Instrumentation & Measurement Magazine 25-6 - 15

Table 3 - Range of variability of the bus voltage
phasor angles in various power transmission
and distribution system of increasing size under
nominal load conditions
Grid size
30 buses
Transmission
systems
Distribution
systems
89 buses (Pegase)
145 buses (IEEE)
1354 bus (Pegase)
37 buses (IEEE)
69 buses
85 buses
141 buses
Phasor angles [mrad]
-39.5 ± 47.5
-27 ± 366
-203 ± 901
-273 ± 508
-2.8 ± 1.6
4.8 ± 11.9
22.0 ± 18.3
-4.2 ± 2.6
◗ Discipline the frequency of the device used to sample the
input AC voltage or current signals; and
◗ Aggregate and to reconstruct the missing data within the
PDC.
The physical quantity that is most directly affected by time
synchronization uncertainty is the synchrophasor angle,
namely the angle of an input ac signal at each UTC reference
timestamp. This problem is particularly critical, because
the phasor angle differences between grid nodes at the same
time are usually very small, at least in ordinary operating
conditions.
For instance, Table 3 shows the range of variability of the
voltage phasor angles at the buses of four different power
transmission and four power distribution systems of growing
size. The bus voltage phasor angle values result from a power
flow analysis performed using the MATPOWER toolbox
under nominal load conditions [8]. The angle values are computed
with respect to the phase angle of the slack bus, which is
usually taken as a reference (i.e., the voltage phasor angle at the
slack bus is assumed conventionally to be 0). Therefore, the obtained
angle values refer to an ideal scenario, and they are not
affected by any measurement uncertainty. The results of Table
3 show that in the case of transmission systems, the phasor angles
generally differ by hundreds of mrad. Therefore, if PMUs
with a resolution of a few mrad and accuracy within ±10 mrad
are used, a transmission system can be adequately monitored.
This result is consistent with the PMU maximum Total Vector
Error (TVE) values specified in the IEC/IEEE Standard 60255118-1:2018

Instrumentation & Measurement Magazine 25-6

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