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
\(R\)	[p.u.]	R	Load resistance
\(X\)	[p.u.]	X	Load reactance

Parameter Validation

None.

Model Derived Parameters

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

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

Wiring

Port	Type	Description
bus	Bus	Connected bus that owns terminal voltage variables and current-balance residuals

Model Equations

Differential Equations

None.

Algebraic Equations

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

Initialization

Initialization solves the algebraic current states from the connected bus voltage. Let \(V_{r0}\) and \(V_{i0}\) be the initialized bus voltage components.

\[\begin{split}\begin{aligned} I_r &= -(G V_{r0} - B V_{i0}) \\ I_i &= -(B V_{r0} + G V_{i0}) \end{aligned}\end{split}\]

The derivative vector entries initialize to zero.

Monitors

Name	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