An advanced method for eliminating impacts from frequency deviations in power system signal processing

Frequency deviation is a common problem for power system signal processing. Many power system measurements are carried out in a fixed sampling rate assuming the system operates in its nominal frequency (50 or 60 Hz). However, the actual frequency may deviate from the normal value from time to time due to various reasons such as disturbances and subsequent system transients. Measurement of signals based on a fixed sampling rate may introduce errors under such situations. In order to achieve high precision signal measurement appropriate algorithms need to be employed to reduce the impact from frequency deviation in the power system data acquisition process. This paper proposes an advanced algorithm to enhance Fourier transform for power system signal processing. The algorithm is able to effectively correct frequency deviation under fixed sampling rate. Accurate measurement of power system signals is essential for the secure and reliable operation of power systems. The algorithm is readily applicable to such occasions where signal processing is affected by frequency deviation. Both mathematical proof and numerical simulation are given in this paper to illustrate robustness and effectiveness of the proposed algorithm. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

Estimação de Fasores para Proteção de Sistemas Elétricos Baseada em Mínimos Quadrados e Morfologia Matemática

This work proposes a new technique for phasor estimation applied in microprocessor numerical relays for distance protection of transmission lines, based on the recursive least squares method and called least squares modified random walking. The phasor estimation methods have compromised their performance, mainly due to the DC exponential decaying component present in fault currents. In order to reduce the influence of the DC component, a Morphological Filter (FM) was added to the method of least squares and previously applied to the process of phasor estimation. The presented method is implemented in MATLABr and its performance is compared to one-cycle Fourier technique and conventional phasor estimation, which was also based on least squares algorithm. The methods based on least squares technique used for comparison with the proposed method were: forgetting factor recursive, covariance resetting and random walking. The techniques performance analysis were carried out by means of signals synthetic and signals provided of simulations on the Alternative Transient Program (ATP). When compared to other phasor estimation methods, the proposed method showed satisfactory results, when it comes to the estimation speed, the steady state oscillation and the overshoot. Then, the presented method performance was analyzed by means of variations in the fault parameters (resistance, distance, angle of incidence and type of fault). Through this study, the results did not showed significant variations in method performance. Besides, the apparent impedance trajectory and estimated distance of the fault were analysed, and the presented method showed better results in comparison to one-cycle Fourier algorithm

Pulsed parabolic equation model of acoustic transmission (PPEMAT)

Underwater sound is very important in the field of oceanography where it is used for remote sensing in much the same way that radar is used in atmospheric studies. One way to mathematically model sound propagation in the ocean is by using the parabolic-equation method, a technique that allows range dependent environmental parameters. More importantly, this method can model sound transmission where the source emits either a pure tone or a short pulse of sound. Based on the parabolic approximation method and using the split-step Fourier algorithm, a computer model for underwater sound propagation was designed and implemented. This computer model differs from previous models in its use of the interactive mode, structured programming, modular design, and state-of-the-art graphics displays. In addition, the model maximizes the efficiency of computer time through synchronization of loosely coupled dual processors and the design of a restart capability. Since the model is designed for adaptability and for users with limited computer skills, it is anticipated that it will have many applications in the scientific community.

An Algorithm for Fresnel Diffraction Computing Based on Fractional Fourier Transform

The fractional Fourier transform (FrFT) is used for the solution of the diffraction integral in optics. A scanning approach is proposed for finding the optimal FrFT order. In this way, the process of diffraction computing is speeded up. The basic algorithm and the intermediate results at each stage are demonstrated.

Fault diagnosis scheme for open-circuit faults in switched reluctance motor drives using fast Fourier transform algorithm with bus current detection

Reliability of power converters is of crucial importance in switched reluctance motor drives used for safety-critical applications. Open-circuit faults in power converters will cause the motor to run in unbalanced states, and if left untreated, they will lead to damage to the motor and power modules, and even cause a catastrophic failure of the whole drive system. This study is focused on using a single current sensor to detect open-circuit faults accurately. An asymmetrical half-bridge converter is considered in this study and the faults of single-phase open and two-phase open are analysed. Three different bus positions are defined. On the basis of a fast Fourier transform algorithm with Blackman window interpolation, the bus current spectrums before and after open-circuit faults are analysed in details. Their fault characteristics are extracted accurately by the normalisations of the phase fundamental frequency component and double phase fundamental frequency component, and the fault characteristics of the three bus detection schemes are also compared. The open-circuit faults can be located by finding the relationship between the bus current and rotor position. The effectiveness of the proposed diagnosis method is validated by the simulation results and experimental tests.

