Model Of Power Transformer Research Articles

A systematic approach to evaluate the overall impact of the electric traction demands of a high-speed railroad on a power system

This paper introduces a systematic approach to the evaluation of the overall impact of the electric traction demands of a high-speed railroad (HSR) on a power system. These large unbalanced traction loads may cause system voltage and current unbalances and, therefore, overheat rotating machines, increase system losses, interfere with neighboring communication systems, and cause protection relays and measuring instruments to malfunction. Some of these problems may significantly affect the operation of the power system and other equipment connected to it. Hence, the proposed approach is oriented toward applications in system operation analysis rather than planning analysis. On the basis of the Newton-Raphson algorithm, a three-phase powerflow program was developed. In this program, most of the component models and solution techniques are those that were developed for three-phase power-flow studies. They are applied to accurately simulate a three-phase high-voltage network supplying the traction loads. Rigorous component models, such as generator, transmission line, power transformer and traction substation models, were incorporated into this program. By combining the electric demands of traction substations along an HSR, this program can be used to evaluate the overall impact of traction loads on a power system. On the basis of the simulation results, related improvement projects can be evaluated and conducted if necessary. This approach has been successfully tested on Taiwan's power system (Taipower system), to which the power-supply system of a planned HSR will be connected in the near future.

High-frequency power transformer model for circuit simulation

A model for the circuit simulation of transformers used in high-frequency power processing is proposed. Many important transformer effects are combined in a single formulation. An Atherton-Jiles model with improved minor-loop handling ability is employed to simulate the hysteresis effect in the magnetic core. Eddy currents and skin and proximity effects are simulated by dynamically approximating the field and flux distributions in the entire structure. Leakage fluxes, capacitive couplings and the influence of temperature on electric and magnetic materials are also included. The parameters needed for simulation are magnetic material characteristics, available in data sheets, core geometry and winding geometry. The model was implemented (built) in the source code of SPICE3.

Analysis of leakage magnetic problems in shell-form power transformer

The principles of minimized magnetic energy and voltage equilibrium have been combined with the finite element method to solve the leakage magnetic field problems coupled with an unknown ampere-turn distribution in shell-form power transformers. Based on the leakage magnetic field calculated, the eddy current and circulating current losses in the coils are further computed. The calculated results are consistent with measured values for a model of a shell-form power transformer. The above principles are applied to the windings design of a 50 MVA three-phase prototype shell-form power transformer. The calculated results show that the largest circulating current in strands of the low-voltage coils near two ends of each phase winding is greatly reduced to 11% from 98% of the rated current in each strand by placing the copper-shieldings on these ends.

Design and performance improvements in power transformers using ribbon cable

An advanced core-form power transformer with significantly lower losses and weight has been produced and brought to commercial status. First, a number of designs and design studies were made on actual medium power transformer specifications. Several windability models were built, as well as a complete 250 kVA core-form advanced power transformer model to develop the new manufacturing technology and to verify many performance characteristics of the new technology. Then extensive thermal, short-circuit strength, and loss studies were made. Finally, a cooperating electric utility ordered two units, one conventional and one advanced, to the same specification to provide ideal conditions for the verification of the new technology. Construction and test of the prototype proceeded without incident. Full verification was achieved for all aspects of the technology: dielectric design, thermal design, short-circuit strength, loss performance, impedance, noise level, and manufacturability. The prototype was installed and energized in 1991 and continues in operation today. Subsequently, other units were built and tested, with performance results confirming the technology.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Shell-form power transformer modelling at high frequencies

The electromagnetic duality principle is used for transformer modelling. The proposed method is presented. The calculation complexity of the rectangular winding parameters is reduced using a conformal mapping method and the boundary element method. The model parameters are directly calculated from the physical geometry by the finite element method or analytical formulations. The transformer modelling provides a good accuracy for the frequency dependent characteristics of the transformers. Comparisons between computation results and measurements are in good agreement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Dynamic model of a three-phase power transformer

