Load

Source: GridKit/Model/PhasorDynamics/Load/README.md

Load Model

Load modeling is one of the more complex aspects of power system dynamics. The simplest model, which is used for this challenge problem, is to model the load as a complex shunt impedance \(R + jX\).

Model Parameters

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

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 Variables

Internal Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(I_r\)	[p.u.]	Terminal current, real component	Read by bus
\(I_i\)	[p.u.]	Terminal current, imaginary component	Read by bus

External Variables

Differential

None.

Algebraic

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

Model Equations

Differential Equations

None.

Algebraic Equations

\[\begin{split}\begin{aligned} 0 &= I_{r} +G V_{r} - B V_{i} \\ 0 &= I_{i} +B V_{r} + G V_{i} \end{aligned}\end{split}\]