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

Orthogonal-least-squares regression: A unified approach for data modelling

A unified approach is proposed for data modelling that includes supervised regression and classification applications as well as unsupervised probability density function estimation. The orthogonal-least-squares regression based on the leave-one-out test criteria is formulated within this unified data-modelling framework to construct sparse kernel models that generalise well. Examples from regression, classification and density estimation applications are used to illustrate the effectiveness of this generic data-modelling approach for constructing parsimonious kernel models with excellent generalisation capability. (C) 2008 Elsevier B.V. All rights reserved.

Numerical investigations of linear least squares methods for derivative estimation

The results of a numerical investigation into the errors for least squares estimates of function gradients are presented. The underlying algorithm is obtained by constructing a least squares problem using a truncated Taylor expansion. An error bound associated with this method contains in its numerator terms related to the Taylor series remainder, while its denominator contains the smallest singular value of the least squares matrix. Perhaps for this reason the error bounds are often found to be pessimistic by several orders of magnitude. The circumstance under which these poor estimates arise is elucidated and an empirical correction of the theoretical error bounds is conjectured and investigated numerically. This is followed by an indication of how the conjecture is supported by a rigorous argument.

Parameter estimation in water-distribution systems by least squares

The weighted-least-squares method using sensitivity-analysis technique is proposed for the estimation of parameters in water-distribution systems. The parameters considered are the Hazen-Williams coefficients for the pipes. The objective function used is the sum of the weighted squares of the differences between the computed and the observed values of the variables. The weighted-least-squares method can elegantly handle multiple loading conditions with mixed types of measurements such as heads and consumptions, different sets and number of measurements for each loading condition, and modifications in the network configuration due to inclusion or exclusion of some pipes affected by valve operations in each loading condition. Uncertainty in parameter estimates can also be obtained. The method is applied for the estimation of parameters in a metropolitan urban water-distribution system in India.

Least Squares Estimation Principle and its Geometrical Interpretation

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Seismic model parameter estimation using least-squares migration

We describe a method for verifying seismic modelling parameters. It is equivalent to performing several iterations of unconstrained least-squares migration (LSM). The approach allows the comparison of modelling/imaging parameter configurations with greater confidence than simply viewing the migrated images. The method is best suited to determining discrete parameters but can be used for continuous parameters albeit with greater computational expense.

Weighted and two-stage least squares estimation of semiparametric truncated regression models

This paper provides a root-n consistent, asymptotically normal weighted least squares estimator of the coefficients in a truncated regression model. The distribution of the errors is unknown and permits general forms of unknown heteroskedasticity. Also provided is an instrumental variables based two-stage least squares estimator for this model, which can be used when some regressors are endogenous, mismeasured, or otherwise correlated with the errors. A simulation study indicates that the new estimators perform well in finite samples. Our limiting distribution theory includes a new asymptotic trimming result addressing the boundary bias in first-stage density estimation without knowledge of the support boundary. © 2007 Cambridge University Press.

Fast sequential multi-element determination of Ca, Mg, K, Cu, Fe, Mn and Zn for foliar diagnosis using high-resolution continuum source flame atomic absorption spectrometry: Feasibility of secondary lines, side pixel registration and least-squares background correction

The fast sequential multi-element determination of Ca, Mg, K, Cu, Fe, Mn and Zn in plant tissues by high-resolution continuum source flame atomic absorption spectrometry is proposed. For this, the main lines for Cu (324.754 nm), Fe (248.327 nm), Mn (279.482 nm) and Zn (213.857 nm) were selected, and the secondary lines for Ca (239.856 nm), Mg (202.582 nm) and K (404.414 nm) were evaluated. The side pixel registration approach was studied to reduce sensitivity and extend the linear working range for Mg by measuring at wings (202.576 nm; 202.577 nm; 202.578 nm; 202.580 nm: 202.585 nm; 202.586 nm: 202.587 nm; 202.588 nm) of the secondary line. The interference caused by NO bands on Zn at 213.857 nm was removed using the least-squares background correction. Using the main lines for Cu, Fe, Mn and Zn, secondary lines for Ca and K, and line wing at 202.588 nm for Mg, and 5 mL min(-1) sample flow-rate, calibration curves in the 0.1-0.5 mg L-1 Cu, 0.5-4.0 mg L-1 Fe, 0.5-4.0 mg L-1 Mn, 0.2-1.0 mg L-1 Zn, 10.0-100.0 mg L-1 Ca, 5.0-40.0 mg L-1 Mg and 50.0-250.0 mg L-1 K ranges were consistently obtained. Accuracy and precision were evaluated after analysis of five plant standard reference materials. Results were in agreement at a 95% confidence level (paired t-test) with certified values. The proposed method was applied to digests of sugar-cane leaves and results were close to those obtained by line-source flame atomic absorption spectrometry. Recoveries of Ca, Mg, K, Cu, Fe, Mn and Zn in the 89-103%, 84-107%, 87-103%, 85-105%, 92-106%, 91-114%, 96-114% intervals, respectively, were obtained. The limits of detection were 0.6 mg L-1 Ca, 0.4 mg L-1 Mg, 0.4 mg L-1 K, 7.7 mu g L-1 Cu, 7.7 mu g L-1 Fe, 1.5 mu g L-1 Mn and 5.9 mu g L-1 Zn. (C) 2009 Elsevier B.V. All rights reserved.