This thesis investigates the capabilities of the Collapse Prediction Relay (CPR-D) and also investigates the use of system identification for detection of oscillatory instability. Both the CPR-D and system identification are based on system measurements and do not require modelling of the power system. Measurement based stability monitors can help to avoid instability and blackouts, in cases where the available system model can not predict instability. The CPR-D uses frequency patterns in voltage oscillation to detect system instability. The relay is based on non-linear dynamics Theory. If a collapse is predicted, measures could be taken to prevent a blackout. The relay was tested using the output of simulators and was later installed in a substation. The data from laboratory tests and site installations is analysed enabling a detailed evaluation of the CPR-D.Oscillatory instability can be detected by monitoring the damping ratio of oscillations in the power system. Poor damping indicates a smaller stability margin. Subspace identification is used to estimate damping ratios. The method is tested under different conditions and using several power system models. The results show that using several measurements gives more accurate estimates and requires shorter data windows. A selection method for measurements is proposed in the thesis.

abstract: This thesis describes an approach to system identification based on compressive sensing and demonstrates its efficacy on a challenging classical benchmark single-input, multiple output (SIMO) mechanical system consisting of an inverted pendulum on a cart. Due to its inherent non-linearity and unstable behavior, very few techniques currently exist that are capable of identifying this system. The challenge in identification also lies in the coupled behavior of the system and in the difficulty of obtaining the full-range dynamics. The differential equations describing the system dynamics are determined from measurements of the system's input-output behavior. These equations are assumed to consist of the superposition, with unknown weights, of a small number of terms drawn from a large library of nonlinear terms. Under this assumption, compressed sensing allows the constituent library elements and their corresponding weights to be identified by decomposing a time-series signal of the system's outputs into a sparse superposition of corresponding time-series signals produced by the library components. The most popular techniques for non-linear system identification entail the use of ANN's (Artificial Neural Networks), which require a large number of measurements of the input and output data at high sampling frequencies. The method developed in this project requires very few samples and the accuracy of reconstruction is extremely high. Furthermore, this method yields the Ordinary Differential Equation (ODE) of the system explicitly. This is in contrast to some ANN approaches that produce only a trained network which might lose fidelity with change of initial conditions or if facing an input that wasn't used during its training. This technique is expected to be of value in system identification of complex dynamic systems encountered in diverse fields such as Biology, Computation, Statistics, Mechanics and Electrical Engineering. / Dissertation/Thesis / M.S. Electrical Engineering 2011

Neste trabalho, é apresentado um estudo sobre um sistema de micro geração de energia a partir da vibração de uma viga em balanço utilizando um transdutor piezoelétrico. A análise é feita levando-se em consideração as dimensões da viga utilizada, tipo de gerador piezoelétrico e diferentes tipos de cargas acopladas a este. O sistema de geração tem sua excitação realizada por um atuador piezoelétrico, que é alimentado por uma fonte de tensão com amplitude, frequência e forma de onda ajustáveis. A avaliação da potência de saída e influência dos diferentes tipos de carga acoplados a saída são analisados. As cargas utilizadas são: puramente resistiva, resistiva-capacitiva e não linear, por meio de um retificador de onda completa. Para avaliar experimentalmente os resultados analíticos foi utilizado um protótipo de uma viga em balanço construída com uma barra de alumínio exposta a uma excitação, induzida por um outro transdutor piezoelétrico ligado a uma placa dSpace controlada por um computador. Os parâmetros do sistema são identificados sendo possível determinar sua influência na saída e realizando assim uma análise pontual do micro gerador piezoelétrico quando submetido a uma carga qualquer. Os resultados da geração com os diferentes tipos de cargas são comparados, bem como a influência destas na dinâmica do sistema. As potências máximas são apresentadas em diferentes modos de vibração depois de otimizadas. Foram obtidos os seguintes resultados: 3;357mW com uma resistência de 200k no primeiro modo; 13;17mW com uma resistência de 50k no segundo modo; para o terceiro e quarto modos de vibração a máxima potência é obtida com a resistência de 10k, sendo 10;22mW e 15;63mW, respectivamente. A alteração da frequência de vibração é de aproximadamente 0;2% para os modos de vibração em função da resistência máxima e mínima. Para a carga resistiva-capacitiva, o comportamento da geração não é afetado significativamente para os valores de resistência de 1M e 100k. Com os valores de 10k e 1k a potência ativa se eleva em 30%, aproximadamente. O comportamento da carga não linear é aproximado por uma impedância com característica capacitiva. Sendo que, com a elevação da frequência, a impedância vista pelo gerador piezoelétrico é diminuída. A energia armazenada é de 0;8039mJ, 2;5245mJ e 1;3041mJ para o primeiro, segundo e terceiro modos de vibração, respectivamente. / This work presents a study of a energy harvesting system based on vibration from a cantilever beam utilizing a piezoelectric generator. The