Appendix: Voltage And Current Harmonics; Theory - Amprobe ACD-55HPQ Manual De Instrucciones

8. APPENDIX: VOLTAGE AND CURRENT HARMONICS

8.1. 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:
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 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
A fundamental element to detect the presence of harmonics is THD defined as:
This index takes all the harmonics into account. The higher it is, the more distorted the
waveform gets.
∞
∑
= +
v(t) V
0
=
k
th
harmonic of v(t)
Effect of the sum of 2 multiple frequencies.
THDv
ω ϕ
+
V sin( t
k k k
1
LEGENDA:
1. Fundamental
2. Third Harmonic
3. Distorted waveform sum of two
previous components.
40
∑
2
V
h
=
h 2
=
V
1
EN - 26
ACD-55HPQ
)
th
harmonic.
(1)