Hioki 3169-20 Instruction Manual 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
P
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:
U
I
Regarding U
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 , I
U
1 2
· ·
· ·
= U I + U I
1 1 2 3
·
· ·
( )I (
= u – u + u
1 2 1
· ·
· ·
(
= u I + u – I
1 1 2 3
· ·
· · ·
= u I + u I + u
1 1 2 2
· · ·
= U – U
3 1 2
· · ·
= – I – I
2 1 3
and I
3 2
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.
,
I
and using power meters,
1 3
( = - ,
U
1
·
· ·
)I
– u
3 2 3
· ·
·
) u
– I + I
(because
1 3 3
the circuit is closed)
·
I
(2)
3 3
, measurement is performed regardless of
= - )
u u U u u
1 2 2 3 2
+ + =0 provided that
I I I
1 2 3