Real-time Accurate Power System Frequency Meter and its Quality Evaluation
Based on Simulations and Large Area System Observations
Tomasz WINEK", Zbigniew STAROSZCZYK* **
"Warsaw University of Technology, Institute of the Theory of Electrical Engineering
and Electrical Measurements, 00-661 Warsaw, P1. Politechniki 1, POLAND
**Military University of Technology, 00-908 Warsaw 49, Kaliskiego 2
only simulation and measurement results are presented,
but they are referenced to parallel measurements made on
local and distanced subsystem supplying lines.
Abstract
In the paper the solution of accurate power system
frequency meterhegistrator is presented. The meter is
equipped with a standard PC DAQ-card which is able to
perform the background data acquisition process. The
method is based on system voltage signal zero-crossings
observations, and zero positions processing targeted to
instant system frequency
estimation. Different
observations of the real power system signals are
presented - local and distanced, where two parallel
observations were made in 25 km distanced subsystems.
The results were verified with the standard signals from
AFG of the known frequency and conJirmed that
presented method accuracy is few hundred pH...
2. Theoretical background of the method
The method is based on voltage signal zero-crossing
observations. Zero-crossings are observed in relation to
DAQ card crystal stabilized oscillator, and even if appear
jittered from period to period have interesting mean value
properties - for fixed frequency systems zero crossings
deliver true fundamental frequency information. In that
meaning the zero-crossings are useful as a fundamental
frequency indicator even if severe distortion in the voltage
signals exists.
The power system fundamental frequency does not differ
too much from 50Hz, and is relatively stationary due to
power system inertia. It is why the zero-crossing method
can be successfully used forfo evaluation.
Let assume that observed voltage signal is given by the
Eqn. 1.
1. Introduction
Power system frequency is a clue factor for power system
regulation, responsible for energy balance in the system.
There are different methods to measure it with high
accuracy [ 1],[2],[3],[4],[5]. Many papers however deal only
with simulated data and are not real systems related [ 1],[3].
Many papers dealing with real measurements present
plots of the fo history not related to the reference data
[2],[6],[7]. From such measurements it is not easy to find
out what is the real system frequency and what is the
measurement noise. The power signals suffer from
untypical, colored and non-stationary noise, for which
gaussian approximation used in standard simulations is
too rough to draw meaningful conclusions concerning
quality of measuring algorithms.
In the paper new, direct interference, method of
fundamental frequency measurement is presented. It has
relatively easy hardware implementation and with a proper
post-registration signal processing gives reliable results
for different measuring conditions (harmonic and noise
pollution of the observed voltage signal). In the paper not
u(t) = U,Sin( q t ) )
(1)
where the current signal frequency in the time instant to is
given by the Eqn.2.
F(t,) = Q(t,>/ 2n
where
a(t,)= d@(t)/dt I t = t o
Let assume that system phase @(t) is observed as it is
explained in the Fig. 1.
If the voltage 5OHz signal is sampled with frequency of
25kHz subsequent zero crossings (phase changes equal
2n) appear distanced 20ms (exactly each 500 samples). For
other frequencies subsequent zero-crossings distance
differs from 500 points (Fig.1).
The current system frequency given by the Eqn.2 is
proportional to phase derivative. If calculated from zero-
0-7803-5890-2/00/$10.00
02000 IEEE
935
to-zero observations this derivative is equal 2dTzero.zero,
where Te,.zero
is the exact value of the current period
calculated from zero crossing observations (Tzero-zem
for the
second period observation is marked with arrows in the
Fig. 1).
In reality, zero-crossings directly describe instant signal
phase information so can be used to local subsystems
phase investigations - that out of the scope of the
presented paper.
In the Fig.2 zero-shifts are presented as recorded parallely
in two distanced, different lines (A and C) voltage signal
observations. Three experiments, numbered 1, 2, 3, show
very exact signal phase correspondence between parallel
observations - two lines for every drawing are almost
indistinguishable.
50
r
I
time [samples]
Fig. 1 Observed phase difference measurements
with zero-crossing observations.
-250;
T,em-zero
value is very close to 20 ms (500 samples) and can
be expressed as:
1
I
500
1000
I
I
I
1500
2000
I
2500
3000
hme [period]
Tzem-zem=To+AT
So the current system frequency is equal:
F,,,=l/ Tzem-rero=l/
(To+AT)sFo(l d T / To)
(3)
Unfortunately there is not easy to exactly measure AT
value due to limited signal sampling resolution and to the
noise in observed power system signals.
