Mega MEg40+ - Appendix No. 1; Methodology of measurement using the monitor MEg40+

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
denition of algorithms of the universal monitors of MEg40+ series but also as a generally
valid description of digital measurements.
e monitor MEg40
+
performs four dierent functions simultaneously. All of them are
based on measurement of three voltages and three currents in a three-phase system. e
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. e 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. e 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. e 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)
e 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.
( )
ku
K
U
K
k
∑
−
=
=
1
0
2
1