Harmonics and THD: What the Numbers Mean for a UPS

Harmonics in one paragraph

Any repeating waveform, however lumpy, can be described as a sum of pure sine waves: one at the fundamental frequency (60 Hz in North America, 50 Hz in much of the world) and others at whole-number multiples of it. Those multiples are the harmonics: the 3rd harmonic is 180 Hz, the 5th is 300 Hz, the 7th is 420 Hz, and so on. A perfect sine wave has only the fundamental. A distorted one has harmonics, and the more distorted it is, the bigger they are.

Total harmonic distortion (THD) condenses all of this into one percentage:

where H1 is the RMS size of the fundamental and H2, H3 and so on are the RMS sizes of each harmonic. Because the harmonics are squared and summed, a few large ones dominate the result.

Worked example: computing voltage THD

A power quality logger on a 120 V office receptacle reports these harmonic voltages:

The square root of 16.20 is about 4.02 V. Divided by 120 V, that is a voltage THD of about 3.4%. That is an ordinary figure for a building full of computers and LED lighting, and nothing to worry about.

Voltage THD and current THD are different things

This is the single most common confusion in harmonics discussions, including on some spec sheets and forum threads.

• Current THD (THDi) is a property of the load. It describes how distorted the current drawn by a device is, regardless of how clean the voltage is.
• Voltage THD (THDv) is a property of the supply at a point. It arises when distorted currents flow through the impedance of transformers and wiring, creating distorted voltage drops that subtract from the sine wave.

A device can draw current with 100% THD while the voltage at its outlet has 3% THD, because the utility's transformer is large and stiff compared with that one device. Put the same device on a small generator, and the voltage THD rises because the source is weaker. The load has not changed; the source has.

The relationship is roughly: voltage distortion = harmonic current x source impedance at that harmonic frequency. Since transformer and generator impedance is mostly inductive, it rises with frequency, so higher harmonics are amplified relative to their current.

Where harmonics come from

The classic source is the capacitor-input rectifier: a diode bridge feeding a large capacitor, which is the front end of almost every electronic power supply that lacks power factor correction. The capacitor only takes current when the incoming voltage rises above its own stored voltage, near the peak of each half cycle. The result is two short, tall current pulses per cycle instead of a smooth sine wave.

In Europe, IEC 61000-3-2 limits harmonic current from equipment drawing up to 16 A per phase, which is a major reason PC power supplies above a modest wattage carry active PFC worldwide. See active PFC power supplies for how they behave on a UPS.

Distortion lowers power factor

Harmonic current carries no useful energy (at least when the voltage is nearly sinusoidal), but it does add to RMS current. That is why a non-PFC supply has a poor power factor even with no phase shift. For a load with negligible phase shift:

With THDi of 94% (0.94), the power factor is 1 / square root of 1.88, about 0.73. This links directly to the VA versus watts distinction: older loads present more VA per watt, so they use up a UPS's VA rating faster.

Triplen harmonics and the overloaded neutral

In a three-phase, four-wire system (the 208Y/120 V service common in US commercial buildings), each phase is 120 degrees apart. At the fundamental, balanced phase currents cancel in the shared neutral, so a neutral sized the same as the phases is normally plenty.

The 3rd harmonic breaks this. Shifting 120 degrees at 60 Hz is a shift of 360 degrees at 180 Hz, so the 3rd harmonic currents from all three phases are in phase with each other. They do not cancel; they add. The same applies to the 9th, 15th and every odd multiple of 3, together called triplen harmonics.

Worked example: neutral current in a server closet

Three 120 V circuits, one per phase, each feed identical older non-PFC loads. Per phase, the current spectrum (scaled to a 1.0 A fundamental) is:

1. Phase current (RMS): square root of (1.000 + 0.563 + 0.250 + 0.063 + 0.010) = square root of 1.886, about 1.37 A. THDi is the square root of 0.886, about 94%.
2. Neutral current: the 3rd harmonics add to 3 x 0.75 = 2.25 A, the 9th to 3 x 0.10 = 0.30 A. The RMS total is the square root of (2.25² + 0.30²), about 2.27 A.
3. Ratio: 2.27 / 1.37 is about 1.65. The neutral carries 65% more current than any phase conductor.

Scale that to 12 A per phase and the neutral carries roughly 20 A, on a conductor sized the same as the phases. The theoretical ceiling for this mechanism is about 1.73 times phase current. This is why the NEC requires the neutral to be counted as a current-carrying conductor when a major portion of the load is nonlinear, and why older office buildings with shared neutrals and many PCs have historically seen overheated neutrals and transformers. K-rated or harmonic-mitigating transformers and oversized neutrals are the standard engineering responses.

Reading UPS harmonic specifications

A UPS data sheet can carry three different harmonic numbers. They answer different questions:

Two caveats. A line-interactive UPS's output THD figure usually applies only on battery; on utility power, it passes the utility waveform through, with whatever distortion that has. And simulated (stepped) sine wave units are distorted by design: their stepped output typically measures tens of percent THD, which most makers do not publish. That is acceptable for many loads for a few minutes, and it is the main subject of pure sine wave versus simulated sine wave.

For a side-by-side view of how topologies differ on output quality, see the UPS topology comparison table.

IEEE 519: what it is and what it is not

IEEE 519 is the main North American recommended practice for harmonic limits. The 2014 revision sets limits at the point of common coupling, normally the boundary between the utility and the customer's system, not at each device. For low-voltage systems (1 kV and below), it recommends voltage THD of no more than 8% with no single harmonic above 5%. Current limits are expressed as total demand distortion and scale with how stiff the utility supply is relative to the customer's load.

What this means in practice: IEEE 519 is a tool for utilities, facility engineers and specifiers of large drives, data centers and industrial plants. It is not a rating for a consumer UPS or a power supply, and a product claiming "IEEE 519 compliant" means at most that it is designed to help an installation meet those limits. A homeowner is very unlikely to encounter it outside a utility dispute.

Generators make harmonics visible

A generator's internal impedance is much higher than a utility transformer's. The same harmonic currents that make 3% voltage distortion on utility power might make 10% or more on a small generator. Generator voltage regulators can also respond poorly to distorted voltage, and frequency on small units drifts with load.

Typical consequences:

• A line-interactive UPS rejects the generator's output as out of tolerance and runs on battery until it is flat. See UPS not working with a generator.
• An online UPS accepts a wider input window and rebuilds a clean output, but its rectifier draw becomes part of the generator's load. Older large UPS units with high input THDi needed generators sized at several times the UPS rating; modern low-THDi units relax that substantially, though maker guidance still commonly calls for meaningful headroom.
• Inverter generators produce a much cleaner waveform and steadier frequency than conventional open-frame units of similar size, which is why they pair better with sensitive electronics.

Practical setup steps are in using a UPS with a generator.

Should a home user worry? A quick checklist

If you want to see your own numbers, a harmonic-capable logger is the tool, but basic monitoring through your UPS and a plug-in meter covers most home questions. See measuring power quality at home.