Single-phase cycloconverter operation

A single-phase cycloconverter converts single-phase AC at frequency $f_i$ directly to single-phase AC at a different frequency $f_o$ (usually $f_o = f_i/n$), with no DC link. It uses a positive group of thyristors for positive load current and a negative group for negative load current.

Circuit (centre-tapped transformer type)

          a o----+---P1->|---+
            |    +---|<-N1---+
  ~ vs    Tr|                |
  (input) O o----[ Load ]----+  (common point K)
            |                |
          b o----+---P2->|---+
                 +---|<-N2---+

Operation ($f_o = f_i/2$, resistive load)

• In halves 1 and 2 the positive group works as a full-wave rectifier, producing two positive humps (positive output half cycle).
• In halves 3 and 4 the negative group gives two negative humps.
• Each thyristor turns off naturally when the supply (and R-load current) reaches zero.

 vs  /\    /\
    /  \  /  \
 --/----\/----\/----\/---
       (alternate humps -ve)
 vo  /\  /\
    /  \/  \
 --/--------\--------/---
             \  /\  /
              \/  \/
    | P1 | P2 | N2 | N1 |
    |<--- To = 2 Ti --->|

Output period = 2 × input period, so 50 Hz gives 25 Hz. For $f_i/3$ or $f_i/4$, each group is kept on for 3 or 4 input half cycles.

Output voltage control

With firing delay $\alpha$ for every SCR (R load):

$$V_o = V_s\sqrt{\frac{1}{\pi}\left(\pi - \alpha + \frac{\sin 2\alpha}{2}\right)}$$

Varying $\alpha$ through each output half cycle (larger at the ends, smaller in the middle) makes the output closer to a sine wave.