Hioki 3196 - Page 210

12.4 Formulae
204
Current unbalance factor Iunb (%)
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
•For I12, I23, and I31, use the fundamental wave RMS current (line-to-line current) from the calculated har-
monics results.
• 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).
• For three-phase 3-wire and three-phase 4-wire configurations this is detected using phase current, but
can be converted and calculated using line-to-line current.
Iunb
136β––
136β–+
---------------------- 100×=
β
I
4
12
I
4
23
I
4
31
++
I
2
12
I
2
23
I
2
31
++()
2
------------------------------
=
Iunb
136β––
136β–+
---------------------- 100×=
β
I
4
12
I
4
23
I
4
31
++
I
2
12
I
2
23
I
2
31
++()
2
------------------------------
=
Harmonic voltage Uk (V rms) (including adjacent inter-harmonics components)
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).
• 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 harmonic voltage content percentage, divide the fundamental wave voltage component by the har-
monic voltage component of the specified order, then multiply by 100.
• When using 60 Hz, the number “10” in the expression above 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
-------------- -
⎝⎠
⎛⎞
⎩⎭
⎨⎬
⎧⎫
2
n1–=
1
∑
=
Harmonic current Ik (A rms) (including adjacent inter-harmonic components)
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).
• For harmonic current content percentage, divide the fundamental wave current component by the har-
monic current component of the specified order, then multiply by 100.
• When using 60 Hz, the number “10” in the expression above 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
10k n+
10
-------------- -
⎝⎠
⎛⎞
⎩⎭
⎨⎬
⎧⎫
2
n1–=
1
∑
=