If we redraw the plotting from the Fig.1 that way that for
every zero crossing observation we draw current AT value
(measured however with very poor accuracy of the signal
sampling period T) we get for the real power system
observations the drawings like in the Fig.2 and Fig.3. The
local derivative of that drawing is the exact, directly nonmeasurable value of AT (and the instant system frequency
according to Eqn.3). Very noised draft data from the Fig.2
and Fig.3 cannot be directly differentiated - some kind of
interpolation has to be used.
Fig. 2 Two parallel session zero crossings shifts
observations on distanced power system nodes
three experiments results.
-
Due to limited value of sampling frequency, only rough
approximation of the true zero positions is directly
accessible. Direct observations (marked with circles in the
Fig.3) are quantizied with the time step of 40 p and suffer
from the noise. It is useless to differentiate direct data to
deliver required frequency information.
3. Real power system signals properties
The main problem in accurate frequency measurements
arises from non-stationarity and noise of power signals.
Zero-crossings are jittered and their time positions cannot
be exactly located. However first experiments made off-line
on the sampled voltage signal assured that zero-crossing
observations contain sufficient fundamental frequency
information and are highly correlated even for distanced
power system observations (Fig.2).
Fig. 3 The details of registered zero-crossing
shifts: beginning part (2s) of experiment 1 (Fig.2)
observations
936
Even if approximations is used to obtain directly more
accurate zero positions, the results are not satisfying.
With interpolations, still non-differentiable, fluctuating
"exact zeros" patterns appear (drawn as a solid line in the
Fig.3).
To verify quality of the method, 50Hz FM signal was
measured. Modulating sinusoidal signal had the
frequency lOOmHz and the deviation was set to 15mHz.
The results presented in the Fig.5 confirm that the
algorithm works correctly giving very good approximation
of the instant signal frequency. The small bias in
observations (=lmHz) is caused by generator and DAQ
card crystal clocks discrepancies.
The method has integral properties, so it smoothes the
peaks in the frequency as can be observed in the Fig.5 for
large size windows (e.g. 200 points).
4. Method description and verification
The method was verified on simulated and real signals in
the Matlab environment and that way verified procedures
were build in the real-time measuring equipment based on
NI-DAQ cards and software. With real-time
instrumentation parallel local and distant registrations of
the power system frequency have been made and
compared. They confirm that independent observations
give very close results and measurement error can be very
low. To verify that, absolute measurements on a
synthesized signal of the known frequency have been
repeated. Field observation made on real power system
and signals confirmed the proper solution of signal
processing built in into the measuring system. Prior to
embedding into instrumentation three methods of DSP,
aimed to make data differentiable, has been tested:
polynomial fitting, lowpass filtering and derivative
averaging. In spite of different complexity, the methods
gave similar quality results. The calculated frequency plot
for the Fig.2 experiment 1 is given in the Fig.4 for the
simplest, derivative averaging method.
50015,
I
I
I
I
.
.
.
.
.
I
H
2
J
1200 1220 1240 1260 1280 1300 1320 1340 1360
bme [penod]
Fig. 5 Derivative averaging method results:
generated signal.
50'
5b0
I
I
I
I
1000
1500
2000
2500
5. Real-time measurements and final results
nme [period]
Fig. 4 Derivative averaging method results:
power system signal.
The method was implemented in LabWindowsICVI
environment and based on a NI-DAQ card. The virtual
panel of the measurement system is presented in the Fig.6.
In that method the fixed size window (50,100,200 and 500
periods) is moved trough the zero-crossing data record.
For every new window position first degree polynomial,
fitted to windowed data, delivers required derivative
information. The method is very simple, easy to implement
in real-time and gives the same quality results as the other,
much more sophisticated methods.
937
______i
;I
49.97 ______1.--!1{
_ _ ._
__
_---...
.
_
__
' ' '
2000 4000 6000
,
49.965
0
Fig. 6 The measurement system virtual panel
The system starts with default values for acquisition rate
(5ok&) and calculation parameters (50 point window).
With every new zero-crossing (each 20ms) new frequency
estimation is found and every fifth measurement is written
to the disk file (10 registrationski). Those settings assure
good quality of frequency measurements and sufficient
measurement response time allowing for tracing power
system phenomena.
