3 Winding Transformer Currents for 12 Pulse Rectifier

[shocked_and_confused]

I'm working on a project that has a Dd0y1 3 winding transformer that feeds a 12 pulse rectifier for conversion to DC. The rectifier is two 3-phase Graetz-bridges connected in parallel with an inter-phase transformer to create the 12 pulses.

What I'm having trouble figuring out is the equivalent AC phase currents at the LV side and HV side of the transformer that corresponds to the DC load current. I've been able to find documentation for a 12 pulse series connected 3-phase bridge, but haven't found anything simplified for a parallel connection.

For the series connection, I've found the following equations:
LV AC current = 0.816 x dc current.
HV AC current = 1.578 x dc current x (LV volts (1 winding)/HV volts).

Does anyone know the equations like this for the parallel connection?

 

[MatthewDB]

I don't know the equations off hand, just be aware that there are many caveats, especially with 12 pulse in parallel. The load will change the equations; for a stiff DC current source (like an induction furnace) the equations are different vs. feeding a capacitor bank or the back EMF of a DC motor (square edges vs. rounded edges).

Also note that with the parallel connection, the 12 pulse rectifier tends to be quite a bit off of ideal. When series connection, the currents are forced to be equal. In parallel connection, the current is not. Since you can't get an exact √3 ration between windings, one winding will carry the current at light load. At full load, the series (leakage) impedance of the transformer helps balance the currents. Most of the time I'm seeing at least 20% imbalance.

Rather than dealing with textbook equations, I tend to head to spice and simulate with real values. Get the best info you can on the load, transformer, interphase transformer and DC link inductors, etc. to simulate what you're really going to see. Don't forget to include line voltage imbalance. Higher pulse number rectifiers are more sensitive to line voltage imbalance.