Performance of parametric spectrum estimation methods

W pracy przedstawiono porównanie dokładności wyznaczania częstotliwości i amplitudy składowych sygnałów harmonicznych odkształconych przy pomocy parametrycznych metod estymacji widma: MUSIC i ESPRIT. Miarą dokładności jest błąd średniokwadratowy estymacji określonego parametru dla wielu symulowanych przebiegów. Przebiegi testowe są charakterystyczne dla zagadnień spotykanych w elektroenergetyce, stąd otrzymane wyniki mogą być zastosowane w praktyce, umożliwiając optymalny dobór parametrów tych metod obliczeniowych. Jako praktyczny przykład zastosowania metod MUSIC i ESPRIT przedstawiono wyznaczanie wskaźników jakości energii. Uzyskano ponad 50% wzrost dokładności po zastąpieniu algorytmu opartego na DFT (dyskretnym przekształceniu Fouriera) parametrycznymi metodami podprzestrzeni. ========Introduction 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 [4]. The methods of power quality assessment in power systems are almost exclusively based on Fourier Transform. The crucial drawback of the Fourier Transform-based methods is that the length of the window is related to the frequency resolution. Moreover, to ensure the accuracy of Discrete Fourier Transform, the sampling interval of analysis should be an exact integer multiple of the waveform fundamental period [3]. Parametric spectral methods, such as ESPRIT or MUSIC [5] do not suffer from such inherent limitations of resolution or dependence of estimation error on the window length (phase dependence of the estimation error). The resolution of these methods is to high degree independent on signal-to-noise ratio and on the initial phase of the harmonic components. The author argues 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 [4]. The paper is composed as follows: After the short description of parametric methods (ESPRIT and MUSIC), the comparison of the frequency and amplitude estimation error, based on numerical simulation is presented. Next part presents basics of selected power quality indices (harmonic sub/groups), followed by comparison of estimation error in the case of application of FFT-based algorithms and parametric methods

Power Quality in Wind Power Systems

Wind power generation systems influence power quality in a specific way making important the need for detailed and accurate evaluation of disturbances caused by wind generators. Wind power system can cause sub- and interharmonic components to appear in the spectrum of voltages and currents. The paper shows different aspects of spectrum estimation in power systems, including the doubly fed induction generator (DFIG) connected to low voltage distribution grid. Harmonic distortions caused by wind generator under various operational conditions regarding wind speed, active and reactive power are shown and discussed. Advanced spectral methods (like ESPRIT) are applied to overcome the drawbacks of Fourier based techniques

Assessing the benefits and risks of application of inverter drives in industry

This paper presents the impact assessment of converters installed in an industrial plant on the power quality in internal power grid of the plant. The analysis of real measurements showed that the installation of inverter drives, despite many benefits, as energy savings, that have been reported in the paper, can also cause many problems. We observed multiple issues related to failures in the control and automation systems that could be due to the interference generated by simultaneous operation of inverter drives

Analysis of Three Phase Signal using Wigner Spectrum

New method of observation and diagnosis of inverter-fed induction motor drives is developed and tested. Unsymmetrical conditions concerning the machine impedances or valves operation are reflected in the spectrum of the current spacephasor. We estimate the spectrum of the space-phasor with the help of the Wigner- Ville distribution (WVD) and we obtain its time-frequency representation with excellent time and frequency resolution. The proposed method is tested with nonstationary multiple-component signals occurring during the fault operation of inverter-fed drives and transmission lines

Determining of Fault Locations with Hilbert – Huang Transformation on XLPE Cables between Land and Offshore Substations

Using of mathematical transformations and digital signal processing (DSP) methods of recorded voltage and currents in power systems in order to extract important informations about physical processes is already known. Higher resolution of measurements and massive introduction of PMU devices in the power systems allows appliance of DSP - based fault location methods in complex power networks. High availability of power systems is required in the modern societies. Fast fault location algorithms and consequent fast repairing of faults is necessary condition for high availability of power networks. Here is represented a numerical procedure for fault location and testing of method already introduced in scientific literature on complex configuration of power network consisting of XLPE underground submarine and land cables between land and offshore substation connecting large wind park with main power system