In the virtual oscilloscope-type screen 500 recently
recorded frequency points are plotted in real-time on
a chart-mode display.
With two such virtual frequency metershecorders the
power system frequency observations (10 min., 30 min.
and 13 hours long) in two distanced 25 km locations were
made. In the Fig.7 half hour long frequency observations
are presented. They are typical to observed system: in
spite of distanced observations the plots are very similar
(as those from the Fig.2). Due to power system nonstationarity, as the observed frequency is not stable, it is
easy to correlate two observations even with very short
correlation window of 50 points ( 5 s long). The
intercorrelation function allows for proper adjusting of the
observation time axes and makes meaningful direct
comparison (subtraction) of two measurements.
I
,
J
i
- . - -_
_._
-_
-_
- .--
#
,
$
0
,
,
I
,
I
8000 10000 12000 14000 16000 18000
time [period x 5 ]
Fig. 7 Large area system observations: two
distanced (25km) parallel recordings.
In the Fig.8 the subplot of the Fig.7 data is presented in
details. One location frequency observation (referenced to
50Hz) is plotted on the background of differences
between two correlated observations. The observed
difference can be treated as the measurement noise,
however it can contain some determined component
related to the power system behavior (different
subsystems).
00151
I
I
I
I
8500
9000
9500
10000
I
bme [period x 51
Fig. 8 Measured frequency and observed
discrepancy for remote observations (Fig.7
signals).
E 4 9 995
=
To verify this parallel, local system observations on the
same and different supplying lines have been made.
Additionally as the signal source of known properties
HP33120A AFG was used. Its frequency was stepped in
the range 49.96S50.015 Hz with 10 and 1 mHz steps and
the output signal frequency was registered by two
recorders. That way absolute values of registered
frequency could be compared to known values. In the
Fig.9 the observations of generator frequency are
presented together with the difference between two
parallel observations (as in the Fig.8).
4999
49 985
c
49 98
49 975
,
I
'
1
49965l
0
'
1
2000 4000
1
'
1
1
,
,
'
1
,
,
'
,
I
,
'
1
6000 8000 10000 12000 14000 16000 18000
time [period x 5]
938
Fig. 10 High
registration
rate system frequency
drop
With different size observation windows it is possible to
adapt conditions of observations to power system
dynamics. More or less smoothed frequency data carry
different kind of power system information. Such
possibility still makes open the question: what is the real
system instant frequency? We can be satisfied with
generator frequency measurements as shown in the Fig. 9,
but can have problems with interpretation of the Fig 8
data.
Two measurement sets discrepancies are less then 1 mHz,
so that value can be treated as the measurement accuracy.
Generator tuning steps of 1 mHz are easily recognized and
the method response time is quite satisfying. There is no
error level change when the generator signal was
exchanged with local power system signals. Such
experiment confirm that the method accuracy for signals
present in the real power system is still of 1 mHz. By
comparison twice bigger discrepancies are observed for
distant system observations (Fig.8). The additional 1 mHz
frequency error component appear due to the additional
phase shifts between power subsystems.
In the Fig.9 the step response of the measuring system
can be observed. The generator immediately switches to
new frequency, while the measurements system respond
with 1 s delay (50 point window). Such the response time
makes no problem in system frequency investigations as
the most rapid high level drop of the system frequency
which has been observed was 70 mHz and lasted 200 s
(Fig.10 ). Of course there are small level local frequency
fluctuations of bigger rates (Fig. 4, 8) but they still can be
registered.
2
2 05
21
bmeIperlodx51
2 15
6. Conclusions
The presented method of very accurate frequency
measurements is simple in realization and can be run on
any computerized system equipped with a standard data
acquisition card. The pJ3z resolution of the meter can be
achieved with no additional hardware and without
complicated signal processing. That makes the method
ideal to target implementations, based on standard
microcontrollers equipped with a/d converter and timers.
The described virtual metedregistrator can trace system
frequency for long hours with parallel data logging on
hard disk. It requires however DAQ card hardware and
software able to make background data acquisition.
References
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System Frequency. IEEE Trans. on Instr. and Meas. Vol. 46,
NO. 2, August 1997,pp. 877-881.
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Frequency Tracking in Power Networks in the Presence of
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22
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