Transformers used in three-phase systems may consist of a ..., Exercises of Topology

Download Transformers used in three-phase systems may consist of a ... and more Exercises Topology in PDF only on Docsity! THREE-PHASE TRANSFORMERS Transformers used in three-phase systems may consist of a bank of three single-phase transformers or a single three-phase transformer which is wound on a common magnetic core. A three-phase transformer wound on a common core offers advantages over a bank of single-phase transformers. A three-phase transformer wound on a common core is lighter, smaller and cheaper than the bank of three single-phase transformers. The common core three-phase transformer also requires much less external wiring than the bank of single-phase transformers and can typically achieve a higher efficiency. The bank of three single-phase transformers does offer the advantage of flexibility. In the case of an unbalanced load, one or more transformer in the bank can be replaced by a larger or smaller kVA-rated transformer. In terms of maintenance, a malfunctioning transformer in the bank of transformers can be easily replaced while the entire common core three- phase transformer would require replacement. The bank of single-phase transformers or the common core three- phase transformer can be connected in one of four combinations relative to the primary and secondary connections. Wye-Delta: Commonly used in a step-down transformer, wye connection on the HV side reduces insulation costs, the neutral point on the HV side can be grounded, stable with respect to unbalanced loads. Delta-Wye: Commonly used in a step-up transformer for the same reasons as above. Delta-Delta: Offers the advantage that one of the transformers can be removed while the remaining two transformers can deliver three-phase power at 58% of the original bank. Wye-Wye: Rarely used, problems with unbalanced loads. Wye-Delta Connection Delta-Wye Connection PER-PHASE ANALYSIS OF THREE-PHASE TRANSFORMERS Assuming the three transformers in the three-phase transformer are identical and the sources and loads in the three-phase problem are balanced, circuits involving a the three-phase transformer can be analyzed on a per- phase basis as illustrated in our study of three-phase circuits. As previously discussed, the easiest three-phase topology to analyze is the wye-wye connection. Thus, given any other configuration for the three- phase transformer other than wye-wye, one should transform the circuit into wye-wye form. The equivalent turns ratio for the transformed wye-wye per-phase equivalent circuit for the transformer is the ratio of the primary line-to-line voltage to the secondary line-to-line voltage for the original configuration. The concept of the equivalent turns ratio can be illustrated by an example transformation of a transformer configuration. The wye-delta and delta-wye configurations of three-phase transformers result in 30o phase shifts between the primary and secondary line-to-line voltages. The industry standard is such that the lower voltages in these configurations should lag the higher voltages by 30o. The wye-wye or delta-delta configurations produce line-to-line voltages in the primary and secondary that are in phase. Example Transform a wye-delta three-phase transformer into the wye-wye configuration and determine the equivalent turns ratio aN of the resulting wye-wye transformer. Draw the per-phase equivalent circuit for the resulting wye-wye transformer. The line-to-neutral voltages across the windings of the equivalent wye- connected secondary are found by dividing the line-to-line voltages across the windings of the of the delta-connected secondary by %&3. Comparing the voltages and currents of the primary and secondary windings, we see the that the equivalent turns ratio of the wye-wye configuration is The equivalent wye-wye model for the wye-delta connected three-phase transformer is In a similar fashion, if we consider the transformation of the the delta- wye and delta-delta configurations to the wye-wye configurations, we find equivalent turns ratios of (c.) To determine the line-to-line voltage on the primary required to produce a secondary line-to-line voltage of 230 V, we must analyze the per-phase equivalent circuit. In the per-phase equivalent circuit, 2the current I is the secondary line current (magnitude = 301.23 A) 2while the voltage V is the secondary line-to-neutral voltage (magnitude = 230/ %&3 = 132.79 V). The power factor of the load 2 2.gives the phase angle difference between V and I Using the secondary line-to-neutral voltage as our reference gives The secondary values can be reflected back to the primary according to the modified turns ratio aN. The resulting primary voltage V1 (line-to-neutral) is The magnitude of the primary line-to-line voltage is (d.) The voltage regulation of this transformer is given by