Converter (Three-Phase)

Controller-driven bidirectional AC/DC three-arm converter

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Libraries:
Simscape / Electrical / Semiconductors & Converters / Converters

Description

The Converter (Three-Phase) block models a six-pulse three-phase controlled converter that consists of three bridge arms. Each bridge arm comprises with two switching devices. The converter circuit connects a three-phase AC network to a DC network.

You can choose from two fidelity levels for the converter model. The equivalent model option does not model the individual switching devices but returns equivalent results. If you need detailed results for the switching device dynamics, use the detailed model option. Otherwise, use the equivalent model for faster simulation. To simulate in real time, use the equivalent model. To validate the results, use the detailed model with a variable-step solver. To use the detailed model, set the Fidelity level parameter to Detailed model - switching devices. To use the equivalent model, set the Fidelity level parameter to Equivalent model - PWM-controlled.

If you choose the detailed model, each component in the three-arm circuit is the same switching device, which you specify by setting the Switching device parameter. The switching devices that you can specify are implementations of blocks in the Simscape > Electrical > Semiconductors & Converters library:

• GTO — Gate turn-off thyristor. For information about the I-V characteristic of the device, see GTO.

• Ideal semiconductor switch — For information about the I-V characteristic of the device, see Ideal Semiconductor Switch.

• IGBT — Insulated-gate bipolar transistor. For information about the I-V characteristic of the device, see IGBT (Ideal, Switching).

• MOSFET — N-channel metal-oxide-semiconductor field-effect transistor. For information about the I-V characteristic of the device, see MOSFET (Ideal, Switching).

• Thyristor — For information about the I-V characteristic of the device, see Thyristor (Piecewise Linear).

• Averaged Switch — Semiconductor switch with an antiparallel diode. The control signal port G accepts values in the interval [0,1]. When G is equal to 0 or 1, the averaged switch is fully opened or fully closed respectively. The switch behaves similarly to the Ideal Semiconductor Switch block with an antiparallel diode. When G is between 0 and 1, the averaged switch is partly opened. You can average the pulse-width modulation (PWM) signal over a specified period. You can then undersample the model and use modulation waveforms instead of PWM signals.

This figure shows the equivalent circuit for a converter with fully controlled switching devices (e.g. IGBTs, GTOs).

This figure shows the equivalent circuit for a converter with partially controlled switching devices (e.g. thyristors).

Control the gate ports of the six switching devices via an input to port G on the Converter (Three-Phase) block:

1. Multiplex all six gate signals into a single vector with a Six-Pulse Gate Multiplexer block.

2. Connect the output of the Six-Pulse Gate Multiplexer block to the Converter (Three-Phase) block G port.

You can specify an integral protection diode for each switching device. An integral diode protects the semiconductor device by providing a conduction path for reverse current. An inductive load can produce a high reverse-voltage spike when the semiconductor device suddenly switches off the voltage supply to the load.

The table shows you how to set the Integral protection diode parameter based on your goals.

Goals		Value to Select	Integral Protection Diode
Do not include protection.		None	None
Include protection.	Prioritize simulation speed.	Diode with no dynamics	The Diode block
	Prioritize model fidelity by precisely specifying reverse-mode charge dynamics.	Diode with charge dynamics	The dynamic model of the Diode block

Note

If you set the Switching device parameter to Averaged Switch, the block automatically models protection diodes with no dynamics and the Integral protection diode parameter is not visible.

You can include a snubber circuit, consisting of a resistor and capacitor connected in series, for each switching device. Snubber circuits protect switching devices against high voltages that inductive loads produce when the device turns off the voltage supply to the load. Snubber circuits also prevent excessive rates of change of current when a switching device turns on.

To use the equivalent model as a rectifier, set all the elements of the PWM signal to zero. The model behaves as a three-phase diode rectifier.

Piecewise Constant Approximation in Averaged Switch for FPGA Deployment

If you set the Switching device parameter to Averaged switch and your model uses a partitioning solver, this block produces nonlinear partitions because the average mode equations include modes, G_sat that are functions of the input G. To make these equations compatible with hardware description language (HDL) code generation, and therefore FPGA deployment, set the Integer for piecewise constant approximation of gate input (0 for disabled) parameter to a value greater than 0. This block then treats the G_sat mode as a piecewise constant integer with a fixed range. This turns the previously nonlinear partitions to linear time varying partitions.

