What a Harmonic Actually Is

Why this matters

"Harmonics" gets used in the field as a name for something invisible and vaguely hostile that arrives from outside and has to be filtered out. That framing produces bad decisions: filters bought for problems they cannot fix, utilities blamed for waveforms the building drew itself, and clamp readings trusted that were never capable of seeing the current in question. A harmonic is not a contaminant. It is a description of a SHAPE, and once you can read the shape you can tell which instrument is lying to you, which number belongs to whom, and whether the value someone quoted you means anything at all.

The claim this card carries: a distortion figure is a statement about a waveform, so it is meaningless until you know whether it describes current or voltage, what it was measured against, and whether the instrument could see it.

A harmonic is arithmetic, not a substance

Any repeating waveform, however strange its shape, can be expressed exactly as a sum of sinusoids at whole-number multiples of its repetition frequency. That is the whole idea. On a 60 Hz system the fundamental is 60 Hz, the third harmonic is 180 Hz, the fifth is 300 Hz, the seventh is 420 Hz, and so on upward.

So when a rectifier-fronted load draws current in short pulses near the voltage peaks instead of as a smooth sinusoid, nothing has been added to the circuit. There is one current, with one shape, and describing it as a fundamental plus a set of harmonics is a way of doing arithmetic on it. The reason we bother is that the system responds to each of those component frequencies differently - a conductor's impedance, a transformer's losses and a motor's rotating field all change with frequency - so decomposing the current tells you what it is going to do.

Current distortion and voltage distortion are two different measurements

This is the distinction that resolves most arguments on site, and the two get quoted interchangeably.

Current distortion belongs to the load. A nonlinear load draws a non-sinusoidal current because of how its front end works. That happens whether the supply is perfect or terrible.

Voltage distortion belongs to the system. That distorted current flows through the impedance of everything upstream, and the voltage drop it produces is itself distorted, so the voltage waveform at the bus stops being a clean sinusoid. How much depends on the upstream impedance, which is why the same load produces different voltage distortion in two buildings. That relationship is what the system-effects card works through.

The practical consequence is where you point the instrument. Current distortion is measured at the load or the branch that serves it. Voltage distortion is measured at the bus. Reporting one as the other is the most common error in a power quality write-up, and the numbers are typically an order of magnitude apart, so it is not a small error.

Which harmonics exist, and what that tells you

Odd only, usually, and the exception is diagnostic. A waveform whose negative half is a mirror image of its positive half contains no even harmonics at all. Most electrical loads are symmetric in that way, so real current spectra are dominated by the third, fifth, seventh and upward. The moment you see significant EVEN harmonics, something has broken that symmetry: a failed leg in a rectifier bridge, a half-wave load, a DC component being injected, or a transformer saturating asymmetrically. Even harmonics are rarely the problem themselves and are frequently a good pointer to which piece of equipment to open.

Each harmonic has a sequence, meaning the way its three phase components line up relative to each other on a three-phase system, and the pattern repeats every sixth harmonic:

Two of those rows point at problems a sibling card owns. The zero-sequence row is why a neutral can carry more than a phase conductor, which the neutral card owns. The negative-sequence row is why harmonic-rich supplies heat motors, which the system-effects card owns. What matters here is that sequence is a property of the harmonic NUMBER rather than of the installation, so you can predict where a given harmonic will make trouble before measuring anything.

Three numbers that describe the same shape

RMS is the value that matters for heating. It is defined as the equivalent direct current that would produce the same heating in a resistance, which means it is the number that heats a conductor, trips a thermal element and loads a transformer, regardless of waveform. For a current made of a fundamental plus harmonics, the total RMS is the fundamental times the square root of one plus the square of the total harmonic distortion expressed as a fraction of the fundamental.

Total harmonic distortion, THD, is the RMS of everything except the fundamental, divided by the fundamental. A THD of 0.66 means the harmonic content by itself is 66 percent as large as the fundamental. Note the base: as a fraction of the FUNDAMENTAL, not of the total.

Crest factor is the peak divided by the RMS. A pure sinusoid is 1.414 by definition. A rectifier's pulsed current commonly runs 2 to 3, which is what "peaky" means numerically, and it is the number that matters for anything that has to supply that peak without saturating or without its voltage collapsing at the top of the cycle.

A fourth term shows up in reports and is worth knowing because it fixes a real weakness in THD. Current THD is computed against the fundamental PRESENT AT THAT MOMENT, so a lightly loaded circuit can show a huge THD that means nothing: 66 percent distortion on a small standby current is not a problem for anything. Total demand distortion, TDD, uses the maximum demand load current as the base instead, which keeps the number proportional to the actual duty. That definition comes from IEEE 519, which binds through a utility service agreement or a project specification rather than on its own authority, in whatever edition that agreement names.

