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180° inverter waveforms VRY, VYB, VBR, VNO, VRN

Short answer

In 180 degree conduction, line voltages are quasi-square waves of plus or minus Vdc for 120 degrees with 60 degree zero intervals, shifted 120 degrees. VNO is a square wave of plus or minus Vdc/6 at triple frequency. Phase voltage VRN is a six-step wave with levels Vdc/3, 2Vdc/3, Vdc/3, minus Vdc/3, minus 2Vdc/3, minus Vdc/3.

For three phase 180 degree conduction inverter, draw the output waveforms for VRY, VYB, VBR, VNO, and VRN, where the notation has their usual meaning.

In the three-phase 180° conduction inverter, each pole (leg) output, measured from the dc mid-point O, is a square wave of ±Vdc/2\pm V_{dc}/2, and the three pole voltages are shifted by 120°. The line voltages, the neutral-point voltage VNOV_{NO} and the phase voltages are obtained from these pole voltages.

Relations used

VRY=VRO−VYO,VYB=VYO−VBO,VBR=VBO−VROVNO=VRO+VYO+VBO3(balanced star load)VRN=VRO−VNO\begin{aligned} V_{RY} &= V_{RO} - V_{YO}, \quad V_{YB} = V_{YO} - V_{BO}, \quad V_{BR} = V_{BO} - V_{RO} \\ V_{NO} &= \frac{V_{RO} + V_{YO} + V_{BO}}{3} \quad (\text{balanced star load}) \\ V_{RN} &= V_{RO} - V_{NO} \end{aligned}

Values in each 60° interval (V=VdcV = V_{dc})

ωt\omega tVROV_{RO}VYOV_{YO}VBOV_{BO}VRYV_{RY}VYBV_{YB}VBRV_{BR}VNOV_{NO}VRNV_{RN}
0–60°+V/2+V/2−V/2-V/2+V/2+V/2VV−V-V0V/6V/6V/3V/3
60–120°+V/2+V/2−V/2-V/2−V/2-V/2VV0−V-V−V/6-V/62V/32V/3
120–180°+V/2+V/2+V/2+V/2−V/2-V/20VV−V-VV/6V/6V/3V/3
180–240°−V/2-V/2+V/2+V/2−V/2-V/2−V-VVV0−V/6-V/6−V/3-V/3
240–300°−V/2-V/2+V/2+V/2+V/2+V/2−V-V0VVV/6V/6−2V/3-2V/3
300–360°−V/2-V/2−V/2-V/2+V/2+V/20−V-VVV−V/6-V/6−V/3-V/3

Waveforms

 wt       0    60   120  180  240  300  360
 VRY    V __________
        0           |____           ____
       -V                |_________|
 VYB    V            _________
        0       ____|         |____
       -V _____|                   |____
 VBR    V                      _________
        0 _____           ____|
       -V      |_________|
 VNO  V/6 _____      ____      ____
     -V/6      |____|    |____|    |____
 VRN 2V/3       ____
      V/3 _____|    |____
        0                |
     -V/3                |____      ____
    -2V/3                     |____|
  • Line voltages VRYV_{RY}, VYBV_{YB}, VBRV_{BR}: quasi-square waves, ±Vdc\pm V_{dc} for 120° and zero for 60°, mutually displaced by 120°.
  • Neutral voltage VNOV_{NO}: square wave of ±Vdc/6\pm V_{dc}/6 at three times the output frequency (it carries all the triplen harmonics).
  • Phase voltage VRNV_{RN}: six-step wave with levels V/3V/3, 2V/32V/3, V/3V/3, −V/3-V/3, −2V/3-2V/3, −V/3-V/3.

Rms values: VRY=0.8165VdcV_{RY} = 0.8165V_{dc}, VRN=0.4714VdcV_{RN} = 0.4714V_{dc}, VNO=Vdc/6V_{NO} = V_{dc}/6.

✓ Answer checked by Claude Opus 5.5 (high effort)

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