# Modular Multilevel Converter Leg

Modular multilevel converter leg with series-connected power submodules

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• Simscape / Electrical / Semiconductors & Converters / Converters

## Description

The Modular Multilevel Converter Leg block models a modular multilevel converter leg as a two arms that are implemented with a number of series-connected power submodules.

Half-Bridge Topology

Full-Bridge Topology

This blocks allows you to select the level of model fidelity by choosing between a detailed model with switching devices or an equivalent model. You can choose from these switching devices are:

• 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 anti-parallel diode. The control signal port, G, accepts values in the `[0,1]` interval. When the value at port G is equal to `0` or `1`, the averaged switch is either fully opened or fully closed, and it behaves similarly to the Ideal Semiconductor Switch block with an anti-parallel diode. When the value at port G is between `0` and `1`, the averaged switch is partly opened. You can then average the PWM signal over a specified period. This allows for undersampling of the model or using modulation waveforms instead of PWM signals.

### Variables

Use the Variables settings to specify the priority and initial target values for the block variables before simulation. For more information, see Set Priority and Initial Target for Block Variables.

## Ports

### Input

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Physical signal port associated with the gate signal for all submodules of the modular multilevel converter leg, specified as a vector of physical signals.

If you set the Converter topology parameter to `Half-bridge`, the output is a vector of length 4 * Nsm, where Nsm is the Number of power submodules.

If you set the Converter topology parameter to `Full-bridge`, the output is a vector of length 8 * Nsm.

#### Dependencies

To enable this port, set Fidelity level to `Detailed model - switching devices` or ```Equivalent model - PWM-controlled```.

Physical signal port associated with the reference waveforms, specified as a vector of physical signals of length 2.

#### Dependencies

To enable this port, set Fidelity level to ```Equivalent model - waveform-controlled```.

### Output

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Physical signal port associated with the capacitor voltages for each submodule in the modular multilevel converter leg, specified as a vector of physical signals.

#### Dependencies

To enable this port, set Capacitor voltages to `Instrumented`.

### Conserving

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Electrical conserving port associated with the positive terminal of the modular multilevel converter leg.

Electrical conserving port associated with the negative terminal of the modular multilevel converter leg.

Electrical conserving port associated with the single-phase terminal of the modular multilevel converter leg.

## Parameters

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### Main

Topology of the modular multilevel converter.

Level of fidelity of the model.

Whether to instrument the capacitor voltages.

Number of power submodules of the modular multilevel converter.

Capacitance of a submodule. If you enter a vector, the vector must be of length 2 * Nsm, where Nsm is the Number of power submodules.

Capacitor effective series resistance. If you enter a vector, the vector must be of length 2 * Nsm, where Nsm is the Number of power submodules.

#### Dependencies

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

Inductance of the arm.

Arm inductance series resistance.

Initial voltage of the capacitor. If you enter a vector, the vector must be of length 2 * Nsm, where Nsm is the Number of power submodules.

### Switching Devices

This table shows how enabled parameters in the Switching Devices settings depend on the Switching device that you select. To learn how to read the table, see Parameter Dependencies. To enable these settings, set Fidelity level to ```Detailed model - switching devices```.

