Why do third-harmonic currents add up in the neutral of a four-wire wye instead of cancelling?

B. Because the three phases’ third harmonics are in step with each other — 3 × 120° is a full 360°

A. Because the neutral has lower resistance

C. Because harmonics only flow in the neutral

D. Because the transformer creates them in the neutral

Which of these is a non-linear load that produces harmonic current?

C. A VFD or LED driver with a rectifier front end

D. An induction motor running across the line

What is a K-factor transformer built for?

B. Carrying harmonic-rich loads without overheating from the extra losses harmonics cause

Fourth year Lesson 3 of 12 · about 15 min

Power quality and harmonics

What you’ll learn

The main power-quality problems — sags, swells, transients, interruptions, unbalance — and their usual causes.
What a harmonic is, which loads make them, and what they do to neutrals, transformers and breakers.
Why third-harmonic (triplen) currents add in the neutral, worked with numbers.
How to work out THD, why you need a true-RMS meter, and the common fixes.

Before this: Unbalanced loads and neutral current · How a VFD works

“Power quality” is everything about the supply that is not simply the right voltage at the right frequency: dips, spikes, outages, unbalance, and wave shapes that are not clean sine waves. Most of it you meet as a symptom — a drive that trips, a neutral that runs hot, lights that flicker — and the skill is recognising which problem the symptom belongs to.

The events, in plain words

Event	What it is	Usual cause
Sag (dip)	Voltage drops for a cycle to a few seconds	A big motor starting; a fault elsewhere on the system
Swell	Voltage rises briefly	A large load dropping off; a fault on another phase
Transient	A spike lasting microseconds	Lightning; capacitor switching; contactors opening inductive loads
Interruption	Voltage gone	A breaker or recloser operating
Unbalance	Three phases not equal	Single-phase loads spread unevenly; a bad connection on one leg
Harmonics	The wave shape itself is distorted	Non-linear loads: rectifiers in drives, LED drivers, electronics

Where harmonics come from

A heater draws current in step with the voltage — a sine wave in, a sine wave of current out. That is a linear load. A rectifier front end (every drive, computer supply and LED driver) only lets current through when the supply voltage is higher than the capacitor behind it, near the peaks. The current comes in short gulps. Any repeating wave shape like that is mathematically the same as a 60 Hz sine plus smaller sines at whole-number multiples — 180 Hz (3rd), 300 Hz (5th), 420 Hz (7th) and so on. Those are the harmonics.

They matter because they are real current: they heat conductors, add losses in transformers (far more than their size suggests), can make thermal-magnetic breakers run warm or trip, and can resonate with power-factor capacitors. They also fool average-responding meters, which assume a sine wave — use a true-RMS meter on anything with electronics on it.

Triplens in the neutral

Balanced phases, but the neutral is far from empty: the fundamentals cancel and the third harmonics, which are in step on all three phases, pile up.

On a balanced four-wire wye, the neutral carries nothing at 60 Hz because the three phase currents are 120° apart. Triple the frequency and those 120° gaps become 360° — the third harmonics on the three phases are in step, and they add. Every multiple of three (the “triplens”: 3rd, 9th, 15th…) behaves the same way. In a delta winding, the same triplens circulate around the delta instead, heating the transformer rather than reaching the supply.

Worked: THD and the neutral

A clamp-on harmonic meter shows, on one phase: fundamental 100 A, 3rd 30 A, 5th 20 A, 7th 10 A.
Harmonic total = √(30² + 20² + 10²) = √(900 + 400 + 100) = √1,400 = 37.4 A. Harmonics add as squares.
Current THD = 37.4 ÷ 100 = 37.4%.
True-RMS current on that phase = √(100² + 1,400) = √11,400 = 106.8 A — the heating value.
If all three phases look the same, the neutral carries 3 × 30 = 90 A at 180 Hz, plus a little 9th, 15th… even though the phases are perfectly balanced.

What gets done about it

Line reactors or DC-bus chokes on drives; drives with multi-pulse or active front ends; harmonic filters; K-factor transformers built to carry harmonic losses; neutrals sized for the triplen current they will actually carry (your code book has rules for this — look up how it treats non-linear loads); and detuned capacitor banks where power-factor correction and drives share a bus. Which fix fits is usually an engineering call, made from a proper power-quality recording.

