Average-Value Rectifier (Three-Phase)

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

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Libraries:
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_c are the respective AC phase voltages.

• v_ref is the DC offset on the AC side. In a balanced AC power system with no DC bias, v_DC is 0 V.

• V_RMS is the RMS AC line-line voltage.

• v_DC is the voltage difference between the positive and negative terminals of the rectifier.

• $$3\sqrt{2}/\pi$$ is the v_DC /V_RMS ratio for a full-wave, six-pulse rectifier.

• v_p, v_n are the voltages at the positive and negative terminals of the rectifier.

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_Rated is the rated AC voltage that you specify on the block mask.

• P_fixed is the fixed power loss that you specify on the block mask.

• R_fixed is the fixed per-phase series resistance in an equivalent wye-connected load.

• i_p, i_n are the currents flowing into the positive and negative terminals of the rectifier.

• P_DC is the power output on the DC side. P_DC has a minimum limit of 0 W.

• R_AC is the per-phase series resistance in an equivalent wye-connected load.

• i_a, i_b, i_c are the respective AC phase currents flowing into the rectifier.

Examples

Marine Full Electric Propulsion Power System

A representative marine half-ship electrical power system with base load, hotel load, bow thrusters and electric propulsion.

• Open Model

Ports

Conserving

~ — Three-phase port

electrical

Expandable three-phase port

Dependencies

To enable this port, set Electrical connection to Composite three-phase ports.

a — a-phase

electrical

Electrical conserving port associated with a-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

b — b-phase

electrical

Electrical conserving port associated with b-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

c — c-phase

electrical

Electrical conserving port associated with c-phase.

Dependencies

To enable this port, set Electrical connection to Expanded three-phase ports.

+ — Positive terminal

electrical

Electrical conserving port associated with the positive terminal.

- — Negative terminal

electrical

Electrical conserving port associated with the negative terminal.

Parameters

Electrical connection — Electrical connection

Composite three-phase ports (default) | Expanded three-phase ports

Whether to have composite or expanded three-phase ports.

AC frequency — AC frequency

Variable (default) | Constant

Whether to have a variable or constant AC frequency:

• Variable — If the frequency at the AC side varies, this option only works in time simulation mode.

• Constant — If the frequency at the AC side is constant, this option works in both time and frequency-and-time simulation modes.

Rated AC voltage — Rated AC voltage

4160V (default)

Rated voltage of the AC system.

Rated electrical frequency — Rated electrical frequency

60 Hz | scalar

Rated electrical frequency. The value of this parameter must be equal to the value of the rated electrical frequencies of other sinusoidal sources in your model, if present.

Dependencies

To enable this parameter, set AC frequency to Constant.

Fixed power loss — Fixed power loss

1e3W (default)

Minimum power drawn on the AC side at rated AC voltage. When the instantaneous AC voltage is equal to the value you specify for the Rated AC voltage, the AC power demand equals the value you specify for the Fixed power loss plus DC power demand.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2014b

R2021b: Electrical connection ports update

From R2021b forward, to switch between composite and expanded ports, set the Electrical connection parameter to either Composite three-phase ports or Expanded three-phase ports.

As a result of these changes, inside a model saved in an earlier release, review the Electrical connection parameter of this block.