Chapter 3, Problem 3.29P

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

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

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

(C) Let $\text{S}’$ and S be the per-phase complex power output and input. respectively. Find $\text{S}’$ in terms of S.