AbstractsComputer Science

This thesis describes the Transfer Function and Eigenfunction Analysis (TFEA) method: an efficient eigenanalysis method for estimating the small signal stability of large interconnected power systems. The method consists of reducing the order of each generator, which is accurately modeled by m state-variables, to only two state-variables, including rotor speed and angle deviations. This efficiency is achieved without loss of dynamic accuracy because the information of the other (m-2) state-variables is compacted into transfer functions in a frequency-dependent state-matrix [A(ω)]2ng×2ng. Because the computation count of QR eigenanalysis increases with the cube of system dimension, computation efficiency arises from evaluating the reduced state matrix [A(ω)]2ng×2ng, instead of the full state matrix [A](m×ng)×(m×ng), in a power system consisting of ng generators. The acceptability of the method is based on the engineering knowledge that the electromechanical modes are the least damped modes, and the system stability depends on these eigenvalues' being on the left side of the complex s-plane. In practice, only a small number of low-frequency electromechanical modes determine stability. Consequently, the accuracy of the TFEA method is improved for selected electromechanical modes by applying the eigenvalue sensitivity formula. In the next step, the TFEA method is combined with the well-known Arnoldi method for further improvement of efficiency.This thesis also develops a method for simultaneous tuning of power system stabilizers (PSSs). The proposed method combines the timesaving TFEA method with the eigenvalue sensitivity concepts and optimization techniques. The key feature of the method is the eigenvalue sensitivity formula, which relates perturbation changes of eigenvalues to perturbation changes of stabilizer parameters. In PSS tuning, the parameters are one amplification gain and the many time constants of each PSS. Tuning consists of formulating an objective function which embeds the desirable improvement in damping of the eigenvalues. To this end, an optimization algorithm (from MATLAB) is applied to satisfy the objective function while meeting the size constraints placed on the parameters.The accuracy, efficiency and robustness of the TFEA method and the PSS tuning method are compared with the benchmark eigenvalues based on the full state matrix [A](m×ng)×(m×ng). The numerical tests use a 16-generator and a 69-generator power system. The test results, demonstrate the effective performance of the proposed methods. Cette thése décrit la Fonction de Transfert et l'Analyse de la méthode de la Fonction propre (TFEA): une méthode efficace d'évaluer stabilité de petits signaux dans les grandes installations électriques connectées. La méthode consiste en réduire l'ordre de chaque générateur qui est précisément modelé par des variables d'état m à seulement variables de deux états incluant la vitesse de rotor et des écarts angulaires. L'efficacité est réalisée sans perte d'exactitude dynamique parce que les…