Generate three-phase, two-level pulse width modulated waveform

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

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

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

Three sinusoidal reference voltages, one per phase

A DC-link voltage

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

Uses the gating times to generate modulation waveforms.

The block provides modes for both continuous and discontinuous pulse width modulation (PWM). The figure shows the general difference between continuous sinusoidal PWM (SPWM) and continuous space vector modulation (SVM) waveforms.

For discontinuous PWM (DPWM), the block clamps the modulation wave to the positive or negative DC rail for a total of 120 degrees during each fundamental period. During the clamping intervals, modulation discontinues.

A waveform with 30-degree DPWM has four 30-degree intervals per fundamental period.

Selecting a positive or negative 30-degree phase shift affects the clamping intervals for 60-degree DPWM.

The figure shows the waveforms for positive and negative DC clamping for 120-degree DPWM.

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 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 two-level, carrier-based PWM method:

Samples a reference wave.

Compares the sample to a triangle carrier wave.

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 two-level carrier-based PWM generator uses these methods to sample the triangle wave:

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

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) and DPWM,

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

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

`1`

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

In the Three-Phase Two-Level PWM
Generator example, the **Two-Level Controller**
subsystem contains a 400–V DC-link input, and a modulation index,
*m*, of 0.8. For SPWM, the maximal input voltage is 400 V/2,
that is, 200 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 1/2 of the DC-link voltage. To highlight overmodulation, the
scope includes simulation results for only one of the six 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,

*V*, clamps to the positive or negative DC rail._{ao}

[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] Hava, A. M., R. J. Kerkman, and T. A. Lipo. “Simple
Analytical and Graphical Methods for Carrier-Based PWM-VSI Drives.”
*IEEE Transactions on Power Electronics*, Vol. 14, No. 1, 1999,
pp. 49–61.