--- title: "Series full converters in rectification mode" subject: "Power Electronics" chapter: 2 key: "semester_7/power_electronics:series-full-converters-rectification" source: https://www.bctengineer.com/q/semester_7/power_electronics/series-full-converters-rectification site: BCT Engineering --- # Series full converters in rectification mode Power Electronics · Chapter 2: Single phase AC to DC conversion - Asked in: 2081 Bhadra, 4 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_electronics/series-full-converters-rectification - Whole chapter: https://www.bctengineer.com/md/semester_7/power_electronics/chapter-2 ## Question Explain the series operation of two single phase full converter in rectification mode. ## Short answer In rectification mode, one converter is kept at α=0° (full positive voltage) while the other’s firing angle is varied from 0° to 180°. Output voltage is Vdc = (2Vm/π)(1+cosα2), adjustable from 4Vm/π down to zero. This series arrangement yields high voltage with better power factor. ## Answer In a **series (dual-transformer) full converter**, two single-phase full converters are fed from two separate secondary windings of the same transformer, and their dc outputs are connected in series so that the load voltage is the sum of the two outputs: $v_o = v_{o1} + v_{o2}$. ```text Sec 1 --> [Converter 1, a1] (+)--------+ (-) | | vo1 | (+) Load Sec 2 --> [Converter 2, a2] (Io) (-) vo2 | +---------------------+ Sec 1, Sec 2: two secondaries of one transformer vo = vo1 + vo2 ``` #### Output voltage With a continuous (highly inductive) load current, each converter gives $\frac{2V_m}{\pi}\cos\alpha$, so $$ V_{dc} = \frac{2V_m}{\pi}\left(\cos\alpha_1 + \cos\alpha_2\right) $$ The maximum output is $\frac{4V_m}{\pi}$ (both $\alpha = 0$), i.e. twice that of one converter. Hence the scheme is used for **high-voltage** loads. #### Operation in rectification mode - Converter 1 is kept fully ON at $\alpha_1 = 0$ (it acts like a diode bridge). - Converter 2's firing angle $\alpha_2$ is varied from $0$ to $\pi$. - The output then varies from $\frac{4V_m}{\pi}$ (at $\alpha_2 = 0$) down to $0$ (at $\alpha_2 = \pi$): $V_{dc} = \frac{2V_m}{\pi}(1 + \cos\alpha_2)$. - During the interval $\pi$ to $\pi + \alpha_2$, $v_{o1} = +|v_s|$ and $v_{o2} = -|v_s|$, so $v_o = 0$: the load current effectively freewheels and no reactive power is drawn in that interval. (For inversion, converter 1 is held at $\alpha_1 = \pi$ and $\alpha_2$ is varied.) #### Advantages - Higher output voltage with lower device voltage rating. - Better input power factor and lower harmonics than a single converter at the same output, because only one converter is phase-controlled at a time. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is the dc output of two series full converters with continuous current? A. (2Vm/pi)(cos a1 + cos a2) B. (2Vm/pi) cos(a1 + a2) C. (Vm/pi)(cos a1 - cos a2) D. (2Vm/pi) cos a1 cos a2 Answer: A. The two outputs add, each being (2Vm/pi) cos a. (Key point: Output of series connection) 2. In rectification mode, which converter is phase-controlled? A. Both equally B. Converter 1 at pi, converter 2 fixed C. Converter 1 fully on (a1 = 0), converter 2 varied from 0 to pi D. Neither; a diode bridge is used Answer: C. Only converter 2 is phase-controlled, giving Vdc = (2Vm/pi)(1 + cos a2), which is why the input power factor improves. (Key point: Control strategy) 3. During pi to pi + a2 what happens to the output voltage? A. vo1 = +|vs| and vo2 = -|vs|, so vo = 0 B. vo doubles C. vo equals vs D. Both converters turn off Answer: A. The two outputs cancel and the load current effectively freewheels with no reactive power drawn. (Key point: Zero-output interval) ## Related in Power Electronics - [Single-phase full converter: rectification and inversion](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Afull-converter-rect-inversion) — Power Electronics, chapter 2 - [Series full converters: rectification and inversion](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Aseries-full-converters-rect-inversion) — Power Electronics, chapter 2, asked 4× - [Series operation of two full converters](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Aseries-full-converters-high-voltage) — Power Electronics, chapter 2 - [Series connection of two full converters](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Aseries-full-converters-waveforms) — Power Electronics, chapter 2, asked 2× - [Single-phase full converter, 10 A, α = 30°](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Afull-converter-10a-30deg) — Power Electronics, chapter 2, asked 4× - [Series full converters: average and rms output](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Aseries-full-converters-avg-rms) — Power Electronics, chapter 2 ## Related in other subjects - [Two semi converters (50 N-m at 1000 rpm)](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Asemi-converters-field-armature-50nm-1000rpm) — Utilization of Electrical Energy, chapter 3, asked 3× - [Two semi converters for field and armature](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Asemi-converters-field-armature-firing-angle) — Utilization of Electrical Energy, chapter 3, asked 3× - [Choppers; single-phase full bridge inverter](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Achoppers-full-bridge-inverter) — Advanced Electronics, chapter 7, asked 2× - [Single-phase fully controlled converter DC motor speed](https://www.bctengineer.com/question.md?key=semester_7%2Futilization_of_electrical_energy%3Afull-converter-dc-motor-speed) — Utilization of Electrical Energy, chapter 3