Hioki PQ3100 - Apparent Power (S) Calculation Formulas; Reactive Power (Q) Calculation Formulas

182
Calculation Formula
11. Harmonic voltage (Uharm), Harmonic current (Iharm), Interharmonic voltage (Uiharm),
Interharmonic current (Iiharm)
Wiring
Item
Single phase
2-wire
1P2W
Single phase
3-wire
1P3W
3-phase 3-wire
3P3W2M
3-phase 3-wire
3P3W3M
3-phase 4-wire
3P4W
Uharm [Vrms]=
U
ck
(including adjacent
interharmonic
components)
U
1k
U
4k
U’
ck
=
( ) ( )
22
ckickr
UU +
U
ck
=
∑
−=






+








1
1
2
1 0
1 0
'
n
nk
c
U
U
1k
U
2k
U
4k
U
1k
U
2k
U
3k
U
4k
U
12k
U
23k
U
31k
U
1k
U
2k
U
3k
U
4k
During 1P3W1U
Without
U
2k
• For 60 Hz measurement, the value 10 in the formula is replaced with 12.
• Harmonic voltage content percentage (%):
U
ck
/U
c1
× 100
(%)
• For 3P3W2M wiring, it is assumed that
U
1s
−U
2s
+U
3s
= 0
•
U
c0
component is treated as DC for 0th order when
k = 0
.
Iharm [Arms]=
I
ck
(including adjacent
interharmonic
components)
I
1k
I
4k
I’
ck
=
( ) ( )
22
ckickr
II +
I
ck
=
∑
−=






+








1
1
2
1 0
1 0
'
n
nk
c
I
I
1k
I
2k
I
4k
I
1k
I
2k
I
3k
I
4k
I
1k
I
2k
I
3k
I
4k
• For 60 Hz measurement, the value 10 in the formula is replaced with 12.
• Harmonic voltage and current content percentage (%):
I
Ck
/I
C1
× 100
(%)
• For 3P3W2M wiring, it is assumed that
I
1s
+I
2s
+I
3s
=0.
•
I
c0
component is treated as DC for 0th order when
k = 0
.
Uiharm [Vrms]=
U
ck
U
1k
U
4k
U’
ck
=
( ) ( )
22
ckickr
UU +
U
ck
=
∑
−=






+








3
3
2
1 0
1 0
'
n
nk
c
U
U
1k
U
2k
U
4k
U
1k
U
2k
U
3k
U
4k
U
12k
U
23k
U
31k
U
1k
U
2k
U
3k
U
4k
During 1P3W1U
Without
U
2k
• For 60 Hz measurement, the value 10 in the formula is replaced with 12; 3, with -3; and 4,
with −4.
• Intermediate harmonic voltage content percentage (%):
U
Ck
/U
C1
× 100
(%)
• For 3P3W2M wiring, it is assumed that
U
1s
−U
2s
+U
3s
= 0
Iiharm [Arms]=
I
ck
I
1k
I
4k
I’
ck
=
( ) ( )
22
ckickr
II +
I
ck
=
∑
−=






+








3
3
2
1 0
1 0
'
n
nk
c
I
I
1k
I
2k
I
4k
I
1k
I
2k
I
3k
I
4k
I
1k
I
2k
I
3k
I
4k
• For 60 Hz measurement, the value 10 in the formula is replaced with 12; 3, with −3; and 4,
with −4.
• Intermediate harmonic current content percentage (%):
I
Ck
/I
C1
× 100
(%)
• For 3P3W2M wiring, it is assumed that
I
1s
+I
2s
+I
3s
=0.
c
: Measurement channel