Analysis of power quality disturbances using the S-Transform

The method presented in this paper employs recently introduced S-transform which is an important development of STFT with improved properties. Proposed methods allow tracking changes in amplitude and frequency with better precision than STFT and Wigner-Ville transform. Possible applications in diagnosis and power quality problems are targeted. The S-transform outperforms the STFT in that it has a better resolution in phase space giving a fundamentally more sound time frequency representation. Investigations of the representation error show that optimally adjusted S-transform can also outperform the Wigner-Ville transform when dealing with time-frequency representations of the signal. The S- transform is also tested on nonstationary electric signals where it shows excellent tracking capability. These properties show that S-transform can be effectively used for analysis of electric signals, especially when dealing with multi-component time-varying waveforms

Application of the Prony Method for Compensation of Errors in Distance Relays

In this paper we propose an application of the Prony method as a filtering technique for distance relays. First, an overview of the Prony method is presented, then the distance relay model and the impact of non-filtered frequency components such as interharmonics and subharmonics by application of typical digital filters in the operation of the distance relay is shown. We apply a solution using Prony method as a filtering technique applied to distance relay algorithms. Finally, an analysis of the proposed algorithm using simulated signals is evaluated to validate the proposed distance relay algorithm in reach error and operation time of the relay, a distorted characteristic of the Mho distance relay is shown in the impedance plane

Model order selection criteria: comparative study and applications

A practical application of information theoretic criteria is presented in this paper. Eigenvalue decomposition of the signal correlation matrixbased AIC, MDL and MIBS criteria are investigated and used for online estimation of time varying parameters of harmonic signals in power systems.===PL===Artykuł przedstawia kryteria i porównanie metod redukcji modelu procesu. Przedstawiono i porównano różne kryteria bazujące na dekompozycji macierzy korelacji według wartości własnych: AIC, MDL i MIBS. Porównania dokonano na sygnałach harmonicznych odpowiadających układowi niestacjonarnemu

Application of higher-order spectra for signal processing in electrical power engineering

In power spectrum estimation, the signal under consideration is processed in such a way, that the distribution of power among its frequency is estimated and phase relations between the frequency components are suppressed. Higher order statistics and their associated Fourier transforms reveal not only amplitude information about a signal, but also phase information. If a non-Gaussian signal is received along with additive Gaussian noise, a transformation to higher order cumulant domain eliminates the noise. These are some methods for estimation of signal components, based on HOS. In the paper we apply the MUSIC method both for the correlation and the 4th order cumulant, to investigate the state of asynchronous running of synchronous machines and the fault operation of inverter-fed induction motors. When the investigated signal is distorted by a coloured noise, more exact results can be achieved by applying cumulants

Measurement of IEC Groups and Subgroups Using Advanced Spectrum Estimation Methods

The International Electrotechnical Commission (IEC) standards characterize the waveform distortions in power systems with the amplitudes of harmonic and interharmonic groups and subgroups. These groups/subgroups utilize the waveform spectral components obtained from a fixed frequency resolution discrete Fourier transform (DFT). Using the IEC standards allows for a compromise among the different goals, such as the needs for accuracy, simplification, and unification. In some cases, however, the power-system waveforms are characterized by spectral components that the DFT cannot capture with enough accuracy due to the fixed frequency resolution and/or the spectral leakage phenomenon. This paper investigates the possibility of a group/subgroup evaluation using the following advanced spectrum estimation methods: adaptive Prony, estimation of signal parameters via rotational invariance techniques, and root MUltiple-SIgnal Classification (MUSIC). These adaptive methods use variable lengths of time windows of analysis to ensure the best fit of the waveforms; they are not characterized by the fixed frequency resolution and do not suffer from the spectral leakage phenomenon. This paper also presents the results of the applications of these methods to three test waveforms, to current and voltage waveforms obtained from simulations of a real dc arc-furnace plant, and to waveforms measured at the point of common coupling of the low-voltage network supplying a high-performance laser printer