An integer value in the range [0,K], where K is the value of the Integer for piecewise constant approximation of gate input (0 for disabled), is now associated with each real value mode in the range [0,1]. The block computes the piecewise constant mode by dividing the original mode by K to normalize it back to the range [0,1]:

$$\begin{array}{l}{u}_I=\left(floor\left(u\cdot K\right)\right)\\ \widehat{u}=\frac{u_I}{K}\end{array}$$

Examples

Asynchronous Machine Direct Torque Control

Control an asynchronous machine (ASM) using the direct-torque control method. A PI-based speed controller supplies the torque reference. The direct-torque controller generates the inverter pulses.

Open Model

Three-Phase Grid-Connected Rectifier Control

Control the DC-link voltage using a grid-connected rectifier. The Rectifier control subsystem uses a PI-based cascade control structure. The Scopes subsystem contains scopes that allow you to see the simulation results. If you have a license for HDL Coder™, you can generate VHDL code for an FPGA using the Simscape™ HDL Workflow Advisor.

Open Model

Three-Phase Grid-Tied Inverter

Control the voltage in a grid-tied inverter system. The Voltage regulator subsystem implements the PI-based control strategy. The three-phase inverter is connected to the grid via a Circuit Breaker. The Circuit Breaker is open at the beginning of the simulation to allow synchronization. At time 0.15 seconds, the Circuit breaker closes, and the inverter is connected to the grid. The Scopes subsystem contains scopes that allow you to see the simulation results. The inverter is implemented using IGBTs. To speed up simulation, or for real-time deployment, the IGBTs can be replaced with Averaged Switches. In this way the gate signals can be averaged over a specified period or replaced with modulation waveforms.

Open Model

Three-Phase Inverter Voltage Control

Control the voltage in a three-phase inverter system. The inverter is implemented using IGBTs. To speed up simulation, or for real-time deployment, the IGBTs can be replaced with Averaged Switches. In this way the gate signals can be averaged over a specified period or replaced with modulation waveforms.

Open Model

Assumptions and Limitations

• If, in the Solver Configuration block inside your model, you set the Solver type parameter to Partitioning, the averaged switches introduce instability during dead time, when all gate inputs are set to 0. Where possible, use the open-zero state by setting all high-side switches to 0 and all low-side switches to 1.

• To use the Converter (Three-Phase) block as an active front end rectifier, if you set the Fidelity level parameter to Equivalent model - PWM-controlled or you set the Switching device parameter to Averaged Switch, you must add a mid-point ground system on the DC side. This figure shows how to build a mid-point ground system with either two resistors or two capacitors.

  

Ports

Conserving

G — Gate terminals

electrical

Vector input port associated with the gate terminals of the switching devices. Connect this port to a Six-Pulse Gate Multiplexer block.

~ — Three-phase port

electrical

Composite three-phase port.

For more information about composite and expanded three-phase ports, see Three-Phase Ports.

Dependencies

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

a — a-phase

electrical

Electrical conserving port associated with the a-phase.

Dependencies

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

b — b-phase

electrical

Electrical conserving port associated with the b-phase.

Dependencies

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

c — c-phase

electrical

Electrical conserving port associated with the c-phase.

Dependencies

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

+ — Positive terminal

electrical

Electrical conserving port associated with the DC positive terminal.

- — Negative terminal

electrical

Electrical conserving port associated with the DC negative terminal.

Parameters

Main

Electrical connection — Electrical connection

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

Option to have composite or expanded three-phase ports. For more information, see Three-Phase Ports.

Fidelity level — Fidelity level

Detailed model - switching devices (default) | Equivalent model - PWM-controlled

Since R2024a

Level of fidelity of the model.

To prioritize simulation accuracy or to obtain results for the individual switching devices, set this parameter to Detailed model - switching devices.

To prioritize simulation speed, set this parameter to Equivalent model - PWM-controlled.

Switching Devices: GTO

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to GTO.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

Forward voltage, Vf — Forward voltage

0.8 V (default)

Minimum voltage required across the anode and cathode block ports for the gradient of the device i-v characteristic to be 1/R_on, where R_on is the value of On-state resistance.

On-state resistance — On-state resistance

0.001 Ohm (default)

Rate of change of voltage versus current above the forward voltage.

