# Transfer function for six-pulse controlled rectifier

I need to determine the transfer function for a six-pulse bridge rectifier, implemented with thyristors.

More precisely, I need to determine the relationship between the output voltage (pulse) and the firing angle (or the conduction angle) of the signal applied to each thyristor.
Obviously, the trigger signal for each of the thyristors is equal, and synchronous with the corresponding supply voltage.

Can anyone suggest a line of research?

Assuming when you say transfer function you are not referring to an S-domain "transfer function" for the behaviour (as this is actually really hard and relies on alot of heaviside functions) but more of a relationship of input to output.

ASUMMUMING the supply is an ideal supply with each voltage sources being 120degree's separated and their amplitudes & freq are all the same and that there is no supply feeder impedance

With the firing angle = 0 and thus the SCR's act like diodes, we know that:

Vd = $\frac{3\sqrt{2}}{\pi}V_L$

Where Vd = DClink voltage and $V_L$ = the Line-Line (rms) voltage from the supply

We want to know what Vd is with regards to some arbitary firing angle $\alpha$

$V_\alpha = Vd - \frac{A_\alpha}{\pi/3}$

$A_\alpha$ is the volts-second area that occurs every 60degrees which reduces the average DClink.

We know that: $V_a = \sqrt{2} V_L Sin(\omega t)$

Thus

$A_\alpha = \int\limits_0^\alpha \sqrt{2}V_LSin(\omega t) d(\omega t)$

$= \sqrt{2}V_L(1-cos\alpha)$

Thus

$V_\alpha = \frac{3\sqrt{2}}{\pi} V_Lcos\alpha$

• With the above development, which is obtained is the ratio between the average output voltage of the rectifier and the firing angle. What would be the approach to obtain the transfer function in the s-domain? Commented Sep 12, 2014 at 14:08
• For a single-phase fully-controlled rectifier it would be (sort-f) possible ... but 3phase, the problem arrises because the voltage that is applied to the DClink is not only dependent on what was delayed BUT what was also conducting out of the other two and which one is higher. YOu would end up with heaviside functions within heaviside.
– user16222
Commented Sep 12, 2014 at 14:36
• Are you saying that to try to determine the transfer function in the s domain should apply a step as firing angle signal and observe the response? Commented Sep 12, 2014 at 15:20