analysis considers the dimensions of the beam, type of piezoelectric generator and di erent types of loads coupled. A piezoelectric actuator is handles for the system excitement, powered by a voltage source with adjustable amplitude, frequency and shape. Are evaluate the output power and the in uence of di erent charge types coupled to the piezoelectric generator. The loads are purely resistive, resistive-capacitive and non-linear, by a full-wave bridge recti er. To check experimentally the analytical results, are used a prototype of a cantilever beam constructed with an aluminum bar exposed to an excitation induced by another piezoelectric transducer attached to a dSpace board controlled by a computer. The system parameters are individually identi ed to determine their in uence on output, allowing the punctual analysis of the piezoelectric harvesting when subjected to any load. The results of power generation are compare with di erent types of loads as well as its in uence on the dynamic of the system. After a optimization, the greatest power delivered to the load happen in di erent vibrational modes. We obtain the following results: 3:357mW with a 200k resistance in the rst mode; 13:17mW with a 50k resistance in the second mode, for the third and fourth vibration modes greatest power is obtained with the 10k resistance, being 10:22mW and 15:63mW, respectively. The modi cation of the vibration frequency are approximately 0:2% for all vibration modes depending on the largest and smallest resistance. For the resistive-capacitive load, the generation behavior are not a ect to the 1M and 100k resistance. With the 10k and 1k values, the active power increases by approximately 30%. The nonlinear load behavior are approach by an impedance with capacitive characteristics. With increasing of frequency, the impedance seen by the piezoelectric harvester is decreased. The energy stored is 0:8039mJ, 2:5245mJ and 1:3041mJ for the rst, second and third vibration modes, respectively.

O escopo desta dissertação é o desenvolvimento de uma metodologia para identificar os modelos de canais da matriz dinâmica que estejam degradando o desempenho de controladores preditivos, ou MPC (Model Predictive Control), baseado nas técnicas de auditoria e diagnóstico deste tipo de controlador propostas por BOTELHO et al. (2015) e BOTELHO; TRIERWEILER; FARENZENA (2016) e CLARO (2016). A metodologia desenvolvida contempla dois métodos distintos. O primeiro, chamado método direto compensado, tem como base o método direto de identificação em malha fechada (LJUNG, 1987)e compensa cada saída medida do processo de modo a se reter apenas a contribuição do canal que se deseja identificar. O segundo, chamado método do erro nominal, utiliza a definição de saída nominal do processo, proposta por BOTELHO et al. (2015), como métrica para se quantificar o quão próximo o modelo está do comportamento da planta através da minimização do erro nominal. Os métodos foram aplicados ao sistema de quatro tanques cilíndricos (JOHANSSON, 2000) para dois cenários distintos, sendo o primeiro um sistema 2x2 em fase não mínima contendo um MPC trabalhando com setpoint e o segundo um sistema 4x4 em fase mínima com o MPC atuando por faixas. Para o sistema 2x2, se avaliou a influência da localização do canal discrepante (dentro ou fora da diagonal principal da matriz dinâmica de transferência) na eficácia dos métodos. Para o sistema 4x4, o estudo foi voltado para a eficácia dos métodos frentes a controladores que atuam dentro de limites para as variáveis. Os modelos identificados foram comparados pela capacidade de identificar um modelo que capturasse o zero de transmissão da planta e o RGA dinâmico, par ao sistema 2x2, e pelas respostas degrau e diagrama de Bode para o sistema 4x4. O método direto compensado resultou em baixo erro relativo no valor do zero para a discrepância na diagonal principal da matriz dinâmica e alto valor quando a discrepância se encontrava fora da diagonal principal. O método do erro nominal, por sua vez, foi capaz de identificar um modelo cujo zero de transmissão possuía baixo erro relativo frente ao zero da planta em ambos os cenários. No cenário do controlador atuando por faixas, os métodos propostos obtiveram melhores estimativas dos modelos quando comparados com o método concorrente, uma vez que apresentou alto percentual de aderência das saídas simuladas com as saídas medidas. Em todos os cenários estudados, o método do erro nominal se mostrou capaz de identificar um modelo mais robusto, pois este apresentou RGA dinâmico compatível com a planta em todo o range de frequências analisado. / The objective of this dissertation is to develop a method to identify the model for the channel of the dynamic matrix that are affecting the performance of model predictive controllers (MPC), based on the assessment and diagnosis techniques for this type of controller proposed by BOTELHO et al. (2015) e BOTELHO; TRIERWEILER; FARENZENA (2016) and CLARO (2016). The proposed methodology includes two different methods. The first, called the compensated direct method, is based on the closed-loop direct identification method (LJUNG, 1987) and compensates each process measured output in order to retain only the contribution of the channel being identified. The second, called nominal error method, uses the definition of the process nominal output, proposed by BOTELHO et al. (2015), as a metric to quantify how close the model is to the actual plant behavior by minimizing the nominal error. The proposed methods were applied to the quadruple-tank system (JOHANSSON, 2000) for two distinct scenarios, the first being a nonminimum-phase 2x2 system containing a MPC working with setpoint and the second a minimum-phase 4x4 system with the MPC working by ranges. For the 2x2 system, the influence of the model mismatch location (inside or outside the main diagonal of