THD
The key idea
Total harmonic distortion is one number for how far a wave is from a clean sine: the size of everything that should not be there, relative to the fundamental. The components combine as the square root of the sum of squares — not by simple addition.
The idea
A harmonic study produces a voltage magnitude for every order at every bus — a lot of numbers. THD compresses each bus's list into one figure of merit: take every harmonic component, square them, add the squares, take the square root, and divide by the fundamental.
Why squares? Because the components live at different frequencies, they add the way the sides of the impedance triangle do — at right angles. A wave with 4% fifth and 3% seventh harmonic is not 7% distorted; it is √(16 + 9) = 5% distorted.
That arithmetic has a practical consequence worth internalizing: the biggest component dominates. Squaring exaggerates the large and buries the small — so halving the dominant harmonic does far more for THD than eliminating a minor one entirely.
Try it
THD = 5.4% · plain sum would say 9.0%
Total harmonic distortion
√(4.0² + 3.0² + 2.0²) = 5.4%The components add at right angles, like the sides of the impedance triangle — so the total is always less than the plain sum. One dominant harmonic sets most of the THD: halving the biggest component does far more than removing a small one entirely.
Why it matters
- Limits are written in THD — and per order. IEEE 519-style practice puts voltage THD around 5–8% at the point of connection and caps each individual order (commonly ~3%). Both checks matter: a single 6% fifth harmonic fails on the individual limit even if THD squeaks by.
- One number is a summary, not a diagnosis. Two buses can share a THD with completely different causes. The fix comes from the dominant order — which points at the source (5th and 7th: six-pulse drives; 3rd: single-phase electronics) or at a resonance amplifying it.
- Voltage THD and current THD are different animals. Current THD describes what a load draws; voltage THD describes what every other customer on the bus receives. Networks exist to keep the second one small while the first one happens.
The math, if you want itOptional — the page reads completely without it
One definition, worth reading closely:
total harmonic distortion
THDV = √( Σh≥2 Vh² )V₁
with each Vh the RMS voltage at order h and V₁ the fundamental. The same definition applies to current. The quadrature sum comes from RMS arithmetic: components at different frequencies are orthogonal, so their powers — the squares — are what add.
See it in Phasor
Phasor's harmonic penetration study reports the per-order voltages, the THD, and the dominant order at every monitored bus — the summary and the diagnosis together. The compliance verdict against your chosen standard stays yours.