Question

Three single-phase \(11\text{kV}/3.3\text{kV}\) transformers are connected to form a three-phase transformer bank, with the HV and LV windings connected as shown.

Considering ABC phase sequence, the vector group of the transformer is:

• A. Dd0
• B. Dd4
• C. Dd6
• D. Dd10

Hint:

Trace both deltas using the dot marks; the LV loop here closes in the opposite rotational sense to the HV loop, giving a clock number of 10, not 0.

Answer 1

The Correct Option is D

Step 1: Draw the HV phasor star.
Place the three HV winding EMFs $120^{\circ}$ apart: $E_A$ at $0^{\circ}$, $E_B$ at $-120^{\circ}$, $E_C$ at $120^{\circ}$. Joining tip to tail in the order A, B, C traces out the HV delta, and the line voltage $V_{AB}$ points along $E_A$, so it sits at $0^{\circ}$, marked as the "12 o'clock" position on a clock face.

Step 2: Draw the LV phasor star at the same angles.
Because each dotted LV winding is in phase with its own HV partner, $e_a$, $e_b$, $e_c$ sit at the same three angles as $E_A$, $E_B$, $E_C$: $0^{\circ}$, $-120^{\circ}$, $120^{\circ}$. Only the way they get stitched into a delta differs.

Step 3: Follow the actual LV wiring.
From the diagram, the LV loop is stitched in the reverse order: the undotted end of one winding lands on the dotted end of the next. Walking the loop this way, the corner-to-corner voltage $V_{ab}$ works out to be $-e_b$ instead of $+e_a$.

Step 4: Place this on the clock.
$-e_b$ points at $-120^{\circ}+180^{\circ}=60^{\circ}$. Reading this on a clock face where 12 is $0^{\circ}$ and the hours increase going clockwise, which is the lagging direction, $60^{\circ}$ of lead is the same position as $300^{\circ}$ of lag, landing exactly on the "10" mark.

Step 5: Double check the lead/lag equivalence.
A phasor at $+60^{\circ}$ and a phasor at $-300^{\circ}$ are the same physical direction, since angles repeat every $360^{\circ}$. So calling $V_{ab}$ "leading by $60^{\circ}$" or "lagging by $300^{\circ}$" are two descriptions of the one result from Step 4.

Step 6: State the vector group.
Since both sides are delta connected and the LV side sits at the 10 o'clock position relative to the HV side, the vector group is Dd10.
\[ \boxed{\text{Dd10}} \]