In a balanced Y–Y (wye–wye) source/load configuration, what is the relationship among the phase current, the line current, and the load current for each phase?

Introduction / Context:
Recognizing current relationships in three-phase connections is essential for sizing conductors, selecting protection, and interpreting measurements. In a wye (Y) connection—on both source and load—the link between line and phase currents is straightforward yet frequently confused with delta relationships.

Given Data / Assumptions:

• Balanced Y-connected source feeding a balanced Y-connected load.
• Ideal lines with negligible impedance.
• Sinusoidal steady state.

Concept / Approach:

In a Y-connected load, each phase element is connected from a line to the neutral point. The current in each line flows directly through the corresponding phase element. Therefore, for each phase: I_line = I_phase (also the load phase current). This is unlike delta, where line current is √3 times phase current.

Step-by-Step Solution:

Verification / Alternative check:

Phasor diagrams for balanced Y systems show equal magnitudes for the three line currents, each aligned with its corresponding phase current. Measurements in practical systems confirm this one-to-one relationship when the load is Y-connected and balanced.

Why Other Options Are Wrong:

Options suggesting 120° phase differences between line and phase currents are incorrect for Y. The 120° separations are between the three phase sets, not between a line and its own phase branch.

Common Pitfalls:

Confusing Y with Δ results; misapplying the √3 factor to currents in Y-connected loads.

Final Answer:

phase current, the line current, and the load current are all equal in each phase