An adequate mathematical model of a three-phase power transformer is one of the important elements in the programs for the computer analysis of power system transients. Featured in this paper is the simulation model of a three-phase, three-limb core-type power transformer. Nonlinear effects of saturation, hysteresis and eddy currents are considered. Two ways of creating major and minor hysteresis loops are presented. The transformer model, described by a system of time dependent differential equations, is solved by an efficient numerical algorithm. The behaviour of the transformer model during switching-in and fault transients, as well as other types of transients, has been tested. The computed transient waveforms are compared with the measured ones and there exists very close agreement between them.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sensitivity analysis for Box-Cox power transformation model: Contrast parameters

SUMMARY Sensitivity analysis is an important tool for the evaluation of scientific models. We consider the Box-Cox power transformation model and study the sensitivity for the estimated slope vector when the transformation parameter is perturbed. This is a key issue in the debate among Bickel & Doksum (1981), Box & Cox (1982) and Hinkley & Runger (1984) on the application of the power transformation model. Hinkley & Runger (1984) conjectured that Box & Cox's (1964) z transformation would eliminate asymptotically the sensitivity for the estimated slope vector. We establish this conjecture under appropriate symmetry conditions on the joint distribution for the regressors, x. When the true transformation is logarithmic, the conjecture holds if the distribution for x is axially symmetric. For other power transformations, the conjecture holds if x is multivariate normal. We also consider a weaker version of Hinkley & Runger's conjecture, namely, the z transformation would achieve the best possible reduction in the sensitivity. We establish this weaker conjecture under less restrictive symmetry conditions which only involve the marginal distribution for xfl. Both conjectures might fail when those symmetry conditions are not satisfied. Two examples are given to illustrate the limitations of the conjectures. Sensitivity analysis is an important tool for the evaluation of scientific models. Many scientific models include some nuisance parameters which are not known precisely. It is usually desirable for the model output to be stable with respect to those parameters. The performance of the model can be questionable if the model output is highly sensitive to those parameters. It is therefore useful to carry out a sensitivity analysis, in which those parameters are perturbed, the model output is derived under the perturbed parameters and compared with the model output prior to the perturbation. We will study the sensitivity analysis for the Box-Cox power transformation model with respect to the specific transformation taken. Let {(yi, xi), i = 1, . . . , n} be the observed data, where yi denotes a positive scalar outcome, and xi denotes a p-dimensional row vector of regressors. Let the transformed outcome be

Transient overvoltage study and model for shell-type power transformers

In order to calculate winding resonances of shell-type power transformers under lightning impulses, an accurate RLC model of the transformer taking into account frequency dependence, is presented. RLC parameters are calculated using analytical and finite element methods. An interactive computer model has been developed and allows automatic generation and calculation of the network elements. The classical network method is used for the frequency study. Transient overvoltages of the transformer are calculated from the frequency response by Fourier transform. Good agreement between experimental and numerical results shows that the model is well adapted to predict windings overvoltages. >

A method for wide frequency range modeling of power transformers and rotating machines

Wide frequency range representation of power system components such as power transformers, reactors and rotating machines is mainly needed for the analysis of electromagnetic transients in power systems. In this paper, a method is presented for state space formulation of machine windings. The described procedure is completely based on external terminal impedance measurements and data related to the internal structure is not required. First, the wide frequency behavior of machine windings is reviewed and the nonlinearity effects of the iron core are discussed. A numerical method is given for calculation of the state equation parameters directly from the measured terminal impedance characteristics. The presented modeling method is applicable to any transformer, reactor or rotating machine in service where sufficient information on the internal design is not available. Besides, the canonical structure of the model offers advantages in terms of computer memory and computation effort in time domain analyses of complex power systems. >

