Two winding transformer equivalent from a three winding transformer

[Stativa Andrei]

Does anyone know if it is possible to determine the two winding equivalent of a three winding transformer with a load connected in the tertiary? I presume that the load and the tertiary must be 'absorbed' somehow into primary and secondary windings. From the leakage impedances, with delta-star transformation, I determined the winding impedances. Then I add the load impedance with the tertiary impedance, and from here I tried two methods:
1. Zeq = Zp + Zs + Zs*Zt/(Zt + Zload)
2. I used Kron reduction in order to remove the tertiary (with the load) impedances (dont know If Kron method is suited for this problem).
None of the approaches gave good results (maybe I did something wrong), so please help me.
A third approach that gave good results was as follows:
3. I treated the problem as an optimization problem, so I used a binary genetic algorithm to optimize R and X (from two winding transformer) so that the power flow from the primary of the two transformers to be as equal as possible (this being the objective function).
The thing is that I want to solve the problem with a method other then the third. If you have ideas, please share them with me...or papers about this matter.

 

[waross]

The directed current in the secondary will cause a directed current in the primary determined by the primary/secondary ratio.
The directed current in the tertiary will cause a directed current in the primary determined by the primary/tertiary ratio.
The directed sum of these currents will be the primary current.
PS: Power factor matters.

 

[Stativa Andrei]

The directed current in the secondary will cause a directed current in the primary determined by the primary/secondary ratio.
The directed current in the tertiary will cause a directed current in the primary determined by the primary/tertiary ratio.
The directed sum of these currents will be the primary current.
PS: Power factor matters.

I tried also with the same power and voltage in all three windings and nothing. I did this just to be sure that the impedances are reported at the same base.

 

[prc]

Please refer to IEC 60076-8,, Transformer Application Guide, or the Transformer Book by L.F. Blume for Theory of Multi circuit Transformers