A possibility for parametric signal estimation by Prony class methods is investigated in this work. So-called exponential-sinusoidal models are considered. These models comprise damped exponentials, damped and undamped sinusoidals, and various their additive combinations. Two main methods – the classical Prony method and Prony method with prefiltering – are studied in this work. The formulas for estimation of parameters of undamped and damped sinusoidals by the classical Prony method are derived. The algorithm for calculation of the impulse response of the filter used in Prony method with prefiltering is given. Software for estimation of exponential-sinusoidal models by Prony class methods is developed (in the MATLAB environment). Numerical experiments are carried out using the software developed. The conclusions on possibilities of application of the classical Prony method and Prony method with prefiltering are stated on the basis of simulation results.

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Orientador: Prof. Dr. Fabiano Fragoso Costa / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2014. / Este trabalho propõe um algoritmo de estimaçãoo fasorial baseado na versão modificada do algoritmo de mínimos quadrados recursivo. Este algoritmo é adequado para proteção de sistemas de potência, uma vez que sua resposta é rapida e robusta 'a presença da componente dc de decaimento exponencial, que é uma interferência comum em condi¸ções de falta atrasando a convergência da estimativa fasorial. Além disso, esta dissertação também investiga o uso do chamado método de Prony, a fim de auxiliar e acelerar a convergência da estimação fasorial do algoritmo dos mínimos quadrados. O método de Prony determina o decaimento exponencial a ser extraído do sinal analisado. As técnicas desenvolvidas nessa disserta¸c¿ao foram comparadas com o tradicional estimador de Fourier de um ciclo atrav'es de simula¸c¿oes realizadas em Matlab e de experimentos realizados com um processador de sinais e um amplificador de sinais. Os resultados mostram melhorias da t'ecnica proposta em comparação ao algoritmo de Fourier e incentivam futuras pesquisas relacionadas a este assunto. / This work proposes a phasor estimation algorithm based on a modified recursive least-squares. This algorithm is suitable for power systems protection once its response quick and robust to the decaying dc component, which is a most usual interference in fault conditions and delays the phasor estimation convergence. Furthermore, this dissertation also investigates the usage of the so-called Prony¿s method in order to aid and to speed up the least-squares phasor estimation convergence. This method determines the exponential decaying to be extracted out of the analyzed signal. The present developed techniques have been compared with the traditional one-cycle Fourier estimation by simulation performed on Matlab and by experiments accomplished with a digital signal processor and a signal amplifier. The results show improvements of the proposed techniques over the Fourier algorithm and encourage further research in this topic.

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