# Modulation Strategies for 3-phase 2-Level Voltage Source Inverters

For 3-phase voltage source converters, to increase the DC voltage utilization (i.e. boost the output AC voltage) or reduce the switching losses, a zero-sequence reference can be inserted in the modulation scheme provided the neutral point of the 3-phase system is floating.

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Modulation depth has a maximal value of 1 in Sine modulation and $\sqrt{2/3} \approx 1.15$ for other modulation strategies which add a third harmonic component.

This example presents the best of these modulation strategies - in terms of linear range and / or harmonic distortion - which can be easily implemented with C-code or control blocks.

The $V_{kO}$ phase voltage can be given by the equation below, where $k = 1, 2, 3$:

V_{kO} = V_{kN} + V_{NO}

The $V_{NO}$ voltage is managed with a zero sequence reference voltage.

Thus, the zero sequence reference voltage $V_{off}$ is added to each phase reference $V_{ref_k}$:

V_{ref_k}^{'} = V_{ref_k} + V_{off}

## Continuous modulation strategies

### Sine modulation (Sine PWM)

With this modulation strategy, the maximum modulation index $m_a$ is equal to 1.

V_{off} = 0

### Third-harmonic injection (THIPWM)

This method adds a sinusoidal zero sequence voltage at three-times the fundamental frequency1. This example proposes the implementation of the 1/6 coefficient third-harmonic injection.

V_{off} = -\frac{m_a}{6} \sin\left({3\omega_{0}t}\right)

### Space vector modulation (SVM)

This modulation strategy is one of the most popular overmodulation methods. It directly defines a sequence of different switching states to follow the complex vector voltage of the three-phase reference system.

The switching pattern of a symmetrical sequence has been implemented in the C-code block.

Caution

It is currently recommended to run this block with the fixed time-step to avoid missing any switching event.

### Space vector modulation "carrier based" (SV-PWM)

This modulation strategy offers a similar pattern as the space vector modulation and can be shown as a triangle-intersection or carrier-based implementation of the conventional Space vector modulation 2, 3.

It is also known as the MIN MAX modulation strategy due to the computation of the zero-sequence:

V_{off} = - \frac{max(V_{ref_1}, V_{ref_2}, V_{ref_3}) + min(V_{ref_1}, V_{ref_2}, V_{ref_3})}{2}

Tip

To get exactly the same swithing pattern as with the conventional SVM, the sampling time of the C-code block which computes the offset voltage must be set at the switching period of the carrier.

## Discontinuous modulation strategies

### DPWM min

In this strategy, each phase does not switch within 120° of the fundamental period and the output is clamped at the negative dc bus voltage. As consequence, the switches connected to the negative dc bus voltage reduce their switching losses.

V_{off} = -1 - min(V_{ref_1}, V_{ref_2}, V_{ref_3})

### DPWM max

In this strategy, each phase does not switch within 120° of the fundamental period and the output is clamped at the positive dc bus voltage. As consequence, the switches connected to the positive dc bus voltage reduce their switching losses.

V_{off} = 1 - max(V_{ref_1}, V_{ref_2}, V_{ref_3})

### DPWM1

In this case the phase leg is clamped 30° symmetricaly from maximal voltage. This method has low harmonic distortion characteristics. The zero-sequence is extracted from the following equations:

V_{off} = sign(V_{max}) - V_{max}
V_{max} = \left\{ \begin{array}{ll} V_{ref_1} & if \: \left|V_{ref_1}\right| \ge \left|V_{ref_2}\right|, \left|V_{ref_3}\right|\\ V_{ref_2} & if \: \left|V_{ref_2}\right| \ge \left|V_{ref_1}\right|, \left|V_{ref_3}\right|\\ V_{ref_3} & if \: \left|V_{ref_3}\right| \ge \left|V_{ref_1}\right|, \left|V_{ref_2}\right|\\ \end{array} \right.

## References

1. G.Buja and G. Indri. “Improvement of pulse width modulation techniques”. Archiv fur Elektrotechnik, 57, pages 281-289, 1975.

2. A.M.Hava, “Carrier based PWM-VSI drives in the overmodulation region”. Vol. 1. University of Wisconsin–Madison, 1998.

3. Ke. Zhou and D. Wang, "Relationship Between Space-Vector Modulation and Three-Phase Carrier-Based PWM: A Comprehensive Analysis", IEEE Transactions On Industrial Electronics, Vol. 49, No. 1, February 2002.