Document 139597
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NEW POWER QUALITY INDICES
Zbigniew LEONOWICZ
Department of Electrical Engineering
Wroclaw University of Technology, Poland
The Seventh IASTED International Conference on
Power and Energy Systems, EuroPES 2007
August 29 – 31, 2007, Palma de Mallorca, Spain
Contents of presentation
• Motivations for applying parametric
spectral analysis in electrical power
engineering
• Power quality assessment - IEC groups
• Performance of applied tools
• The ESPRIT & MUSIC methods
• Results of investigations
• Conclusions
Motivations
• The quality of voltage waveforms is nowadays an
issue of the utmost importance for power
utilities, electric energy consumers and also for
the manufactures of electric and electronic
equipment. The proliferation of nonlinear loads
connected to power systems has triggered a
growing concern with power quality issues.
• The inherent operation characteristics of these
loads deteriorate the quality of the delivered
energy, and increase the energy losses as well as
decrease the reliability of a power system.
Motivations
• Methods of power quality assessment in power systems
are almost exclusively based on Fourier Transform, which
has many limitations.
• Parametric spectral methods, such as ESPRIT or MUSIC do
not suffer from inherent limitations of resolution or
dependence of estimation error on the window length
(phase dependence of the estimation error) of FFT.
• The authors argue that the use of high-resolution
spectrum estimation methods instead of Fourier-based
techniques can improve the accuracy of measurement of
spectral parameters of distorted waveforms encountered
in power systems, in particular the estimation of the
power quality indices.
IEC groups & subgroups
• Amplitudes
G sg2 n
Used for calculating
7th harmonic group, Cg-7
Used for calculating
8th harmonic group, Cg-8
1
2
C
10n k
Harmonic
Amplitude
k 1
8
Frequency [Hz]
2
2
Cisg
C
10n k
n
325 330 335 340 345 350 355 360 365 370 375 380 385 390 395 400 405 410
Spectral components
Time window of 200ms
k 2
Used for calculating
7th harmonic
Used for calculating
8th harmonic
Used for calculating
7th harmonic sub-group, Csg-7
Spectral components
Time window of 200ms
Used for calculating
8th harmonic sub-group, Csg-8
Spectral components
Time window of 200ms
Harmonic
Amplitude
355 360 365 370 375 380 385 390 355
340 345
350
405 410
Frequency [Hz]
400
Harmonic
Amplitude
360 365 370 375 380 385 390
340
345 350 355
Frequency [Hz]
395 400 405
Interharmonic
Amplitude
Used for calculating
7.5 Interharmonic group, Cg-7.5
410
Interharmonic
Amplitude
Used for calculating
7.5 Interharmonic sub-group, Csg-7.5
Progressive average of the harmonic
subgroups of currents and voltages
Fifth harmonic
subgroup of the
voltage
Results
Results of calculation of PQ indices
Basic performance characteristics
CC – computational cost
AC – accuracy
RF – risk of false estimates
Harmonic decomposition methods
• MUSIC (Multiple Signal Classification) method
Esignal
1
e
e2
Enoise eM 1 eM 2 e N
e p
T
noise
Pnoise EnoiseE
I Psignal
• MUSIC pseudospectrum
j
1
T
T
T
P e w Pnoisew w E noiseE noisew
Harmonic decomposition methods
• ESPRIT method
A waveform can be approximated by:
M
y[n] Ak e
jk n
w[n]
k 1
Two selector matrices
shift invariance between discrete time series
S1 Γ1U
parameters in :
S2 Γ2 U
e j1
0
Φ
0
0
e j2
0
S1 ΦS 2
0
0
jM
e
Performance of MUSIC and ESPRIT
•MUSIC uses the noise subspace to estimate the signal
components
•ESPRIT uses the signal subspace.
Several experiments with simulated, stochastic signals were
performed, in order to compare performance aspects of
both parametric methods MUSIC and ESPRIT. Testing signal is
designed to belong to a class of waveforms most often
present in power systems. Each run of spectrum and power
estimation is repeated many times (Monte Carlo approach)
and the mean--square error (MSE) is computed.
Error of estimation
Results of error comparison
• Problem of masking of the higher low–amplitude
harmonics components by a strong fundamental
component was investigated.
• The results show an extremely high masking effect in the
case of power spectrum, while MUSIC and ESPRIT methods
show very little dependence (almost no dependence in
the case of ESPRIT method).
• This is a very important feature which partially explains
excellent performance of parametric methods in the task
of calculation of power quality indices.
Conclusions
• In practical applications, one of the most important
•
•
questions concerns the optimal choice of analysis
methods when taking into account known parameters of
the signal and limitations of the chosen analysis
technique.
Performance comparison showed that both parametric
methods show similar values of accuracy wich greatly
outperform the accuracy of FFT–based non–parametric
method.
Parametric methods show almost complete immunity to
masking effect, to variable initial phase of harmonic
components and to many other deficiencies off FFT–
based techniques, as shown in the relevant literature.
Conclusions
• For all results presented previously, it can be seen that
the use of ESPRIT method for calculation of power quality
indices offers reduction of the error of estimation of
harmonic subgroups by 53% and the use of MUSIC method
reduces the error by 49%, when comparing to STFT (FFT–
based method).
• Even higher gains in accuracy can be achieved when
analyzing waveforms with high inter/sub–harmonic
contents.