# Average-Value Rectifier (Three-Phase)

Average-value three-phase AC voltage to DC voltage converter with fixed power loss

**Library:**Simscape / Electrical / Semiconductors & Converters / Converters

## Description

The Average-Value Rectifier (Three-Phase) block models an average-value, full-wave, six-pulse rectifier. It converts instantaneous three-phase AC voltages to DC voltage and DC power demand to three-phase AC power demand. The corresponding AC power demand is equal to the sum of the fixed power loss and the DC power demand.

You can use the Average-Value Rectifier (Three-Phase) block only as a six-pulse rectifier. You cannot combine two Average-Value Rectifier blocks to represent a twelve-pulse rectifier.

The figure shows the equivalent circuit for the rectifier as a full-wave, six-pulse rectifier. The Average-Value Rectifier (Three-Phase) block does not yield the harmonics that are typically associated with the detailed representation, however, because it performs an average-value power conversion.

This block can work in both time and frequency-and-time simulation modes. If you set
the **AC frequency** parameter to `Variable`

,
this block works only in time simulation mode. If you select
`Constant`

, this block works in both time and
frequency-time simulation modes. For more information, see Frequency and Time Simulation Mode.

### Electrical Defining Equations

The voltages are defined by:

$${v}_{ref}=\frac{{v}_{a}+{v}_{b}+{v}_{c}}{3},$$

$${V}_{RMS}=\sqrt{\frac{{\left({v}_{a}-{v}_{b}\right)}^{2}+{\left({v}_{b}-{v}_{c}\right)}^{2}+{\left({v}_{c}-{v}_{a}\right)}^{2}}{3}},$$

$${v}_{DC}=3\frac{\sqrt{2}}{\pi}{V}_{RMS},$$

$${v}_{p}={v}_{ref}+\frac{{v}_{DC}}{2},$$

and

$${v}_{n}={v}_{ref}-\frac{{v}_{DC}}{2},$$

where:

*v*,_{a}*v*,_{b}*v*are the respective AC phase voltages._{c}*v*is the DC offset on the AC side. In a balanced AC power system with no DC bias,_{ref}*v*is_{DC}`0`

V.*V*is the RMS AC line-line voltage._{RMS}*v*_{DC}is the voltage difference between the positive and negative terminals of the rectifier.$$3\sqrt{2}/\pi $$ is the

*v*/_{DC }*V*ratio for a full-wave, six-pulse rectifier._{RMS}*v*,_{p}*v*are the voltages at the positive and negative terminals of the rectifier._{n}

The resistance, power, and currents are defined by

$${R}_{fixed}=\frac{{V}_{Rated}^{2}}{{P}_{fixed}},$$

$${P}_{DC}=-{v}_{p}{i}_{p}-{v}_{n}{i}_{n},$$

$${R}_{AC}=\frac{{V}_{RMS}^{2}}{{P}_{DC}+\frac{{V}_{RMS}^{2}}{{R}_{fixed}}},$$

and

$\left[\begin{array}{ccc}{i}_{a}& {i}_{b}& {i}_{c}\end{array}\right]=\frac{\left[\begin{array}{ccc}{v}_{a}& {v}_{b}& {v}_{c}\end{array}\right]-{v}_{ref}}{{R}_{AC}},$

where:

*V*is the rated AC voltage that you specify on the block mask._{Rated}*P*is the fixed power loss that you specify on the block mask._{fixed}*R*is the fixed per-phase series resistance in an equivalent wye-connected load._{fixed}*i*,_{p}*i*are the currents flowing into the positive and negative terminals of the rectifier._{n}*P*is the power output on the DC side._{DC}*P*has a minimum limit of_{DC}`0`

W.*R*is the per-phase series resistance in an equivalent wye-connected load._{AC}*i*,_{a}*i*,_{b}*i*are the respective AC phase currents flowing into the rectifier._{c}

## Ports

### Conserving

## Parameters

## Model Examples

## Extended Capabilities

## Version History

**Introduced in R2014b**