Hioki PQ3198 - Page 287

A23
Appendix
Since equations (1) and (2) agree, it is possible to prove that 2-wattmeter measurement can
be used to measure the power of a 3-
phase, 3-wire line. The circuit allowing 3-phase power
measurements with this method is a only closed cir
cuit without leakage current. Since there are no
special conditions other than the above, it is possib
le to calculate 3-phase power regardless of the
balanced or unbalanced state of
the electric circuit.
Additionally, since the sum of the voltage and current vectors always equals 0 under these
conditions, the instrument internally
calculates the third voltage and current values as follows:
However, because the three phases are calculated from two po
wer values in 2-wattmeter measurement,
it is not possible to check the power balance between respective phases. If you wish to check the power
balance for individual phases, use 3-wattmeter (3P3W3M) measurement.
In 3P3W2M measurement, the instrument inputs the 3
-phase line’s T-phase current as each current’s I2
parameter. For display purposes, a current value of Phase T in the 3-phase line is displayed as the cur-
rent I2;
and a calculated value of Phase S in the 3-phase line, as the current I3.
U
·
3
I
·
2
U
·
3
U
·
2
U
·
1
–=
I
·
2
I
·
1
– I
·
3
–=
Item 3P3W2M
Relative
merits
3P3W3M
Voltage
U1
=
,
U2
,
U3
,
Current
I1
=I2
I3
Active power
P1
Since the three phases are
ca
lculated from 2-wattme-
ter,it is not possible to check
the
active power balance for
individual phases.
<
It is possible to check the
a
ctive power balance for
individual phases.
P2
P3 -
P
See equation (2).
=
Apparent
power
S1
Since calculations are
b
ased on the line-to-line
voltage and phase (line) cur-
rent,apparent power values
a
re not generated for indi-
vidual phases.
<
Since calculations are
b
ased on the phase voltage
and phase (line) current, it is
possible to check the appar-
ent power for individual
p
hases.
S2
S3
S =
U
·
1
U
·
1
u
·
1
U
·
1
U
·
3
–()
3
---------------------=
U
·
2
U
·
2
u
·
2
U
·
2
U
·
1
–()
3
---------------------=
U
·
3
U
·
2
U
·
1
–=
U
·
3
u
·
3
U
·
3
U
·
2
–()
3
---------------------=
I
·
1
I
·
1
I
·
3
I
·
2
I
·
2
I –
·
1
I
·
3
–=
I
·
3
U
·
1
I
·
1
u
·
1
I
·
1
U
·
2
I
·
3
u
·
2
I
·
2
u
·
3
I
·
3
U
·
1
I
·
1
U
·
2
I
·
3
+ u
·
1
I
·
1
u
·
2
I
·
2
u
·
3
I
·
3
++=
u
·
1
I
·
1
u
·
2
I
·
2
u
·
3
I
·
3
++
U
·
1
I
·
1
u
·
1
I
·
1
U
·
2
I
·
3
u
·
2
I
·
2
U
·
3
I
·
2
u
·
3
I
·
3
3
3
-------
U
·
1
I
·
1
U
·
2
I
·
3
U
·
3
I
·
2
++()
3
3
-------
U
·
1
I
·
1
U
·
2
I
·
2
U
·
3
I
·
3
++()
HIOKI PQ3198A961-02