Bus

A bus owns the terminal voltage components \(V_r\) and \(V_i\) and the current-balance residuals. Each connected device adds its current injection after the bus resets the residuals to zero.

Notes

Current entering the bus has positive sign, and current exiting the bus has negative sign.

Block Diagram

Figure 1: Bus-variable diagram. This should be updated to represent current balance instead of power balance.

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(V_\mathrm{base}\)	[kV]	kv	Nominal bus voltage		Unused

Parameter Validation

None.

Model Derived Parameters

None.

Model Ports

None.

Model Variables

Internal Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(V_r\)	[p.u.]	Bus voltage, real component
\(V_i\)	[p.u.]	Bus voltage, imaginary component

External Variables

Differential

None.

Algebraic

None.

Model Equations

Internal Equations

Differential

None.

Algebraic

Let \(\mathcal{D}\) denote the set of components connected to the bus, and let \(G_f\), \(B_f\) be the conductance and susceptance of a fault applied to the Bus, respectively, with \(G_f + jB_f = 1/(R_f + jX_f)\), both zero when no fault is applied.

\[\begin{split}\begin{aligned} 0 &= -(G_f V_r - B_f V_i) + \sum_{d \in \mathcal{D}} I_{r,d} \\ 0 &= -(B_f V_r + G_f V_i) + \sum_{d \in \mathcal{D}} I_{i,d} \end{aligned}\end{split}\]

External Equations

None.

Initialization

Internal Initialization

Bus initializes its algebraic voltage variables as

\[\begin{split}\begin{aligned} V_r &\leftarrow \text{bus voltage, real component} \\ V_i &\leftarrow \text{bus voltage, imaginary component} \end{aligned}\end{split}\]

The derivative vector entries initialize to zero.

Monitors

Monitor	Units	Description	Note
Vr	[p.u.]	Bus voltage, real component
Vi	[p.u.]	Bus voltage, imaginary component
Vm	[p.u.]	Bus voltage magnitude	\(\sqrt{V_r^2+V_i^2}\)
Va	[rad]	Bus voltage angle	\(\operatorname{atan2}(V_i,V_r)\)