The following rules must be obeyed in order to successfully connect two or more transformers in parallel with each other:
1. The turn ratios of all of the transformers must be nearly equal.
2. The phase angle displacements of all of the transformers must be identical.
3. The series impedances of all transformers must be nearly equal, when expressed as ‘‘%Z’’ using the transformer impedance base.
The first two rules are required so that the open-circuit secondary voltages of the transformers are closely matched in order to avoid excessive circulating currents when the parallel connections are made.
The last rule is based on the fact that for a given voltage rating and %Z, the ohmic impedance of a transformer is inversely proportional to its KVA rating. When transformers having the same %Z are connected in parallel, the load currents will split in proportion to the KVA ratings of the units. Therefore, transformers with different KVA ratings can be successfully operated in parallel as long as their %Z values are all approximately the same.
According to IEC 60076-8 , a mismatch of relative loading of no more than about 10% between two transformers of non-identical designs should be regarded as reasonable.
Regarding the impedance mismatch we can write:
Sra , Srb : Rated power of a and b power transformer
Za , Zb : Relative impedance of a and b power transformer
Sa , Sb : Take up load by of a and b power transformer
S : Shard load
According to ABB switchgear manual, approximately the impedance voltages Uk maximum permissible discrepancies is ± 10 %. In the event of larger differences, an inductance (reactor) can be connected ahead of the transformer with the lower impedance voltage. Also the following conditions must be satisfied in order to avoid dangerous transient currents:
1. Vector groups should have the same phase angle number; terminals of the same designation must be connected together on the HV and LV sides; Exception: Phase angle numbers 5 and 11
2. The ratios should be as similar as possible, i.e. the same rated voltages on the HV and LV sides;
3. Rated output ratio smaller than 3:1.
In the other hand, when connecting single-phase transformers in three-phase banks, proper impedance matching becomes even more critical. In addition to following the three rules for parallel operation, it is also a good practice to try to match the X/R ratios of the three series impedances to keep the three-phase output voltages balanced.
If single-phase transformers are connected in a Y-Y bank with an isolated neutral, then the magnetizing impedances should also be equal on an ohmic basis. Otherwise, the transformer having the largest magnetizing impedance will have a highest percentage of exciting voltage, increasing the core losses of that transformer and possibly driving its core into saturation.
When single-phase transformers with the same KVA ratings are connected in a Y-Δbank, impedance mismatches can cause a significant load unbalance among the transformers. The general case where all three transformers have different impedances is derived below.
Define the following ratios of impedances, w and x, as follows.
(Note: In general, these ratios are complex numbers because the impedances are complex numbers.)
With a balanced three-phase load of 1 per unit applied, the phase currents are as follows
The bank is balanced if w = 1 and x = 1. Even when the impedance magnitudes are all equal, if the X/R ratios are unequal then w ≠ or x≠ and the transformer currents will not be equal. The most heavily loaded transformer limits the maximum load that can be applied to the bank, so any unbalance will reduce the load rating of the bank.
Let us examine the specific case where the X/R ratios of all three transformers are equal, and transformer B is identical to transformer C but the impedance of transformer A is not equal to the impedances of the other two transformers. In this case Zb/Za = Zc/Za =x and x is a real number. The currents ia, ib, and ic are multiplied by 1.732 to obtain the per-unit loading due to the Y-Δconnection.