Three single-phase two-winding transformers, each rated \(3 \mathrm{kVA}, 220 / 110\) volts, \(60 \mathrm{~Hz}\), with a 0.10 per-unit leakage reactance, are connected as a three-phase extended \(\Delta\) autotransformer bank, as shown in Figure 3.36 (c). The low-voltage \(\Delta\) winding has a 110 volt rating.

(a) Draw the positivesequence phasor diagram and show that the high-voltage winding has a 479.5 volt rating.

(b) A three-phase load connected to the low-voltage terminals absorbs \(6 \mathrm{~kW}\) at 110 volts and at 0.8 power factor lagging. Draw the per-unit impedance diagram and calculate the voltage and current at the high-voltage terminals. Assume positive-sequence operation.

Figure 3.36 (c)

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2N turns N turns HA HB XB HC (c) Extended A autotransformer