## Question

The three-phase inverter shown in figure operates such that each switch gets a gating signal for 120°. The gating sequence is: S₁: 0120, S2: 60-180, S3: 120 240 … and so on. The source voltage is 300V and the load is a resistance of 5092/phase. 1) Complete the table below. 2) Sketch the following (showing all values, angles and conducting devices on the curves): – – – Solution Interval 0 →60 60 120 120 →180 180→240 V 240 →300 300-360 a S₁ D, Conducting devices Va DA The gating signals for the six switches The three phase voltages: Va, Vb, Vc The three line-line voltages: Vab, Vbe, Vea 3) Calculate the rms values of the phase and line-line voltages. 4) Find the power delivered to the load. + 1 ia Va b O N D S So Do S₂ D₂ Vb + 1 Ve Vp ib – C n DS Z ic Ve Z.

## Answer

**1. Completing the table:**

Solution Interval | Phase Voltage (Va) | Conducting Devices | Line Voltage (VL) |
---|---|---|---|

0° → 60° | 0 V | D1, D6 | Vab |

60° → 120° | 300 V | D1, D3 | Vab + Vc |

120° → 180° | 0 V | D3, D6 | Vc |

180° → 240° | 300 V | D3, D5 | Vc + Vab |

240° → 300° | 0 V | D5, D6 | Vab |

300° → 360° | 300 V | D5, D1 | Vab + Vc |

**2. Sketching the curves:**

**a. Phase Voltage (Va):**

- A triangular wave with amplitude 300 V.
- Conducting devices:
- During 0° – 60° and 240° – 300°, D1 conducts (Va = 0).
- During 60° – 120° and 180° – 240°, D3 conducts (Va = 300 V).

**b. Gating Signals for Switches:**

- Three square waves with 120° phase shift.
- S1: High for 0° – 60° and 240° – 300°.
- S2: High for 60° – 180°.
- S3: High for 120° – 240°.

**c. Three-Phase Voltages (Va, Vb, Vc):**

- Three shifted copies of Va, with phase differences of 120°.
- Vb lags Va by 120°.
- Vc lags Vb by another 120°.

**d. Three Line-Line Voltages (Vab, Vbc, Vca):**

- Obtained by subtracting phase voltages.
- Vab = Va – Vb.
- Vbc = Vb – Vc.
- Vca = Vc – Va.

**3. Calculating RMS Values:**

- Phase voltage RMS: Vrms = Vpeak / √2 = 300 V / √2 ≈ 212.13 V.
- Line voltage RMS: Vrms = √3 * Vphase RMS ≈ 367.39 V.

**4. Calculating Power Delivered to Load:**

- Per-phase power: P = Vrms^2 / R = (212.13 V)^2 / 5092 Ω ≈ 8.88 W.
- Total power: Ptotal = 3 * P = 3 * 8.88 W ≈ 26.64 W.