47113964.2.023
РЭ
13
Notes
1 There are following designations:
Ci
Bi
Ai
u
u
u
,
,
- samples of instantaneous line-to-neutral voltages;
Ci
Bi
Ai
i
i
i
,
,
- samples of instantaneous phase currents;
PHi
PHi
i
u
,
- samples of instantaneous line-to-neutral voltages
U
A
,U
B
,U
C
and respective samples of in-
stantaneous phase currents
I
A
,I
B
,I
C
;
PHi
u
⊥
- samples of instantaneous line-to-neutral voltages subjected to Hilbert transformer;
N – quantity of samples per
≈
0.1638 s time interval
2 The generalizing designation «
PH
» is applied for the phase indexes
А,В,С
for the calculation of phase
parameter
Table 9 Formulas for the calculation of parameters of three-phase three-wire system
Name of parameter
Designation
Formula
True RMS value of line-to-line
voltage
U
AB
U
BC
U
CA
(
)
,
1
1
0
2
∑
−
=
−
=
N
i
Bi
Ai
AB
u
u
N
U
(
)
,
1
1
0
2
∑
−
=
−
=
N
i
Ci
Bi
BC
u
u
N
U
(
)
∑
−
=
−
=
1
0
2
1
N
i
Ai
Ci
CA
u
u
N
U
Average value of line-to-line
voltage
U
AV
(
)
CA
BC
AB
AV
U
U
U
U
+
+
=
3
1
True RMS values of phase
current
I
A
I
B
I
C
∑
−
=
=
1
0
2
1
N
i
Ai
A
i
N
I
;
∑
−
=
=
1
0
2
1
N
i
Bi
B
i
N
I
;
∑
−
=
=
1
0
2
1
N
i
Ci
C
i
N
I
Average values of phase cur-
rent
I
AV
(
)
C
B
A
AV
I
I
I
I
+
+
=
3
1
Active power of three-phase
system
P
(
)
(
)
[
]
∑
−
=
⋅
−
+
⋅
−
=
1
0
1
N
i
Ci
Bi
Ci
Ai
Bi
Ai
i
u
u
i
u
u
N
P
Reactive power of three-phase
system
Q
(
)
(
)
[
]
∑
−
=
⊥
⊥
⊥
⊥
⋅
−
+
⋅
−
=
1
0
1
N
i
Ci
Bi
Ci
Ai
Bi
Ai
i
u
u
i
u
u
N
Q
Apparent power of three-
phase system
S
2
2
Q
P
S
+
=
Note
The following designations employed:
Ci
Bi
Ai
u
u
u
,
,
- samples of instantaneous voltages;
Ci
Bi
Ai
i
i
i
,
,
- samples of instantaneous phase currents;
Ai
u
⊥
,
Bi
u
⊥
,
Ci
u
⊥
- samples of instantaneous voltages subjected to Hilbert transformer;
N – quantity of samples per
≈
0.1638 s time interval
1.4.4 Frequency measurement
The input signal of measured frequency (Ubc) arrives at an analog comparator input of a microcon-
troller. The frequency measurement is based on measuring of a fundamental frequency period. For this
purpose, time clocks of the microcontroller are used. These are clocked from the internal source 16 MHz.
The measured period value arrives at the digital filter which reduces noise content. The digital filter out-
