PQA819 - PQA820
EN – 23
12.2. 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
(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)
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 how in (1) the index of the
summation goes from 1 to infinity. What actually happens is that each signal has an
unlimited number of harmonics: there is always a sequence number beyond which the
value of the harmonics is negligible.
CAPTION:
1.
Fundamental
2.
Third Harmonic
3.
Distorted waveform sum of two previous
components.
Effect of the sum of 2 multiple frequencies.
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.