Off-state Conductance — Off-state conductance

1e-6 1/Ohm (default)

Anode-cathode conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

Gate trigger voltage, Vgt — Gate trigger voltage

1 V (default)

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

Gate turn-off voltage, Vgt_off — Gate turn-off voltage

-1 V (default)

Gate-cathode voltage threshold. The device turns off when the gate-cathode voltage is below this value.

Holding current — Holding current

1 A (default)

Current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

Switching Devices: Ideal Semiconductor Switch

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to Ideal semiconductor switch.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

On-state resistance — On-state resistance

0.001 Ohm (default)

Anode-cathode resistance when the device is on.

Off-state Conductance — Off-state conductance

1e-6 1/Ohm (default)

Anode-cathode conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

Threshold voltage, Vth — Threshold voltage

6 V (default)

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

Switching Devices: IGBT

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to IGBT.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

Forward voltage, Vf — Forward voltage

0.8 V (default)

Minimum voltage required across the collector and emitter block ports for the gradient of the diode i-v characteristic to be 1/R_on, where R_on is the value of On-state resistance.

On-state resistance — On-state resistance

0.001 Ohm (default)

Collector-emitter resistance when the device is on.

Off-state Conductance — Off-state conductance

1e-6 1/Ohm (default)

Collector-emitter conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

Threshold voltage, Vth — Threshold voltage

6 V (default)

Gate-emitter voltage at which the device turns on.

Switching Devices: MOSFET

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to MOSFET.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

Drain-source on resistance, R_DS(on) — Drain-source on resistance

0.001 Ohm (default)

Drain-source resistance when the device is on.

Off-state Conductance — Off-state conductance

1e-6 1/Ohm (default)

Drain-source conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

Threshold voltage, Vth — Threshold voltage

6 V (default)

Gate-source voltage threshold. The device turns on when the gate-source voltage is above this value.

Switching Devices: Thyristor

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to Thyristor.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

Forward voltage, Vf — Forward voltage

0.8 V (default)

Forward voltage at which the device turns on.

On-state resistance — On-state resistance

0.001 Ohm (default)

Anode-cathode resistance when the device is on.

Off-state Conductance — Off-state conductance

1e-6 1/Ohm (default)

Anode-cathode conductance when the device is off. The value must be less than 1/R, where R is the value of On-state resistance.

Gate trigger voltage, Vgt — Gate trigger voltage

1 V (default)

Gate-cathode voltage threshold. The device turns on when the gate-cathode voltage is above this value.

Holding current — Holding current

1 A (default)

Current threshold. The device stays on when the current is above this value, even when the gate-cathode voltage falls below the gate trigger voltage.

Switching Devices: Averaged Switch

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to Averaged switch.

Switching device — Switching device

Ideal Semiconductor Switch (default) | GTO | IGBT | MOSFET | Thyristor | Averaged Switch

Converter switching device.

Dependencies

To enable this parameter, set Fidelity level to Detailed model - switching devices.

On-state resistance — On-state resistance

0.001 Ohm (default)

Anode-cathode resistance when the device is on.

Integer for piecewise constant approximation of gate input (0 for disabled) — Integer mode for FPGA deployment

0 (default) | nonnegative scalar

Integer used to perform piecewise constant approximation of the gate input for FPGA deployment.

Dependencies

To enable this parameter, set Switching device to Averaged Switch.

Integral Diodes

To enable these parameters, set Fidelity level to Detailed model - switching devices.

Integral protection diode — Integral protection diode model

None | Diode with no dynamics | Diode with charge dynamics

Integral protection diode for each switching device.

Forward voltage — Forward voltage

0.8 V (default)

Minimum voltage required across the + and - block ports for the gradient of the diode I-V characteristic to be 1/R_on, where R_on is the value of On resistance.

Dependencies

To enable this parameter, choose one of these options:

• Set Switching device to Averaged Switch.

• Set Integral protection diode to Diode with no dynamics or Diode with charge dynamics.

On resistance — On resistance

0.001 Ohm (default)

Rate of change of voltage versus current above the Forward voltage.

Dependencies

To enable this parameter, choose one of these options:

• Set Switching device to Averaged Switch.

• Set Integral protection diode to Diode with no dynamics or Diode with charge dynamics.

