Rockwell Automation 1412-PP21xx PowerPad Portable Powermonitor - Manual (Page 87)

Rockwell Automation Publication 1412-UM001D-EN-P - September 2012 87
Mathematical Formulas For Various Parameters Appendix C
THD Calculation
• i: phase (0, 1, 2)
• n: range (2 to 50)
Calculation of Harmonic Bins Harmonic bins are calculated by FFT with 16 bit resolution (1024 samples on 4
cycles) without windowing (IEC 1000-4-7). From real and imaginary
components, each bin ratio is calculated on each phase Vharm [3][51], Uharm
[3][51] and Aharm [3][51] in proportion to the fundamental value and the
phase angles Vph [3][51], Uph [3][51] and Aph [3][51] between each bin and
the fundamental.
This calculation is accomplished by using the following principle:
• ck: amplitude of the component with a frequency of
• Fs: sampled signal
• co: DC component
• k: ordinal number (spectral bin)
Vthd[i] =
[i][n] Vharm
[i][1] Vharm
∑
n=2
50
2
Uthd[i] = , ,
[i][n] Uharm
[i][1] Uharm
∑
n=2
50
2
Athd[i] =
[i][n] Aharm
[i][1] Aharm
∑
n=2
50
2
⎝
⎛
⎝
⎛
cos
sin
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
=
⎟
⎠
⎞
⎜ + Ч =
⎟
⎠
⎞
⎜ + Ч =
+ = + =
∑
∑
∑
=
=
=
1024
0
0
1024
0
1024
0
2 2
1024
1
512 512
1
512 512
1
s
s
s
k s k
s
k s k
k k k k k
F c
s
k
F a
s
k
F b
b a ja b c
ϕ
π
ϕ
π
100 mod
1
× =
c
c
k
k
⎟⎟⎠
⎞
⎜⎜⎝
⎛
=
k
k
k b
a
arctan
ϕ
module in %:
with
angle in degree:
1
4
f
k
f
k
=