How can we calculate positive, negative and zero sequence currents in a transformer?

The application of symmetrical components is not so much to model the currents within the transformer, but to apply impedance modeling techniques to see how positive. negeative and zero sequence currents flow in a power system in which the transformer is connected. The impedance you use for the tranformer in a negative seqquence diagram is handled the same was as a positive sequence impedance. It's just conected in series with other negative sequence impedances in the negative sequence network. Zero sequence impedance modeling depends on the transformer winding connection. A delta wye winding is modeled by an open circuit in the zero sequence network. No zero sequence connection between primary and secondary. Whereas wye-wye there is a zero sequence path between the two windings Often negative sequence impedance and zero sequence impedance for a transformer is the same as the positive sequence impedance. There are cases where the zero sequence impedance could be less, and secondary ground faults would be higher than secondary three-phase bolted faults. I think Stevenson, "Elements of Power System Analysis" is still regarded as a good reference for symmetrical component theory.

I think your question is how can we find those values in practice isn't ?

Symmetrical component analysis is used in calculating the current valuess during unsymmetrical faults and loading conditions.

If you want to find out the positive sequence impedance

Apply a balanced 3 phase voltage in the winding with out neutral and short circuit the other winding ( the winding to which the % impedance is required ) keeping all other windings windings open circuited . ( if there is delta teritiary it can be kept as it is with out any external short circuit - The ratio of the Applied voltage and current will give you the positive sequence impedance between the Two

These experiment can be done between each and every pair of windings to find out the positive and negative sequence impedance

To find the zero sequence impedance ( Star- Star )

Apply the a single phase voltage to all the three phases with neutral connected short circuit the secondary side with neutral - The % zero sequence impedance is 3 V/I ( if there is any delta winding , it shall be kept open circuited - This is not normally possible at site )
To find the zero sequence impedance ( Star- delta )

Apply the a single phase voltage to all the three phases with neutral connected . Keep the delta in delta mode with out any short circuit externally - The % zero sequence impedance is 3 V/I ( if there is any other delta winding , it shall be kept open circuited - This is not normally possible at site . If there is any other star winding it shall be kept open )

After measuring the impedances in this way , you have substitute the values in the positive sequence or zero sequence as the case may be and proceed with calculation

In case of 3 winding with tertiary winding , the values shall be put in T equivalent values before proceeding further

Hope I have complicated you enough !

if you know the phasor of the 3 phases currents u can have the "phase a" compenents by multiplying the cuurents column by the "A matrix " for phase b and c the positive sequance is 120 shifted for b and 240 for c ,the negative the sequence will be acb