Hioki 3197 - Power Measurement by the Two-Meter Method, and U3, I3 Measurement Theory

Appendix 9 Definitions
A 16
(3P3W2M Wiring Configuration Mode)
Three-phase power P is usually calculated as the sum of the power of
each phase.
P =
u

1
I

1
+ u

2
I

2
+ u

3
I

3
......................................................................... (1)
However, because there is no central point in three-phase, 3-wire lines,
there is no way to measure the power of each phase independently, and
even if there was, three wattmeters would be required to measure simul-
taneously. The two-wattmeter method is therefore commonly used
(
measuring two voltages and two currents).
Power can then be theoretically calculated by the following formulas:
When measuring U

1
, U

2
, I

1
and I

2
using wattmeters,
P= U

1
I

1
+ U

2
I

3
(where U

1
= u

1
u

2
and U

2
= u

3
u

2
) ............................. (1)
= (
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
(where the closed-circuit condition is I

1
+I

2
+I

3
=0)
= u

1
I

1
+ u

2
I

2
+ u

3
I

3
......................................................................... (2)
Here, formulas (1) and (2) match, proving the 2-wattmeter method of
measuring three-phase, 3-wire power.
Also, there are no special requirements other than the closed circuit and
no leakage circuit, so 3-phase power can be measured regardless of
whether the phases are balanced.
The 3P3W2M wiring configuration mode of this instrument employs this
method.
Power Measurement by the Two-Meter Method, and U3, I3 Measure-
ment Theory
Central
Point
Three-Phase,
3-Wire
Source Side
Three-Phase,
3-Wire Load Side
1
2
3
→I

3
I

2
→
→
I

1
U

1
U

3
U

2
u

1
u

2
u

3
Circuit Concept of Three-Phase, 3-Wire Lines
U

1
, U

2
, U

3
: Inter-line voltage vectors
I

1
, I

2
, I

3
: Line (phase) current vectors
u

1
, u

2
, u

3
: Phase voltage vectors