the dynamic transfer matrix) on the effectiveness of the methods was evaluated. For the 4x4 system, the study was focused on the effectiveness of the methods with controllers that operate within limits for the variables. The identified models were compared by the capability of identifying a model with accurate plant transmission zero and dynamic RGA, for the 2x2 system, and by the step responses and Bode diagram for the 4x4 system. The compensated direct method resulted in low relative error in the value of the transmission zero for the model mismatch located in the main diagonal of the dynamic matrix and high relative error when the mismatch was outside the main diagonal. On the other hand, the nominal error method was able to identify a model whose transmission zero had low relative error against the plant zero in both scenarios. In the scenario of a controller working by range, the proposed methods obtained better estimates of the models when compared to the concurrent method, since it presented a high percentage of adherence of the simulated outputs with the measured outputs. In all the studied scenarios, the nominal error method was able to identify a more robust model, since it presented dynamic RGA compatible with the plant in the entire range of analyzed frequencies.

Monitoramento da integridade estrutural (Structural health monitoring - SHM) está relacionado à implementação de alguma estratégia para a detecção de dano em estruturas de engenharia. Este estudo geralmente envolve a observação do sistema no tempo, utilizando amostras periódicas de medições da resposta dinâmica, a partir de um grupo de sensores, a fim de verificar alterações nos parâmetros modais, que podem indicar a presença do dano. Entretanto, especialmente para estruturas treliçadas, este processo tornase difícil principalmente porque nem todos os deslocamentos ou rotações nodais modelados numericamente podem ser medidos experimentalmente. Desta forma, o presente estudo tem por objetivo tratar algumas das ainda correntes questões dos sistemas de monitoramento da integridade estrutural baseados em registros de vibração. Primeiramente aborda-se um tema que, apesar de recentemente ter se mostrado importante, ainda apresenta muito poucos estudos: a influência da variação dos efeitos ambientais, especialmente a temperatura, sobre as características dinâmicas de estruturas. Com o intuito de verificar tal influência em pontes metálicas, os resultados apresentados por Ni et al. (2005) são utilizados para a realização de estudos de correlação, através de uma comparação entre equações de regressão linear e um modelo, proposto no presente trabalho, em Redes Neurais Artificiais (RNA). A seguir são estudados procedimentos de identificação estocástica de sistemas, passo fundamental para o monitoramento da integridade estrutural. Realiza-se uma revisão bibliográfica nesta área abordando a evolução dos métodos que utilizam apenas dados de resposta para a identificação. Enfoque principal é dado nos métodos de identificação estocástica de subespaço (SSI), pois se mostram os mais práticos e robustos para a determinação dos parâmetros modais da estrutura.Finalmente, o método dos vetores de localização de dano (Damage locating vector method- DLV), introduzido por Bernal (2002), é extensivamente discutido. Esta é umatécnica eficaz quando operando com um número arbitrário de sensores, modos truncados e em cenários de dano múltiplo, mantendo as operações numéricas simples. Além disto, a influência do ruído na precisão do método dos vetores de localização de dano é avaliada. Com o intuito de verificar o comportamento do método DLV perante diferentes intensidades de dano e, principalmente, na presença de ruído de medição, um estudo paramétrico é conduzido. Distintas excitações, como também diferentes cenários de dano, são numericamente testadas em uma treliça Warren contínua considerando um limitado conjunto de sensores, através de cinco níveis de ruído. Além disto, é proposto um caminho alternativo para determinar os vetores de localização de dano no procedimento do método DLV. A idéia é oferecer uma opção alternativa para a solução do problema utilizando um método algébrico amplamente difundido. A formulação original via decomposição em valores singulares é subsituída pela solução mais trivial de um problema de valores próprios. Isto é possível graças à relação algébrica entre a decomposição em valores singulares de uma matriz e a solução do problema de autovalores desta matriz pré-multiplicada por sua transposta. Os resultados finais mostraram que o método DLV, considerando a soluça alternativa, foi capaz de corretamente localizar as barras danificadas, utilizando dados somente de resposta da estrutura, mesmo considerando pequenas intesidades de dano e moderados níveis de ruído. / Structural health monitoring (SHM) refers to the implementation of some strategy for damage detection in engineering structures. This study generally involves the observation of a system over time using periodically sampled dynamic response measurements from a set of sensors in order to verify changes in modal parameters, which may indicate damage or degradation. However, especially for truss structures this process sounds difficulty mainly because not all nodal displacements or rotations in the numerical model can be experimentally measured. In this context, the present thesis aims to address some still current issues of the vibration-based structural health monitoring systems. Firstly it is introduced a subject that, although has recently shown important, still presents very few studies: the environmental effects, mainly temperature, on the structural modal properties. Seeking to address this influence on steel bridges, the results presented by Ni et al. (2005) are used to conduct correlations studies, comparing linear equation regression with an artificial neural