Question

In developing per-unit equivalent circuits for three-phase transformers, under balanced three-phase operation.

(i) A common ${\mathit{S}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}}$is selected for both the H and X terminals.

(ii) The ratio of the voltage bases $\frac{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{H}}}{{\mathbf{V}}_{\mathbf{b}\mathbf{a}\mathbf{s}\mathbf{e}\mathbf{X}}}$is selected to be equal to the ratio of the rated line-to-line voltages $\frac{{\mathbf{V}}_{\mathbf{ratedHLL}}}{{\mathbf{V}}_{\mathbf{ratedXLL}}}$.

(a) Only one of the above is true.

(b) Neither is true

(c) Both statements are true.

Short answer

Answer

Therefore, the correct option is (c) Both the statements are true.

Step-by-step solution

 Check statement (i).

(i)

The MVA power base for entire system is always common.

Suppose that, for an ideal transformer, H is high-voltage side and X is low voltage side.

For this H and X sides, the $S_{base}$will be same.

Therefore, first option is correct.

Check statement (ii)

(ii)

Suppose that, for an ideal transformer, H is high-voltage side and X is low voltage side.

Let, $V_{ratedHLL}$is a voltage across the line connected to H terminal of transformer and $V_{ratedXLL}$is a voltage across the line connected to X terminal of transformer

Also, $V_{baseH}$and $V_{baseX}$are the rated voltage or base voltages of H and X side of transformer.

HLL is connected to H and XLL is connected to X, therefore, the ratio $\frac{V_{baseH}}{V_{baseX}}$is same as the ratio of $\frac{V_{ratedHLL}}{V_{ratedXLL}}$.

Therefore, second statement is correct.

Hence, correct option is (c) Both the statements are true