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The majority of three‐phase dynamic transformer models used in commercially available electric power system transient simulation programs offer only saturated three‐phase transformer models built from three single‐phase transformer models. This paper sets out to deal with the modelling and transient analysis of a saturated three‐limb core‐type transformer.

Three iron core models I‐III are given by the current‐dependent characteristics of flux linkages. In the first model, these characteristics are given by a set of piecewise linear functions, which include saturation. In the second model, the piecewise linear functions are replaced by the measured nonlinear characteristic. The more complex third model is given by a set of measured flux linkage characteristics.

The behaviour of transformers used in electric power applications depends considerably on the properties of magnetically nonlinear iron core. The best agreement between the calculated and measured results is obtained by use of the most complex iron core model III, which takes into account magnetic cross‐couplings between different limbs, caused by saturation.

Measurement of the current‐dependent flux linkage characteristics of the 0.4 kV, 3.5 kVA laboratory transformer requires corresponding excitation of windings by three independent linear amplifiers. Current‐dependent flux linkage characteristics of the larger power transformer can be determined either by similar measurement with linear amplifiers of an appropriate power or by extracting them from the calculated magnetic field, which is done by the finite element method.

A three‐phase dynamic transformer model with the obtained iron core model III is suitable for the numerical analysis of nonsymmetric transient states in power systems.

This paper presents a three‐phase dynamic transformer model with an original iron core model III, which accounts for magnetic cross‐couplings between different limbs, caused by saturation.

The purpose of this paper is to investigate the applicability of a direct current (DC) hysteresis measurement on power transformer terminals for the subsequent hysteresis model parametrization in transformer grey box topology models.

Two transformer topology models with two different hysteresis models are used together with a DC hysteresis measurement via the power transformer terminals to parameterize the hysteresis models by means of an optimization. The calculated current waveform with the derived model in the transformer no-load condition is compared to the measured no-load current waveforms to validate the model.

The proposed DC hysteresis measurement via the power transformer terminals is suitable to parametrize two hysteresis models implemented in transformer topology models to calculate the no-load current waveforms.

Different approaches for the measurement and utilization of transformer terminal measurements for the hysteresis model parametrization are discussed in literature. The transformer topology models, derived with the presented approach, are able to reproduce the transformer no-load current waveform with acceptable accuracy.

This paper aims to improve the finite element modelling of transformers subjected to DC excitation, by including core joint details.

Geomagnetically induced currents (GICs) or leakage DC can cause part-cycle, half wave saturation of a power transformer’s core. Practical measurements and finite element matrix (FEM) simulation were carried out using three laboratory-scale, untanked single-phase four limb transformers resembling real power transformers in terms of the core steel and parallel winding assemblies. “Equivalent air gaps” at the joints, based on AC measurements, were applied to the FEM models for simultaneous AC and DC excitation.

Measurements confirm that introducing equivalent air gaps at the joints improves the FEM simulation of transformers carrying DC.

The FEM simulations based on the laboratory transformers are exemplary, showing the difference between modelling core joints as solid or including equivalent air gaps. They show that, for more representative results, laboratory transformers used for research should have mitred core joints (like power transformers).

This research shows why joint details are important in FEM models for analysing transformer core saturation in the presence of DC/GICs. Extending this, other core structures of power transformers with mitred joints should improve the understanding of the leakage flux during half-wave saturation.

The purpose of this paper is to describe a technique for modeling transformer internal faults using transmission line modeling (TLM) method. In this technique, a model for simulating a two winding single phase transformer is modified to be suitable for simulating an internal fault in both windings.

TLM technique is mainly used for modeling transformer internal faults. This was first developed in early 1970s for modeling two‐dimensional field problems. Since, then, it has been extended to cover three dimensional problems and circuit simulations. This technique helps to solve integro‐differential equations of the analyzed circuit. TLM simulations of a single phase transformer are compared to a custom built transformer in laboratory environment.

It has been concluded from the real time studies that if an internal fault occurs on the primary or secondary winding, the primary current will increase a bit and secondary current does not change much. However, a very big circulating current flows in the shorted turns. This phenomenon requires a detailed modeling aspect in TLM simulations. Therefore, a detailed inductance calculation including leakages is included in the simulations. This is a very important point in testing and evaluating protective relays. Since, the remnant flux in the transformer core is unknown at the beginning of the TLM simulation, all TLM initial conditions are accepted as zero.

