Hioki 3169-20 - Page 204

196
A three-phase 3-wire line, however, doesn't have a neutral point,
and the power of each phase cannot be measured directly. If a
neutral point hypothetically existed, three power meters must be
used simultaneously. For this reason, the 2-power-meter method
(2 voltages and 2 currents) using the line voltage is generally used
instead. Theoretically, the power of each phase is obtained using
the following equation:
If measuring and using power meters,
( = - , = - )
(because + + =0 provided that
the circuit is closed)
(2)
Equation (1) coincides with equation (2). This proves that the
power of a three-phase 3-wire line is measured by the 2-power-
meter method. In addition, there is no special precondition
required, except that the circuit must be closed and without leak-
age current. Therefore, three-phase power can be obtained
regardless of whether the cable way is balanced or unbalanced.
The 3P3W2M mode of the 3169-20/21 employs this method. In
addition, because the sum of the voltage (current) vectors is
always zero, the 3169-20/21 internally implements the following
equations to measure the 3rd voltage and current:
Regarding U
3
and I
2
, measurement is performed regardless of
whether distortion is present. These values are reflected in the
three-phase apparent power and power factor (when the reactive-
power-meter method is not used).
U
1
, U
2
, I
1
,
I
3
PU
·
1
I
·
1
U
·
2
I
·
3
+=
U
1
u
1
u
2
U
2
u
3
u
2
u
·
1
u
·
2
–()
I
·
1
u
·
3
u
·
2
–()
I
·
3
+=
u
·
1
I
·
1
u
·
2
I
·
3
–
I
·
1
–()
u
·
3
I
·
3
++=
I
1
I
2
I
3
u
·
1
I
·
1
u
·
2
I
·
2
u
·
3
I
·
3
++=
U
·
3
U
·
1
U
·
–
2
=
I
·
2
I
·
1
–
I
·
3
–=
In the 3P3W2M mode of the 3169-20/21, the phase C current of
the three-phase line is input to I2 of each circuit. On the display,
the current measurement of phase C is shown as I2, and the cal-
culation result of phase B is shown as I3.