Maamar Bettayeb

Recursive estimation of power system harmonics

This paper presents the application of well known recursive estimation techniques to the important problem of power system harmonics in a noisy environment. on-line estimation of harmonic amplitudes and phases is performed using several variants of recursive least square (RLS) algorithms, known for their simplicity of computation and good convergence properties. The estimates are updated recursively as samples of the harmonic signals are received. A noisy harmonic signal from the AC bus of a six pulse rectifier is used as a test signal in the simulation. The various RLS algorithms are evaluated under different signal to noise ratios (SNR) and are shown to produce good harmonic magnitude and phase estimates even for a 0 dB SNR. Due to their simplicity, these algorithms are appropriate for on-line implementation in polluted power systems.

Characterization of the solution to the optimal H∞ model reduction problem

Abstract In this paper the H ∞ norm approximation of a given stable, proper, rational transfer function by a lower order stable proper rational transfer function is studied. The solution method is based on the authors observation that the H ∞ model reduction problem can be converted into a Hankel norm model reduction problem. A simple characterization of the solution to the optimal H ∞ model reduction problem is developed.

Controllability and Observability of Linear Discrete-Time Fractional-Order Systems

Controllability and Observability of Linear Discrete-Time Fractional-Order Systems In this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

A Hybrid Least-Squares GA Based Algorithm for Harmlonic Estimation

Harmonic estimation in a distorted signal along with additive noise has been an area of interest for researchers in many disciplines of science and engineering. This paper presents a new algorithm to estimate the harmonics in power systems using genetic algorithms (GA). The harmonic estimation problem is linear in amplitude and nonlinear in phase. The proposed hybrid algorithm takes advantage of this structure and iterates between linear least-squares amplitude estimation and the nonlinear GA-based phase estimation. Improvement in both convergence for solution as well as processing time is demonstrated from this algorithm.

New model reduction scheme for bilinear systems

A new method for the approximation of bilinear systems is proposed. The reduction scheme applies to both stable and unstable bilinear systems. The technique uses generalized input normal representations to retain the dominant part of the original system. The algorithm is evaluated on a synchronous induction generator and is shown to lead to acceptable reduced approximations of the original system. A frequency weighting is also introduced in the reduction scheme to further improve the approximation.

Multilayer perceptron-based DFE with lattice structure

The severely distorting channels limit the use of linear equalizers and the use of the nonlinear equalizers then becomes justifiable. Neural-network-based equalizers, especially the multilayer perceptron (MLP)-based equalizers, are computationally efficient alternative to currently used nonlinear filter realizations, e.g., the Volterra type. The drawback of the MLP-based equalizers is, however, their slow rate of convergence, which limit their use in practical systems. In this work, the effect of whitening the input data in a multilayer perceptron-based decision feedback equalizer (DFE) is evaluated. It is shown from computer simulations that whitening the received data employing adaptive lattice channel equalization algorithms improves the convergence rate and bit error rate performances of multilayer perceptron-based DFE. The adaptive lattice algorithm is a modification to the one developed by Ling and Proakis (1985). The consistency in performance is observed in both time-invariant and time-varying channels. Finally, it is found in this work that, for time-invariant channels, the MLP DFE outperforms the least mean squares (LMS)-based DFE. However, for time-varying channels comparable performance is obtained for the two configurations.

Adaptive echo cancellation using least mean mixed-norm algorithm

A novel algorithm for echo cancellation is presented in this work. The algorithm consists of simultaneously applying the least mean square (LMS) algorithm to the near-end section of the echo canceller and the least mean fourth (LMF) algorithm to the far-end section. This new scheme results in a substantial performance improvement over the LMS algorithm and other algorithms.

Power system harmonic estimation: a comparative study

In this work, the discrete Fourier transform, the least-square and least-absolute-value techniques are applied to the voltage harmonic estimation of a three-phase six-pulse converter. The algorithms are evaluated and compared with respect to the signal/ noise ratio, number of samples, sampling frequency, computation time and missing data. The results of the estimation show an overall superiority of the least-absolute-value technique and an acceptable performance for the least-square method

A new model reduction scheme for k-power bilinear systems

A model reduction scheme of k-power bilinear systems is proposed in this work. The canonical state space structure of k-power systems is used to simplify a balancing like model reduction scheme for bilinear systems. The derived model reduction algorithm reduces to computational steps similar in complexity to the balanced approximation of linear systems. Controllability and observability gramians turn out to have simple block diagonal structures and their properties are easily derived. The simulation of an 11th order system shows good performances of the reduced order models.<<ETX>>

A NOTE ON THE CONTROLLABILITY AND THE OBSERVABILITY OF FRACTIONAL DYNAMICAL SYSTEMS

Abstract In this paper, we give some new results on the controllability and the observability of linear dynamical systems with a fractional derivative of order α , where α is a non integer number. We show that the observability and the controllability Gramians, recently introduced for a fractional order system, are solutions of fractional differential Lyapunov equations, thus generalizing the classical result for the integer case ( α = 1). Our results can be considered as a generalization of the known corresponding results in the integer order case to the fractional order one since for α = 1, the results for the integer case are recovered.