Hioki 3196 - Page 212

12.4 Formulae
206
Harmonic power Pk (W)
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
P1k P1k
P2k
P1k
P2k
P1k
P2k
P3k
Psumk=
P
1k+P2k
Psumk=
P
1k+P2k
Psumk=P1k+P2k+P3k Psumk=
P
1k+P2k+P3k
• Calculate the Discrete Fourier Transform of harmonic power (harmonic active power) at 2048 points for
voltage and current (about once every 10 cycles at 50 Hz or every 12 cycles at 60 Hz).
• For harmonic power content percentage, divide the fundamental wave power component by the harmonic
power component of the specified order, then multiply by 100.
c: measured channel, k: order for analysis, r: resistance after FFT, i: reactance after FFT
Pck Uckr Ickr× Ucki Ick
i
×+=
P
1k
1
3
-- -
U
1kr U3kr–()I1kr×
1
3
-- -
U1ki U3ki–()I1k
i
×+=
P
2k
1
3
-- -
U
2kr U1kr–()I2kr×
1
3
-- -
U2ki U1ki–()I2k
i
×+=
P
3k
1
3
-- -
U
3kr U2kr–()I3kr×
1
3
-- -
U
3ki U2ki–()I3k
i
×+=
Harmonic reactive power Qk (var) (only for use with internal calculation)
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
Q1k Q1k
Q2k
Q1k
Q2k
Q1k
Q2k
Q3k
Qsumk=
Q
1k+Q2k
Qsumk=
Q
1k+Q2k
Qsumk=Q1k+Q2k+Q3k Qsumk=
Q
1k+Q2k+Q3k
• Calculate the Discrete Fourier Transform of harmonic reactive power at 2048 points for voltage and cur-
rent (about once every 10 cycles at 50 Hz or every 12 cycles at 60 Hz).
c: measured channel, k: order for analysis, r: resistance after FFT, i: reactance after FFT
Qck Uckr Icki× Ucki Ick
r
×–=
Q
1k
1
3
-- -
U
1kr U3kr–()I1kr
1
3
-- -
U
1ki U3ki–()I1
ki
×–×=
Q
2k
1
3
-- -
U
2kr U1kr–()I2kr
1
3
-- -
U
2ki U1ki–()I2
ki
×–×=
Q
3k
1
3
-- -
U
3kr U2kr–()I3kr×
1
3
-- -
U3ki U2ki–()I3k
i
×–=
K factor KF
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
KF1
KF4
KF1
KF2
KF4
KF1
KF2
KF4
KF1
KF2
KF3
KF4
KF1
KF2
KF3
KF4
• The K factor is also called the multiplication factor, and indicates the power loss using the harmonic RMS
current for the electrical transformer.
• 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).
c: measured channel, k: order for analysis
KFc
k
2
I×
2
ck
()
k1=
50
∑
I
2
ck
k1=
50
∑
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