network model (ANN), proposed in the present thesis. Procedures for stochastic systems identification are studied next, which is a fundamental phase for the SHM systems. A literature review in this field addressing the evolution of the methods that just use response data for identification is carried out. Main focus is given in the stochastic subspace identification methods (SSI), because they have been known as the most practical and robust methods to determine the structure’s modal parameters. Finally, the damage locating vector (DLV) method, introduced by Bernal (2002), is extensively discussed. This is a useful approach because is effective when operating with an arbitrary number of sensors, a truncated modal basis and multiple damage scenarios, while keeping the calculation at a low level. In addition, the noise influence on the accuracy of the damage locating vector method is evaluated. In order to verify the DLV behavior in front of different damages intensities and, mainly, in presence of measurement noise, a parametric study had been carried out. Different excitations as well as damagescenarios are numerically tested in a continuous Warren truss structure with a set of limited measurement sensors through five noise levels. Besides this, it is proposed another way to determine the damage locating vectors in the DLV procedure. The idea is to offer an alternative option to solve the problem with a more widespread algebraic method. The original formulation via singular value decomposition (SVD) is replaced by a common solution of an eigenvector and eigenvalue problem. This is possible thanks to the algebraic relationship between the singular value decomposition of a matrix and the eigenproblem solution of this matrix pre-multiplied by its transpose. The final results show that the DLV method, adopting the alternative, was able to correct locate the damaged bars, using an output-only system identification procedure, even considering small intensities of damage and moderate noise levels.

With the growing installation of surveillance video cameras in both private and public areas, it is an immediate requirement to develop intelligent video analysis system for the large-scale camera network. As a prerequisite step of person tracking and person retrieval in intelligent video analysis, person re-identification, which targets in matching person images across camera views is an important topic in computer vision community and has been received increasing attention in the recent years. In the supervised learning methods, the person re-identification task is formulated as a classification problem to extract matched person images/videos (positives) from unmatched person images/videos (negatives). Although the state-of-the-art supervised classification models could achieve encouraging re-identification performance, the assumption that label information is available for all the cameras, is impractical in large-scale camera network. That is because collecting the label information of every training subject from every camera in the large-scale network can be extremely time-consuming and expensive. While the unsupervised learning methods are flexible, their performance is typically weaker than the supervised ones. Though sufficient labels of the training subjects are not available from all the camera views, it is still reasonable to collect sufficient labels from a pair of camera views in the camera network or a few labeled data from each camera pair. Along this direction, we address two scenarios of person re-identification in large-scale camera network in this thesis, i.e. unsupervised domain adaptation and semi-supervised learning and proposed three methods to learn discriminative model using all available label information and domain knowledge in person re-identification. In the unsupervised domain adaptation scenario, we consider data with sufficient labels as the source domain, while data from the camera pair missing label information as the target domain. A novel domain adaptive approach is proposed to estimate the target label information and incorporate the labeled data from source domain with the estimated target label information for discriminative learning. Since the discriminative constraint of Support Vector Machines (SVM) can be relaxed into a necessary condition, which only relies on the mean of positive pairs (positive mean), a suboptimal classification model learning without target positive data can be those using target positive mean. A reliable positive mean estimation is given by using both the labeled data from the source domain and potential positive data selected from the unlabeled data in the target domain. An Adaptive Ranking Support Vector Machines (AdaRSVM) method is also proposed to improve the discriminability of the suboptimal mean based SVM model using source labeled data. Experimental results demonstrate the effectiveness of the proposed method. Different from the AdaRSVM method that using source labeled data, we can also improve the above mean based method by adapting it onto target unlabeled data. In more general situation, we improve a pre-learned classifier by adapting it onto target unlabeled data, where the pre-learned classifier can be domain adaptive or learned from only source labeled data. Since it is difficult to estimate positives from the imbalanced target unlabeled data, we propose to alternatively estimate positive neighbors which refer to data close to any true target positive. An optimization problem for positive neighbor estimation from unlabeled data is derived and solved by aligning the cross-person score distributions together with optimizing for multiple graphs based label propagation. To utilize the positive neighbors to learn discriminative classification model, a reliable multiple region metric learning method is proposed to learn a target adaptive