Rotation-discriminating template matching based on Fourier coefficients of radial projections with robustness to scaling and partial occlusion

We consider brightness/contrast-invariant and rotation-discriminating template matching that searches an image to analyze A for a query image Q We propose to use the complex coefficients of the discrete Fourier transform of the radial projections to compute new rotation-invariant local features. These coefficients can be efficiently obtained via FFT. We classify templates in ""stable"" and ""unstable"" ones and argue that any local feature-based template matching may fail to find unstable templates. We extract several stable sub-templates of Q and find them in A by comparing the features. The matchings of the sub-templates are combined using the Hough transform. As the features of A are computed only once, the algorithm can find quickly many different sub-templates in A, and it is Suitable for finding many query images in A, multi-scale searching and partial occlusion-robust template matching. (C) 2009 Elsevier Ltd. All rights reserved.

Hand detection in cluttered scene images using Fourier-Mellin invariant features

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-based image segmentation and an interest point detector based on corners are used in order to identify regions of interest that contains possible matches. A sliding window algorithm is then used to scan the image at different scales performing the FMT calculations only in the previously detected regions of interest and comparing the extracted FM descriptor of the windows with a hand descriptors database obtained from a train image set. The results of the performed experiments suggest the use of Fourier-Mellin invariant features as a promising approach for automatic hand detection.

Hand detection in cluttered scene images using Fourier-Mellin invariant features

This paper proposes an automatic hand detection system that combines the Fourier-Mellin Transform along with other computer vision techniques to achieve hand detection in cluttered scene color images. The proposed system uses the Fourier-Mellin Transform as an invariant feature extractor to perform RST invariant hand detection. In a first stage of the system a simple non-adaptive skin color-based image segmentation and an interest point detector based on corners are used in order to identify regions of interest that contains possible matches. A sliding window algorithm is then used to scan the image at different scales performing the FMT calculations only in the previously detected regions of interest and comparing the extracted FM descriptor of the windows with a hand descriptors database obtained from a train image set. The results of the performed experiments suggest the use of Fourier-Mellin invariant features as a promising approach for automatic hand detection.

Fourier-Matrizen und Ringe mit Basis

Bei der Bestimmung der irreduziblen Charaktere einer Gruppe vom Lie-Typ entwickelte Lusztig eine Theorie, in der eine sogenannte Fourier-Transformation auftaucht. Dies ist eine Matrix, die nur von der Weylgruppe der Gruppe vom Lie-Typ abhängt. Anhand der Eigenschaften, die eine solche Fourier- Matrix erfüllen muß, haben Geck und Malle ein Axiomensystem aufgestellt. Dieses ermöglichte es Broue, Malle und Michel füur die Spetses, über die noch vieles unbekannt ist, Fourier-Matrizen zu bestimmen. Das Ziel dieser Arbeit ist eine Untersuchung und neue Interpretation dieser Fourier-Matrizen, die hoffentlich weitere Informationen zu den Spetses liefert. Die Werkzeuge, die dabei entstehen, sind sehr vielseitig verwendbar, denn diese Matrizen entsprechen gewissen Z-Algebren, die im Wesentlichen die Eigenschaften von Tafelalgebren besitzen. Diese spielen in der Darstellungstheorie eine wichtige Rolle, weil z.B. Darstellungsringe Tafelalgebren sind. In der Theorie der Kac-Moody-Algebren gibt es die sogenannte Kac-Peterson-Matrix, die auch die Eigenschaften unserer Fourier-Matrizen besitzt. Ein wichtiges Resultat dieser Arbeit ist, daß die Fourier-Matrizen, die G. Malle zu den imprimitiven komplexen Spiegelungsgruppen definiert, die Eigenschaft besitzen, daß die Strukturkonstanten der zugehörigen Algebren ganze Zahlen sind. Dazu müssen äußere Produkte von Gruppenringen von zyklischen Gruppen untersucht werden. Außerdem gibt es einen Zusammenhang zu den Kac-Peterson-Matrizen: Wir beweisen, daß wir durch Bildung äußerer Produkte von den Matrizen vom Typ A(1)1 zu denen vom Typ C(1) l gelangen. Lusztig erkannte, daß manche seiner Fourier-Matrizen zum Darstellungsring des Quantendoppels einer endlichen Gruppe gehören. Deswegen ist es naheliegend zu versuchen, die noch ungeklärten Matrizen als solche zu identifizieren. Coste, Gannon und Ruelle untersuchen diesen Darstellungsring. Sie stellen eine Reihe von wichtigen Fragen. Eine dieser Fragen beantworten wir, nämlich inwieweit rekonstruiert werden kann, zu welcher endlichen Gruppe gegebene Matrizen gehören. Den Darstellungsring des getwisteten Quantendoppels berechnen wir für viele Beispiele am Computer. Dazu müssen unter anderem Elemente aus der dritten Kohomologie-Gruppe H3(G,C×) explizit berechnet werden, was bisher anscheinend in noch keinem Computeralgebra-System implementiert wurde. Leider ergibt sich hierbei kein Zusammenhang zu den von Spetses herrührenden Matrizen. Die Werkzeuge, die in der Arbeit entwickelt werden, ermöglichen eine strukturelle Zerlegung der Z-Ringe mit Basis in bekannte Anteile. So können wir für die meisten Matrizen der Spetses Konstruktionen angeben: Die zugehörigen Z-Algebren sind Faktorringe von Tensorprodukten von affinen Ringe Charakterringen und von Darstellungsringen von Quantendoppeln.

