Harmonics and Cable Derating: The Modern Load Nobody Designed For

The electrical distribution systems in most buildings were designed for linear loads: motors, heaters, incandescent lamps. These loads draw sinusoidal current at the supply frequency — 50 or 60 Hz. The cable sizing tables in our standards, the transformer ratings, the switchgear specifications — all are based on the assumption that current waveforms are sinusoidal.

Modern loads have shattered that assumption. LED drivers, variable frequency drives (VFDs), switched-mode power supplies (SMPS) in computers and data centres, battery chargers — these are all non-linear loads. They draw current in sharp pulses rather than smooth sine waves. These distorted waveforms contain harmonic frequencies (multiples of the fundamental) that cause problems the original cable designers never anticipated.

The most counterintuitive of these problems: in a perfectly balanced three-phase system feeding identical non-linear loads, the neutral conductor — which would carry zero current with linear loads — can carry more current than the phase conductors. This single fact has caught out countless engineers and caused overheated neutrals, tripped breakers, and even fires.

A linear load (resistor, motor at steady state) draws current proportional to the applied voltage. If the voltage is sinusoidal, the current is sinusoidal. The only frequency present is the fundamental — 50 or 60 Hz.

A non-linear load draws current that is not proportional to voltage. The most common example is a rectifier circuit: it only conducts when the supply voltage exceeds the DC bus capacitor voltage, creating short pulses of current near the peaks of the voltage waveform.

By Fourier analysis, any periodic waveform can be decomposed into a sum of sinusoidal components at the fundamental frequency and its integer multiples:

i(t) = I₁sin(ωt + φ₁) + I₃sin(3ωt + φ₃) + I₅sin(5ωt + φ₅) + … — (Eq. 1)

Most power electronic loads have symmetrical positive and negative half-cycles (the rectifier conducts identically on both halves). This symmetry means even harmonics (2nd, 4th, 6th) cancel out, leaving predominantly odd harmonics: 3rd, 5th, 7th, 9th, 11th, 13th.

A typical single-phase SMPS might have a current spectrum like:

The total harmonic distortion (THD) of such a current waveform can exceed 100% — meaning the harmonic content has more energy than the fundamental.

In a balanced three-phase system with linear loads, the neutral current is zero. The three phase currents, displaced by 120°, sum to zero at the neutral point:

I_N = I_A + I_B + I_C = I sin(ωt) + I sin(ωt − 120°) + I sin(ωt + 120°) = 0 — (Eq. 2)

This is why older installations were designed with reduced-size neutrals — if the neutral carries no current (or minimal current from slight imbalance), why use a full-sized conductor?

But here is where harmonics break this assumption. The triplen harmonics — 3rd, 9th, 15th, 21st, and all multiples of 3 — have a special property. In a three-phase system, these harmonics from each phase are in phase with each other. Instead of cancelling, they add algebraically in the neutral.

The 3rd harmonic has three complete cycles for every one cycle of the fundamental. Phase A’s 3rd harmonic: sin(3ωt). Phase B’s 3rd harmonic: sin(3(ωt − 120°)) = sin(3ωt − 360°) = sin(3ωt). Phase C’s 3rd harmonic: sin(3(ωt + 120°)) = sin(3ωt + 360°) = sin(3ωt).

All three are identical. They do not cancel. Instead:

I_N(3rd) = 3 × I₃ — (Eq. 3)

The neutral current at the 3rd harmonic frequency is three times the per-phase 3rd harmonic current.

A commercial building has a balanced three-phase lighting circuit feeding identical LED luminaires. Each phase carries 40 A of fundamental current with a 3rd harmonic content of 60% (24 A per phase at 150 Hz).

Phase current (total RMS):

The RMS current in each phase conductor includes both fundamental and harmonic components. Including the 3rd and 5th harmonics (5th at 25% = 10 A):

I_phase = √(40² + 24² + 10²) = √(1600 + 576 + 100) = √2276 = 47.7 A — (Eq. 4)

Neutral current:

The fundamental cancels. The 5th harmonic cancels (non-triplen). But the 3rd harmonic adds:

I_neutral = 3 × I₃ = 3 × 24 = 72 A — (Eq. 5)

The neutral carries 72 A while each phase carries only 47.7 A. The neutral current is 151% of the phase current.

If the original installation was designed with a reduced neutral (say, half the phase conductor size, which was common practice for “balanced” systems), the neutral conductor is drastically overloaded. A conductor sized for 24 A (half of the design phase current) is now carrying 72 A — three times its rating.

If the 3rd harmonic content is exactly 1/√3 of the fundamental (approximately 57.7%), the neutral current equals the phase current. If the 3rd harmonic is higher — as it commonly is with LED drivers and SMPS — the neutral current exceeds the phase current.

For a theoretical worst case where the 3rd harmonic equals the fundamental:

I_neutral / I_phase = 3 × I₁ / (I₁ × √2) = 3/√2 = 2.12 — (Eq. 6)

The neutral would carry 212% of the phase current. In practice, with typical LED driver 3rd harmonic content of 60–80%, the ratio is commonly between 150% and 175%.

A data centre rack PDU feeds 20 servers, each drawing 3 A from a single-phase 230 V supply. All servers use SMPS with THD of 95% and 3rd harmonic content of 72%.

