Hioki PW3360-21 - Appendix2 Three-Phase 3-Wire Measurement

A2
An artificial circuit of a three-phase 3-wire line
: The vectors of line-to-line voltage
: The vectors of phase to neutral voltage
: The vectors of line (phase) current
3-phase/3-wire/3-wattmeter measurement (3P3W3M)
In 3-wattmeter measurement, three phase voltages ( ) and three line
(phase) currents ( ) are measured. Because the lack of a neutral point in 3-
phase, 3-wire lines makes it impossible to meas
ure actual phase voltages, phase
voltages are measured from a virtual neutral point.
The 3-phase active power P is calculated as t
he sum of all the phase active power
values.
P = + + (1)
3-phase/3-wire/2-wattmeter measurement (3P3W2M)
In 2-wattmeter measurement, two line-to-line voltages ( ) and three line
(phase) currents ( ) are measured. The 3-phase active power P can be derived
from two voltage and current values, as shown below:
P = + ( = - , = - )
= ( - ) + ( - )
= + (- - ) + 
(because + + =0 due to precondition of a closed circuit)
= + + (2)
Since equations (1) and (2) agree, it is possibl
e to prove that 2-wattmeter measure-
ment can be used to measure the power of a 3-phase, 3-wire line. Since the only
special conditions are that the target be a closed circuit without leakage current, it is
possible to calculate 3-phase power without regard to the balance or unbalance
state of the electric circuit.
Appendix2 Three-phase 3-wire Measurement
Three-phase 3-wire
Power-supply side
Three-phase 
3-wire Load side
I
1
1
U
1
U
3
u
1
Neutral
point
u
3
u
2
U
2
I
3
I
2
23
U
1
, U
2
, U
3
u
1
, u
2
, u
3
I
1
, I
2
, I
3
u
1
, u
2
, u
3
I
1
, I
2
, I
3
u
1
I
1
u
2
I
2
u
3
I
3
U
1
, U
2
I
1
, I
3
U
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
1
I
3
u
3
I
3
I
1
I
2
I
3
u
1
I
1
u
2
I
2
u
3
I
3