Numerical methods for eddy currents modeling of planar transformers

2010 ◽  
Author(s):  
Jeremie Aime ◽  
Bruno Cogitore ◽  
Gerard Meunier ◽  
Edith Clavel ◽  
Yves Marechal
Keyword(s):  
Numerical Methods ◽  
Eddy Currents

scholarly journals Application of Selected Numerical Methods to Model the Fractional-Order System Behavior of Nonlaminated Magnetic Actuators

2021 ◽  
Author(s):  
Martin Hecht ◽  
Robert Seifert ◽  
Wilfried Hofmann
Keyword(s):  
Numerical Methods ◽  
Fractional Order ◽  
Eddy Currents ◽  
Tracking Error ◽  
Measurement Data ◽  
Analytical Approximation ◽  
Fractional Order System ◽  
Order System ◽  
Model Accuracy ◽  
Magnetic Actuators

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.

scholarly journals Application of Selected Numerical Methods to Model the Fractional-Order System Behavior of Nonlaminated Magnetic Actuators

2021 ◽  
Author(s):  
Martin Hecht ◽  
Robert Seifert ◽  
Wilfried Hofmann
Keyword(s):  
Numerical Methods ◽  
Fractional Order ◽  
Eddy Currents ◽  
Tracking Error ◽  
Measurement Data ◽  
Analytical Approximation ◽  
Fractional Order System ◽  
Order System ◽  
Model Accuracy ◽  
Magnetic Actuators

The electromagnetic dynamics of nonlaminated magnetic actuators are highly influenced by eddy currents and minor perturbations like core saturation, hysteresis as well as fringing and leakage fluxes. In the literature, analytical high-fidelity models describing these phenomena are known, which lead to complex reluctance networks or transcendental system descriptions with fractional-order characteristics. Therefore, they are not suitable for a direct implementation within the actuator control. Previously, we provided appropriate analytical rational approximations that allow a digital real-time implementation of these models on a microcontroller. However, the inclusion of the minor perturbations, if possible, leads to impractical model orders requiring simplifications, which compromise the model accuracy. This article studies numerical methods to reduce high model orders or directly approximate the transcendental systems or empirical measurement data. The greater degree of freedom allows for a possible higher model accuracy with sufficiently low orders. We review and improve existing approaches like Levy's method and Vector Fitting and apply them to the frequency response of the underlying fractional-order system. Furthermore we propose an order reduction algorithm based on a pole-zero-cancellation with tracking error compensation. Using measurement data, a comparison shows that the numerical approaches match or excel our previously studied analytical approximation.

Numerical Methods for Eddy Currents Modeling of Planar Transformers

2011 ◽  
Vol 47 (5) ◽  
pp. 1014-1017 ◽  
Author(s):  
Jérémie Aime ◽  
Bruno Cogitore ◽  
Gérard Meunier ◽  
Edith Clavel ◽  
Yves Marechal
Keyword(s):  
Numerical Methods ◽  
Eddy Currents

Numerical Methods

2019 ◽  
Author(s):  
Rajesh Kumar Gupta
Keyword(s):  
Numerical Methods

Determination of eddy current losses and hysteresis losses in magnetic circuits of electrical machines

2020 ◽  
pp. 54-58
Author(s):  
S. M. Plotnikov
Keyword(s):  
Eddy Current ◽  
Magnetization Reversal ◽  
Eddy Currents ◽  
Technical Problem ◽  
Electrical Machines ◽  
Eddy Current Losses ◽  
Hysteresis Losses ◽  
Magnetic Circuits ◽  
Core Losses ◽  
Reversal Frequency

The division of the total core losses in the electrical steel of the magnetic circuit into two components – losses dueto hysteresis and eddy currents – is a serious technical problem, the solution of which will effectively design and construct electrical machines with magnetic circuits having low magnetic losses. In this regard, an important parameter is the exponent α, with which the frequency of magnetization reversal is included in the total losses in steel. Theoretically, this indicator can take values from 1 to 2. Most authors take α equal to 1.3, which corresponds to the special case when the eddy current losses are three times higher than the hysteresis losses. In fact, for modern electrical steels, the opposite is true. To refine the index α, an attempt was made to separate the total core losses on the basis that the hysteresis component is proportional to the first degree of the magnetization reversal frequency, and the eddy current component is proportional to the second degree. In the article, the calculation formulas of these components are obtained, containing the values of the total losses measured in idling experiments at two different frequencies, and the ratio of these frequencies. It is shown that the rational frequency ratio is within 1.2. Presented the graphs and expressions to determine the exponent α depending on the measured no-load losses and the frequency of magnetization reversal.

THE METHODS OF DEVELOPING COMPUTATIONAL THINKING OF STUDENTS WHILE STUDYING THE COURSE "NUMERICAL METHODS" BASED ON BLENDED LEARNING

2019 ◽  
pp. 34-41
Author(s):  
M. M. Klunnikova
Keyword(s):  
Numerical Methods ◽  
Blended Learning ◽  
Computational Thinking ◽  
Individual Characteristics ◽  
Diagnostic Model ◽  
Mathematics Students ◽  
Professional Activities ◽  
Cognitive Component ◽  
Professional Field ◽  
The Individual

The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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