# PWM Generator (Three-phase, Three-level)

Generate three-phase, three-level pulse width modulated signal or waveform for gating switching devices

**Library:**Simscape / Electrical / Control / Pulse Width Modulation

## Description

The PWM Generator (Three-phase, Three-level) block controls switching behavior for a three-phase, three-level power converter. The block:

Calculates on- and off-gating times based on the block inputs:

Three sinusoidal reference voltages

A DC-link voltage

A DC-link neutral point balance control signal

Uses the gating times to generate 12 switch-controlling pulses.

Uses the gating times to generate modulation waveforms.

### Sampling Mode

This block allows you to choose natural, symmetric, or asymmetric sampling of the modulation wave.

The PWM Generator (Three-phase, Two-level) block does not perform carrier-based pulse width modulation (PWM). Instead, the block uses input signals to calculate gating times and then uses the gating times to generate both the switch-controlling pulses and the modulation waveforms that it outputs.

Carrier-based PWM is, however, useful for showing how the sampling mode that you select relates to the switch-on and switch-off behavior of the pulses that the block generates. A generator that uses a three-level, carrier-based PWM method:

Samples a reference wave.

Compares the sample to two parallel triangle carrier waves, separated by one level.

Generates a switch-on pulse if a sample is higher than the carrier signal or a switch-off pulse if a sample is lower than the carrier wave.

To determine switch-on and switch-off pulse behavior, a three-level carrier-based PWM generator uses these methods to sample each of the triangle waves:

Natural — The sampling and comparison occur at the intersection points of the modulation wave and the carrier wave.

Asymmetric — Sampling occurs at the upper and lower boundaries of the carrier wave. The comparison occurs at the intersection that follows the sampling.

Symmetric — Sampling occurs only at the upper boundary of the carrier wave. The comparison occurs at the intersection that follows the sampling.

### Overmodulation

The modulation index, which measures the ability of the power converter to output a given voltage, is defined as

$$m=\frac{{V}_{M}}{{V}_{C}},$$

where

*m*is the modulation index.*V*is the peak value of the modulation wave._{m}*V*is the peak value of the triangle carrier wave._{c}

For three-phase SPWM,

$${V}_{peak}=m\frac{{v}_{dc}}{2},$$

where

*V*is the peak value of the fundamental component of the phase-to-neutral voltage._{peak}*v*is the DC-link voltage._{dc}

For three-phase space-vector PWM (SVM),

$${V}_{peak}=m\frac{{v}_{dc}}{\sqrt{3}}.$$

For normal steady-state operation, `0`

<*m* ≤
`1`

. If a transient, such as a load increase, causes the
amplitude of *V _{m}* to exceed the amplitude of

*V*, overmodulation (

_{c}*m*>

`1`

) occurs If overmodulation occurs, the output voltage of the power converter clamps to the positive or negative DC rail.

In the Three-Phase Three-Level PWM
Generator example, the **Three-Level Controller**
subsystem contains a 1800–V DC-link input, and a modulation index,
*m*, of 0.8. For SVM, the maximal input voltage is $$1800/\sqrt{3}$$V, that is 1039.23 V. To demonstrate overmodulation, a transient is
added at the beginning of the simulation. The transient forces the amplitudes of the
reference voltages to exceed the amplitude of $$1/\sqrt{3}$$ of the DC-link voltage. To highlight overmodulation, the scope
includes simulation results for only one of the 12 output pulses and only the
*a*-phase of the reference voltages, modulation waveforms, and
output voltages.

The modulation index is greater than one between 0.03–0.09 seconds. During overmodulation:

The pulse remains in the on or off position.

The output voltage clamps to the positive or negative DC rail.

## Ports

### Input

### Output

## Parameters

## Model Examples

## References

[1] Chung, D. W., J. S. Kim, and S. K. Sul. “Unified
Voltage Modulation Technique for Real Time Three-Phase Power Conversion.”
*IEEE Transactions on Industry Applications*, Vol. 34, No. 2,
1998, pp. 374–380.

[2] Seo, J. H., C. H. Choi, and D. S. Hyun. “A new
simplified space-vector PWM method for three-level inverters.” *IEEE
Transactions on Power Electronics*, Vol. 16, No. 4, 2001, pp.
545-550.

## Extended Capabilities

## Version History

**Introduced in R2016b**