What are harmonics in electrical systems?

Harmonics are voltage or current components at integer multiples of the fundamental frequency. If the fundamental is 50 Hz, the 3rd harmonic is 150 Hz, the 5th is 250 Hz and so on. When these harmonics add to the fundamental, the once-smooth sine wave becomes distorted. Harmonics are created mainly by nonlinear loads such as rectifiers, variable frequency drives and switch-mode power supplies.

What is total harmonic distortion (THD)?

Total harmonic distortion (THD) measures how distorted a waveform is. It is the ratio of the combined RMS value of all the harmonics to the RMS value of the fundamental, THD = square root of (V2 squared + V3 squared + V4 squared + ...) divided by V1, expressed as a percentage. A pure sine wave has THD = 0 percent; a higher THD means more distortion.

What is the formula for THD?

THD = square root of the sum of the squares of the harmonic RMS values, divided by the fundamental RMS value, times 100 percent. In symbols, THD = sqrt(V2^2 + V3^2 + V4^2 + ...) / V1. The same formula applies to current using I2, I3, I4 and I1.

What is the difference between odd, even and triplen harmonics?

Odd harmonics are the 3rd, 5th, 7th and so on; they dominate in most power systems because typical loads have half-wave symmetry. Even harmonics (2nd, 4th, 6th) usually cancel and are small. Triplen harmonics are the odd multiples of three (3rd, 9th, 15th); in a three-phase system they are in phase and add up in the neutral conductor instead of cancelling.

Why are harmonics a problem?

Harmonics cause extra heating in cables, motors and transformers, overload the neutral conductor with triplen harmonics, trip breakers, distort the supply voltage, cause capacitor failures and resonance, reduce the true power factor and can disturb sensitive electronics. This is why standards such as IEEE 519 set limits on THD.

What is an acceptable level of THD?

For voltage, IEEE 519 recommends a THD below 5 percent for general systems, with each individual harmonic below 3 percent. Below about 5 percent is considered clean; above 8 percent often causes problems. Current THD limits depend on the ratio of short-circuit current to load current.

How are harmonics reduced or mitigated?

Harmonics are reduced with passive harmonic filters (tuned LC traps), active harmonic filters that inject cancelling currents, line reactors or DC chokes on drives, phase-shifting or K-factor transformers, 12- or 18-pulse rectifiers, and by keeping harmonic-heavy loads on separate feeders.

How do harmonics affect power factor?

Harmonics lower the true power factor by adding a distortion component. The true power factor is the displacement power factor (cos phi) multiplied by the distortion factor, which falls as THD rises. So even a load whose current is in phase with the voltage can have a poor power factor if its current is badly distorted.

Harmonics & THD (Total Harmonic Distortion): Orders, Formula & Effects

Q: What causes harmonics?

Harmonics are caused by nonlinear loads that draw current in pulses rather than smoothly following the voltage. Common sources include diode and thyristor rectifiers, variable frequency drives, switch-mode power supplies, computers, LED and fluorescent lighting, welders, arc furnaces and saturated transformers.

What are Harmonics?

Harmonics are unwanted voltage or current components at integer multiples of the fundamental frequency. If the fundamental (1st harmonic) is 50 Hz, the 3rd harmonic is 150 Hz, the 5th is 250 Hz, and so on. When they add to the fundamental, a clean AC sine wave becomes distorted.

A perfect power supply would be a pure sinusoid at one frequency. In reality, nonlinear loads pull current in bursts, and by Fourier analysis any repeating distorted wave is exactly a fundamental sine plus a series of harmonic sines.

Fundamental sine wave plus 3rd and 5th harmonics summing to a distorted flat-topped waveform

A fundamental plus a 3rd and a 5th harmonic add up to a distorted, flat-topped wave. The extra frequencies riding on the fundamental are the harmonics.

n×f

Harmonic frequency

150 Hz

3rd of 50 Hz

THD

Distortion measure

< 5%

Clean supply target

Fundamental = 1st harmonic

The fundamental (the 50 or 60 Hz supply frequency) is itself the 1st harmonic. The word "harmonics" in day-to-day use means the higher-order components (2nd, 3rd, 5th…) that distort the wave.

Harmonic Orders: Odd, Even & Triplen

The harmonic order n tells you the frequency: harmonic n sits at n × fundamental. Orders group into three families that behave very differently.

