LoadZIP

Static ZIP load model with constant impedance, constant current, and constant power fractions. LoadZIP owns terminal current states and adds their current contribution to the connected bus residual.

Model Parameters

Symbol	Units	JSON	Description	Typical Value
\(P_\text{nom}\)	[p.u.]	Pnom	Nominal consumed real power	0.0
\(Q_\text{nom}\)	[p.u.]	Qnom	Nominal consumed reactive power	0.0
\(V_\text{nom}\)	[p.u.]	Vnom	Nominal voltage magnitude	1.0
\(\alpha_I\)	[-]	alphaI	Constant current load fraction	0.0
\(\alpha_P\)	[-]	alphaP	Constant power load fraction	0.0

Parameter Validation

None.

Model Derived Parameters

\[\begin{split}\begin{aligned} G &= \frac{P_\text{nom}}{V_\text{nom}^2} \\ B &= \frac{Q_\text{nom}}{V_\text{nom}^2} \\ \alpha_Z &= 1 - \alpha_I - \alpha_P \end{aligned}\end{split}\]

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

Let \(V = \sqrt{V_r^2 + V_i^2}\).

Differential Equations

None.

Algebraic Equations

\[\begin{split}\begin{aligned} 0 &= I_r + (G V_r + B V_i) \left[ \alpha_Z + \alpha_I \frac{V_\text{nom}}{V} + \alpha_P \frac{V_\text{nom}^2}{V^2} \right] \\ 0 &= I_i + (G V_i - B V_r) \left[ \alpha_Z + \alpha_I \frac{V_\text{nom}}{V} + \alpha_P \frac{V_\text{nom}^2}{V^2} \right] \end{aligned}\end{split}\]

Initialization

Initialization solves the algebraic current states from the connected bus voltage. Let \(V_{m0} = \sqrt{V_{r0}^2 + V_{i0}^2}\).

\[\begin{split}\begin{aligned} I_r &= -(G V_{r0} + B V_{i0}) \left[ \alpha_Z + \alpha_I \frac{V_\text{nom}}{V_{m0}} + \alpha_P \frac{V_\text{nom}^2}{V_{m0}^2} \right] \\ I_i &= -(G V_{i0} - B V_{r0}) \left[ \alpha_Z + \alpha_I \frac{V_\text{nom}}{V_{m0}} + \alpha_P \frac{V_\text{nom}^2}{V_{m0}^2} \right] \end{aligned}\end{split}\]

The derivative vector entries initialize to zero.

Monitors

Name	Units	Description	Note
ir	[p.u.]	Terminal current, real component	Added to connected bus residual
ii	[p.u.]	Terminal current, imaginary component	Added to connected bus residual
im	[p.u.]	Terminal current magnitude
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