Analytical model of a T-connected three-phase transformer

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Abstract

Three-phase transformers usually consist of three sets of windings connected in Wye, delta or zigzag on three individual cores or on a single three-phase one. Two single-phase transformers can also be used in a less than well-known way called the T-connection. Depending on the actual connection, as in conventional three-phase transformers, secondary voltages are in phase or displaced by ±30°. Due to the reduced number of windings, the T-connected transformer can be economically produced. However, since it is an asymmetrical connection, the short-circuit impedances of the individual phases are not identical, leading to unbalanced load voltages and short-circuit currents. An analytical model of the T-connected transformer has been developed to evaluate the effects of the impedance unbalance. This model based on single-phase short-circuit tests can be used to determine voltage unbalances, active and reactive transformer losses and short-circuit impedances.

Introduction

The T-connected three-phase transformer was first introduced by E.W. Manning in 1958 [1]. As can be seen in Fig. 1, it consists of two single-phase transformers with both primary and secondary windings connected in the same way as the primary of a Scott connected transformer. The first winding, called the main winding, is connected across two lines and one end of the second winding, the teaser, is connected to the third line while the other end is connected to the midpoint of the first winding. The main windings should be rated for the line-to-line voltage and the teasers for √3/2 times the line-to-line voltage or one and a half the phase voltage. If needed, a neutral point can be realized with a tap at one-third of the teaser winding. Depending how the secondary windings are connected in relation to the primary windings, three basic configurations exist. The first one, identified as Tt0, introduces no phase-shift between the primary and secondary voltages while for the two others, identified as Tt1 and Tt11, the secondary voltages are respectively displaced by 30° and −30°. In fact, the first configuration behaves exactly like conventional delta–zigzag transformer while the last two emulate delta–Wye connections with ±30° phase-shift.

The same equations as for the conventional cases apply to the relations between primary and secondary voltages and currents.ForTt0:Eab=EABaandIA=IaaEbc=EBCaandIB=IbaEca=ECAaandIC=IcaForTt11:Eab=EAB∠−30°aandIA=Ia−Ica3Ebc=EBC∠−30°aandIB=Ib−Iaa3Eca=ECA∠−30°aandIC=Ic−Iba3ForTt1:Eab=EAB∠30°aandIA=Ia−Iba3Ebc=EBC∠30°aandIB=Ib−Ica3Eca=ECA∠30°aandIC=Ic−Iaa3where a is the voltage ratio: Eab/EAB

Even though, in most of the cases, the use of a T-connected transformer rather than a more common configuration is completely transparent to the user, this connection is seldom seen in North America and is completely unknown in Europe. In Canada, at least one company offers a full line of low-voltage, dry-type, distribution transformers based on the T-connection. The range of their products extends from 15 kVA to more than 500 kVA. Voltages up to 4.6 kV are available. These transformers are routinely used for commercial, institutional and industrial applications.

Section snippets

Impedance unbalance

In usual three-phase transformers, it is assumed that the short-circuit impedances of the individual phases are identical. Therefore, their single line model is a simple impedance. However, because its construction is based on two single-phase transformers, the short-circuit impedance of a T-connected transformer is more complex. Each individual phase presents a different impedance and, moreover, these impedances are coupled. This asymmetrical short-circuit impedances are probably the cause of

Application

In order to assess its validity, the model was applied to several commercial transformers with capacity ranging from 30 to 112.5 kVA. Similar results were obtained with all units. Typical results obtained for a 112.5 kVA, 60 Hz, 600/120–208 V transformer are given. All calculations were done for a temperature winding of 20 °C. Table 1 gives, the turn ratios, the short-circuit impedances and the winding resistances of the transformer at 20 °C. Appendix A gives the numerical values of matrices G and N.

Conclusion

A new analytical model of T-connected transformers have been presented. This model, is based on simple short-circuit tests done on individual pairs of windings, enables the calculation of, transformer losses and impedance, secondary voltage unbalance and short-circuit currents. Results show that the T-connected transformer can satisfactory replace conventional units in most of the applications.

Acknowledgements

This work was supported in part by the National Research Council Canada and, in part, by Marcus Transformer Canada.

References (4)

  • E.W. Manning, The T-Connected Three-Phase Transformer, AIEE Transactions on Power Apparatus and Systems, Part III, vol....
  • R.D. Chenoweh, A.K. Ayeub, Equivalent circuits for multi winding transformers: a general procedure, in: Proceedings of...
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