Family	Orders	Frequency (50 Hz base)	Behaviour
Fundamental	1	50 Hz	The real supply frequency
Odd	3, 5, 7, 11, 13…	150, 250, 350… Hz	Dominant in most systems
Even	2, 4, 6…	100, 200, 300… Hz	Usually cancel (small)
Triplen	3, 9, 15…	150, 450, 750… Hz	Add up in the neutral

Most loads have half-wave symmetry (the negative half mirrors the positive), which mathematically eliminates the even harmonics — so real-world distortion is dominated by the odd harmonics: 3rd, 5th and 7th.

Quick rule

Harmonic order n at fundamental f has frequency n × f. Example: the 7th harmonic of a 60 Hz supply is 7 × 60 = 420 Hz.

Total Harmonic Distortion (THD)

Total Harmonic Distortion (THD) puts one number on how distorted a wave is: the combined size of all the harmonics compared with the fundamental. A pure sine has THD = 0%.

THD formula: square root of sum of squares of harmonic RMS values divided by fundamental RMS value, with interpretation

THD is the RMS of all the harmonics divided by the RMS of the fundamental. Below 5% is clean; above 8% usually spells trouble.

THD = √(V₂² + V₃² + V₄² + …) / V₁ × 100%

V₁ is the fundamental RMS; V₂, V₃… are the harmonic RMS values (same formula for current with I)

Worked example

A current has a fundamental of 100 A and harmonics: 3rd = 33 A, 5th = 20 A, 7th = 14 A.

THD = √(33² + 20² + 14²) / 100 = √(1089+400+196)/100 = √1685/100 ≈ 41%. Try the THD Calculator.

The Harmonic Spectrum (FFT)

A distorted wave is easiest to read in the frequency domain. An FFT (fast Fourier transform) breaks it into a harmonic spectrum — a bar for each order showing its size as a percentage of the fundamental.

Harmonic spectrum bar chart: fundamental 100 percent, 3rd 33 percent, 5th 20 percent, 7th 14 percent, higher orders smaller, THD about 45 percent

A typical six-pulse rectifier spectrum: strong 3rd, 5th and 7th harmonics tail off with order. The taller the harmonic bars, the higher the THD.

The spectrum instantly shows which harmonics dominate. A classic six-pulse rectifier, for example, produces characteristic harmonics of order 6k ± 1 (5th, 7th, 11th, 13th…). Engineers use spectra to design the right filter.

Where Harmonics Come From: Nonlinear Loads

Harmonics are created by nonlinear loads — devices that draw current in sharp pulses instead of smoothly following the voltage. A resistor draws a clean sine; a diode rectifier does not.

Clean sinusoidal voltage feeding a nonlinear load that draws a distorted harmonic-rich current

A clean voltage into a nonlinear load (rectifier, VFD, SMPS) comes out as a distorted, harmonic-rich current — the load, not the supply, creates the harmonics.

Rectifiers & drives

Diode/thyristor rectifiers, VFDs and UPS front-ends — the biggest industrial source.

Electronics & SMPS

Computers, chargers and switch-mode supplies draw pulsed current rich in 3rd harmonic.

LED & fluorescent

Electronic ballasts and LED drivers add harmonic current across many small loads.

Arcing & saturation

Arc furnaces, welders and saturated transformers inject harmonics too.

Effects & Problems of Harmonics

Harmonics waste energy and stress equipment. The most notorious problem is triplen harmonics overloading the neutral of a three-phase system.

Third harmonic currents of three phases in phase, adding up in the neutral conductor instead of cancelling

Unlike the fundamental, the 3rd-harmonic currents of the three phases are in phase, so they add in the neutral — which can carry more current than the phases and overheat.

Overheating

Higher-frequency currents raise I²R and eddy losses in cables, motors and transformers.

Neutral overload

Triplen harmonics sum in the neutral, sometimes exceeding the phase current.

Capacitor & resonance

PF-correction capacitors attract harmonic current and can resonate and fail.

Poor power factor

Distortion lowers the true power factor, wasting supply capacity.

How to Reduce Harmonics (Mitigation)

Once you know the spectrum, you can filter or design out the worst harmonics.

Passive filters

Tuned LC traps shunt a specific harmonic (e.g. 5th) to ground — cheap and reliable.

