8.5 Calculation Formulas
160
Harmonic Formulas
Wiring
Configuration
Parameter
Single-
Phase
2-Wire
Single-Phase
3-Wire
Three-phase, 3-wire
Three-Phase
4-Wire
1P2W 1P3W 3P3W2M 3P3W3M
3P4W,
3P4W2.5E
Harmonic
Voltage
U
k
[Vrms]
*1
U
1k
U
1k
U
2k
Inter-Line
Voltage
U
1k
U
2k
U
3k
(
U1s+(-U2s)+U3s=0
are assumed)
Phase Voltage
U
1k
U
2k
U
3k
Phase
Voltage
U
1k
U
2k
U
3k
Harmonic
Current
I
k
[Arms]
I
1k
I
1k
I
2k
I
1k
I
2k
I
3k
(Assuming
I
1s
+I
2s
+I
3s
=0 )
I
1k
I
2k
I
3k
Harmonic
Power
*2
P
k
[W]
P
1k
P
sumk
=P1k + P2k
P
sumk
=P
1k
+ P
2k
+ P
3k
(U is phase voltage for FFT)
c: Measurement channel, k: Analysis order, r: Amount of resistance after FFT, i: Amount of reactance after
FF
T
*1. Harmonic content percentage (harmonic voltage) divide each value by the fundamental
waveform amplitude to make 100%.
*2. The phase value from the virtual neutral point is used to calculate Pk and Qk for 3P3W3M.
Wiring
Configuration
Parameter
Single-
Phase
2-Wire
Single-Phase
3-Wire
Three-phase, 3-wire
Three-Phase
4-Wire
1P2W 1P3W 3P3W2M 3P3W3M
3P4W,
3P4W2.5E
For internal
calculations
*1
Harmonics
Reactive Power
Q
k
[var]
Q
1k
Q
sumk
=Q
1k
+ Q
2k
Q
sumk
=Q
1k
+ Q
2k
+ Q
3k
(U is phase voltage for FFT)
*1. The phase value from the virtual neutral point is used to calculate Pk and Qk for 3P3W3M.
*2. Phase angles of the fundamental voltage and current waveforms are calculated using only the
fi
rst-order calculated harmonic, and are displayed by normalizing fundamental waveform U1 to
0°
.
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