Switching Devices Parameter Dependencies

Parameters and Options
Switching device
```Ideal Semiconductor Switch````GTO``IGBT``MOSFET``Thyristor````Averaged Switch```
On-state resistanceForward voltageForward voltageDrain-source on resistanceForward voltageOn-state resistance
Off-state conductanceOn-state resistanceOn-state resistanceOff-state conductanceOn-state resistance
Threshold voltageOff-state conductanceOff-state conductanceThreshold voltageOff-state conductance
Gate trigger voltage, VgtThreshold voltageGate trigger voltage, Vgt
Gate turn-off voltage, Vgt_offHolding current
Holding current

Switching device type for the converter.

#### Dependencies

See the Switching Devices Parameter Dependencies table.

For the different switching device types, the Forward voltage is the:

• GTO — Minimum voltage required across the anode and cathode block ports for the gradient of the device I-V characteristic to be 1/Ron, where Ron is the value of On-state resistance

• IGBT — Minimum voltage required across the collector and emitter block ports for the gradient of the diode I-V characteristic to be 1/Ron, where Ron is the value of On-state resistance

• Thyristor — Minimum voltage required for the device to turn on

#### Dependencies

See the Switching Devices Parameter Dependencies table.

For the different switching device types, the On-state resistance is the:

• GTO — Rate of change of the voltage versus the current above the forward voltage

• Ideal semiconductor switch — Anode-cathode resistance when the device is on

• IGBT — Collector-emitter resistance when the device is on

• Thyristor — Anode-cathode resistance when the device is on

• Averaged switch — Anode-cathode resistance when the device is on

#### Dependencies

See the Switching Devices Parameter Dependencies table.

Resistance between the drain and the source. The gate-to-source voltage also affects the Drain-source on resistance parameter.

#### Dependencies

See the Switching Devices Parameter Dependencies table.

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

For the different switching device types, the On-state resistance is the:

• GTO — Anode-cathode conductance

• Ideal semiconductor switch — Anode-cathode conductance

• IGBT — Collector-emitter conductance

• MOSFET — Drain-source conductance

• Thyristor — Anode-cathode conductance

#### Dependencies

See the Switching Devices Parameter Dependencies table.

Gate voltage threshold. The device turns on when the gate voltage is above this value. The voltage threshold applies to different devices depending on the switching device used:

• Ideal semiconductor switch — Gate-emitter voltage

• IGBT — Gate-cathode voltage

• MOSFET — Gate-source voltage

#### Dependencies

See the Switching Devices Parameter Dependencies table.

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

#### Dependencies

See the Switching Devices Parameter Dependencies table.

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

#### Dependencies

See the Switching Devices Parameter Dependencies table.

Gate 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.

#### Dependencies

See the Switching Devices Parameter Dependencies table.

### Protection Diodes

Diode type. The options are:

• `None` — The block does not model diode dynamics.

• `Diode with no dynamics` — Select this option to prioritize simulation speed using the Diode block.

• `Diode with charge dynamics` — Select this option to prioritize model fidelity in terms of reverse mode charge dynamics using the commutation diode model of the Diode block.

Note

If you set Switching device to `Averaged Switch` in the Switching Device settings, the `Diode with no dynamics` setting is automatically selected.

#### Dependencies

To enable this parameter, set Switching device to `GTO`, `Ideal Semiconductor Switch`, `IGBT`, `MOFSET`, or `Thyristor`.

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

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with no dynamics` or `Diode with charge dynamics`.

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

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with no dynamics` or `Diode with charge dynamics`.

Conductance of the reverse-biased diode.

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with no dynamics` or `Diode with charge dynamics`.

Diode junction capacitance.

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with charge dynamics`.

Peak reverse current measured by an external test circuit. This value must be less than zero.

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with charge dynamics`.

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

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with charge dynamics`.

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

#### Dependencies

To enable this parameter, set Model dynamics to `Diode with charge dynamics`.

Determines how you specify reverse recovery time.

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 Model dynamics to `Diode with charge dynamics`.

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 Model dynamics to `Diode with charge dynamics` and Reverse recovery time parameterization to ```Specify reverse recovery time directly```.

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 Model dynamics to `Diode with charge dynamics` and Reverse recovery time parameterization to `Specify stretch factor`.

Value that the block uses to calculate Reverse recovery time, trr. Use this parameter if the data sheet for your diode 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:

• iRM 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 Model dynamics to `Diode with charge dynamics` and Reverse recovery time parameterization to `Specify reverse recovery charge`.

### Snubbers

To enable the Snubbers settings, set Fidelity level to ```Detailed model - switching devices``` and Switching device to `GTO`, ```Ideal Semiconductor Switch```, `IGBT`, `MOFSET`, or `Thyristor`.

Snubber for each switching device:

• `None`

• `RC snubber`

Snubber resistance.

#### Dependencies

To enable this parameter, set Snubber to `RC snubber`.

Snubber capacitance.

#### Dependencies

To enable this parameter, set Snubber to `RC snubber`.

## References

[1] Saad, Hani, Sebastien Dennetiere, and Jean Mahseredjian. “On Modelling of MMC in EMT-Type Program.” 2016 IEEE 17th Workshop on Control and Modeling for Power Electronics (COMPEL), 1–7. Trondheim, Norway: IEEE, 2016. https://doi.org/10.1109/COMPEL.2016.7556717.

## Version History

Introduced in R2020b