Total Harmonic Distortion (THD)
Enter the fundamental and harmonic percentages to get THD or TDD, the dominant harmonic and an IEEE 519 limit check.
Step-by-step
- Enter valid values to begin.
Harmonic magnitudes are percentages of the fundamental and h = 2 to 15 (even orders and h = 8, 10, 12, 14 are not listed; enter their root-sum-square into a nearby order if needed). Voltage limits are typed from memory (THD 8 / 5 / 2.5 / 1.5 %, individual 5 / 3 / 1.5 / 1.0 % by bus class): verify against IEEE 519-2022 before you rely on them. Current mode computes TDD = √(ΣIh²) / IL and compares it with the total limit for the Isc/IL ratio (5 / 8 / 12 / 15 / 20 %); the individual current limits, which differ by harmonic order and are lower for even harmonics, are not checked here. Real limits apply at the point of common coupling.
Total Harmonic Distortion: Measuring What Non-Linear Loads Do to the Waveform
Core Engineering Principles
Any load that draws current in pulses instead of a smooth sine pushes harmonics back into the system: variable frequency drives with diode rectifiers, switch-mode supplies in servers, LED drivers, battery chargers and arc furnaces. Each harmonic is a sine at a whole-number multiple of the line frequency, and THD is their root-sum-square divided by the fundamental, not by the total RMS. Current distortion is the cause; voltage distortion is the symptom, produced as that current flows through the source impedance.
The damage is mostly heat and resonance. Harmonic currents raise eddy-current losses in transformers, so we derate them or buy K-rated units. Triplen harmonics (3rd, 9th, 15th) from single-phase loads add in the neutral instead of cancelling; we have seen undersized neutrals cook on office floors full of computers. A capacitor bank and the source inductance form a parallel resonance, and if it lands near the 5th or 7th, a modest harmonic current becomes a large voltage. We judge current as TDD, normalised to demand current, because a lightly loaded drive shows a terrible THD on a tiny current.
RMStotal = X1 × √(1 + THD²) • Distortion factor = 1 / √(1 + THD²)
NEC & Standard References
IEEE 519-2022 sets harmonic limits at the point of common coupling (PCC), the point where the utility and other customers connect: voltage limits by bus voltage class, and current limits by short-circuit-to-demand current ratio. IEC 61000-2-4 defines compatibility levels for industrial plants. EN 50160 describes public supply voltage characteristics, including harmonics. The limits in this calculator are typed from memory, so verify against IEEE 519-2022 and your adopted edition before signing a compliance report.1. Squares: 2.25 + 12.25 + 4.84 + 1.21 + 0.49 = 21.04.
2. THD = √21.04 = 4.587%, which is under the 8% limit.
3. Dominant harmonic is the 5th at 3.5%, or 277 × 0.035 = 9.70 V; it is under the 5% individual limit.
4. RMS total = 277 × √(1 + 0.04587²) = 277.29 V.
5. Distortion factor = 1 / 1.00105 = 0.9989.
6. Compliant, but the 5th is 70% of its limit.
- Light-load THDi misleads. A drive at 10% load can show 60% THD on a trivial current; judge it by TDD.
- Measure at the right point. Limits apply at the PCC, not at the drive terminals.
- Check for capacitor resonance. Use detuning reactors on harmonic-rich buses.
- Watch the neutral. Triplen currents add there, so size it at 200% where single-phase electronics dominate.
- Use a true-RMS meter. Average-responding meters read low on distorted current.