_2 \in \mathbb{R}^N\)
\(\mathrm{open}\)	open	Input	[-]	Ganged switch command	Required Boolean; true open, false closed
\(\mathbf{i}_1\)	i1	Output	[A]	Current injection at terminal 1	\(\mathbf{i}_1 \in \mathbb{R}^N\)
\(\mathbf{i}_2\)	i2	Output	[A]	Current injection at terminal 2	\(\mathbf{i}_2 \in \mathbb{R}^N\)

Submodels

None.

Submodel Validation

None.

Submodel Wiring

None.

Model Variables

Internal Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(\mathbf{i}_{12}\)	[A]	Series current from terminal 1 to terminal 2	\(\mathbf{i}_{12} \in \mathbb{R}^N\)

External Variables

Differential

Symbol	Units	Description	Note
\(\mathbf{v}_1\)	[V]	Terminal 1 voltage owned by EMT bus	\(\mathbf{v}_1 \in \mathbb{R}^N\)
\(\mathbf{v}_2\)	[V]	Terminal 2 voltage owned by EMT bus	\(\mathbf{v}_2 \in \mathbb{R}^N\)

Algebraic

None.

Model Equations

Internal Equations

Differential

None.

Algebraic

\[\begin{split}\begin{cases} \mathbf{i}_{12} = \mathbf{0}, & \text{open}\\ \mathbf{v}_2-\mathbf{v}_1 = \mathbf{0}, & \text{closed} \end{cases}\end{split}\]

External Equations

\[\begin{split}\begin{aligned} \mathbf{i}_1 &\leftarrow -\mathbf{i}_{12} \\ \mathbf{i}_2 &\leftarrow \mathbf{i}_{12} \end{aligned}\end{split}\]

Initialization

The open command is applied at \(t_0\) before enforcing the algebraic equations. The switch has no additional model-specific initialization.

Monitors

Monitor	Units	Description	Note
open	[-]	Switch command	Boolean; true open, false closed
i12	[A]	Series current from terminal 1 to terminal 2	\(\mathbf{i}_{12} \in \mathbb{R}^N\)