eeworldonline.com | designworldonline.com 6 • 2019 DESIGN WORLD — EE NETWORK 35Because of the alternating magnetic field, there is a normal
temperature rise in the iron core due to eddy current and hysteresis
loss. That is a given, and the iron core is by design sufficiently
massive to dissipate this heat. But as it happens, the amount of eddy
current loss varies with the square of the frequency. When high-
frequency harmonics come along, the heat rises dramatically and, as
it dissipates, a significant portion migrates into the windings, adding
to the excess heat generated there by the unwanted harmonics and
further stressing the winding insulation. Hysteresis varies directly with
the frequency, not with its square, but still, it adds to the total.
Another factor, even more harmful, is a loss within the windings.
This source of heat varies with the square of the current (I^2 R) and the
harmonics have a significant negative impact. Additionally, these high-
frequency components exhibit harmful skin effect, reducing effective
conductor size.
If a generator is to supply nonlinear loads, it should be derated
because it has higher reactance and impedance than a similar size
motor. Combined with high-frequency magnetic flux resulting from the
presence of powerful harmonics, they boost the stator temperature.
Rotor heating also results from these high-frequency currents.
Additionally, harmonics set the stage for often catastrophic
transformer failure. Generally trouble-free, transformers without
warning may explode as big nonlinear loads abruptly switch on. The
problem is compounded in older transformers containing toxic PCB-
laden cooling oil.
Copper and iron losses combine to create a hazardous situation.
Eddy current rises when harmonics enter a transformer from line
or load. Because eddy current is proportional to the square of
the applied current and the square of its frequency, a transformer
catastrophe can happen suddenly and without warning.
Harmonic current in transformers is a source of electromagnetic
interference that can degrade nearby communication circuits.
Shielding, increased spatial separation and suppression of the
harmonics are used to mitigate these effects.
To summarize, Fourier analysis (as opposed to Fourier synthesis),
of a periodic signal reveals the harmonic frequencies that are
components and integer multiples of the signal. This is where THD
appears.
The reason that a voltage and its associated current are purely
sinusoidal is that they consist of a single frequency. Multiple higher
frequency components contribute to the observed THD. A square
wave has a great amount of this distortion while a sine wave that is
in the real, non-ideal world has a small amount of it. In most cases,
that component is not visible in the time domain, but it can usually be
observed just above the noise floor in the frequency domain.
THD is a constant concern in power systems. Low power factor,
higher peak currents and low efficiency accompany high THD. In audio
reproduction, a low THD equates to better fidelity. In communications
systems, high THD means a potential for interference with nearby
equipment and greater power consumption at the transmitter.
A THD analyzer can be used to measure the distortion of a waveform in comparison to a distortion-free sine wave. The instrument
breaks the wave under investigation into its harmonics and compares
each harmonic to the fundamental. An alternate procedure is to
remove the fundamental by means of a notch filter, then measuring
the remaining signal which will be the THD plus noise.
In audio equipment development, a low-distortion arbitrary
function generator is used to insert an input into the unit being
evaluated. Distortion at constituent frequencies is then measured for
comparison of prototypes. In such procedures, crossover distortion
for any given THD level is more audible and thus tends to outweigh
clipping distortion, which produces higher-order harmonics.
Generally, harmonics are beneficial only to the musician, who
uses them in a flute or guitar to produce sounds that would otherwise
be beyond the capability of the instrument.
The best way to mitigate harmonics is to suppress them at the
source. An alternative is to create shielding or filters at the equipment
that is affected by the harmonics. Then, measuring the amount of
THD, the success of these measures can be evaluated. Tektronix PA3000 power analyzer
https://www.tek.com/power-analyzer/pa3000THD
Herres — Test and Measurement HB 06-19.indd 35 6/7/19 1:47 PM