Měřící Energetické Aparáty
36
appendix no. 1
Methodology of measurement using the monitor MEg40
+
Appendix made by prof. Ing. Vladislav Matyáš, CSc. We understand it not only as a universal
definition of algorithms of the universal monitors of MEg40+ series but also as a generally
valid description of digital measurements.
The monitor MEg40
+
performs four different functions simultaneously. All of them are
based on measurement of three voltages and three currents in a three-phase system. The
basis is numerical measurement of instantaneous values of these voltages and currents in
regular time intervals given by the sampling rate that is an integer multiple of the mains
frequency. The data sequence
u
(
k
) representing instantaneous values of this voltage is
derived by sampling and digitalizing from the voltage waveform
u
(
t
); where
k
= 0, 1, 2, …
is a serial number. The sequence of instantaneous values
i
(
k
) is derived from the current
waveform
i
(
t
) in the same way.
For three of the monitor functions, the sampling rate is used that is 32-multiple of the
mains frequency, and therefore every network period
T
s
receives 32 data for each voltage
and current referring its instantaneous values. The RMS values are calculated from data
sequences. So for the voltage from the data sequences
u
(
k
) with
K
data with the serial
numbers
k
= 0, 1, 2, …,
K –
1, the RMS value is calculated using the following formula
(1)
The formula is gradually used for all three voltages. If instantaneous values
u
1
(
k
) of the
voltage of phase 1 are used instead of
u
(
k
) in the formula, you receive the RMS value
U
1
of this voltage that applies to the
K
given data group. Similarly, from the group of
instantaneous values
u
2
(
k
) of the voltage in phase 2, you get its RMS value
U
2
and from
the group of instantaneous values
u
3
(
k
) of the voltage in phase 3 you get its RMS value
U
3
.
It is also possible to evaluate delta voltages instead of phase voltages. When you substitute
u
12
(
k
) =
u
1
(
k
) –
u
2
(
k
) in the formula (1) instead of
u
(
k
), you can calculate the RMS value
U
12
of the voltage between phases 1 and 2. Similarly, from the instantaneous values
u
23
(
k
)
=
u
2
(
k
) –
u
3
(
k
) you get the RMS value
U
23
of the voltage between phases 2 and 3 and from
the instantaneous values
u
31
(
k
) =
u
3
(
k
) –
u
1
(
k
) you get the RMS value
U
31
of the voltage
between the phase 3 and 1.
( )
k
u
K
U
K
k
∑
−
=
=
1
0
2
1
Содержание MEg40+
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