Page 70 - Power Quality in Electrical Systems

Harmonics and Interharmonics 53

individual currents is the sum of the squares of the rms values of the
individual components, or:

2
2
2
I rms 5 2I 1,rms 1 I 2,rms 1 I 3,rms 1 ???
Total Harmonic Distortion
Total harmonic distortion or THD is a measure of how much harmonic
content there is in a waveform. The total harmonic distortion of a wave-
form is

2
2
V rms 2 V 1,rms
THD 5
2
Å V 1,rms
where V RMS is the rms value of the total waveform, and V 1,RMS is the rms
value of the first harmonic. The THD of a sine wave is 0 percent, and
the THD of a square wave is 48 percent.

Crest Factor
Crest factor is another term sometimes used in power systems analysis,
and represents the ratio of the peak value to the rms value of a waveform.
For a sine wave (Figure 4.14a), the peak value is 1.0 and the rms value is
0.707. Thus, the crest factor is 1.414. For a square wave (Figure 4.14b),
the peak and rms values are both 1.0—hence, the crest factor is 1.0.

Example 4.1: A truncated square wave. Asquare wave with peak value +1
has the Fourier series:
` 4
vstd 5 a b sin s2pntd
n51 np

A truncated Fourier series approaches the ideal waveform. We’ll next
find the rms value and total harmonic distortion for a square wave
waveform with harmonics present up to the seventh. The total waveform
for this example is

4 4 4 4
vstd 5 a b sinsvtd 1 a b sins3vtd 1 a b sins5vtd 1 a b sins7vtd
p 3p 5p 7p

The rms value of the first harmonic is

4
V 1,rms 5 5 0.9
π!2