Three-phase variable, lagging load wired in wye configuration

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• Simscape / Electrical / Passive / RLC Assemblies

## 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:

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

### Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see System Scaling by Nominal Values.

## Ports

### Input

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Physical signal input port associated with the real power.

Physical signal input port associated with the reactive power.

### Conserving

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Electrical conserving port associated with the neutral phase.

## Parameters

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Whether to model composite or expanded three-phase ports.

Composite three-phase ports represent three individual electrical conserving ports with a single block port. You can use composite three-phase ports to build models that correspond to single-line diagrams of three-phase electrical systems.

Expanded three-phase ports represent the individual phases of a three-phase system using three separate electrical conserving ports.

### Main

RMS, rated line-line voltage for the resistance equation.

Nominal AC electrical frequency for the inductance equation.

Minimum real power that the three-phase load dissipates when supplied at the rated voltage. The value must be greater than 0.

Minimum reactive power that the three-phase load dissipates when supplied at the rated voltage. The value must be greater than 0.

### Parasitics

Conductance that the block adds, in parallel, to the series RL.

## Version History

Introduced in R2014b