Consider three ideal single-phase transformers (with a voltage gain of \(\eta\) ) put together as a \(\Delta-\Omega\) three-phase bank as shown in Figure 3.35. Assuming positive-sequence voltages for \(V_{a w}, V_{b n}\), and \(V_{c n}\), find \(V_{a^{\prime} n^{\prime}}, V_{b^{\prime} n^{\prime}}\), and \(V_{C^{\prime} n^{\prime}}\) in terms of \(V_{a n}, V_{b n}\), and \(V_{c n}\), respectively.

(a) Would such relationships hold for the line voltages as well?

(b) Looking into the current relationships, express \(I^{\prime}{ }_{a}, I^{\prime}{ }_{b}\), and \(I^{\prime}{ }_{c}\) in terms of \(I_{a}, I_{b}\), and \(I_{c}\), respectively.

(c) Let \(S^{\prime}\) and \(S\) be the per-phase complex power output and input, respectively. Find \(\mathrm{S}^{\prime}\) in terms of \(S\).

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