Instrumentation & Measurement Magazine 25-6 - 16

Table 4 - Examples of 50/60-Hz maximum synchrophasor angle estimation errors due to both
time limited synchronization accuracy and sampling jitter assuming that all the systematic phase
delays are compensated and the random fluctuations due to finite clock resolution are made
negligible through coherent sampling.
Synchronization
Accuracy
PTP with SW timestamping (typical
case)
PTP with SW timestamping (best
case) or IRIG-B
GPS or PTP with HW timestamping
over short lines
PTPv2.1-HA
10 μs
1 μs
100 ns
1 ns
±100 ns over very short chains of devices, then it follows that

 31 μrad at 50 Hz or  38 μrad at 60 Hz. These vals
s
ues
are small enough even for accurate distribution systems
monitoring. The use of the PTP protocol with standard software
timestamping (whose accuracy is within ±10 μs) may
cause phase errors up to ±3 mrad at 50 Hz and ±4 mrad at
60 Hz. These values are borderline for transmission systems
state monitoring and they are definitely too large for distribution-level
state estimation. However, such uncertainty
contributions can be roughly decreased by a factor 10 if just
a few cascaded PTP-compliant switches are used for substation
automation. Indeed, in such conditions it is possible to
constrain |τs
s
(·)| ≤ 1 μs, and, consequently,  314 μrad at
s
50 Hz or  380 μrad at 60 Hz. Such values are also consis
tent
with the results achievable with the traditional solutions
based on the IRIG-B protocol. Some researchers also explored
the possibility to use the PTP HA profile to make 
s
 1 μrad
[9]. However, in this case a dedicated communication infrastructure
and a local disciplined servo-clock with superior
frequency stability in the PMU signal acquisition stage have to
be used. In general, terms φj
and φc
in (1) depend on jitter and
frequency of the sampling signal. Recalling that the PMU sampling
frequency usually ranges from some kHz to a few tens of
kHz, the value of random variable φc
can potentially be so large
as to prevail over all the other contributions, i.e., from tens to
hundreds μrad, which would be unacceptable. To make
c
  0,
it is essential that the sampling frequency is an integer multiple
of power system frequency. For this purpose, the 1-PPS
reference signal produced by the GPS or the PTP-compliant
modules has to be used to discipline the sampling clock signal.
This can be done through a Phase-Locked Loop (PLL), a
frequency synthesizer or the same servo-clock used for time
synchronization. Nowadays, digital PLLs are often used since
a Direct-Digital Synthesizer (DDS) driven by a TemperatureControlled
Crystal Oscillator (TCXO) or, even better, by an
Oven-Controlled Crystal Oscillator (OCXO) that provides a
much higher frequency stability than any classic analog Voltage-Controlled
Crystal Oscillator (VCXO).
Quite importantly, if the PMU sampling frequency is in the
order of several kHz, then the phase comparator of the PLL
16
Max. φs
range
[μrad]
≈±3142/3770
≈±314/377.0
≈±31/38
≈±0.3/0.4
Max. φj
range
[μrad]
≈±3
≈±3
≈±3
≈±0.1
Max. γφ
range
[μrad]
≈±3140/3770
≈±315/378
≈±32/39
≈±0.4/0.5
(namely the component that measures the phase difference
between the synthesized sampling signal and the 1-PPS input
reference signal) can feed the PLL loop filter with just one
phase comparison every several thousands of cycles of the
DDS clock signal. As a consequence, φj
is dominated by the local
stability of the local TCXO/OCXO, and it depends instead
just weakly on the frequency stability of the reference 1-PPS
signal, which is nonetheless essential to avoid long-term drift
phenomena.
Thus, assuming for instance that the digital PPL generates
a 12-kHz sampling clock signal [10], if the DDS is driven by a
TCXO with frequency stability within ±1 ppm, then the sampling
period fluctuations are in the order of ±83 ps, i.e., with a
standard deviation of about 28 ps. If such fluctuations are normally
distributed and white (i.e., uncorrelated in time, which
is reasonable over short time intervals), the ±3σ Time Interval
Errors (TIE) limits over 1-s intervals can be conservatively

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