# Documentation

Three-phase variable, lagging load wired in wye configuration

## Library

Passive Devices / Time Varying

## Description

The Wye-Connected Variable Load (lagging) block models a three-phase variable, lagging load wired in a wye configuration. Each limb of the load contains a resistor (R) and an inductor (L) connected in series. The block calculates the resistance and inductance required to draw the real and reactive powers of the physical signal inputs P and Q at the rated voltage and rated frequency that you specify. Therefore, the block can represent a real and lagging reactive load.

To ensure that the resistance and inductance are always greater than zero, you specify the minimum real power and the reactive power that the load consumes. The minimum real power and the reactive power must be greater than zero.

## Electrical Defining Equations

The per-phase series resistance and inductance are defined by

`$R=\frac{P{V}_{Rated}^{2}}{{P}^{2}+{Q}^{2}}$`

and

`$L=\frac{Q{V}_{Rated}^{2}}{2\pi {F}_{Rated}\left({P}^{2}+{Q}^{2}\right)},$`

where:

• R is the per-phase series resistance.

• L is the per-phase series inductance.

• VRated is the RMS, rated line-line voltage.

• FRated is the nominal AC electrical frequency.

• P is the three-phase real power required.

• Q is the three-phase lagging reactive power required.

The inductance is defined as the ratio of the magnetic flux, φ, to the steady-state current:

`$L\left(i\right)=\frac{\varphi \left(i\right)}{i}.$`

Therefore the current-voltage relationship for the inductor is:

`$v=\frac{dL}{dt}i+L\frac{di}{dt}.$`

## Parameters

### Main Tab

Rated voltage

RMS, rated line-line voltage for the resistance equation. The default value is `24e3` `V`.

Rated electrical frequency

Nominal AC electrical frequency for the inductance equation. The default value is `60` `Hz`.

Minimum real power

Minimum real power that the three-phase load dissipates when supplied at the rated voltage. The value must be greater than 0. The default value is `1e3` `W`.

Minimum reactive power

Minimum reactive power that the three-phase load dissipates when supplied at the rated voltage. The value must be greater than 0. The default value is `1e3` `V*A`.

### Parasitics

Parasitic parallel conductance

Conductance that the block adds, in parallel, to the series RL. The default value is `1e-6` `1/Ohm`.

### Variables Tab

Use the Variables tab to set the priority and initial target values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables (Simscape) .

Unlike block parameters, variables do not have conditional visibility. The Variables tab lists all the existing block variables. If a variable is not used in the set of equations corresponding to the selected block configuration, the values specified for this variable are ignored.

## Ports

The block has the following ports:

`P`

Physical signal input port for real power

`Q`

Physical signal input port for reactive power

`~`

Expandable three-phase port

`n`

Electrical conserving port associated with the neutral phase.