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Parallel operation of autotransformers

Q:
We have 2 no 160MVA 220/132/11 kV transformers with short circuit impedance 46.06 ohm, and one 160MVA transformer, 220/132/11 kV with % impedance 15.02%. Can we parallel these three transformers?

A:
Indeed, the vector group is an important (mandatory) consideration when connecting transformers in parallel. And also important if a transformer is going to close a loop in either the HV or LV sides.

But it is perfectly OK to parallel transformers with different impedances. All it is going to happen is an uneven distribution of the power flow, among the parallel transformers. The unit with the lowest impedance would carry a larger share of the load.

Regarding "same ratio": are you talking about the transformer ratio, such as 138/230 kV? Or are you talking about tap positions? Within certain constraints, it is possible to parallel transformers with different ratios (let's think, for a second, of identical transformers at different tap positions). This is not recommended, though, because of reactive power circulation.

So, without disagreeing with the factors that you have listed, I would like to re-order, if you will, the conditions you have described:
1) Mandatory: making sure that the vector group and nominal voltages of transformers being considered for parallel operation are indeed adequate and compatible with the intended parallel operation
2) Desirable: ability to operate parallel transformers at the same tap positions or as close as possible, to minimize reactive current circulation
3) Almost indifferent: identical impedances on the parallel transformers simplify things a bit, but this is not a "show stopper" for parallel operation of these transformers. Actually, it is more realistic to expect some differences in impedances, even for otherwise "identical" transformers (same manufacturer, same nameplate ratings, etc.)

For the "Y-Y- Delta" transformers operated in parallel, there exist two kinds of the circulating currents between the tanks and between the banks of the delta side. As the circulating current between the tanks is 90 degree out of phase of the load current, it is estimated by decomposing the line current into the component 90 degree out of phase of the load current. The circulating current between the banks in the delta side is estimated from the delta winding current and the line currents.

The estimated circulating current depends on the power factor of the system even with the same tank currents. This characteristic is derived from the view point of the active and reactive power. Also, it needs the voltage as well as the tank and the load currents.

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