On the job

Tips

Measure the neutral, not just the phases. A hot neutral with balanced phases is the harmonic giveaway.
Use a true-RMS meter everywhere electronics live; know whether yours is.
For intermittent trips and flicker, a power-quality recorder left for a week beats a spot reading.
Note when problems happen. Sags that line up with a motor start point at that motor.

Common mistakes

Adding harmonic currents straight instead of as squares.
Assuming a balanced wye means an idle neutral.
Blaming the breaker for heat that the harmonics are making.
Adding power-factor capacitors to a bus full of drives without checking for resonance.
Trusting an average-responding meter on a drive or computer load.

Check yourself

0 right of 0 answered 8 questions · pick one answer each

1.Why do third-harmonic currents add up in the neutral of a four-wire wye instead of cancelling?
2.On a 60 Hz system, what frequency is the 5th harmonic?
3.A balanced office panel has 20 A of third-harmonic current on each phase. Ignoring other harmonics, about how much current is in the neutral?
4.A current has a 100 A fundamental, 24 A of 5th harmonic and 18 A of 7th. What is its current THD?
5.Which meter gives a correct current reading on a badly distorted waveform?
6.Which of these is a non-linear load that produces harmonic current?
7.The lights dim for a second every time a large compressor starts. That event is best described as a…
8.What is a K-factor transformer built for?

Answers

B. Because the three phases’ third harmonics are in step with each other — 3 × 120° is a full 360° — The fundamentals are 120° apart and cancel in the neutral on a balanced load. Triple their frequency and the 120° shifts become 360° — the third harmonics line up and add. The same is true of every "triplen" (3rd, 9th, 15th…).
C. 300 Hz — A harmonic is a whole-number multiple of the fundamental: 5 × 60 = 300 Hz. On a 50 Hz system it would be 250 Hz.
D. 60 A — The fundamentals cancel, but the three 20 A third-harmonic currents are in step and add: 3 × 20 = 60 A at 180 Hz — in a conductor that a balanced-load rule of thumb says should carry nothing.
B. 30% — THD = √(sum of each harmonic squared) ÷ fundamental: √(24² + 18²) = √(576 + 324) = √900 = 30 A; 30 ÷ 100 = 30%. You add harmonics as squares, not straight — 24 + 18 = 42 is the trap.
B. A true-RMS meter — An average-responding meter assumes a sine wave and scales its reading by a fixed factor; on a peaky, distorted current it usually reads low. A true-RMS meter measures the heating value of whatever wave is there.
C. A VFD or LED driver with a rectifier front end — Rectifier front ends only draw current near the peaks of the voltage wave, in short gulps — that is what makes harmonic current. Heaters and incandescent lamps draw current in proportion to voltage (linear).
B. voltage sag — A sag is a short drop in RMS voltage lasting from a cycle or so up to a few seconds — motor starting current through the supply impedance is the classic cause. A transient is a much faster spike, measured in microseconds.
B. Carrying harmonic-rich loads without overheating from the extra losses harmonics cause — Harmonic currents raise eddy-current losses in a transformer far more than their size suggests. A K-rated transformer is designed (and often has a bigger neutral terminal) to carry them without overheating.

Questions people ask

Can the neutral really carry more current than the phases?

Yes, on a four-wire wye feeding lots of single-phase electronic loads — computers, LED drivers, small power supplies. Their third-harmonic currents add in the neutral, and it can carry more than any one phase. That is why neutral sizing on harmonic-rich loads is its own topic in your code book, and why an overheated neutral with "balanced" phases is a harmonic clue.

Do three-phase drives put third harmonics in the neutral?

A three-phase drive with no neutral connection cannot put current in the neutral at all. Its rectifier mostly makes 5th and 7th harmonics (and 11th, 13th…), which flow in the phases. Triplen neutral trouble comes from single-phase, line-to-neutral electronic loads.

What is a line reactor for?

A small inductor in series with a drive’s input. It slows down the gulps of current the rectifier takes, which lowers the harmonic current, and it softens voltage notches and transients on the way in. Many drives have one built in as a DC-bus choke doing a similar job.

Unbalanced loads and neutral current — the balanced-neutral rule this lesson breaks
Voltage unbalance calculator
Power factor correction calculator
How a VFD works — the rectifier that makes the harmonics
Using a multimeter — true RMS

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