The modeling technique presented in this paper is based on a low frequency (up to a few kHz) model of the custom‐built transformer. A detailed capacitance model must be added to obtain a high‐frequency model of the transformer. A detailed arc model, aging problem of the windings will be applied to model with TLM + finite element method.

Using TLM technique for dynamical modeling of transformer internal faults is the main contribution. This is an extended version of an earlier referenced paper of the authors and includes inductance calculation, leakages calculation, and BH curve simulation while the referenced paper only includes piecewise linear inductance values. This modeling approach may help power engineers and power system experts understand the behavior of the transformer under internal faults.

The purpose of this study is to develop a topological model of a three-phase, three-limb transformer for low-frequency transients. The processes in the core limbs and yokes are reproduced individually by means of a dynamic hysteresis model (DHM). A method of accounting for the transformer tank with vertical magnetic shunts at the tank walls is proposed and tested on a 120 MVA power transformer.

The model proposed has been implemented independently in a dedicated Fortran program and in the graphical pre-processor ATPDraw to the ATP version of the electromagnetic transient program.

It was found that the loss prediction in a wide range of terminal voltages can only be achieved using a DHM with variable excess field component. The zero sequence properties of the transformer can be accurately reproduced by a duality-derived model with Cauer circuits representing tank wall sections (belts).

In its present form, the model proposed is suitable for low-frequency studies. Its usage in the case when transformer capacitances are involved should be studied additionally.

The presented model can be used either as an independent tool or serve as a reference for subsequent simplifications.

The model proposed is aimed at meeting the needs of electrical engineering and ecology-minded customers.

Till date, there were no experimental data on zero-sequence behavior of three-phase, three-limb transformer with vertical magnetic shunts, so no verified transient model existed. The model proposed is probably the first that matched this behavior and reproduced measured no-load losses for a wide voltage range.

To make easier and faster the designing of transformers using scale models.

The scale modeling in designing of transformers is included. Both computer and physical models of high leakage reactance (HLR) and 3‐phase (TP3C) transformers have been considered. The 3D field computations have been executed for the scaled models, and the results were recalculated to the full‐scaled ones.

It is possible to calculate the scale coefficients for nonlinear models of transformers using finite element method (FEM) software. Obtained coefficients are useful in the designing process. Measurements confirm correctness of the scaling laws.

The calculations were done only for transformers and the eddy current was not taken into account.

Presented formulae for scale model calculation are very useful for designing of transformers by the engineers. It is possible to design a series of transformers. Only one physical model must be manufactured for experimental verification.

This paper offers an innovative approach to non‐linear scaled modelling of transformers using FEM.

The aim is to develop a nonlinear transformer model to achieve an accurate model to obtain the frequency components of the magnetizing current based on the harmonic voltages at the primary and secondary side. So, it can easily be implemented in a harmonic load‐flow program.

The transformer model is based on the harmonic balance method. The electric and magnetic equations of the transformer are derived from the electric and magnetic equivalent circuits.

The transformer model can be easily implemented in a harmonic load‐flow program. The accuracy of the model has been shown by comparing it with a finite element simulation. The transformer model can be used with asymmetrical supply voltages, because different saturation levels of the phases can occur. There is a coupling between the phases which can be concluded out of the asymmetrical currents in the transformer under symmetrical supply voltages.

The transformer model does not consider the iron losses and the interharmonics. In future work the transformer model will be used to study the harmonic losses in distribution networks, so the transformer losses due to these harmonics have to be considered. This can be achieved with a postcalculation process where the magnetic flux density is used to calculate the eddy current losses and the magnetic field intensity will be applied in a static Preisach model to quantify the hysteresis losses.

The model can be used in a harmonic load‐flow program in order to obtain more accurate simulations for the power system analysis and design.

The model presented in this paper is more detailed than similar papers found in literature (saturation of the yokes, coupling between the phases, interaction between different harmonics) and still it takes a brief simulation time.

COVID-19 continues to spread, and cause increasing deaths. Physicians diagnose COVID-19 using not only real-time polymerase chain reaction but also the computed tomography (CT) and chest x-ray (CXR) modalities, depending on the stage of infection. However, with so many patients and so few doctors, it has become difficult to keep abreast of the disease. Deep learning models have been developed in order to assist in this respect, and vision transformers are currently state-of-the-art methods, but most techniques currently focus only on one modality (CXR).

