Hioki 3169-20 - Maintenance and Troubleshooting; Cleaning, Storage, and Disposal Procedures

13.1 Formulae
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Basic Formulae for Harmonic
•
U
: Line to line voltage (phase to neutral voltage for a three-
phase 4-wire line);
I
: Line to line current;
U
ave
/
I
ave
: Average
voltage/average current within the circuit;
si
: Polarity of lead/lag
(detected by the reactive-power-meter method, no indication
for lag, or a minus sign indicated for lead);
u
: Phase voltage
from a virtual neutral point;
i
: Measurement channel;
M
: Num-
ber of samples;
s
: Sample point No.;
m
: Number of samples in
a cycle (128)
• The power flow direction is indicated using the polarity signs
for active power
P
: "+" indicates consumption and "-" indicates
regeneration.
• If
S
<|
P
| due to a measurement error, unbalance, or other factor,
the 3169-20/21 will process data such that
S
=|
P
|,
Q
=0, and PF
= 1.
• If
S
=0, the instrument processes the data such that PF = over.
Processing
Item
k
th harmonic
Total up to the 40th
Voltage
U
[Vrms]
U
k
U
K
Voltage
phase
angles
φ
U
[deg]
φ
U
k
tan
-1
*1
-- --
Current
I
[Arms]
I
k
I
K
Current
phase
angles
φ
I
[deg]
φ
I
k
tan
-1
*1
-- --
Power
P
[W]
P
k
U
kr
x
I
kr
+
U
ki
x
I
ki
P
K
Reactive
power
Q
[var]
*3
Q
k
The reactive-power-meter
method is used.
U
kr
x
I
ki
-
U
ki
x
I
kr
*2
The reactive-power-meter
method is not used.
-- --
Apparent
power
S
[VA]
*3
S
k
U
k
x
I
k
-- --
Harmonic
voltage
content
[%]
Voltage
U
k
/
U
1
x 100 (%)
-- --
Current
I
k
/
I
1
x 100 (%)
Power
P
k
/
P
1
x 100 (%)
U
kr
2
U
ki
2
+
U
k
()
2
k 1=
40
∑
U
kr
U
ki
–
-------------



I
kr
2
I
ki
2
+
I
k
()
2
k 1=
40
∑
I
kr
I
ki
–
----------



P
k
k 1=
40
∑
S
k
2
P
k
2
–
P
k
2
Q
k
2
+