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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
FFT
*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.
Uck
U
k r
2
U
ki
2
+
=
Ick
I
kr
2
I
k i
2
+
=
Pck
U
kr
I
kr
×
U
ki
I
ki
×
+
=
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
first-order calculated harmonic, and are displayed by normalizing fundamental waveform U1 to
0°.
Qck
U
kr
I
ki
×
U
ki
I
kr
×
–
=
Summary of Contents for 3197
Page 1: ...3197 POWER QUALITY ANALYZER May 2012 Revised edition 7 3197A981 07 12 05H Instruction Manual ...
Page 2: ......
Page 8: ...Contents vi ...
Page 30: ...1 3 Measurement Flowchart 22 ...
Page 44: ...2 5 Internal Operating Status and Memory Usage 36 ...
Page 86: ...4 6 Initializing the Instrument System Reset 78 ...
Page 134: ...6 4 Viewing Recorded Data REVIEW State 126 ...
Page 176: ...9 4 Disposing of the Instrument 168 ...
Page 199: ......
Page 200: ...3197 POWER QUALITY ANALYZER May 2012 Revised edition 7 3197A981 07 12 05H Instruction Manual ...