Off conductance — Off conductance

1e-5 1/Ohm (default)

Conductance of the reverse-biased diode.

Dependencies

To enable this parameter, choose one of these options:

• Set Switching device to Averaged Switch.

• Set Integral protection diode to Diode with no dynamics or Diode with charge dynamics.

Junction capacitance — Junction capacitance

50e-9 F (default)

Diode junction capacitance.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics.

Peak reverse current, iRM — Peak reverse current

-235 A (default) | negative scalar

Peak reverse current measured by an external test circuit. This value must be less than zero. The default value is -235 A.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics.

Initial forward current when measuring iRM — Initial forward current when measuring iRM

300 A (default) | positive scalar

Initial forward current when measuring peak reverse current. This value must be greater than zero.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics.

Rate of change of current when measuring iRM — Rate of change of current when measuring iRM

-50A/μs (default) | negative scalar

Rate of change of current when measuring peak reverse current. This value must be less than zero.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics.

Reverse recovery time parameterization — Reverse recovery time parameterization

Specify reverse recovery time directly (default) | Specify stretch factor | Specify reverse recovery charge

Determines how you specify reverse recovery time in the block. The default value is Specify reverse recovery time directly.

If you select Specify stretch factor or Specify reverse recovery charge, you specify a value that the block uses to derive the reverse recovery time. For more information on these options, see How the Block Calculates TM and Tau.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics.

Reverse recovery time, trr — Reverse recovery time

15 μs (default)

Interval between the time when the current initially goes to zero (when the diode turns off) and the time when the current falls to less than 10% of the peak reverse current. The value of the Reverse recovery time, trr parameter must be greater than the value of the Peak reverse current, iRM parameter divided by the value of the Rate of change of current when measuring iRM parameter.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics and Reverse recovery time parameterization to Specify reverse recovery time directly.

Reverse recovery time stretch factor — Reverse recovery time stretch factor

3 (default)

Value that the block uses to calculate Reverse recovery time, trr. This value must be greater than 1. Specifying the stretch factor is an easier way to parameterize the reverse recovery time than specifying the reverse recovery charge. The larger the value of the stretch factor, the longer it takes for the reverse recovery current to dissipate.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics and Reverse recovery time parameterization to Specify stretch factor.

Reverse recovery charge, Qrr — Reverse recovery charge

1500 μAs (default)

Value that the block uses to calculate Reverse recovery time, trr. Use this parameter if the data sheet for your diode device specifies a value for the reverse recovery charge instead of a value for the reverse recovery time.

The reverse recovery charge is the total charge that continues to dissipate when the diode turns off. The value must be less than $$-\frac{i^2{}_{RM}}{2a},$$

where:

• i_RM is the value specified for Peak reverse current, iRM.

• a is the value specified for Rate of change of current when measuring iRM.

Dependencies

To enable this parameter, set Integral protection diode to Diode with charge dynamics and Reverse recovery time parameterization to Specify reverse recovery charge.

For more information on these parameters, see Diode.

Snubbers

To enable these parameters, set Fidelity level to Detailed model - switching devices and Switching device to one of these options:

• Ideal Semiconductor Switch

• GTO

• IGBT

• MOSFET

• Thyristor

Snubber — Snubber

None (default) | RC snubber

Snubber for each switching device.

Snubber resistance — Snubber resistance

0.1 Ohm (default)

Snubber resistance.

Dependencies

To enable this parameter, set Snubber to RC snubber.

Snubber capacitance — Snubber capacitance

1e-7 F (default)

Snubber capacitance.

Dependencies

To enable this parameter, set Snubber to RC snubber.

Extended Capabilities

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

Version History

Introduced in R2013b

R2024a: Increase simulation speed using an equivalent model

You can now choose from two fidelity levels for the converter model. The equivalent model option does not model the individual switching devices but returns equivalent results. If you need detailed results for the switching device dynamics, use the detailed model option. Otherwise, use the equivalent model for faster simulation. To simulate in real time, use the equivalent model. To validate the results, use the detailed model with a variable-step solver.

To use the detailed model, set the Fidelity level parameter to Detailed model - switching devices. To use the equivalent model, set the Fidelity level parameter to Equivalent model - PWM-controlled.

Before R2024a, you can use the detailed model only.

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.