HT instruments SOLAR300N - Manual (Page 190)

SOLAR300 - SOLAR300N
EN - 188
10.5. VOLTAGE AND CURRENT HARMONICS
10.5.1. Theory
Any periodical no-sine wave can be represented as a sum of sinusoidal waves having
each a frequency that corresponds to an entire multiple of the fundamental, according to
the relation:
) t sin( V V v(t)
k k
1 k
k 0
    



(1)
where:
V
0
= Average value of v(t)
V
1
= Amplitude of the fundamental of v(t)
V
k
= Amplitude of the k
th
harmonic of v(t)
In the mains 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 constant problem and should not be confused with short events such as
sags, swells or fluctuations.
It can be noted that in (1) the index of the sigma is from 1 to the infinite. What happens in
reality is that a signal does not have an unlimited number of harmonics: a number always
exists after which the harmonics value is negligible.
CAPTION:
1. Fundamental
2. Third Harmonic
3. Distorted
Waveform
Effect of the sum of 2 multiple frequencies.
The EN50160 standard recommends to stop the index in the expression (1) corresponding
to the 40
th harmonic. A fundamental element to detect the presence of harmonics is THD
defined as:
100 %
1
40
2
2
x
V
V
THDV
h
h

 
This index takes all the harmonics into account. The higher it is, the more distorted the
waveform results.