Generalised modelling of power transformers in the harmonic domain

The periodic nonlinear behavior of a multilimb three-phase transformer is modeled in the harmonic domain, a frame of reference which allows cross-couplings between phases and between harmonics to be explicitly represented. The magnetic equivalent circuit is derived from the individual magnetizing characteristics of the core branches. The linearized transformer model, in the form of a harmonic Norton equivalent, is combined with the linear part of the electric network, and solved using a unified iterative procedure. The numerical solution involves a Newton-type iterative algorithm and a novel sparsity-oriented hybrid technique. Use of the proposed model in a practical transmission system has shown that the harmonic distortion caused by individual and multilimb core transformers is very different, with noticeable reduction in the multilimb case.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Box-coxVs. modulus power family of response transformations

Economic theory provides researchers little guidance when selecting the appropriate estimating functional form model, given the data. The flexible Box and Cox [J. Roy. Stat. Soc., 1964] power transformation model is one relatively simple device for minimizing functional approximation errors in single-equation, least-squares models. However, the Box-Cox may induce heteroscedastic residuals [Sarkar, Comm. Stats.Theory and Methods, 1985] and is only operational for strictly positive data values. Dynamic econometric models often involve variables calibrated in differences--not levels. Difference data containing negative values incapacitate Box-Cox transformations. Therefore, John and Draper [Appl. Stats., 1980] proposed the modulus alternative power family of transformations. Currently, implementation of the Modulus for econometric modelling does not exist in the literature. The purpose of this note is to increase the awareness of the Modulus and point out its usefulness when the Box-Cox is incapacitated. Consider the general linear model:

A note on the cost of estimating the ratio of regression parameters after fitting a power transformation

Abstract The inflation in variance of the ratio of regression parameters, due to estimation of the transformation, in a power transformation model with two independent variables is considered. It is shown that the cost of estimating the transformation parameter is generally small and frequently zero. This is in contrast to the results of Bickel and Doksum (1981), who show that the inflation in variance of a single regression parameter can be extremely large. A small study of the effect of the design and parameter values on the inflation in variance of the ratio of parameters, shows that the design of the independent variables is an important determinant of the variance inflation. If the design contains no outlying or influential observations the cost of estimating the transformation parameter is very small; however for designs with outliers the cost can be significant, although nowhere near as large as those found by Bickel and Doksum.

Transformations and Influential Observations in Minimum Sum of Absolute Errors Regression

The Box-Cox power transformation model is considered for minimum sum of absolute errors (MSAE) regression. A long-tailed error distribution, specifically the Laplace distribution, is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation. The log-likelihood procedure of Box and Cox (1964) for obtaining the optimal transformation parameter is adapted for Laplace errors and MSAE regression. Graphical methods for detecting the influence of individual observations on the choice of transformation are described. Application to examples illustrates that this approach can provide valuable additional information to the data analyst.

Transformations and Influential Observations in Minimum Sum of Absolute Errors Regression

The Box-Cox power transformation model is considered for minimum sum of absolute errors (MSAE) regression. A long-tailed error distribution, specifically the Laplace distribution, is included and could accommodate observations that in the normal case are outlying or unduly influencing a choice of transformation. The log-likelihood procedure of Box and Cox (1964) for obtaining the optimal transformation parameter is adapted for Laplace errors and MSAE regression. Graphical methods for detecting the influence of individual observations on the choice of transformation are described. Application to examples illustrates that this approach can provide valuable additional information to the data analyst.

An Extension of Partial Likelihood Methods for Proportional Hazard Models to General Transformation Models

Estimates of the linear model parameters in a linear transformation model with unknown increasing transformation are obtained by maximizing a partial likelihood. A resampling scheme (likelihood sampler) is used to compute the maximum partial likelihood estimates. It is shown that for a certain local parameter set where the to noise ratio is small, it is asymptotically possible to estimate the linear model parameters using the partial likelihood as well as if the transformation were known. In the case of the power transformation model with symmetric error distribution, this result is shown to also hold when the distribution of the error in the transformed linear model is unknown and is estimated. Monte Carlo results are used to show that for moderate sample size and small to moderate signal to noise ratio, the asymptotic results are approximately in effect and thus the partial likelihood estimates perform very well. Estimates of the transformation are introduced and it is shown that the estimates, when centered at the transformation and multiplied by $\sqrt{n}$, converge weakly to Gaussian processes.

