Bus

Source: GridKit/Model/EMT/Bus/README.md

Bus Model

Bus represents a three-phase bus in instantaneous abc coordinates. The bus voltages are differential variables, and the model equations enforce three-phase current balance at the bus.

Model Parameters

None.

Model Derived Parameters

None.

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(\mathbf{v}\)	[V]	Bus voltage vector	\(\mathbf{v} = [v_a, v_b, v_c]^T \in \mathbb{R}^3\)

Algebraic

None.

External Variables

Differential

None.

Algebraic

None.

Model Equations

Differential Equations

An explicit representation for \(\dot{\mathbf{v}}\) is not used because the effective shunt admittances depend on connected components and are not known at the bus level. The implicit DAE solver operates directly on the accumulated KCL residual:

\[\begin{aligned} 0 &= \sum_{e \in \mathcal{E}} \mathbf{i}^\text{inj}_e \end{aligned}\]

where \(\mathbf{i}^\text{inj}_e\) is the vector of phase-current injections of connected component \(e\) into the bus, which are a function of the bus voltage and bus voltage derivative.

Algebraic Equations

None.

Initialization

For a balanced three-phase initialization derived from the phasor voltage \(V = |V| \angle \phi\) and nominal angular frequency \(\omega_0 = 2 \pi f_0\),

\[\begin{split}\mathbf{v}(0) = \sqrt{2}\,|V| \begin{bmatrix} \cos(\phi) \\ \cos(\phi - \tfrac{2\pi}{3}) \\ \cos(\phi + \tfrac{2\pi}{3}) \end{bmatrix}\end{split}\]

and

\[\begin{split}\dot{\mathbf{v}}(0) = -\sqrt{2}\,|V|\,\omega_0 \begin{bmatrix} \sin(\phi) \\ \sin(\phi - \tfrac{2\pi}{3}) \\ \sin(\phi + \tfrac{2\pi}{3}) \end{bmatrix}\end{split}\]

Model Outputs

Phase voltages \(v_a\), \(v_b\), and \(v_c\) are monitorable model outputs.

Phase-voltage derivatives \(\dot{v}_a\), \(\dot{v}_b\), and \(\dot{v}_c\) are also available as monitorable outputs.