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Total Harmonic Distortion (THD) measures how much a real (distorted) AC waveform deviates from a pure sine wave, by comparing the combined RMS magnitude of all harmonic components (2nd, 3rd, 4th, 5th, ...) to the RMS magnitude of the fundamental (1st harmonic, the intended 50/60Hz component). A THD of 0% means a perfect sine wave; higher THD means more distortion from switching converters, non-linear loads, or saturating transformers.
| Quantity | Formula |
|---|---|
| THD from RMS values | THD = √(V2²+V3²+V4²+…+Vn²) / V1 × 100% |
| THD from harmonic % | THD = √(h2%²+h3%²+…+hn%²) |
| Total RMS (fundamental + harmonics) | Vrms = √(V1²+V2²+V3²+…) |
| Relation to total RMS | Vrms = V1×√(1+THD²) |
THD can be defined relative to the fundamental (THD-F, used here and most common) or relative to the total RMS (THD-R); the two are nearly identical for low distortion but diverge at high THD. Most standards (e.g. IEEE 519) specify limits using THD-F.
A measure of how much a waveform deviates from a pure sine wave, expressed as the ratio of the combined RMS of all harmonic components to the RMS of the fundamental component, usually as a percentage.
For grid voltage, typically <5% is considered good and often required by standards; for VFD/inverter current it can be much higher (10–30%+) without filtering, since motor and inverter loads are inherently non-linear.
Non-linear loads and switching devices — rectifiers, VFDs, switch-mode power supplies, LED drivers, arc furnaces, and saturating transformers — draw current in pulses rather than a smooth sine, generating harmonic frequencies.
Voltage THD (THD-V) measures distortion of the supply voltage waveform; current THD (THD-I) measures distortion of the load current waveform. Non-linear loads primarily cause current THD, which then causes voltage THD through the system impedance.
Most non-linear loads have waveforms symmetric about the zero-crossing (half-wave symmetry), which mathematically eliminates even harmonics, leaving only odd harmonics (3rd, 5th, 7th, etc.) as the dominant distortion.
IEEE 519 sets voltage THD limits (typically 5% at the point of common coupling for general systems) and current THD limits that scale with the short-circuit ratio of the connection, to control harmonic pollution back onto the grid.
High THD indicates poor power quality: it causes extra heating in transformers/motors, nuisance tripping of protective devices, interference with sensitive electronics, and reduced overall system efficiency.
Yes — line reactors, harmonic filters (passive or active), higher-pulse rectifier topologies (12-pulse, 18-pulse), and better inverter PWM techniques all reduce THD at the source.
No real-world converter or non-linear load produces a perfectly pure sine wave; 0% is a theoretical reference. Well-designed grid-tie inverters can achieve THD below 3%, which is considered excellent.
Harmonic currents cause additional eddy-current and skin-effect losses in transformer windings and cores beyond what the fundamental current alone would cause, requiring K-factor-rated (harmonic-rated) transformers for heavily distorted loads.
THD-F (used here) divides by the fundamental RMS; THD-R divides by the total RMS instead. They agree closely for low THD but THD-R is always slightly lower and the two diverge more as distortion increases.
Only modestly at typical THD levels — the total RMS equals the fundamental times √(1+THD²), so even 10% THD increases total RMS by only about 0.5%.
A power quality analyzer or true-RMS meter with harmonic analysis (FFT) capability measures each harmonic's magnitude directly; this calculator then combines those readings into the overall THD figure.
THD is a standard measure of how faithfully an amplifier reproduces its input signal; lower THD (often <0.1% for hi-fi amplifiers) means less audible distortion added to the original audio.
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