Amprobe DM-4 Power-Quality-Recorder - Manual (Page 49)

15.2 VOLTAGE AND CURRENT HARMONICS
15.2.1 THEORY
Any periodical non-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:
v(t) = V
0
+
∑ V
k
sin (w
k
t + Ø
k
) (1)
Where:
V0 = Average value of v (t)
V1 = Amplitude of the fundamental of v (t)
Vk = Amplitude of the kth harmonic of v (t)
Effect of the sum of 2 multiple frequencies.
In the main voltage, the fundamental has a frequency of 60 Hz, the second harmonic
has a frequency of 120 Hz, the third harmonic has a frequency of 180 Hz and so on.
Harmonic distortion is a constant problem and should not be confused with short
events such as sags, surges 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. The EN 50160 standard recommends to stop the index in the
expression (1) in correspondence of the 40
th
harmonic.
48
DM-4 Power Quality Recorder
LEGEND:
1. Fundamental
2. Third Harmonic
3. Distorted Waveform
∞
k=1