---
title: "Transformer running hot: harmonics and K-factor"
description: "The ammeter reads 70 % of nameplate and the transformer is too hot to touch. Why eddy loss follows frequency squared, and what K-factor really tells you."
date: "2026-09-02"
author: "Divakar B"
source: "https://energycalchq.com/blog/transformer-running-hot-harmonics"
license: "© 2026 Divakar B. Quote with attribution to https://energycalchq.com/blog/transformer-running-hot-harmonics"
---

A transformer that runs hot at an ammeter reading well inside its nameplate is
one of the more disorienting things to find on a site visit. The load is
650 kVA on a 1000 kVA unit. The ventilation is clear. The taps are right. The
oil or winding temperature says otherwise, and if you go by current alone there
is nothing to explain it.

The current is not the problem. The **shape** of it is.

## Heating follows the square of the frequency

A transformer has two kinds of load loss. The **I²R loss** in the winding
resistance depends only on the RMS current, and it does not care what shape the
waveform is. The **eddy current loss** — circulating currents induced in the
conductors and the structural steel — rises with the square of frequency.

That second term is what harmonics do to a transformer. A 5th harmonic
component is at 250 Hz, so for the same current magnitude it produces
**twenty-five times** the eddy loss of the fundamental. The 7th produces
forty-nine times.

Run the arithmetic on an ordinary six-pulse drive load and the result is
counterintuitive:

![Grouped bar chart comparing each harmonic's share of RMS current against its share of eddy-current heating, showing the fundamental at 92 percent of current but 13 percent of heating while the fifth harmonic is 32 percent of current and 40 percent of heating](https://hhfiunqrrmpuctcnlwnk.supabase.co/storage/v1/object/public/blog-images/harmonics-transformer-heating.svg "The clamp meter and the winding are measuring different things. Only one of them decides how long the transformer lasts.")

The fundamental carries **92 % of the current and causes 13 % of the eddy
loss**. The 5th carries a third of the current and causes **40 %** of it. Your
ammeter is dominated by the component that barely heats anything, and is nearly
blind to the ones doing the damage.

This is the whole phenomenon. Everything below is bookkeeping on top of it.

## What K-factor actually is

K-factor puts a single number on that spectrum. Under IEEE C57.110 it is:

```
K = Σ (Ih(pu)² × h²)
```

where `Ih(pu)` is each harmonic's current as a fraction of the total RMS
current, and `h` is the harmonic order. It is a weighted sum in which every
term is scaled by the square of its frequency — precisely the eddy loss
weighting above.

For the spectrum in the diagram — a typical 6-pulse drive at 42 % current
distortion — **K works out at about 6.5**. A purely linear load is K = 1 by
definition.

Two things about K-factor are worth being clear on, because both are commonly
muddled:

**K-factor is a property of the load, not the transformer.** You calculate it
from a measured current spectrum. A "K-13 transformer" is one *built to
tolerate* a load of K up to 13 — larger conductors, transposed windings,
oversized neutral, more core steel. Buying a K-rated transformer does not
reduce your harmonics; it means the transformer survives them.

**K-factor is not THD, and they do not convert.** Two loads with the same THD
can have very different K-factors depending on which harmonics carry the
distortion, because of that h² weighting. THD tells you how distorted the
waveform is. K tells you how much it will heat a transformer. Quoting one when
you mean the other is the most common error in this area.

## Derating: the honest version

The rule you will find repeated is "derate the transformer". The number
attached to it varies wildly between sources, and most of them are guessing.

The real calculation in C57.110 needs one parameter you cannot infer from the
nameplate: **PEC-R**, the winding eddy current loss as a fraction of I²R loss
at rated current. It is typically a few percent for a distribution transformer
and much higher for a large unit with heavy conductors. The derating for a
given K depends strongly on it, which is why a 1000 kVA transformer might carry
750 kVA under one drive load and 850 kVA under the same K with a different
construction.

