Question

In delta-star connection, the phase displacement between the primary voltage and secondary emfs is

• A. \( 30^\circ \)
• B. \( -60^\circ \)
• C. \( 60^\circ \)
• D. \( -30^\circ \)

Hint:

Whenever you see a mismatch in the primary and secondary connection types (one side is Delta and the other side is Star), the phase displacement will always involve an odd multiple of $30^\circ$ (typically $\pm 30^\circ$). If the connections are identical on both sides (Star-Star or Delta-Delta), the shift is always $0^\circ$ or $180^\circ$.

Answer 1

The Correct Option is A

Concept: In three-phase transformers, the phase displacement is defined as the angle by which the secondary line voltage lags behind the primary line voltage when viewed from a phasor diagram perspective. This displacement is standardized using clock convention notations, where the primary voltage phasor is fixed at the $12$ o'clock position ($0^\circ$). Common combinations include:
• Star-Star (Y-y) or Delta-Delta (D-d): Typically yield $0^\circ$ or $180^\circ$ phase shifts (Yy0, Dd0, Yy6, Dd6).
• Delta-Star (D-y) or Star-Delta (Y-d): Introduce an inherent structural phase shift of $\pm 30^\circ$ due to the mixing of line and phase values between the two configurations (Dy1, Dy11).

Step 1: Analyze the phasor configurations of Delta and Star windings.
Let the primary side be connected in Delta ($\Delta$) and the secondary side be connected in Star ($Y$). In a Delta connection, the line voltage is equal to the phase voltage: $$V_{\text{line, primary}} = V_{\text{phase, primary}}$$ In a Star connection, the line voltage is $\sqrt{3}$ times the phase voltage, and it leads the phase voltage by $30^\circ$: $$V_{\text{line, secondary}} = \sqrt{3} \cdot V_{\text{phase, secondary}} \angle 30^\circ$$

Step 2: Account for the magnetic coupling between primary and secondary phases.
The voltage induced in the secondary phase winding is exactly in phase with the voltage across the corresponding primary phase winding because they are wound on the same magnetic core limb. $$V_{\text{phase, secondary}} \propto V_{\text{phase, primary}}$$ Since the primary line voltage is equal to the primary phase voltage, but the secondary line voltage is shifted from the secondary phase voltage by $30^\circ$, it directly implies a phase displacement between the primary line voltage and the secondary line voltage.

Step 3: Determine the value of the displacement angle.
Standard Delta-Star connections are designed as either a $+30^\circ$ lead (Dy11 connection, corresponding to 11 o'clock) or a $-30^\circ$ lag ($+330^\circ$, Dy1 connection, corresponding to 1 o'clock). Looking at the options provided:
• (1) $30^\circ$
• (2) $-60^\circ$
• (3) $60^\circ$
• (4) $-30^\circ$ Among the standard configurations, a phase shift magnitude of $30^\circ$ is the universally recognized value for delta-star arrangements. Therefore, option (1) is correct.