3-D high frequency computation of transformer R, L parameters (original) (raw)
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Fast computation of R, L parameters of high frequency multi-winding magnetic components
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2011
Purpose-The purpose of this paper is to propose a numerical procedure for the extraction of RL equivalent circuits of high frequency multi-winding transformers with a low computational time. Design/methodology/approach-Rigorous RL equivalent circuits of multi-winding transformers can be obtained by performing open and short-circuit tests. In this work, the finite element method (FEM) is employed as a virtual laboratory in order to derive such circuits. However, an accurate modeling of skin and proximity effects in the windings requires extremely dense meshes at high frequencies. Therefore, a 2D frequency-domain homogenization of the windings, which conducts to coarser meshes, is applied in order to decrease the computational burden. The fine and homogenized models are compared in terms of simulation time as well as accuracy. Findings-A significant decrease in simulation times is observed with the homogenized model (one order of magnitude at high frequencies for 2D models), while keeping acceptable relative error values (below 8 percent in the worst case, taking the fine model as reference). Furthermore, it is shown that the skin effect could contribute in a significant way to the total values of the circuit parameters, especially for high frequencies and for small fill factors. It should therefore not be neglected compared to the proximity effect when gathering such conditions, as commonly assumed in the literature. Originality/value-Equivalent circuits which capture the skin and proximity effects are obtained at an acceptable computational cost, thanks to the use of homogenization techniques in FE simulations. To the best of the authors knowledge, such a procedure has not yet been published.
High frequency transformer model derived from limited information about the transformer geometry
International Journal of Electrical Power & Energy Systems, 2018
To represent transformer behaviour during a transient state which includes high frequencies, it is necessary to consider the resonances which occur inside the transformer. One strategy is to deduce the transformer model from the measurements of the transformer's frequency response, another one is to construct the model based on a careful representation of the inside of the apparatus. In the paper a model is presented which is compatible with EMTP-type software programs based on a finite element method (FEM) calculations and the complex permeability approximation. The model can be classified as a Grey Box transformer model, according to the terminology of the CIGRE. The model's frequency dependent parameters are derived from limited information about the transformer geometry. State space equations are used to input the model into an electromagnetic transient calculation software program. This approach requires specific mathematical treatments to avoid stability issues during simulations. The model is validated for lightning impulse studies using the field test measurements of overvoltages that had occurred at the external transformer's terminals.
Quasi-3-D Finite-Element Modeling of a Power Transformer
A strong circuit-field coupling technique that can analyze multiple magnetic field systems (2-D Cartesian and axisymmetric) is adapted to study power transformers. The technique is based on finite-element (FE) and modified nodal analyses, leading to a multi-field system approach that can effectively take account of the 3-D magnetic field existing inside and outside the transformer core. Hence, cumbersome 3-D FE simulations are circumvented, overcoming high computational costs. A 2-D Cartesian FE model is set up to represent the cross section of the transformer core and its three-phase winding, whereas an axisymmetric representation is employed for the end sections of each set of windings (one per phase). All models and their associated circuit systems are simultaneously solved, providing a circuit-field method that is easy to implement at low computational cost, keeping the well-known advantages of 2-D FE modeling. Electrical currents and local values of magnetic flux density are calculated for two limiting conditions: rated load and short-circuit operation. Our approach shows a remarkably small difference (no higher than 1%) with a full 3-D FE model. Index Terms— End-winding effects, finite-element (FE) analysis, power transformer, short-circuit condition, strong coupling method.
Difficulties in high frequency transformer modeling
Electric Power Systems Research, 2016
Traditional transformer models available in EMTP-like software packages are not capable of representing transformer behavior during a transient state, which includes high frequencies, since they usually do not adequately take into account the transformer resonant behavior caused by its highly complicated design. Therefore, more complex "Black box" models are developed. Those models can be established without any knowledge of transformer geometry, based on the fitting of the measured admittance matrix of the transformer versus frequency. Unfortunately, the measurement and exploitation of a transformer's admittance matrix are not straightforward. The existing fitting methods include solving a non-convex constrained problem. Hence, it is not always easy to find an optimal solution of the problem. The difficulties, which can arise when building a high frequency "Black box" transformer model, are described in this paper together with a comparison of the performance and fitting accuracy of different numerical packages.
