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Standard three-phase unbalanced-current phasor formula7 min read

Worked Example: Neutral Current from an Unbalanced Three-Phase Panel Load

Three unevenly loaded phases in a distribution board — computing the resulting neutral current directly from the phasor relationship, not just estimating it as the difference between the busiest and quietest phase.

Scenario

Phase L1 current45 A
Phase L2 current38 A
Phase L3 current52 A

Step-by-step calculation

Step 1: Compute the average phase current and each phase's deviation from it

average = (IL1 + IL2 + IL3) / 3
(45 + 38 + 52) / 3
average = 45 A

Step 2: Find the maximum deviation as a percentage of average

maxDeviation% = max(|IL_n - average|) / average x 100
L3 deviates most: |52-45| = 7 A; 7 / 45 x 100
maxDeviation = 15.6%

Step 3: Compute neutral current using the phasor (120°-apart) formula

The three phase currents are 120° apart, not simply summed or subtracted — the neutral current formula accounts for this phase relationship directly.

In = √(IL1² + IL2² + IL3² - IL1·IL2 - IL2·IL3 - IL1·IL3)
√(45² + 38² + 52² - 45x38 - 38x52 - 45x52)
In = 12.12 A

Step 4: Identify the most and least loaded phases

Result summary

CheckRequirementActualStatus
Panel balance (max deviation from average)n/a (informational — lower is better practice)15.6%, on phase L3✓ PASS
Resulting neutral currentn/a (this is the computed result)12.12 A✓ PASS
This panel's phase imbalance produces 12.12 A of neutral current — noticeably less than the raw 14 A difference between the busiest (L3, 52 A) and quietest (L2, 38 A) phase, because the phasor formula correctly accounts for the 120° phase relationship rather than treating currents as if they were simply additive.

Key insight: Neutral current from a balanced linear load is exactly zero even though each phase carries substantial current — it's specifically the imbalance between phases (not the absolute current level) that drives neutral current on a linear-load panel. This is a fundamentally different mechanism from the harmonic-driven neutral current from non-linear loads (like the Data Centre UPS Output scenario elsewhere on this site), where even perfectly balanced phase loading doesn't eliminate neutral current.

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Frequently asked questions

How could this panel be rebalanced?

Moving some circuits from the most-loaded phase (L3, 52 A) to the least-loaded phase (L2, 38 A) — even a rough rebalancing to bring all three phases closer to the 45 A average — would reduce both the percentage imbalance and the resulting neutral current, which matters for neutral conductor sizing and for reducing losses on shared neutral runs.

Is 15.6% imbalance a problem?

There's no single universal hard limit for panel-level phase imbalance the way there is for supply voltage unbalance, but persistent imbalance like this increases neutral conductor loading and can indicate an opportunity to rebalance circuits for better overall system efficiency and more even conductor utilization — it's worth addressing as good practice even without a specific code violation.

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