On the Computation of Fourier Coefficients

In this paper we derive an identity for the Fourier coefficients of a differentiable function f(t) in terms of the Fourier coefficients of its derivative f'(t). This yields an algorithm to compute the Fourier coefficients of f(t) whenever the Fourier coefficients of f'(t) are known, and vice versa. Furthermore this generates an iterative scheme for N times differentiable functions complementing the direct computation of Fourier coefficients via the defining integrals which can be also treated automatically in certain cases.

Hybrid Water Demand Forecasting Model Associating Artificial Neural Network with Fourier Series

This paper addressed the problem of water-demand forecasting for real-time operation of water supply systems. The present study was conducted to identify the best fit model using hourly consumption data from the water supply system of Araraquara, Sa approximate to o Paulo, Brazil. Artificial neural networks (ANNs) were used in view of their enhanced capability to match or even improve on the regression model forecasts. The ANNs used were the multilayer perceptron with the back-propagation algorithm (MLP-BP), the dynamic neural network (DAN2), and two hybrid ANNs. The hybrid models used the error produced by the Fourier series forecasting as input to the MLP-BP and DAN2, called ANN-H and DAN2-H, respectively. The tested inputs for the neural network were selected literature and correlation analysis. The results from the hybrid models were promising, DAN2 performing better than the tested MLP-BP models. DAN2-H, identified as the best model, produced a mean absolute error (MAE) of 3.3 L/s and 2.8 L/s for training and test set, respectively, for the prediction of the next hour, which represented about 12% of the average consumption. The best forecasting model for the next 24 hours was again DAN2-H, which outperformed other compared models, and produced a MAE of 3.1 L/s and 3.0 L/s for training and test set respectively, which represented about 12% of average consumption. DOI: 10.1061/(ASCE)WR.1943-5452.0000177. (C) 2012 American Society of Civil Engineers.

Programmable logic design of a compact Genetic Algorithm for phasor estimation in real-time

The main objective of this work is to present an efficient method for phasor estimation based on a compact Genetic Algorithm (cGA) implemented in Field Programmable Gate Array (FPGA). To validate the proposed method, an Electrical Power System (EPS) simulated by the Alternative Transients Program (ATP) provides data to be used by the cGA. This data is as close as possible to the actual data provided by the EPS. Real life situations such as islanding, sudden load increase and permanent faults were considered. The implementation aims to take advantage of the inherent parallelism in Genetic Algorithms in a compact and optimized way, making them an attractive option for practical applications in real-time estimations concerning Phasor Measurement Units (PMUs).

Quality Assessment and Enhancement Method for high-resolution Fourier-Domain OCT Imaging of Retina Laser Lesions

We present an image quality assessment and enhancement method for high-resolution Fourier-Domain OCT imaging like in sub-threshold retina therapy. A Maximum-Likelihood deconvolution algorithm as well as a histogram-based quality assessment method are evaluated.

Automatic estimation of noise parameters in Fourier-domain optical coherence tomography cross sectional images using statistical information

We present an application and sample independent method for the automatic discrimination of noise and signal in optical coherence tomography Bscans. The proposed algorithm models the observed noise probabilistically and allows for a dynamic determination of image noise parameters and the choice of appropriate image rendering parameters. This overcomes the observer variability and the need for a priori information about the content of sample images, both of which are challenging to estimate systematically with current systems. As such, our approach has the advantage of automatically determining crucial parameters for evaluating rendered image quality in a systematic and task independent way. We tested our algorithm on data from four different biological and nonbiological samples (index finger, lemon slices, sticky tape, and detector cards) acquired with three different experimental spectral domain optical coherence tomography (OCT) measurement systems including a swept source OCT. The results are compared to parameters determined manually by four experienced OCT users. Overall, our algorithm works reliably regardless of which system and sample are used and estimates noise parameters in all cases within the confidence interval of those found by observers.

A new algorithm to accelerate harmonic analysis of time series

The Lomb periodogram has been traditionally a tool that allows us to elucidate if a frequency turns out to be important for explaining the behaviour of a given time series. Many linear and nonlinear reiterative harmonic processes that are used for studying the spectral content of a time series take into account this periodogram in order to avoid including spurious frequencies in their models due to the leakage problem of energy from one frequency to others. However, the estimation of the periodogram requires long computation time that makes the harmonic analysis slower when we deal with certain time series. Here we propose an algorithm that accelerates the extraction of the most remarkable frequencies from the periodogram, avoiding its whole estimation of the harmonic process at each iteration. This algorithm allows the user to perform a specific analysis of a given scalar time series. As a result, we obtain a functional model made of (1) a trend component, (2) a linear combination of Fourier terms, and (3) the so-called mixed secular terms by reducing the computation time of the estimation of the periodogram.