metric using regularized affine hulls of positive neighbors as positive regions. Experimental results demonstrate the effectiveness of the proposed method. In the semi-supervised learning scenario, we propose a discriminative feature learning using all available information from the surveillance videos. To enrich the labeled data from target camera pair, image sequences (videos) of the tagged persons are collected from the surveillance videos by human tracking. To extract the discriminative and adaptable video feature representation, we propose to model the intra-view variations by a video variation dictionary and a video level adaptable feature by multiple sources domain adaptation and an adaptability-discriminability fusion. First, a novel video variation dictionary learning is proposed to model the large intra-view variations and solved as a constrained sparse dictionary learning problem. Second, a frame level adaptable feature is generated by multiple sources domain adaptation using the variation modeling. By mining the discriminative information of the frames from the reconstruction error of the variation dictionary, an adaptability-discriminability (AD) fusion is proposed to generate the video level adaptable feature. Experimental results demonstrate the effectiveness of the proposed method.

abstract: It is possible in a properly controlled environment, such as industrial metrology, to make significant headway into the non-industrial constraints on image-based position measurement using the techniques of image registration and achieve repeatable feature measurements on the order of 0.3% of a pixel, or about an order of magnitude improvement on conventional real-world performance. These measurements are then used as inputs for a model optimal, model agnostic, smoothing for calibration of a laser scribe and online tracking of velocimeter using video input. Using appropriate smooth interpolation to increase effective sample density can reduce uncertainty and improve estimates. Use of the proper negative offset of the template function has the result of creating a convolution with higher local curvature than either template of target function which allows improved center-finding. Using the Akaike Information Criterion with a smoothing spline function it is possible to perform a model-optimal smooth on scalar measurements without knowing the underlying model and to determine the function describing the uncertainty in that optimal smooth. An example of empiric derivation of the parameters for a rudimentary Kalman Filter from this is then provided, and tested. Using the techniques of Exploratory Data Analysis and the "Formulize" genetic algorithm tool to convert the spline models into more accessible analytic forms resulted in stable, properly generalized, KF with performance and simplicity that exceeds "textbook" implementations thereof. Validation of the measurement includes that, in analytic case, it led to arbitrary precision in measurement of feature; in reasonable test case using the methods proposed, a reasonable and consistent maximum error of around 0.3% the length of a pixel was achieved and in practice using pixels that were 700nm in size feature position was located to within ± 2 nm. Robust applicability is demonstrated by the measurement of indicator position for a King model 2-32-G-042 rotameter. / Dissertation/Thesis / Measurement Results (part 1) / Measurement Results (part 2) / General Presentation / M.S. Mechanical Engineering 2012

In modern manufacturing, industrial robots are essential components that allow saving cost, increase quality and productivity for instance. To achieve such goals, high accuracy and speed are simultaneously required. The design of control laws compliant with such requirements demands high-fidelity mathematical models of those robots. For this purpose, dynamic models are built from experimental data. The main objective of this thesis is thus to provide robotic engineers with automatic tools for identifying dynamic models of industrial robot arms. To achieve this aim, a comparative analysis of the existing methods dealing with robot identification is made. That allows discerning the advantages and the limitations of each method. From those observations, contributions are presented on three axes. First, the study focuses on the estimation of the joint velocities and accelerations from the measured position, which is required for the model construction. The usual method is based on a home-made prefiltering process that needs a reliable knowledge of the system’s bandwidths, whereas the system is still unknown. To overcome this dilemma, we propose a method able to estimate the joint derivatives automatically, without any setting from the user. The second axis is dedicated to the identification of the controller. For the vast majority of the method its knowledge is indeed required. Unfortunately, for copyright reasons, that is not always available to the user. To deal with this issue, two methods are suggested. Their basic philosophy is to identify the control law in a first step before identifying the dynamic model of the robot in a second one. The first method consists in identifying the control law in a parametric way, whereas the second one relies on a non-parametric identification. Finally, the third axis deals with the home-made setting of the decimate filter. The identification of the noise filter is introduced similarly to methods developed in the system identification community. This allows estimating automatically the dynamic parameters with low covariance and it brings some information about the noise circulation through the closed-loop system. All the proposed methodologies are validated on an industrial robot with 6 degrees of freedom. Perspectives are outlined for future developments on robotic systems identification and other complex problems.

