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8. APPENDIX: VOLTAGE AND CURRENT HARMONICS
8.1.
THEORY
Any periodical non-sine wave can be represented as a sum of sinusoidal waveforms each
having a frequency that corresponds to an integer multiple of the fundamental frequency,
according to the relation:
where:
V
= Average value of v(t)
0
V
= Amplitude of the fundamental of v(t)
1
V
= Amplitude of the k
k
In the mains 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 durations events
such as sags, surges or spikes.
It can be noted that in (1) the index of sigma is from 1 to the infinity. 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
the index end in (2) in correspondence of the 40
A fundamental element to detect the presence of harmonics is THD defined as:
This index takes all the harmonics into account. The larger it is, the more distorted the
waveform gets.
∞
∑
=
+
v(t)
V
0
=
k
1
th
harmonic of v(t)
Effect of the sum of 2 multiple frequencies.
THDv
ω
ϕ
+
V
sin(
t
k
k
k
LEGENDA:
1. Fundamental
2. Third Harmonic
3. Distorted waveform sum of two
previous components.
th
harmonic.
40
∑
2
V
h
=
=
h
2
V
1
EN - 31
ACD-51HP - ACD-56HPQ
)
(1)
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