Active filters

Power electronics inject equal-and-opposite harmonic current in real time.

Line reactors / chokes

Series inductance on drives smooths the current pulse and cuts THD.

Multi-pulse & K-factor

12/18-pulse rectifiers and phase-shift or K-rated transformers cancel harmonics.

Distortion power factor

True power factor = displacement factor (cosφ) × distortion factor. As THD rises, the distortion factor falls, so mitigating harmonics also improves the real power factor.

Harmonic Standards & Limits

Utilities cap harmonics so one customer's distortion does not disturb the grid. The key references are IEEE 519 and IEC 61000.

Metric	Typical limit	Meaning
Voltage THD (< 1 kV)	≤ 8% (often ≤ 5%)	Overall voltage distortion at the point of common coupling
Individual voltage harmonic	≤ 5% (often ≤ 3%)	Any single harmonic order
Current TDD	5%–20%	Depends on short-circuit-to-load ratio (I_SC/I_L)

Current limits use TDD (total demand distortion), referenced to peak demand current rather than the instantaneous fundamental — a close cousin of THD.

Key Terms at a Glance

The essential harmonics vocabulary students and engineers search for.

Harmonic

Component at n× the fundamental frequency.

Harmonic order (n)

The multiple: 3rd = 3×f.

THD

√(∑V_n²)/V₁; distortion %.

Triplen

3rd, 9th, 15th; add in neutral.

Spectrum

Amplitude vs harmonic order.

Nonlinear load

Draws non-sinusoidal current.

Frequently Asked Questions

Quick, expert answers to the questions people ask most about harmonics and THD.

What are harmonics in simple words?

Harmonics are extra voltage or current waves at whole-number multiples of the mains frequency. A 50 Hz supply can carry a 150 Hz (3rd), 250 Hz (5th) and higher waves. Added together they distort the smooth sine into a jagged or flat-topped shape.

What is THD (total harmonic distortion)?

THD is one number for how distorted a wave is: the combined RMS of all harmonics divided by the fundamental RMS, as a percentage. THD = √(V₂²+V₃²+…)/V₁. A pure sine is 0%; higher means more distortion.

How do I calculate THD?

Square each harmonic RMS value, add them, take the square root, and divide by the fundamental RMS. Example: fundamental 100 A, harmonics 33, 20, 14 A gives √(33²+20²+14²)/100 ≈ 41%. The THD Calculator does it for you.

What are triplen harmonics and why do they overload the neutral?

Triplen harmonics are the odd multiples of three (3rd, 9th, 15th). In a balanced three-phase system the fundamentals cancel in the neutral, but the triplens of all three phases are in phase, so they add. The neutral can then carry up to three times the per-phase triplen current and overheat.

What causes harmonics?

Nonlinear loads that draw pulsed current: diode/thyristor rectifiers, variable frequency drives, switch-mode power supplies, computers, LED and fluorescent lighting, welders, arc furnaces and saturated transformers.

Why are odd harmonics more common than even ones?

Most loads have half-wave symmetry — the negative half-cycle mirrors the positive. That symmetry mathematically cancels the even harmonics (2nd, 4th…), leaving the odd harmonics (3rd, 5th, 7th) to dominate.

What is an acceptable THD level?

IEEE 519 recommends voltage THD below 5% for general systems, with any single harmonic under 3%. Under ~5% is clean; above ~8% often causes overheating and nuisance tripping. Current limits (TDD) depend on the short-circuit-to-load ratio.

How are harmonics reduced?

With passive LC filters tuned to a harmonic, active filters that inject cancelling current, line reactors or DC chokes on drives, 12- or 18-pulse rectifiers, and phase-shifting or K-factor transformers.

Conclusion & Key Takeaways

Harmonics are the higher-frequency multiples that distort AC waves, and THD is the single number that quantifies that distortion.

Harmonic = n×f

Integer multiples of the fundamental.

Odd dominate

3rd, 5th, 7th; evens cancel.

THD = √(∑V_n²)/V₁

Distortion as a percentage.

Triplens add

Overload the neutral.

Nonlinear loads

Rectifiers, VFDs, SMPS.

Keep THD < 5%

Filter to meet IEEE 519.

Harmonics & THD

Complete Learning Path — Harmonics & THD