212
Specifications of Equations
10.5
Specifications of Equations
Equations for basic measurement items
Wiring
Item
1P2W
1P3W
3P3W2M
3V3A
3P3W3M
3P4W
Voltage RMS
value
Urms
(
i
)
=
Urms
(
i
)(
i
+1)
=
1
2
(
Urms
(
i
)
+
Urms
(
i
+1)
)
Urms
(
i
)(
i
+1)(i+2)
=
1
3
(
Urms
(
i
)
+
Urms
(
i
+1)
+
Urms
(
i
+2)
)
RMS equivalent
of voltage
average rectified
value
Umn
(
i
)
=
π
2 2
1
0
1
M
U
M
-
=
∑
(
i
)
s
Umn
(
i
)(
i
+1)
=
1
2
(
Umn
(
i
)
+
Umn
(
i
+1)
)
Umn
(
i
)(
i
+1)(
i
+2)
=
1
3
(
Umn
(
i
)
+
Umn
(
i
+1)
+
Umn
(
i
+2)
)
Voltage AC
component
Uac
(
i
)
=
Urms
−
Udc
2
2
(
) (
)
(
i
)
(
i
)
Voltage simple
average
Udc
(
i
)
=
1
0
1
M
U
i s
s
M
( )
-
=
∑
Voltage
fundamental
wave component
Harmonic voltage
U
1(
i
)
in harmonic equation
Voltage peak
Upk
+
(
i
)
=
U
(
i
)
s
maximum of
M
data points
Upk
−
(
i
)
=
U
(
i
)
s
maximum of
M
data points
Total voltage
harmonic
distortion
Uthd
(
i
)
in harmonic equation
Voltage ripple
factor
Voltage phase
angle
θU
1(
i
)
in harmonic equation
Voltage
unbalance rate
Uunb
(
i
)(
i
+1)(
i
+2)
=
1− 3 −
6
1+
3 −
6
×
100
β
β
β =
+
+
)
(
U
U
U
(
i
)(
i
+1)
2
(
i
+1)(
i
+2)
2
(
i
+2)(
i
)
2
2
+
+
U
U
U
(
i
)(
i
+1)
4
(
i
+1)(
i
+2)
4
(
i
+2)(
i
)
4
Example: If Ch. 1 to Ch. 3 are used
β =
+
+
+
+
(
)
U
U
U
U
U
U
12
4
23
4
31
4
12
2
23
2
31
2 2
•
U
12
,
U
23
, and
U
31
are fundamental wave voltage
RMS values (line voltage), which are obtained
from harmonic calculation results.
•In 3P4W wiring mode, phase voltage is
detected, but converted to line voltage before
calculation.
(
i
)
: measurement channel,
M
: number samples between sync timings,
s
: sample point number
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