Parameter Estimation for Power Transformer Models from Time-Domain Data

The existence of power system harmonics has been realized for many years. With the advent of new technologies and more solid state loads, power system harmonics are certain to increase both in amplitude and frequency bandwidth. Signal propagation in power systems depends on transformer impedances. Transformer impedances, on the other hand, are functions of signal frequency as well as input voltage and loading condition. Present power transformer models with single-valued parameters obtained from tests cannot adequately represent the transformer in the presence of harmonics. Accurate modeling of transformers must account for changes in signal frequencies and loading conditions as they occur. This paper presents algorithms for estimation of the parameters of a structurally known transformer model. These algorithms use time-domain data and continuously update the estimates, thereby accounting for changes in operating conditions. The techniques presented here can be applied to three-phase and single-phase N-winding transformers. The results of model identification for a single-phase two-winding transformer is given. The data acquisition system used and the problem of identification in a noisy environment are discussed. The simulated response of the identified model is compared with the transformer actual response.

Power-Transformation for Ordered Categorical Data

We consider in this paper a model of asymmetric power-transformation of response probability explained by linear function of some covariates. This model includes logistic and complementary log-log transformation models as its specific case, so we can use the model to evaluate the appropriateness or the goodness of fit of these models. Then the performances of the asymmetric power-transformation model are evaluated and examined, based on data used in published literatures. And we discuss various issues of diagnoses which may occur in the process of applying the model. Further we consider alternative transformations, and then in comparison with them, we point out the advantages of the asymmetric power-transformation.

Transformations in Regression: A Robust Analysis

We consider two approaches to robust estimation for the Box–Cox power-transformation model. One approach maximizes weighted, modified likelihoods. A second approach bounds a measure of gross-error sensitivity. Among our primary concerns is the performance of these estimators on actual data. In examples that we study, there seem to be only minor differences between these two robust estimators, but they behave rather differently than the maximum likelihood estimator or estimators that bound only the influence of the residuals. These examples show that model selection, determination of the transformation parameter, and outlier identification are fundamentally interconnected.

Transformations in Regression: A Robust Analysis

We consider two approaches to robust estimation for the Box–Cox power-transformation model. One approach maximizes weighted, modified likelihoods. A second approach bounds a measure of gross-error sensitivity. Among our primary concerns is the performance of these estimators on actual data. In examples that we study, there seem to be only minor differences between these two robust estimators, but they behave rather differently than the maximum likelihood estimator or estimators that bound only the influence of the residuals. These examples show that model selection, determination of the transformation parameter, and outlier identification are fundamentally interconnected.

A procedure for the statistical evaluation of Ames Salmonella assay results comparison of results among 4 laboratories

Ames Salomonella test data collected in our laboratory and 3 National Cancer Institue contract laboratories were analyzed to study the distribution of experimental errors associated with the test. It is shown that the Poisson distribution is not appropriate, and that the power transformation model Y = ( Krevertants/plate) λ , with λ = 0.2 as estimated by the methods of Box and Cox, produced a measurement scale of which the experimental errors could be adequately described by a normal (Gaussian) distribution with a constant variance. The modeling procedure enables one to properly use analysis of variance, regression analysis, and Student's t test to analyze Ames Salmonella test results, and well-known statistical quality control procedures to monitor laboratory performance. The method detects weak mutagenic activity and measures the amount and uncertainty of the increase in revertants/plate. The development of the power transformation model in discussed and examples of its use in interpretation of Ames Salmonella assay results are included.