[pt] Este trabalho descreve uma metodologia para modelagem de cargas elétricas, utilizando dados de tensão e corrente registrados durante distúrbios no sistema de potência. Estes modelos são utilizados na representação de subsistemas da rede elétrica em simulações computacionais que preveem o comportamento dinâmico do sistema de potência após perturbações em suas condições normais de operação.São apresentados resultados práticos da metodologia proposta, onde a carga é definida como um sistema cuja saída é a variação da potência consumida e a entrada é a variação da tensão, ambas medidas em barramentos de 69 kV da Companhia Hidroelétrica do São Francisco (CHESF), ponto de entrega de energia para concessionárias distribuidoras de energia do nordeste brasileiro. Estas distribuidoras são modeladas como cargas, supridas pelo sistema de transmissão da CHESF e todos os elementos consumidores de energia são agregados nestes modelos equivalentes, parametrizados para simular o maior número de contingências típicas medidas em cada um destes barramentos de carga.A técnica de estimação de parâmetros dos modelos de cargas é o Algoritmo Genético (AG) cujos resultados apresentaram precisão para a simulação de contingências de características bem distintas, caracterizando a abrangência alcançada no processo de identificação de sistemas.Ao final do trabalho são apresentadas curvas de desvios de potência ativa e reativa causadas por afundamentos de tensão, ambos registrados nos barramentos das subestações da CHESF. Estas curvas foram utilizadas para estimar os parâmetros dos modelos, obtidos individualmente para cada uma das subestações estudadas. / [en] This work describes a measurement-based load modeling methodology, using voltage and current data registered during power system disturbances. These load models are used on computational simulations for predicting power system stability after disturbances of system operational points. Practical results are presented of the proposed methodology, defining load as a system whose output is power deviation from its operational state and input is voltage sags, both measured at 69 kV bus bars of São Francisco Hydroelectric Company (CHESF), points of common coupling (PCC) between CHESF and local distribution utilities. Therefore, distribution utilities are seen as loads supplied by CHESF’s transmission system. All devices consuming power from the PCC are aggregated into an equivalent model, parameterized to simulate most typical contingencies measured by these 69kV load bars. Optimization technique used for load model parameter estimation is Genetic Algorithm (GA), showing his flexibility on implementation and good coverage and accuracy in the final results. At the end, it will be presented a set of active and reactive power curves during and after voltages sags, measured on CHESF’s substations. These curves were used as estimation data to parameterize load models for each substation chosen.

[pt] Este trabalho apresenta um método recursivo de identificação dos parâmetros de um sistema linear, invariante no tempo, a tempo discreto, determinístico e monovariável. Como característica desse método pode-se destacar: O número de passos é igual ao número de parâmetros a determinar. Não há necessidade de inversões de matrizes nem de cálculos de determinantes. O sistema não precisa estar previamente relaxado; as condições iniciais podem ser diferentes de zero. A ordem pode ser determinada durante o processamento das amostras. A implementação em computadores digitais é simples. / [en] This work presents a method for on-line identification of the parameters of a linear, time-invariant, discrete time, monovariable, deterministic system. The caracteristics of the method are: number of steps equal to the number of unknown parameters. no matrices need to be inverted and no determinants need to be calculated. no system need to be previouly relaxed, the inicial conditions could be different from zero. the system order determination could be done during the sample processing. the implementation in a computer is simple.