HT9022
EN - 52
9.4.
VOLTAGE AND CURRENT HARMONICS
Any periodic non-sinusoidal wave may be represented by a sum of sinusoidal waves, each
with a frequency which is a whole multiple of the fundamental, according to the
relationship:
)
t
sin(
V
V
v(t)
k
k
1
k
k
0
ϕ
ω
+
+
=
∑
∞
=
(1)
where:
V
0
= Average value of v(t)
V
1
= Amplitude of the fundamental of v(t)
V
k
= Amplitude of the k-nth harmonic of v(t)
CAPTION:
1. Fundamental
2. Third Harmonic
3. Distorted waveform sum of two
previous components.
Effect of the sum of 2 multiple frequencies.
For network voltage, the fundamental has a frequency of 50 Hz, the second harmonic has
a frequency of 100 Hz, the third harmonic has a frequency of 150 Hz and so on.
Harmonic
distortion is a continuous problem and must not be confused with short-duration
phenomena such as peaks, drops or fluctuations.
It can be seen from (1) that each signal consists of the summation of infinite harmonics.
However, an order number exists beyond which the value of the harmonics may be
considered as negligible. Standard EN 50160 suggests cutting the summation in the
expression (1) at the 40th harmonic.
A fundamental index to detect the presence of harmonics is the THD defined as:
1
40
2
2
V
V
THDv
h
h
∑
=
=
This index takes into consideration the presence of all harmonics, and the more distorted
is the waveform, the higher is the index.
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