Triplen Harmonic Neutral Current Calculator
Enter the three fundamental phase currents, the per-phase triplen harmonic percentages, and the adjusted neutral ampacity. The calculator reports true-RMS neutral current, harmonic contribution, largest phase true-RMS current, and whether the entered neutral ampacity is exceeded.
Total neutral RMS current36.58
- Fundamental imbalance current
- 0
- Triplen harmonic neutral current
- 36.58
- Neutral ampacity used
- 91.44%
- Largest phase true-RMS current
- 41.82
- Neutral-to-largest-phase current
- 87.47%
- Neutral loading status
- Within entered neutral ampacity.
Neutral current components
| Component | Neutral current |
|---|---|
| Fundamental imbalance | 0 |
| 3rd harmonic | 36 |
| 9th harmonic | 6 |
| 15th harmonic | 2.4 |
Assumes the entered triplen harmonic percentages are the same on each phase and are zero-sequence components that add in the neutral.
Different harmonic frequencies are combined by root-sum-square because their RMS currents are orthogonal.
How to use this calculator
- Enter the fundamental RMS current on phases A, B, and C.
- Enter the 3rd, 9th, and 15th harmonic RMS currents as percentages of each phase fundamental current.
- Enter the adjusted neutral conductor ampacity after applicable correction and adjustment factors.
- Read the total neutral RMS current, ampacity use, and harmonic breakdown.
How the neutral current is calculated
This calculator separates the 50 Hz or 60 Hz fundamental neutral current from the zero-sequence triplen harmonic current. The fundamental part is the vector sum of three phase currents spaced 120 electrical degrees apart. With phase-current magnitudes IA, IB, and IC, the fundamental neutral current is:
IN1 = sqrt(IA^2 + IB^2 + IC^2 - IA x IB - IB x IC - IC x IA)
Triplen harmonics are odd multiples of the third harmonic. In a four-wire wye system, balanced 3rd, 9th, and 15th harmonic currents are zero-sequence components, so they are in phase with each other across A, B, and C for that harmonic order. Instead of canceling in the neutral, each order adds arithmetically:
IN3 = p3 x (IA + IB + IC)
IN9 = p9 x (IA + IB + IC)
IN15 = p15 x (IA + IB + IC)
Here p3, p9, and p15 are the entered percentages divided by 100. Different harmonic frequencies do not peak at the same instant in a fixed way, so their RMS contributions are combined by root-sum-square:
INT = sqrt(IN3^2 + IN9^2 + IN15^2)
The total neutral RMS current is then IN = sqrt(IN1^2 + INT^2). The phase true-RMS check uses Ix,rms = Ix x sqrt(1 + p3^2 + p9^2 + p15^2), and the neutral utilization is 100 x IN / INrated.
What moves the result most
The 3rd harmonic usually dominates because it is often much larger than the 9th or 15th, and because the neutral contribution is based on the sum of the three phase fundamentals. A perfectly balanced three-phase load can therefore have zero fundamental neutral current while still putting substantial RMS current in the neutral. Phase imbalance matters most when harmonic percentages are small or zero.
What this calculator leaves out
The calculation assumes each phase has the same harmonic percentage and that each entered triplen component is aligned as a zero-sequence current. Real measurements may show unequal harmonic spectra, different harmonic phase angles, displacement power-factor differences, non-triplen zero-sequence components, and current distortion from multiple loads. This tool also does not select a conductor size or apply code-specific ampacity, bundling, ambient-temperature, termination, or equipment rules.
Worked example
Suppose phases A, B, and C each carry 40 A of fundamental current. The 3rd harmonic is 30%, the 9th is 5%, the 15th is 2%, and the adjusted neutral ampacity is 40 A.
The fundamental imbalance current is 0 A because the phase currents are balanced. The phase-current sum is 120 A, so the neutral harmonic currents are 36 A at the 3rd, 6 A at the 9th, and 2.4 A at the 15th. Their root-sum-square is 36.58 A, so the total neutral RMS current is also 36.58 A. Neutral ampacity use is 91.44%, and the largest phase true-RMS current is 41.82 A.
Common questions
Why do third harmonics add instead of cancel in the neutral?
In a balanced three-phase system, the fundamental currents are 120 degrees apart, so they cancel in the neutral. Third harmonics are three times the fundamental frequency, which makes the three phase components line up as zero-sequence currents. Because they are in phase in the neutral, they add instead of canceling.
Can neutral current exceed phase current?
Yes. A balanced nonlinear load can have little or no fundamental neutral current while the triplen harmonic currents add in the neutral. With high 3rd-harmonic content, the neutral RMS current can be greater than the RMS current in any one phase.
Should the harmonic percentages use fundamental current or total RMS current?
Use each harmonic RMS current as a percentage of that phase fundamental RMS current. That matches the formula used here and the way many harmonic spectra are reported. If your instrument reports harmonic current in amperes, divide that harmonic amperage by the phase fundamental amperage before entering the percentage.
Why are the 3rd, 9th, and 15th harmonics combined by root-sum-square?
They are separate frequency components, so their RMS heating contribution is combined as the square root of the sum of their squared RMS currents. The calculator first adds each triplen order across the phases, then combines those different orders by root-sum-square.
When should neutral current be measured with a power-quality analyzer?
Measure it when conductor loading is close to a limit, loads are nonlinear, spectra differ by phase, or equipment is overheating. A power-quality analyzer can capture harmonic magnitudes, phase relationships, crest factor, and time variation that a simplified calculator cannot see.
Does the NEC require an oversized neutral for nonlinear loads?
Code treatment depends on the wiring method, load type, harmonic content, and applicable edition and local adoption. This calculator only estimates current and ampacity use from the entered data. Use the applicable electrical code and qualified engineering judgment for conductor selection.