Instrumentation & Measurement Magazine 25-6 - 17

an OCXO with ±10 ppb frequency stability. Also, in this case
the possible residual uncompensated delays may be comparable
with the γφ
values.
Further Uncertainty Contributions Affecting
Synchrophasor Angle Estimation
When the PMU measurement data are collected and forwarded
to a PDC, a variety of further latencies and uncertainty contributions
may affect the data records aggregated by the PDC.
The latencies are due to possible waiting times of the incoming
PMU streams of data at the PDC input channels (e.g., because
of heterogeneous networking delays) as well as to message
propagation and processing times through the PDC. However,
since the PDCs are also usually synchronized to the UTC, such
latencies are not critical. In fact, they do not affect the PMU measurement
data directly and, in any case, they can be estimated
and corrected by measuring the differences between the ingress
and egress timestamps of input and output messages. A
subtler and more crucial accuracy problem may instead arise
when the reporting rates of the PMU data collected by the
PDC are different. In fact, the IEEE/IEC Standard 60255-1181-2018
specifies that the PMU reporting rate can range from
10 frame/s up to 100 or 120 frame/s depending on whether
the system frequency is 50 Hz or 60 Hz. If the PMU data rates
are different, those collected at a lower rate should be interpolated
to be aligned with those collected at a higher rate. Thus,
the missing phasor angles at generic time tr
+Δt have to be reconstructed.
For instance, by applying the Taylor's series of the
phasor angle function truncated to the second order, the phasor
angle at time tr
+Δt can be estimated from:
  f t t ROCOF tr
2
ˆ t    2
t
where 
ˆ
r
r
both 
r rrˆ  
t   
ft and 
ˆ
r
ROCOF tr
2t 
ˆ


(2)
ROCOF t are the frequency and ROCOF
. Since
values measured by the PMU at the reference time tr
ft and  are affected by measurement uncertainty,
the synchrophasor phase angle value reconstructed
at time tr
+Δt suffers from the additional phase uncertainty
contribution:

 t RFE t

ar
t  t  2
  (3)


FE tr
  
t
2

r
where FE(tr) and RFE(tr) are the frequency and ROCOF errors
at time tr. Equation (3) shows that the phase reconstruction error
grows with Δt. For instance, assuming to interpolate the
PMU data by a factor 5 (i.e., from 10 frame/s to 50 frame/s) and
keeping into considerations the FE and RFE limits specified in
[7], it follows that, if Δt=80 ms:
◗ For P Class PMUs 
tions (i.e., if FE 
 10.6 mrad in steady-state condi5
mHz and RFE 
a
0.4 Hz/s)
◗ For M Class PMUs  4.5 mrad in steady-state condi5
mHz and RFE 
and 
RFE 
a
a
tions (i.e., if FE 
a
September 2022
0.1 Hz/s)
and  106.6 mrad under the effect of amplitude
 27.1 mrad under the effect of amplitude
or phase modulations (i.e., for
0.6 Hz/s);
FE 
30 mHz and
2
or phase modulations (i.e., for FE 
RFE 
2.3 Hz/s).
This analysis shows that the uncertainty of synchrophasor
phase angle reconstruction over intervals consisting of a few
power line cycles can be dominated by the indirect effect of frequency
and ROCOF measurement uncertainty contributions.
As a result, the overall phase measurement uncertainty may
become unacceptably large for Class A applications, especially
under dynamic operating conditions, since it is likely to exceed
the accuracy requirements described in the Impact of Time Synchronization
Uncertainty section.
Conclusions
This paper presents an overview of the time synchronization
accuracy requirements for power systems monitoring applications
as well as the related crucial uncertainty issues in the
context of synchrophasor measurement. Special attention is devoted
to the effect of time synchronization uncertainty in PMUs
and its potential impact on smart grid state estimation. In
particular, the paper explains why sub-microsecond time synchronization
accuracy is needed. The direct and indirect effect
of time synchronization uncertainty on synchrophasor phase
measurements is analyzed. If the signal propagation delays affecting
PMU signal acquisition and preprocessing are properly
estimated and compensated, the accuracy of the time reference
used to timestamp individual synchrophasor values (and particular
the phase angle ones) prevails over other time-related
uncertainty contributions such as the sampling jitter and the
sampling time resolution errors, provided that the same time
synchronization module adopted for timestamping is also
used to discipline the sampling clock signal and that a coherent
sampling of the input waveforms is achieved. Under standard
operating conditions, sub-microsecond accuracy is adequate
not only for transmission systems, but also for distribution
systems real-time monitoring and state estimation. However,
when the data collected by a PDC from multiple PMUs at different
rates are aggregated and aligned in time, the uncertainty of
the frequency and ROCOF measurement values used to reconstruct
the missing synchrophasor data may unexpectedly boost
the phase measurement uncertainty regardless of how accurate
the adopted time synchronization technique is.
References
[1] IEC Communication networks and systems for power utility
automation - Part 5: communication requirements for functions and
device models, IEC 61850-5:2013, Jan. 2013.
[2] IEC/IEEE International Standard - Precision clock synchronization
protocol for networked measurement and control systems, IEC/IEEE
61588-2021, pp. 1-504, Jun. 2021.
[3] IEC/IEEE International Standard - Communication networks and
systems for power utility automation - Part 9-3: precision time protocol
profile for power utility automation, IEC/IEEE 61850-9-3:2016, pp.
1-18, May 2016.
[4] M. Rizzi, M. Lipinski, P. Ferrari, S. Rinaldi, and A. Flammini,
" White rabbit clock synchronization: ultimate limits on
close-in phase noise and short-term stability due to FPGA
IEEE Instrumentation & Measurement Magazine
17
120 mHz and
Instrumentation & Measurement Magazine 25-6

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