So the practical position is:

- If you are **specifying a new transformer** for a known drive load, ask the
  manufacturer for the derating at your measured spectrum, or buy a K-rated
  unit and size normally. Both are answerable questions for them and guesswork
  for you.
- If you are **assessing an existing one**, stop calculating and measure the
  temperature. Winding or top-oil temperature against the rated rise is the
  direct answer, and it accounts for every effect at once — including the ones
  no formula on this page covers.

The [THD and harmonic losses calculator](/tools/thd-losses) will take a
measured spectrum and give you the loss picture; the [transformer sizing
calculator](/tools/transformer-sizing) covers the conventional side of the
question.

## Reading your own installation

**Measure with the right instrument.** An averaging clamp meter reads a
distorted waveform low — sometimes 20 % low. You want **true RMS**, and for the
spectrum itself a power quality analyser rather than a multimeter. If the only
number you have is from an averaging meter, you do not yet know the load
current, let alone its shape.

**Measure at the transformer secondary, not at the drive.** Harmonics from
several loads do not simply add; some cancel, particularly between drives on
different phases or with different DC bus loading. The spectrum that matters is
the one arriving at the transformer.

**Check the neutral.** Triplen harmonics — 3rd, 9th, 15th — do not cancel in
the neutral of a four-wire system; they add. A neutral running hotter than the
phases, or carrying more current than any phase, is that, and it is a wiring
capacity problem as well as a transformer one. Six-pulse drives are
three-wire and produce little triplen content, but single-phase SMPS loads
produce a great deal.

**Look at the load mix before blaming the drives.** A floor of LED drivers and
SMPS supplies can produce a worse spectrum than one large VFD, and it does not
announce itself the way a drive panel does.

## The capacitor bank makes it worse, not better

If the site has power factor correction, harmonics stop being purely a heating
problem and become a resonance problem.

A capacitor bank and the supply transformer's leakage inductance form a
parallel resonant circuit at some frequency. If that frequency lands near a
harmonic the load is producing — the 5th and 7th are the usual suspects —
current at that harmonic circulates between the two and is **amplified**, not
absorbed. Capacitors overheat and fail, fuses blow with no obvious fault, and
the transformer gets hotter than the load alone explains.

Switching a capacitor step changes the resonant frequency, which is why this
often looks like an intermittent fault correlated with nothing obvious.
[APFC panels: sizing the steps, and avoiding
resonance](/blog/apfc-panel-step-sizing) covers how the steps interact and what
detuned reactors are for.

## What to actually do

In rough order of cost:

- **Move loads between transformers** so the drive load is not concentrated on
  one unit. Free, if you have the spare capacity.
- **Detune the capacitor bank** with series reactors, usually at 7 % or 14 %,
  which shifts the resonance below the 5th harmonic. This is the standard fix
  and is often the whole answer on sites where PFC is present.
- **Fit line reactors or DC link chokes** on the drives. A 3 % line reactor
  typically takes a 6-pulse drive's THDi from about 80 % down to 35–40 %. This
  is the cheapest real harmonic reduction available and is often omitted to
  save money at panel build.
- **Passive or active filters**, when the above is not enough.
- **12-pulse or active front-end drives** for new large installations, which
  cancel the 5th and 7th at source.
- **A K-rated transformer**, which does not reduce harmonics but stops them
  shortening the transformer's life.

## What this does not cover

This is about heating in the transformer. Harmonics also cause motor heating
and torque pulsation, nuisance tripping of protective devices, and metering
error — that last one matters commercially, since a distorted waveform can put
your meter and the utility's meter in disagreement.

It also does not address the utility's limits on what you may inject. IEEE 519
sets injection limits at the point of common coupling based on your demand
relative to the supply's short circuit capacity, and an installation can be
comfortable internally while being outside those limits.

And it assumes the heat is harmonics. It might not be. Overloading, a blocked
radiator, a failing fan, high ambient, a loose connection or degraded oil all
produce a hot transformer too, and several of them progress faster than
harmonic heating does. [Why distribution transformers
fail](/blog/why-distribution-transformers-fail) covers the other routes —
worth reading first if the temperature rose suddenly rather than creeping up
over months as load was added.