JUPITER
IT - 41
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
(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 components
Fig. 46: Effect of overlapping of two frequencies, one multiple of the other
For network voltage, the fundamental has a frequency of 50Hz, the second harmonic has
a frequency of 100 Hz, the third harmonic has a frequency of 150Hz 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 EN50160
suggests cutting the summation in the expression (1) at the 40th harmonic. A fundamental
index to detect the presence of harmonics is the THD% (Total Harmonic Distortion)
defined as:
100
%
1
40
2
2
x
V
V
THD
h
h
This index takes into consideration the presence of all harmonics, and the more distorted
is the waveform, the higher is the index.
Limit values for harmonics
Standard EN50160 prescribes the limits for the Harmonic voltages the Supplier may put in
network. In normal operating conditions, at any time in a week, 95% of the efficient values
of each harmonic voltage, averaged to 10 minutes, must be lower than or equal to the
values indicated in Table 3. The overall harmonic distortion (THD%) of supply voltage
(including all harmonics up to the 40th) must be lower than or equal to 8%.