Find the current in the neutral of a three-phase four-wire system from unbalanced phase currents, their power factors and the third-harmonic content of non-linear loads, and get the current to size the cable with the IEC 60364-5-52 harmonic factors.
| 3rd harmonic in phase current | Size on | Factor |
|---|
In a balanced three-phase system the three phase currents cancel in the neutral. When the phases are loaded differently, the neutral carries the difference. With equal power factors on all phases:
Example: 100 A, 80 A and 60 A give IN = √(10,000 + 6,400 + 3,600 − 8,000 − 4,800 − 6,000) = √1,200 = 34.6 A. When the power factors differ, the currents are added as vectors with their own angles; the calculator does this automatically.
Non-linear loads such as LED drivers, computers and single-phase power supplies draw third-harmonic currents (150 Hz on a 50 Hz system). These "triplen" harmonics are in phase on all three lines, so instead of cancelling they add up in the neutral: with 30% third harmonic on three balanced 100 A phases, the neutral carries about 86 A even though the fundamental currents cancel completely. With heavy IT loads the neutral current can exceed the phase current.
| Third harmonic content of phase current | Select size on | Reduction factor |
|---|---|---|
| 0–15% | Phase current | 1.0 |
| 15–33% | Phase current | 0.86 |
| 33–45% | Neutral current | 0.86 |
| Above 45% | Neutral current | 1.0 |
Divide the current by the factor and size a 4- or 5-core cable for the result with the Cable Size Calculator. Under the NEC, the neutral of a three-phase four-wire wye circuit serving mainly non-linear loads counts as a current-carrying conductor for ampacity adjustment (310.15(E)).
With equal power factors, IN = √(I1² + I2² + I3² − I1·I2 − I2·I3 − I3·I1). For 100 A, 80 A and 60 A this gives 34.6 A. With different power factors add the currents as vectors, and add triplen harmonic currents arithmetically.
Yes. With non-linear loads the third-harmonic currents of the three phases add in the neutral. Above about 33% third harmonic in the phase current the neutral current exceeds the phase current, and IEC 60364-5-52 then sizes the cable on the neutral current.
Not from the fundamental: balanced currents cancel. But if the loads are non-linear, their third harmonics still add up in the neutral even when the phases are perfectly balanced.
LED drivers often have 25–40% third harmonic. Between 15% and 33% IEC sizes on the phase current divided by 0.86; between 33% and 45% on the neutral current divided by 0.86. Use a full-size neutral and check with the calculator.
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