This work aims to leverage the benefits of both CT and CXR to improve COVID-19 diagnosis. This paper studies the differences between using convolutional MobileNetV2, ViT DeiT and Swin Transformer models when training from scratch and pretraining on the MedNIST medical dataset rather than the ImageNet dataset of natural images. The comparison is made by reporting six performance metrics, the Scott–Knott Effect Size Difference, Wilcoxon statistical test and the Borda Count method. We also use the Grad-CAM algorithm to study the model's interpretability. Finally, the model's robustness is tested by evaluating it on Gaussian noised images.

Although pretrained MobileNetV2 was the best model in terms of performance, the best model in terms of performance, interpretability, and robustness to noise is the trained from scratch Swin Transformer using the CXR (accuracy = 93.21 per cent) and CT (accuracy = 94.14 per cent) modalities.

Models compared are pretrained on MedNIST and leverage both the CT and CXR modalities.

This paper aims to present and define a factor to assess the severity supported along transformer windings when the transformer is subjected to a transient voltage waveform due a switching operation of a vacuum circuit breaker (VCB). This factor is identified as time domain severity factor (TDSF).

Since each of switching waveforms depend on the electrical interaction between transformer and the VCB, it implies that each of those combinations is characterized by a TDSF. To obtain the TDSF implies to manage two different models of the transformer under consideration. Firstly, a terminal model (black box model) of the transformer is built to compute the switching waveform at transformer terminals during VCB operation. Then, a detailed model (white box model) of the transformer is used to compute the internal transient voltage distribution along transformer windings.

A practical application of a power system consisting of a real transformer connected to a VCB is performed to show the sensibility of the TDSF coefficient.

Previous works found in the literature already consider the evaluation of the overvoltages in transformer associated to switching transient by coefficients, such as the frequency domain severity factor (FDSF). But this factor, as a global coefficient, could not assess the severity along windings to localize dielectrically weak points. Therefore, this paper overcomes this limitation proposing an alternative coefficient identified as time domain severity factor (TDSF).

The paper presents a mathematical model for the hysteresis phenomenon in a multi-winding single-phase core type transformer. The set of loop differential equations was developed for Kth winding transformer model where the flux linkages of each winding includes a flux common Φ to all windings as function of magneto motive force Θ of all windings. The purpose of this paper is to first determine a hysteresis nonlinearity involved in Φ(Θ) function using modified Preisach theory and second to develop new analytical formula of Preisach distribution function (PDF).

It is assumed in this paper that flux linkage characteristics Ψ(i) of each winding have nonlinear component due to the magnetization characteristic of the steel core and sum of linear components due to the self and mutual leakage fluxes. This nonlinear component of Ψ(i) characteristic can be expressed as a flux common Φ to all windings vs ampere-turns Θ of all windings. The nonlinear flux linkage characteristics Ψ(i) of the tested transformer are calculated from the set of measured terminal voltages and terminal currents. To simulate magnetic behavior of the iron core the feedback scalar Preisach model of hysteresis is proposed which gives more accurate predictions than classical model. For this hysteresis model the PDF and feedback function are needed. The intend of this paper is to find these function as an analytical formulas which are convenient for numerical simulations. For identification of the PDF and feedback function parameters of the considered iron core of tested transformer the Levenberg-Marquardt optimization algorithm was used.

The flux common to all windings is calculated by integrating the induced voltages of the appropriate windings. In this paper the PDF is proposed as a functional series including two dimensional Gauss expressions. In order to proper approximation of hysteresis nonlinearity of the tested iron core the first three terms of functional series of the PDF have been used. In the optimization algorithm only initial and descending limiting hysteresis curves Φ(Θ) were utilized. The feedback function for proposed hysteresis model is assumed as third-order polynomial. The hysteresis model has been successfully validated by comparing the calculated and measured results of Φ(Θ) hysteresis curves. This hysteresis model can be used in transient and steady state simulations of tested transformer taking into account the hysteresis phenomenon. The developed hysteresis model can be also used for analysis of the influence of remnant flux on the operation of tested transformer especially in transient states.

In this paper the feedback Preisach hysteresis model is involved in the flux common to all windings vs ampere-turns of all windings. The new PDF is proposed as functional series including two dimensional Gauss expressions. For tested transformer the three first terms of this functional series may be used for proper approximation of hysteresis nonlinearities.