Question

Determine the positive- and negative-sequence phase shifts for the three phase transformers shown in Figure 3.36.

Short answer

The positive and negative sequence phase shifts for figure (a) are drawn below:

The positive and negative sequence phase shifts for figure (b) are drawn below:

The positive and negative sequence phase shifts for figure (c) are drawn below:

Step-by-step solution

Determine the positive and negative phase sequence

Assume that A, B and C represent the balanced three-phase system.

For the positive sequence set, the phase displacement is in order ABC.

For the negative sequence set, the phase displacement is in order ACB.

Determine the positive and negative phase shifts for figure (a)

(a)

In the first part of figure (a), the positive sequence phase shift is drawn below.

In the second part of figure (a), the positive sequence phase shift is drawn below.

In the third part of figure (a), the positive sequence phase shift is drawn below.

For positive sequence, $V_{H1}$leads $V_{M1}$by role="math" localid="1655180598327" $90°$, and $V_{H1}$lags $V_{X1}$by $90°$.

For negative sequence, $V_{H2}$lags $V_{M2}$by $90°$, and $V_{H2}$leads $V_{X2}$by $90°$.

Determine the positive and negative phase shifts for figure (b)

(b)

In the first part of figure (b), the positive sequence phase shift is drawn below.

In the second part of figure (b), the positive sequence phase shift is drawn below.

In the third part of figure (b), the positive sequence phase shift is drawn below.

For positive sequence, $V_{H1}$leads$V_{X1}$ by$90°$ ,and$V_{X1}$is in phase with$V_{M1}$.

For negative sequence, $V_{H2}$lags$V_{X2}$ by $90°$, and $V_{X2}$is in phase with $V_{M2}$.

Determine the positive and negative phase shifts for figure (c)

(c)

The positive sequence phase shift is drawn below.

For positive sequence, $V_{H1}$leads $V_{X1}$by $23.4°$.

For negative sequence, $V_{H2}$lags $V_{X2}$by $23.4°$.