Harmonics
The key idea
A distorted wave is not a new kind of wave. It is the clean 50 or 60 Hz wave plus smaller clean waves at exact multiples of it — the harmonics. Electronics draw current this way, and the network turns those currents into voltage distortion everywhere.
The idea
A heater draws a clean sine-wave current. A variable speed drive, a rectifier, an LED driver does not — it gulps current in pulses. That pulsed shape looks complicated, but it hides a beautiful fact: any repeating wave is exactly a stack of clean sine waves at integer multiples of the fundamental frequency.
The multiples are the harmonic orders: the 5th harmonic is 250 Hz on a 50 Hz system, the 7th is 350 Hz, and so on. Six-pulse converters — the workhorse drive circuit — inject mostly 5th, 7th, 11th and 13th.
Here is the part that makes it a network problem rather than a local one. Those harmonic currents flow through the network's impedance, and current through impedance makes voltage. So every bus the current passes drops a little harmonic voltage — and the distortion appears everywhere, including at customers who own nothing but clean loads.
Try it
THD = 22.4%
- composite
- 5th
- 7th
The distorted wave is nothing mysterious — it is exactly the clean sine plus the harmonics you dialed in. Every distorted wave on a real network decomposes the same way, which is why harmonic studies work order by order.
Why it matters
- Distortion is a delivered product defect. Motors heat and vibrate on harmonic voltage, capacitors age early, electronics misfire. Standards such as IEEE 519 and EN 50160 set limits on it, order by order and in total.
- It solves order by order. Because the distorted wave is its harmonic stack, a study can solve the network one order at a time — a 250 Hz problem, a 350 Hz problem — and add the results. That is exactly how a harmonic penetration study works.
- The impedance is half the story. The same injected current can be harmless on a stiff bus and severe on a weak one — and catastrophic where a resonance sits on an injected order.
The math, if you want itOptional — the page reads completely without it
A repeating wave decomposes into its harmonic stack — the Fourier series:
the Fourier series
v(t) = Σh Vh · sin( h·ωt + φh )
A six-pulse converter injects the characteristic orders h = 6k ± 1 (5, 7, 11, 13…), with magnitudes falling roughly as 1/h. At each order the network is solved as an ordinary AC circuit at frequency h·f, with reactances scaled by h:
one order at a time
Vh = Z(h·f) · Ih
See it in Phasor
Phasor runs both halves of the study: a frequency scan that shows where the network amplifies, and a harmonic penetration solve that injects your loads' measured spectra and reports the voltage distortion bus by bus.