Worked case: reading a waveform off three instruments

A branch circuit serving a bank of electronic equipment is read three ways in the same minute.

These are readings on energized conductors, so 29 CFR 1910.333(a)(1) applies: de-energize before working on or near exposed live parts unless the employer can demonstrate that de-energizing introduces additional or increased hazards or is infeasible due to equipment design or operational limitations, and a load current reading does not exist on a dead circuit. Work under the employer's energized-work program with boundaries and PPE selected under NFPA 70E-2021 130.5 and 130.7, in the edition your employer's program or your authority having jurisdiction has adopted. Use an instrument and test leads rated for the measurement category and voltage of the point you are testing, and inspect the leads for damage before every use; a clamp jaw closed around a conductor still puts your hands inside the enclosure, so the boundary and PPE decision applies to a "non-contact" reading exactly as it does to a probe.

• True-RMS clamp: 24.0 A.
• Average-responding, RMS-calibrated clamp: 18.0 A.
• Power analyser, fundamental component: 20.0 A.

What the second instrument did. An average-responding meter rectifies the waveform, averages it, and multiplies by 1.111, which is the ratio of RMS to average for a SINUSOID. If it displayed 18.0 A, the average it actually measured was 18.0 divided by 1.111, or 16.2 A. Against a true RMS of 24.0 A, the real waveform's ratio of RMS to average is 24.0 divided by 16.2, or 1.48, well above a sinusoid's 1.111. That is the signature of a peaky waveform, and it is why the meter read low: it was calibrated on a shape this current does not have.

Check the direction at the other end, because this is the part that gets remembered backwards. An averaging meter reads LOW on a peaky waveform and HIGH on a flat-topped one, because the error is entirely in which shape the 1.111 assumed. It is not a meter that "reads low on harmonics"; it is a meter that reads correctly on one shape only.

What the third instrument adds. With a fundamental of 20.0 A and a true RMS of 24.0 A, the harmonic content is the square root of 24.0 squared minus 20.0 squared, which is the square root of 576 minus 400, or the square root of 176, which is 13.3 A. THD is 13.3 divided by 20.0, or 66 percent. Check it back the other way: 20.0 times the square root of one plus 0.66 squared is 20.0 times the square root of 1.436, which is 20.0 times 1.198, or 24.0 A. It closes.

Now the part that decides what you do. The conductor, the terminations and the breaker's thermal element all respond to RMS, so the current this circuit is actually running is 24.0 A. The averaging clamp understated the conductor's duty by 6.0 A, which is 25 percent of the true value, and a tech sizing or evaluating from that reading would conclude the circuit had headroom it does not have. Nothing in the panel was wrong. The instrument answered a question about a sinusoid that nobody asked.

And the number that gets quoted upward. If someone reports "66 percent THD" to a facility manager, that is a CURRENT distortion figure measured on one branch. It says nothing about the voltage at the bus, and it cannot be compared against a voltage distortion limit. Establishing whether the same load is doing anything to the system is a different measurement in a different place, and it is what the system-effects card is for.

What changes the answer

• A lightly loaded circuit. High current THD on a small fundamental is arithmetic, not a problem, which is what TDD exists to express.
• Diversity across many devices. Harmonic components from a population of different devices are not perfectly in step, so a floor of mixed equipment usually measures less total distortion than the sum of its individual devices' spec sheets would predict. Measure the aggregate rather than adding up datasheets.
• A drive with a line reactor or a multi-pulse front end draws a different shape than a bare six-pulse rectifier, so the equipment's own configuration changes its spectrum. That is the manufacturer's information, not something to estimate.

How to verify you got this right

Take the same reading with a true-RMS instrument and confirm it is a true-RMS instrument by its documentation rather than by the words on the case. Read the neutral as well as the phases when the load is single-phase and nonlinear, because a neutral above the phase currents confirms triplen content by itself. Write down, next to every distortion figure you record, whether it is current or voltage, where it was taken, and what its base was. A THD number without those is not a measurement, it is a rumour, and it will be quoted back to you in six months as if it were.

References

• IEEE 519, definitions of total harmonic distortion and total demand distortion, as it binds through a utility service agreement or project specification, in the edition that agreement names
• 29 CFR 1910.333(a)(1), general industry electrical safety-related work practices and the de-energizing gate
• NFPA 70E-2021, 130.5 and 130.7, as adopted by your employer's electrical safety program or your authority having jurisdiction
• Instrument manufacturer documentation for measurement category rating and true-RMS capability
• See related: Why a Neutral Can Carry More Than You Expect; What Non-Linear Loads Do to a System