Open-Delta or V-V Connection

The open-delta, also known as the V-V connection, is a 3-phase arrangement that makes use of only two, instead of three, single-phase transformers, as shown in Fig. 6-27. The open-delta connection is sometimes used in the case of instrument potential transformers for economy. It is also used initially in load centers, the full growth of which may require several years, at which time a third transformer is added for the conventional delta-delta operation.

Figure 6-27. Open-delta or V-V connection, (a) Common physical arrangement; (b) schematic diagram

The rating of two identical transformers operating delta-delta is 1/ of the rating of three similar transformers, but connected delta-delta. It would seem that this rating should be 2/3 instead of 1/. However, the line current is also the current in the transformer winding and, if I is the rated current of each of the two transformers and V the rated voltage, then the rated 3-phase power is VI. In the case of three transformers, the line current is times the current in the transformers windings when connected delta and when the load is balanced. The 3-phase rating of the three transformers is, therefore, 3VI, where I is the rated current of the transformer winding.

If it were not for the leakage impedance of the transformers, the secondary voltages of an open-delta connection would be balanced when balanced 3-phase voltage is applied to the primary. This is evident when we let V_AB V_BC and V_CA be the balanced 3-phase primary applied voltages. Then

and

If the transformer leakage impedances are neglected, and their ratio is a, then the secondary voltages are

but from Kirchhoff's law

from which

showing that the secondary voltages V_ab, V_bc, and V_ca are equal in magnitude and displaced from each other by an angle of 120°. This is characteristic of balanced 3-phase systems, and is true only for ideal transformers. In the case of actual transformers, the secondary voltages will not be balanced exactly, even when balanced voltages are applied to the primary in an open-delta arrangement because there are only two transformers and, therefore, only two, instead of three, leakage impedance voltage drops.