Y-connected generator phasors – Line vs phase voltage angles Statement: “In a Y-connected generator, there is a 120° difference between each line voltage and the nearest phase voltage.” Determine the correctness of this statement.

Difficulty: Easy

Correct Answer: False

Explanation:


Introduction / Context:
Understanding the phasor relationships between phase and line quantities in Y (wye) systems is essential for measurements and design. The phase angle between line and phase voltages is a common exam point that tests phasor geometry, not just magnitudes.


Given Data / Assumptions:

  • Balanced, three-phase, Y-connected generator.
  • Phase voltages VaN, VbN, VcN are 120° apart and equal in magnitude.
  • Line voltages Vab, Vbc, Vca are differences between phase voltages.


Concept / Approach:

In a balanced Y system, line voltage leads its corresponding phase voltage by 30° (not 120°). Magnitude relationship: |V_line| = √3 * |V_phase|. Angle relationship: each line-to-line voltage is the vector difference of two phase voltages and is shifted by ±30° relative to a phase voltage.


Step-by-Step Solution:

Let VaN = V∠0°, VbN = V∠−120°, VcN = V∠+120°.Compute Vab = VaN − VbN = √3V ∠+30°.Thus Vab leads VaN by 30°; similar results hold cyclically for Vbc and Vca.Therefore, the stated 120° difference is incorrect.


Verification / Alternative check:

Draw the phasor diagram to visualize the 30° lead/lag and the √3 magnitude factor. Measurements on a balanced Y-connected alternator corroborate this geometry.


Why Other Options Are Wrong:

Conditions like unbalance or power factor do not change the inherent phase relation between instantaneous line and phase voltages in the source; the 30° relation is geometric.


Common Pitfalls:

Confusing the 120° separation between phase voltages with the line-to-phase angle. Remember: 120° is between phases; 30° is between a line voltage and its nearest phase voltage.


Final Answer:

False.

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