Per-server analysis:

• Fundamental current: 3 A at 50 Hz
• 3rd harmonic: 0.72 × 3 = 2.16 A at 150 Hz
• 5th harmonic: 0.50 × 3 = 1.50 A at 250 Hz
• 7th harmonic: 0.30 × 3 = 0.90 A at 350 Hz

Phase current (balanced distribution, ~7 servers per phase):

I_phase = 7 × √(3² + 2.16² + 1.50² + 0.90²) = 7 × √16.73 = 7 × 4.09 = 28.6 A — (Eq. 7)

Neutral current (triplens only):

I_neutral = 3 × 7 × √(2.16² + 0.648²) = 21 × √5.09 = 21 × 2.26 = 47.4 A — (Eq. 8)

The neutral carries 47.4 A versus 28.6 A per phase — a ratio of 166%. The neutral conductor must be at least as large as the phase conductors and probably larger.

The standards address this problem through derating factors. When a cable system supplies non-linear loads, the current-carrying capacity tables must be adjusted.

AS/NZS 3008.1.1:2017, Table 27 provides derating factors for cables supplying harmonic-rich loads:

BS 7671:2018, Table 4C1 (Appendix 4) provides a more detailed breakdown:

When the 3rd harmonic exceeds 45%, the standard effectively says: forget the phase current — size the cable for the neutral current, then verify that the phase conductors are adequate for the (lower) phase current.

AS/NZS 3008.1.1:2017, Section 3.5.3 and Table 27; BS 7671:2018+A2, Table 4C1 and Regulation 523.6.

There is a subtler effect beyond the increased RMS current. Higher-frequency harmonic currents experience greater skin effect and proximity effect (see Skin Effect and Proximity Effect). At the 5th harmonic (250 Hz), the skin depth in copper drops to about 4.2 mm. At the 7th harmonic (350 Hz), it is 3.5 mm.

This means the AC resistance of the conductor is higher for harmonic currents than for fundamental current. The I²R losses at harmonic frequencies are worse than the harmonic current magnitude alone would suggest:

Total losses = I₁² × R_ac(50Hz) + I₃² × R_ac(150Hz) + I₅² × R_ac(250Hz) + … — (Eq. 9)

For large cables where skin effect is already significant at 50 Hz, this harmonic-enhanced AC resistance can increase total losses by an additional 5–15% beyond what a simple RMS current calculation predicts.

1. Oversize the neutral: The simplest approach. Install a neutral conductor at least equal to the phase conductor size, and for installations with known high harmonic content (data centres, LED lighting circuits, broadcast facilities), consider a neutral that is 150–200% of the phase conductor size.
2. Use separate neutrals per phase: Instead of a shared four-core cable, use single-core cables with individual neutral conductors for each phase. This eliminates triplen harmonic addition in the neutral — each neutral carries only its own phase’s harmonics.
3. Install harmonic filters: Active or passive harmonic filters at the distribution board can reduce harmonic content before it reaches the cable system. This reduces both phase and neutral currents.
4. Select equipment with low THD: Modern LED drivers are available with THD below 10% (compared to 70–100% for cheap drivers). Specifying low-THD equipment at the design stage avoids the cable derating problem entirely. VFDs with active front ends can achieve THD below 5%.
5. Use K-rated transformers: Standard transformers experience additional heating from harmonic currents (eddy current losses increase with frequency squared). K-rated transformers are designed to handle harmonic-rich loads without derating. A K-13 transformer can handle the harmonic spectrum from typical office/IT loads.

While the neutral conductor problem is the most dramatic consequence of harmonics, phase conductors are also affected:

1. Higher RMS current: Even in the phase conductors, the harmonic content adds to the total RMS current (see the square root of sum of squares calculation above)
2. Increased AC resistance: Higher harmonic frequencies mean more skin effect
3. Additional voltage drop: Harmonic currents flowing through cable impedance create harmonic voltage drops, distorting the voltage waveform at the load
4. Resonance risk: Cable capacitance and system inductance can create resonant circuits at harmonic frequencies, amplifying specific harmonics

1. Non-linear loads (LED drivers, VFDs, SMPS) draw current in pulses rather than smooth sine waves, creating harmonic currents at multiples of the supply frequency.
2. In a balanced three-phase system feeding identical non-linear loads, the fundamental current cancels in the neutral — but triplen harmonics (3rd, 9th, 15th) add, producing neutral current up to 173% or more of the phase current.
3. Cable derating factors for harmonic-rich environments reduce the allowable current capacity by approximately 14% (factor of 0.86) for moderate harmonic content. When 3rd harmonic exceeds 45%, the cable must be sized based on the neutral current, not the phase current.
4. Harmonics compound the skin effect problem — higher-frequency currents experience greater AC resistance, increasing I²R losses beyond what the RMS current alone would predict.
5. The most cost-effective mitigation is specifying low-THD equipment at the design stage. Retroactively addressing harmonic problems through cable replacement or filter installation is always more expensive.

Standards referenced: AS/NZS 3008.1.1:2017, Section 3.5.3 and Table 27; BS 7671:2018+A2, Table 4C1 and Regulation 523.6; IEC 60364-5-52:2009, Annex E; IEEE Std 519-2022, Recommended Practice for Harmonic Control.