Space Vector PWM

Purpose

Generate PWM signals for 3-phase inverter using space-vector modulation technique

Library

Control / Modulators

Description

The space vector modulator generates a reference voltage vector, \(\overrightarrow{V_{\mathrm{s}}}\), at the ac terminals of a three-phase voltage source converter shown below. The reference vector is defined in the \(\alpha\beta\) coordinate system: \(\overrightarrow{V_{\mathrm{s}}}=V_{\alpha}^{*}+j\, V_{\beta}^{*}\).

Fig. 174 Three-phase voltage source converter

Operation

The conventional construction of the reference voltage vector, \(\overrightarrow{V_{\mathrm{s}}}\), is graphically depicted in Fig. 175.

Fig. 175 Construction of the reference vector

Rather than calculating the relative on-times \(\tau_{\rm a},\tau_{\rm b},\tau_{0}\) for the switching vectors \(\overrightarrow{V_{\rm a}},\overrightarrow{V_{\rm b}}\) and the zero vector, this block uses an equivalent index-based modulation approach to achieve different SVPWM modulation strategies by manipulating the three-phase sinusoidal modulation indices with different injected zero-sequence patterns.

This block is implemented with a 3-Phase Index-Based Modulation block in series with a Symmetrical PWM block. The Symmetrical PWM block is configured to use the Regular (single update at min.) sampling scheme, where the incoming modulation index is sampled only at the minimum of the symmetrical triangular carrier.

The following figures show the switching patterns for different SVPWM strategies. Every figure shows only one switching cycle that resides in the first half of Sector 1, i.e. between \(0\) and \(30\) degrees of the AC period. This is when \({u_{\rm a}}(t) > 0 > {u_{\rm b}}(t) > {u_{\rm c}}(t)\).

• The Symmetrical strategy always uses both zero vectors \(\overrightarrow{V_{0}}\) (000) and \(\overrightarrow{V_{7}}\) (111), by placing one in the center of the period and the other one evenly split at the beginning and the end of the period.

• DPWM1, DPWM2 and DPWMMAX happen to result in the same switching pattern inside this 30-degree interval. In this interval they only utilize one zero vector \(\overrightarrow{V_{7}}\) (111), evenly split at the beginning and the end of the period.

• DPWM0, DPWM3 and DPWMMIN happen to result in the same switching pattern inside this 30-degree interval. In this interval they only utilize one zero vector \(\overrightarrow{V_{0}}\) (000), placed in the center of the period.

Fig. 176 Switching pattern for different SVPWM modulation strategies, example for one switching cycle inside the first half of Sector 1 with an angle between \(0\) to \(30\) degrees of the AC period (i.e. \({u_{\rm a}}(t) > 0 > {u_{\rm b}}(t) > {u_{\rm c}}(t)\))

To see how the modulation index pattern evolves throughout the other sectors for each modulation strategy, please refer to the documentation of the 3-Phase Index-Based Modulation block.

Parameters

Modulation strategy

The modulation strategy can be set to Symmetrical, DPWM0, DPWM1, DPWM2, DPWM3, DPWMMIN, and DPWMMAX using a combo box. All these strategies follow the same space vector modulation theory, the major difference is in the utilization of the two available zero vectors - \(\overrightarrow{V_{0}}\) (000) and \(\overrightarrow{V_{7}}\) (111) inside each switching period regarding different sector intervals.

Switching frequency

The switching frequency in hertz \((\mathrm{Hz})\).

Output values

The switch output values in the high and low state. The values should be selected to match the inverter’s gate control logic so that a high value turns on the upper switch in the leg and the low value turns on the lower switch. The default values are \([-1\;1]\).

Inputs and Outputs

DC voltage

The input signal \(V_{\rm dc}\) is the voltage measured on the dc side of the inverter.

Reference voltage

This input, labeled \(V_{\alpha\beta}^{*}\), is a two-dimensional vector signal comprising the elements \([V_{\alpha}^{*},V_{\beta}^{*}]\).

Switch output

The output labeled \(sw\) is formed from three switch control signals, \([S_{\rm a},S_{\rm b},S_{\rm c}]\), which control the inverter legs A, B, and C. Each switch signal controls the upper and lower switches in the respective leg.

Probe Signals

3-phase modulation index

A vector signal consisting of the three-phase modulation indices, \([m_{\rm a}, m_{\rm b}, m_{\rm c}]\) for the chosen space vector modulation strategy.