Space Vector PWM (3-Level)

Purpose

Generate PWM signals for a 3-phase 3-level neutral-point clamped inverter using space-vector modulation technique

Library

Control / Modulators

Description

../../_images/svpwm.svg

The 3-level space-vector modulator generates a voltage vector on the ac terminals of a neutral-point clamped 3-phase inverter according to a reference signal provided in the stationary \(\alpha \beta\) reference frame.

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Fig. 177 Neutral-point clamped 3-phase inverter schematic

By controlling the semiconductor gate signals, each ac terminal can be connected either to the high (+), low (-) or neutral (o) point of the dc link. This results in \(27\) vectors including \(12\) short vectors, \(6\) medium vectors and \(6\) long vectors, as well as \(3\) zero vectors. Under the assumption of balanced voltages on the capacitors \(V_{\mathrm{dc+}}\) and \(V_{\mathrm{dc-}}\) the space-vector diagram is graphically depicted in Fig. 178.

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Fig. 178 3-level space vector diagram

The hexagon area can be divided in to six sectors (1 to 6), each of which has four zones (1 to 4). As an example, consider the reference voltage \(\vec{V}^*\) to be located in zone 2 of sector 1. In order to generate the reference voltage \(\vec{V}^*\) on the ac terminals, the adjacent vectors \(\vec{V}_{1}\), \(\vec{V}_{3}\) and \(\vec{V}_{5}\) are selected and weighted by time. The on-time of each vector with respect to the switching period is calculated as:

../../_images/svpwm3level_sector1zone2.svg

Fig. 179 Sector 1 Zone 2 vector diagram

\[\tau_{\mathrm{a}} = 1 - 2k\,\sin\left(\theta\right)\]
\[\tau_{\mathrm{b}} = 2k\,\sin\left(\frac{\pi}{3} + \theta\right) - 1\]
\[\tau_{\mathrm{c}} = 1 - 2k\,\sin\left(\frac{\pi}{3} - \theta\right)\]

This block implements a symmetrical sequence to achieve minimum total harmonic distortion (THD). The short vectors have redundant switch states, e.g. \(\vec{V}_{1}\) can be either generated by the combination (+oo) or (o–). In order to keep the dc link voltages balanced, both switch states must be applied for the same duration during one switching period. The resulting switch pattern is illustrated in Fig. 180.

../../_images/svpwm3level_sw_pattern.svg

Fig. 180 3-level switching pattern

Parameters

Switching frequency

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

Output values

The switch output values in the high, neutral and low state. The default values are [-1 0 1].

Inputs and Outputs

DC voltage

The input signal \(V_{\rm dc}\) is the sum of the two dc link voltages \(V_{\rm dc+}\) and \(V_{\rm dc-}\).

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 the three switch signals \([S_{\rm a}, S_{\rm b}, S_{\rm c}]\), which control the converter legs A, B and C. Each switch signal determines if the corresponding ac terminal shall be connected to the positive, neutral or negative side of the dc link.

Probe Signals

sector

A value in the set of \([1..6]\) that indicates the sector in which the reference vector, \(\vec{V}^*\), is located.

zone

A value in the set of \([1..4]\) that indicates the zone in which the reference vector, \(\vec{V}^*\), is located.

tau

A vector signal comprising the three relative on-time values, \([\tau_{\mathrm{a}}, \tau_{\mathrm{b}}, \tau_{\mathrm{c}}]\).

sw

A vector signal consisting of the three gate signals for the inverter legs, \([S_{\mathrm{a}}, S_{\mathrm{b}}, S_{\mathrm{c}}]\).