You've accurately identified the core of the problem: the shared leg. Simply adding the single-phase currents is incorrect because the currents are out of phase. Your intuition about not simply doubling the current is spot on.Let's break down the best approach and why your suggested method has some merit but isn't perfect.

Understanding the Vector Addition

The key is understanding that the currents in each single-phase transformer are shifted 120 degrees from each other (relative to the three-phase system). You can't just add them arithmetically. You need to consider their phase relationship.

A More Accurate Approach: Vector Sum and Calculation

Here's how to calculate the currents in each phase line:1. Single-Phase Transformer Currents

As you correctly calculated, each 25kVA transformer draws 52.1A at 480V.
2.

Define the Phases

Let's call the three phases A, B, and C. Transformer 1 is connected between phases A and B. Transformer 2 is connected between phases B and C.3.

Calculate the Currents in each Phase



Phase A

52.1A (due to Transformer 1)

Phase B

This is the shared leg. It carries current from both transformers. The current from Transformer 1 flows into Phase B, and the current from Transformer 2 flows out of Phase B. To calculate the current in Phase B, you need to do a vector subtraction. This requires a bit more math: Convert the currents to complex numbers: Current from Transformer 1 (flowing into B): 52.1∠0° Current from Transformer 2 (flowing out of B): -52.1∠120° Vector sum (subtraction in this case because we're considering the direction of flow):52.1∠0° - 52.1∠120° = 52.1 - 52.1 (-0.5 + j0.866) = 52.1 + 26.05 - j45.12 = 78.15 - j45.12 Magnitude of the vector sum:√(78.15² + (-45.12)²) = √(6107.42 + 2035.81) = √8143.23 = 90.24 A

Phase C

52.1A (due to Transformer 2)4.

Add the 3-Phase Load Currents

Assume your 21.6A 3-phase load is balanced (equal current in each phase). Convert the 3-phase load current to a single phase value: 21.6A / √3 = 12.47A Add the 3-phase current to each phase:

Phase A

52.1A + 12.47A = 64.57A

Phase B

90.24A + 12.47A = 102.71A

Phase C

52.1A + 12.47A = 64.57A

Therefore, the calculated phase currents are approximately: Phase A = 64.57A, Phase B = 102.71A, Phase C = 64.57AWhy Your "75kVA 3-Phase" Approach is Close (but Not Perfect)

Your 75kVA 3-phase approximation is actually quite clever and, in many cases, a reasonable estimate. Here's why:

Total Power

It correctly accounts for the total power being drawn (25kVA + 25kVA = 50kVA; assuming balanced three-phase is drawing very little real power.)

Averaging

It essentially averages the effect of the single-phase loads across all three phases.

Limitations

It doesn't perfectly capture the fact that the current is heavily concentrated on Phase B. The real situation creates a larger current imbalance than assuming a balanced 75kVA load.

When to Use the Approximation

For quick, back-of-the-envelope calculations. When you don't have all the information needed for a full vector analysis. As a way to check the reasonableness of more detailed calculations. For initial sizing estimates when there is significant slack in the system.

When to Use the Vector Analysis

For critical applications where accuracy is paramount (e.g., sizing circuit breakers, conductors, transformers, etc.). When dealing with a significant imbalance in the single-phase loads. When you need to perform a power system study or analysis.

Key Takeaways: Don't simply add single-phase currents arithmetically in a three-phase system. Vector analysis provides the most accurate solution. The "75kVA three-phase" approximation can be useful for quick estimates, but be aware of its limitations.* Pay special attention to the shared leg, as it will carry the highest current.Remember to always consult with a qualified electrical engineer for critical design decisions. They will be able to consider all relevant factors, including safety, code compliance, and the specific characteristics of your system. Flag for review