
I am working on a static transfer switch which aim is to allow supplying a load with 2 different sources in order to have a redundancy when feeding the load. The head to tail assembly allow the current to flow in 2 directions (for each alternative of the input current)
The working condition is the following:
When both input are connected to the supply grid and if we want to supply the load at the output with Input 2 supply, the thyristors of Switch group 1 are openned (off state) and thyristors of switch group 2 will be closed (on state). So that at the output line voltages U12in2, U23in2 and U31in2 are applied.
I am trying to find out an equation that helps to calculate the value of the off state voltage across the thyristor switch Vt1, Vt2 and Vt3 in the following condition:
-Input 1 and input 2 connected to 2 different power supply
-Thyristors of switch group 2 in on state (closed) => triggering signal on so Vt1' = Vt2' = Vt3' =0
-Thyristors of switch group 1 openned (off state) => triggering signal off
I have 3 equations but I am not sure about my results:

Thank you in advance for the advices