Harmonic Distortion Loss Calculator

Why the spectrum, not just THD

A single THD number tells you how much distortion there is, not what it will do. Two plants at 20 % THD behave completely differently if one is 20 % fifth harmonic from drives and the other is 20 % third harmonic from single-phase electronics — the first heats the transformer, the second overloads the neutral.

Everything below follows from the spectrum by definition, so it is worth ten minutes with a power quality analyser rather than an assumption.

THD    = √(Σ Ih²) / I₁
I_rms  = I₁ × √(1 + Σ(Ih/I₁)²)

Losses go with the square, so they add up quickly

Copper loss is I²R, and R does not care whether the current is doing useful work. Since the harmonic currents add in quadrature, the extra loss over the clean-sine case is exactly the sum of the squared harmonic ratios:

extra loss = base loss × Σ(Ih/I₁)²

At 25 % THD that is a 6 % increase in copper loss — modest as a percentage, and a real number in kilowatt-hours on a feeder running six thousand hours a year. It is also 3 % more RMS current in a cable you sized for the fundamental.

Skin effect makes it slightly worse than this, because higher frequencies see more resistance than the 50 Hz figure. The calculation here is the floor.

The neutral is where triplens go

Third harmonic — and its multiples, the triplens — is in phase across all three lines. In the neutral the three contributions do not cancel like the fundamental does. They add:

I_neutral ≈ 3 × I₃

So 35 % third harmonic gives a neutral current slightly above the line current, on a balanced load. A neutral carrying more than the phases is not a fault condition — it is arithmetic — and it is why a 3.5-core cable with a reduced neutral is the wrong cable for an office block full of LED drivers and switch-mode supplies.

Where third harmonic exceeds about 33 %, IEC 60364-5-52 has you size the cable on the neutral current rather than the line current. That is the case this calculator flags, and the derating detail is in cable derating factors.

K-factor and transformer derating

Harmonic currents drive eddy-current losses in a transformer's windings that rise with the square of frequency. The K-factor captures that:

K = Σ (Ih / I_rms)² × h²

A pure sine wave gives K = 1. Typical office and drive loads land between 4 and 13. A K-rated transformer is built to carry that without derating; a standard transformer has to be derated instead, and IEEE C57.110 puts the capability at:

derating = √[(1 + P_EC) / (1 + K × P_EC)]

with P_EC the eddy loss at rated current, taken here as 0.05 for a typical oil-filled distribution transformer. Dry-type units have higher eddy losses and derate harder — if the transformer is dry-type, treat the figure shown as optimistic.

Feed the result into the transformer calculator: a unit at 92 % capability that you had planned to load to 85 % is actually running at 92 % of what it can now do.

The symptoms, in the order they appear

• Capacitors failing repeatedly. The first and most expensive symptom. Capacitors are a low impedance to high frequencies, and a plain bank resonating with the supply inductance amplifies whatever harmonic sits near the resonant point. The fix is detuned reactors — APFC panels.
• Neutral conductors and terminals running hot, on a circuit whose phases are comfortable.
• Transformer humming and running warm at loads it used to handle.
• Nuisance tripping of thermal-magnetic devices responding to true RMS current the design never allowed for.
• Metering disagreement. Different meter designs measure distorted current differently, which is one reason a submeter total drifts from the utility bill — metering accuracy.

What to do about it

1. Measure first. At the point of common coupling and at the largest non-linear loads. IEEE 519 sets 8 % current THD for most industrial consumers at the PCC, and the limits are stricter on stiffer supplies.
2. Line reactors on drives — 3 % or 5 % impedance. Cheap, passive, and typically halves a drive's current distortion.
3. Detuned reactors on capacitor banks, 7 % as standard, before harmonics destroy them.
4. Full-size or oversized neutrals where triplens are significant, and separate neutrals rather than shared ones.
5. Twelve-pulse or active front-end drives on large loads, which cancel the 5th and 7th at source.
6. Active harmonic filters where distortion is severe and the load varies. Expensive, effective, and the last resort rather than the first.

Measuring it without being misled

Harmonic problems are diagnosed with an instrument, and the wrong instrument will tell you there is nothing wrong.

An averaging clamp meter — which is most inexpensive clamp meters — assumes a sine wave. It measures the average of the rectified waveform and multiplies by a fixed form factor to report an rms value. On a distorted current that factor is wrong, and the meter under-reads, commonly by 20 to 40 per cent on the pulsed current a rectifier draws. The cable that is overheating measures as comfortably within rating.

A true-RMS instrument computes the actual heating value and gets the magnitude right, which is enough to find an overloaded neutral. It still will not tell you the spectrum. Deciding between a reactor, a passive filter and an active filter needs the individual harmonic magnitudes, not a single THD figure, and that requires a power quality analyser logging over a full production cycle. A snapshot taken during a quiet hour is the most common reason a harmonic survey concludes there is no problem.

Where the limits actually come from

IEEE 519 is the document usually cited, and it is routinely misapplied. Its limits are set at the point of common coupling — the boundary between your installation and the utility — and not at an individual load inside your plant. A drive drawing 40 per cent current distortion is not in breach of anything if the aggregate at the incomer is within limits.

The current limits are also expressed relative to the short-circuit ratio at that point, not as a single number. A stiff supply with a high fault level tolerates more harmonic current from a given load than a weak one, because the resulting voltage distortion is what actually matters to other customers. This is why the same equipment can be acceptable on one site and a problem on another with no change to the equipment at all.

Voltage distortion limits are the ones with teeth: commonly 5 per cent total harmonic distortion for systems below 69 kV, with a limit on any individual harmonic as well. In India, CEA regulations set the obligation and state utilities enforce it through the connection agreement, so the practical answer to what limit applies is whatever the agreement for that connection says — and it is worth reading before specifying mitigation, because the cost difference between meeting 5 per cent and meeting 3 per cent is substantial.