Neutral current in an unbalanced four-wire LT feeder
A 415 V, three-phase, four-wire LT feeder supplied from a 630 kVA distribution transformer serves a commercial block with mixed single-phase loads. The cable is 4-core 95 mm² aluminium XLPE, 300 m long, installed in a duct; the neutral is the same size as the phase conductors. At the feeder pillar, a clamp meter reads R = 120 A, Y = 100 A and B = 80 A, all at approximately unity power factor, while the neutral reads 58 A. The neutral bar is noticeably warm and 230 V equipment on the far end resets intermittently. The upstream MCCB is 250 A. The block has many LED drivers and switched-mode power supplies. Ambient temperature is 40°C and the cable derating factor is 0.85. The electrician proposes simply tightening the neutral and increasing the MCCB rating.
1. Calculate the fundamental neutral current from the three line currents using phasor addition and compare it with the measured 58 A. What does the difference tell you?
Read the worked answer
Take R as reference:
- IR = 120∠0° = 120 + j0 A
- IY = 100∠-120° = -50 - j86.6 A
- IB = 80∠120° = -40 + j69.3 A
Sum = 30 - j17.3 A, so |IN| = √(30² + 17.3²) ≈ 34.6 A.
At unity power factor the fundamental neutral current should be about 34.6 A, not 58 A. The measured value is roughly 23 A higher, about 68% above the fundamental estimate. A clamp meter on a harmonic-rich load reads true RMS, so the extra current is consistent with triplen harmonics - 3rd, 9th, 15th - which are in phase in all three phases and add in the neutral instead of cancelling. Phase-angle differences and neutral-to-earth leakage can add a little, but they do not explain a 23 A gap. The result points to a power-quality problem, not just loose torque. A true-RMS analyser should record neutral current, neutral-earth voltage and harmonic spectrum before deciding the remedy.
2. Is the 95 mm² neutral thermally adequate for the measured 58 A? Explain the specific harmonic risk and why the MCCB does not protect the neutral.
Read the worked answer
On the face of it, 58 A in 95 mm² aluminium is only about 0.61 A/mm², so fundamental heating is modest. That does not close the issue. Triplen harmonic currents add arithmetically in the neutral, and at 150 Hz and above the skin and proximity effects raise the effective resistance. The neutral can therefore run hotter than the same RMS current at 50 Hz. The neutral is also not opened by a three-pole MCCB, so a loose neutral joint or rising harmonic current can overheat without any protective device operating. The warm neutral bar and the intermittent 230 V resets fit a neutral shift or distorted neutral-earth voltage. Increasing the MCCB rating would make the protection worse: it would not protect the neutral and would reduce phase-fault sensitivity. The correct check is thermal imaging plus true-RMS neutral current and THD, not a bigger breaker.
3. Recommend two corrective actions and one measurement to verify effectiveness.
Read the worked answer
Two practical actions are: first, rebalance the single-phase loads across R, Y and B; second, provide a neutral with adequate harmonic rating - either a separate neutral per phase, an oversized neutral, or a neutral rated for the measured harmonic spectrum. If the spectrum confirms high triplen content, add a tuned harmonic filter or active filter at the feeder pillar. Do not simply increase the MCCB; verify the cable and neutral first.
One verification measurement is a before-and-after power-quality survey using a true-RMS analyser: record neutral current, neutral-earth voltage, phase current THD and neutral current THD at the feeder pillar and at the far-end distribution board under normal and peak load. Supplement it with thermal imaging of the neutral bar after steady operation. Effective remediation should reduce both the neutral RMS current and the neutral-earth voltage distortion, not merely make the bar feel cooler.