LoadZ

Static constant-impedance load model. LoadZ owns terminal current states and adds their current contribution to the connected bus residual.

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(R\)	[p.u.]	R	Load resistance
\(X\)	[p.u.]	X	Load reactance

Parameter Validation

None.

Model Derived Parameters

\[\begin{split}\begin{aligned} G &= \dfrac{R}{R^2 + X^2} \\ B &= -\dfrac{X}{R^2 + X^2} \end{aligned}\end{split}\]

Model Ports

Name	Port	Init	Description
bus	Bus	Known	Connected bus that owns terminal voltage variables and current-balance residuals

Model Variables

Internal Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(I_r\)	[p.u.]	Terminal current, real component	Added to connected bus residual
\(I_i\)	[p.u.]	Terminal current, imaginary component	Added to connected bus residual

External Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(V_r\)	[p.u.]	Terminal voltage, real component	Owned by connected bus
\(V_i\)	[p.u.]	Terminal voltage, imaginary component	Owned by connected bus

Model Equations

Internal Equations

Differential

None.

Algebraic

\[\begin{split}\begin{aligned} 0 &= I_r + G V_r - B V_i \\ 0 &= I_i + B V_r + G V_i \end{aligned}\end{split}\]

External Equations

\[\begin{split}\begin{aligned} I_r^{\mathrm{bus}} &\leftarrow I_r^{\mathrm{bus}} + I_r \\ I_i^{\mathrm{bus}} &\leftarrow I_i^{\mathrm{bus}} + I_i \end{aligned}\end{split}\]

Initialization

The initial bus voltage determines the terminal currents:

\[\begin{split}\begin{aligned} I_r &\leftarrow -G V_r + B V_i \\ I_i &\leftarrow -B V_r - G V_i \end{aligned}\end{split}\]

The derivative vector entries initialize to zero.

Monitors

Monitor	Units	Description	Note
p	[p.u.]	Active power at the connected bus terminal	Positive for injection into the connected bus
q	[p.u.]	Reactive power at the connected bus terminal	Positive for injection into the connected bus