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Using appropriate solution techniques for transformer inrush current transient study is of great prominence owing to the inevitable inclusion of differential equations leading to complicated analysis procedures. This study aims to propose an analytical-numerical method to accurately analyze the three-phase three-limb core-type transformer inrush current in different cases considering the nonlinear behavior of the iron core.

The proposed method focuses on acquiring equations for inrush current and also the magnetic core flux by the application of a simulation-based iterative approach. In this regard, multiple integral equations are solved taking the time intervals into account. Then several derivations and integrations of matrix terms are substituted into the obtained results so as to simplify the solution process.

The method provides notable enhancements in computation time and also excellent qualities of accuracy compared with conventional numerical methods.

The proposed method is simulated for two three-phase transformers via MATLAB software. The obtained simulation results have been also compared with experimental tests.

Actually, the analytical-numerical method is capable of computing higher number of iterations in a shorter time efficiently, while making use of the conventional numerical procedures may not result in expected convergences. The simulation results of the proposed analytical-numerical technique illustrate a close agreement with the experimental test, and hence, verify the method preciousness.

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.

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.

Calculation of flux distribution in three‐phase three‐limb transformer core has been made using 2D finite element method. The calculation has been performed with and without taking into account lthe hysteresis of magnetic material. Anisotropy of magnetic material has been modelled through the so‐called elliptic permeability model. Comparison of results of calculation and results of measurement has been performed for a scale model of transformer core. An agreement better than 3 per cent has been obtained, for calculated and measured results of third harmonics and of flux distortion factors, when hysteresis has been taken into account. The CPU‐time was 6–10 times longer when hysteresis has been included into calculation.

This paper deals with a coupled field‐circuit simulation of transients in a three‐phase, three‐limb power transformer taking non‐linearity into consideration. A comparative analysis of the results obtained from the application of 3D and 2D field models has been carried out. Owing to core saturation and the non‐periodic components of the magnetic fluxes, the magnetic field exists also within the space surrounding the core. Hence, three‐dimensional description is necessary. It has been proved that assuming the 2D model significantly overstated peak values of currents are obtained.

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.

To maintain quality, performance and competitiveness, the eddy current losses in metal parts of power transformers in the range of 50‐200 MVA are investigated in a more detailed form. The finite element calculations utilize different modelling strategies for the current carrying metal parts. Several global and local results are further used to obtain simplified calculation approaches for an inclusion in the initial design and the design optimization. The results from two finite element approaches using nodal and edge based formulations will be compared with measurements.

The finite element technique has been used to develop a software package which, with the help of an IBM/PC 386 computer, can determine two dimensional magnetic fields and power loss in transformer cores. The program takes into account both the non‐linear B‐H characteristic and the anisotropy of the core material.

The purpose of this paper is to present a new type of equivalent scheme of multi‐winding transformers.

An inventory representation of relations between currents and flux linkages has been interpreted as a multi‐port purely inductive circuit.

An equivalent scheme in the form of a multi‐port circuit, and a method of its parameters determination from field computations.

Core losses are not considered in the multi‐port equivalent scheme.

A new equivalent scheme could become a basic tool for modeling multi‐winding transformers.

The introduced multi‐port equivalent scheme eliminates disadvantages of classical T‐type equivalent scheme of transformers.

This paper deals with the modelling of transformer supply in the two‐dimensional (2D) finite element (FE) simulation of rotating electrical machines. Three different transformer models are compared. The reference one is based on two 2D FE models, considering a cross‐section either parallel or perpendicular to the laminations of the magnetic core. The parameters of the two other transformer models, a magnetic equivalent circuit and an electrical equivalent circuit, can be derived from the reference model. Particular attention is paid to some common features of the transformer models, e.g. with regard to the inclusion of iron losses. The three models are used in the 2D FE simulation of the steady‐state load operation and the starting from stand‐still of an induction motor.