User manual
5 Power quality - a guide
77
measured even order harmonics are of minimal value. If we consider this property, it turns out that
the group of harmonics with the most undesirable properties is the 3rd, 9th, 15th (zero sequence),
and the 5th, 11th, and 17th (negative sequence).
The current harmonics which are multiples of 3 cause additional problems in some systems. In
4-wire systems, they have a very undesirable property of summing up in the neutral conductor. It
turns out that, contrary to other order harmonics, in which the sum of instantaneous current values
is zeroed, the waveforms of these harmonics are in phase with each other which causes adding of
the phase currents in the neutral conductor. This may lead to overheating of this conductor (partic-
ularly in the distribution systems where the conductor has a smaller cross-section than the phase
conductors, as it was widely practiced until recently). Therefore, in systems with non-linear loads
and large current distortions, it is now recommended that the cross section of neutral conductor is
larger than that of the phased conductors.
In the delta systems, the harmonics of these orders are not present in the line currents (provided
these are balanced systems), but they circulate in the load branches, also causing unnecessary
power losses.
The nature of individual harmonics as shown in the table is fully accurate only in three-phase
balanced systems. Only in such systems, the fundamental component has the exclusively positive
sequence character. In actual systems, with some degree of supply voltage unbalance and the load
unbalance, there are non-zero positive and negative sequence components. The measure of such
unbalance is so-called unbalance factors. And this is due to this unbalance of the fundamental
component and additionally the differences in amplitudes and phases of the higher harmonics, that
also these harmonics will have the positive, negative and zero sequence components. The larger
the unbalance, the higher the content of remaining components.
IEC 61000-4-30 standard recommends that the harmonic subgroup method is used in power quality
analyzers for calculating harmonic components.
5.4.4 Total Harmonic Distortion
Total Harmonic Distortion (THD) is the most widely used measure of waveform distortion. Two
versions of this factor are applied in practical use:
THD
F
(THD-F or simply THD) – total harmonic distortion referred to the fundamental component,
THD
R
(THD-R) – total harmonic distortion referred to the RMS value.
In both cases, THD is expressed in percent. Definitions are presented below:
where: A
h
– RMS of the h-th order harmonic,
A
1
– RMS of the fundamental component,
A
RMS
– RMS of the waveform.
Limitation of the number of harmonics used to calculate THD is conventional and results mainly
from measuring limitations of the device. As the analyzer is capable of measuring the harmonic
components up to the 50th order, the harmonics of the 50th or 40th order are used to calculate THD
(the user can select either 40
th
or 50
th
order as the limit).
Please note that when the waveforms are very distorted, the two definitions presented above
will give significantly different results. THD
R
cannot exceed 100%, while THD
F
has no such limit and
may be 200% or more. Such a case may be observed when measuring very distorted current. The
voltage harmonic distortion usually does not exceed a few percent (both THD
F
and THD
R
); e.g. EN
50160 standard defines the limit of 8% (THD
F
).