Recent Developments in the Modelling of Transformer Windings
2021
The paper provides a review of the modelling techniques used to simulate the frequency response of transformer windings. The aim of the research and development of modelling methods was to analyze the influence of deformations and faults in the windings on the changes in the frequency response. All described methods are given with examples of the modelling results performed by the authors of this paper and from literature sources. The research is prefaced with a thorough literature review. There are described models based on lumped parameters with input data coming from direct calculations based on the winding geometry and obtained from FEM modelling software and models considering the wave phenomena in the windings. The analysis was also performed for practical problems in winding modelling: the influence of windings other than the modelled one and the influence of parallel wires in a winding.
Applied Sciences
One of the standard diagnostic methods for power transformers is frequency response analysis (FRA). This paper deals with progress in the frequency response interpretation of these very important appliances in the power network. Simulations of the frequency response of the transformer windings are a useful way to improve the correct assessment of FRA results. One of the disadvantages of FRA modelling is time-consuming analysis, especially of large multilayer windings. The aim of this article is to develop a numerical model, which would reduce the duration of the electromagnetic field analysis of the winding with hundreds of turns. The approach introduced in the paper describes the simple two-dimensional (2D) finite elements method (FEM) model, which provides the results comparable to the three-dimensional (3D) model. Moreover, the paper presents the numerical models, which demonstrate the influence of the remaining windings on the inductance of tested winding. As a result of the con...
IEEE Transactions on Magnetics, 2000
This paper presents a 2-D finite-element model to analyze the iron losses in a three-phase transformer. In this model, the effects of nonlinear core behavior are taken into account by means of a vector hysteresis model incorporated in the finite-element formulation by using a magnetic differential reluctivity tensor. The reluctivity tensor emerges naturally from the vectorized Jiles-Atherton model. The complete model includes eddy current losses and the anomalous losses. The magnetization currents are calculated and compared with the measured ones. Calculations of hysteresis loops at spotted points of the transformer are also performed. The comparisons between the iron losses measured and calculated with vectorial hysteresis, including the eddy current and the anomalous losses, are presented. Index Terms-Anomalous losses, eddy current losses, finite-element method (FEM), three-phase transformer, vector hysteresis model.
High frequency transformer design and modelling using finite element technique
2000
The field of high power density power supplies has received much attention in recent years. The area of the most concern is to increase the switching frequency so as to achieve a reduction in the power supply size. Such concern in high frequency power conversion units has led to many resonant structures (quasi, multi, and pseudo). In all resonant types, the power transfer from the source to the load is controlled by varying the ratio of operating to resonant frequencies. Every effort has been made to reduce the switching losses using zero voltage and/or zero current techniques. In contrast, little attention has been given to the area of the design of the magnetic components at high frequency operation. It is usually accepted that the weak point in further high frequency power supply design is in the magnetic devices ( transformer and inductor ). No accurate model of the transformer taking into account the high frequency range has been performed yet. It is well known that as the freq...
The simulation of a new high frequency transformer
Journal of Energy Systems
Core losses of transformers motivate many engineers and scientists to design and implement different transformers for their specific aims. Since there exists a growing interest on high frequency applications in today’s world, design and optimization studies of a magnetic fluid core transformer (MFCT), having an easy and cheap production approach in high frequency applications, are considered in the present paper. The desired design should operate in a more efficient way within a wide frequency band. The MFCT considered here can be a solution to the eddy currents and core losses encountered in the conventional transformers with its low conductivity, oil-based magnetic fluid and super paramagnetic characteristic. The magnetic fluid in the proposed work consists of a combination of ferromagnetic particles made by iron in an averaged diameter of 70 µm with an adjustable magnetism compared to the traditional magnetic fluids and an engine oil, thereby the magnetic permeability of the over...