Three-phase six-step (180° conduction) inverter

In the 180° conduction mode of a three-phase bridge inverter each switch conducts for 180°, three switches are ON at any time (one from each leg), and switches are gated in the order S1, S2, …, S6 at 60° intervals. The output phase voltage is a six-step wave and the line voltage is a 120° quasi-square wave.

Circuit

      +----+--------+--------+
      |    |        |        |
 Vdc/2   S1 D1    S3 D3    S5 D5
  ---  |    |        |        |
  O    +-a  +--b     +--c     |
  ---  |    |        |        |
 Vdc/2   S4 D4    S6 D6    S2 D2
      |    |        |        |
      +----+--------+--------+
        a, b, c -> 3-phase load

Switches S1, S3, S5 connect phases a, b, c to the positive rail; S4, S6, S2 to the negative rail. S1 and S4 (same leg) are complementary.

Conduction table and phase voltages (star resistive load, each phase $R$)

($V = V_{dc}$.) Example, mode 1: phases a and c are on the positive rail, b on the negative. The equivalent circuit is $R/2$ (a, c in parallel) in series with $R$: current $i = \dfrac{V}{1.5R}$, so $v_{bn} = -iR = -2V/3$ and $v_{an} = v_{cn} = iR/2 = V/3$.

Waveforms

 gates: S1 |######......|   (0-180)
        S2  ..|######...|   (60-240)
        S3  ....|######.|   (120-300)
 van 2V/3      __
      V/3   __|  |__
        0 -|--------|-------------
     -V/3            |__    __|
    -2V/3               |__|
 vab   +V  |_____|
        0 -|     |__|      |__|--
       -V           |_____|
           0  60 120 180 240 300 360

• Phase voltage $v_{an}$: $V/3$, $2V/3$, $V/3$, $-V/3$, $-2V/3$, $-V/3$ in successive 60° steps. $v_{bn}$, $v_{cn}$ are the same wave shifted by 120° and 240°.
• Line voltage $v_{ab} = v_{an} - v_{bn}$: $+V$ for 0–120°, 0 for 120–180°, $-V$ for 180–300°, 0 for 300–360°. $v_{bc}$, $v_{ca}$ are shifted by 120°, 240°.

Important values

$$\begin{aligned} V_{ph,rms} &= \frac{\sqrt2}{3}V_{dc} = 0.4714\,V_{dc}, \qquad V_{L,rms} = \sqrt{\frac23}\,V_{dc} = 0.8165\,V_{dc} \\ v_{an} &= \sum_{n=6k\pm1}\frac{2V_{dc}}{n\pi}\sin n\omega t \end{aligned}$$

Triplen harmonics are absent. Because two switches of a leg must not conduct together, a small dead time is given between turning S1 off and S4 on.