12.4 Formulae
205
Inter-harmonic voltage Uk (V rms)
Single-phase 2-wire
1P2W
Single-phase 3-wire
1P3W
Three-phase 3-wire
3P3W2M
Three-phase 3-wire
3P3W3M
Three-phase 4-wire
3P4W
U1k
U4k
U1k
U2k
U4k
U12k
U32k
U4k
U12k
U23k
U31k
U4k
U1k
U2k
U3k
U4k
• Calculate the Discrete Fourier Transform of harmonic RMS voltage at 2048 points (about once every 10
cycles at 50 Hz or every 12 cycles at 60 Hz).
• In the equation above, 3 and -3 are used at 50 Hz, and 4 and -4 are used at 60 Hz. k = 0.5, 1.5, 2.5, 3.5,,,
• Indicates the results of the harmonic calculations of line-to-line voltage for three-phase 3-wire configura-
tions and the results of harmonic calculations of phase-to-neutral voltage for three-phase 4-wire configu-
rations.
• For inter-harmonic voltage content percentage, divide the fundamental wave voltage component by the
inter-harmonic voltage component of the specified order, then multiply by 100.
• When using 60 Hz, the number “10” in the above expression is “12.”
c: measured channel, k: order for analysis, r: resistance after FFT, i: reactance after FFT
U′ck Uckr()
2
Ucki()
2
+=
Uck
U′
c
10k n+
10
-------------- -
⎝⎠
⎛⎞
⎩⎭
⎨⎬
⎧⎫
n3–=
3
∑
=
Inter-harmonic current Ik (A rms)
Single-phase 2-wire
1P2W
Single-phase 3-wire
1P3W
Three-phase 3-wire
3P3W2M
Three-phase 3-wire
3P3W3M
Three-phase 4-wire
3P4W
I1k
I4k
I1k
I2k
I4k
I1k
I2k
I4k
I1k
I2k
I3k
I4k
I1k
I2k
I3k
I4k
• Calculate the Discrete Fourier Transform of harmonic RMS current at 2048 points (about once every 10
cycles at 50 Hz or every 12 cycles at 60 Hz).
• In the equation above, 3 and -3 are used at 50 Hz, and 4 and -4 are used at 60 Hz. k = 0.5, 1.5, 2.5,
3.5,,,
• For inter-harmonic current content percentage, divide the fundamental wave current component by the
inter-harmonic current component for the specified order, then multiply by 100.
• When using 60 Hz, the number “10” in the above expression is “12.”
c: measured channel, k: order for analysis, r: resistance after FFT, i: reactance after FFT
I′ck Ickr()
2
Icki()
2
+=
Ick
I′
c
10
kn+
10
-------------- -
⎝⎠
⎛⎞
⎩⎭
⎨⎬
⎧⎫
2
n
3
–=
3
∑
=
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