Ferromagnetic coil frequency response and dynamics modeling with fractional elements

Sowa, Marcin

doi:10.1007/s00202-020-01190-5

Cited by 7 publications

(5 citation statements)

References 41 publications

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“…According to the arrival time of the peak point and zero crossing point of the current wave relative to the sinusoidal voltage input wave, the i − u curves can be sorted into four typical shapes: With the change of the fractional orders α, β, the i − u curve of FOE varies from one type to another. The rich dynamic characteristics make the FOE model a good way to fit and model some real physical devices, such as ferromagnetic core coils [28,29] with hysteresis loops and capacitive-coupled memristive devices [4,46] with various i − u curves similar to the discoveries here.…”

Section: Numerical Examplesupporting

confidence: 57%

“…Recently, much research [17,18] has emerged on the practical realization of FOE and fractional-order systems, such as resistor and capacitor networks [19,20], singlecomponent realization [21], field-programmable gate arrays (FPGAs) [22] and generalized impedance converter [23]. The FOE model has demonstrated its applicability in fitting physical devices or systems, such as supercapacitors [24][25][26][27], ferromagnetic core coils [28,29], and on-chip inductors [30], and so on [31,32] producing more satisfactory fitting results than the conventional integer-order model.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Fractional-order Electrical Element: Modeling, Response Characteristic Analysis and Circuit Simulation

Gong,

Si,

et al. 2023

Preprint

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Fractional-order electrical properties are ubiquitous in physical devices, and investigating the features of fractional-order elements (FOEs) is imperative. This paper presents a comprehensive investigation of a generalized FOE model with nonlinear fractional-order constitutive relation. We analyze the response characteristics of FOEs among the four basic integer-order electrical elements, and derive analytic expressions for the step input, zero input, and sinusoidal input responses. The step input response consists of a sequence of power functions, indicating that nonlinear FOEs exhibit an extended power-law step response. The zero input response manifests in three different modes: impulsive, discontinuous, and continuous. Moreover, the sinusoidal input response can be expressed as a series of harmonic additions with calculable amplitude and phase, suggesting a constant phase-shift characteristic of nonlinear FOEs. Our numerical examples demonstrate that FOEs with nonlinear constitutive relations exhibit more intricate dynamic characteristics than linear elements. Additionally, we propose an equivalent analog circuit to achieve the FOE model approximately. The circuit simulation results validate the equivalent circuit's effectiveness and the theoretical conclusion's accuracy. This generalized FOE model extends the existing integer-order nonlinear circuit theory and simplifies the modeling of physical devices in the real world.

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Section: Numerical Examplesupporting

confidence: 57%

Section: Introductionmentioning

confidence: 99%

Generalized Fractional-order Electrical Element: Modeling, Response Characteristic Analysis and Circuit Simulation

Gong,

Si,

et al. 2023

Preprint

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“…The deviation of the measurement voltage r N e 16) was adopted as the criterion for selecting the reluctance R mδ . In practical implementation, a comparison between measured and simulated waveforms can be made using a variety of criteria (for instance, as in [32], when sums of squares are used or through an integral error [33]).…”

Section: Phase Imbalancementioning

confidence: 99%

“…The value of this shunt is selected in such a way as to obtain the maximum value (Figure 16) was adopted as the criterion for selecting the reluctance m R δ . In practical implementation, a comparison between measured and simulated waveforms can be made using a variety of criteria (for instance, as in [32], when sums of squares are used or through an integral error [33]). The new and corrected transformer model differs from the model given in [13] based on the presence of a carefully selected air shunt R mδ .…”

Section: Phase Imbalancementioning

confidence: 99%

Practical Experiments with a Ready-Made Strategy for Energizing a Suitable Pre-Magnetized Three-Column Three-Phase Dy Transformer in Unloaded State for Inrush Current Computations

Łukaniszyn,

Majka,

Baron

et al. 2024

Energies

Self Cite

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This article presents the results of an experimental verification of three-phase Dy transformer dynamics under no-load conditions. This study is motivated by previous ferroresonance analyses where the occurrence of inrush currents has been observed. The measurements covered all available electrical quantities in a transient state (12 measured and 3 additionally computed waveforms) during the device’s start-up under no-load conditions, as well as in a long-term steady state. A detailed analytical analysis is carried out for the obtained comprehensive set of measurement results. As a result of the conducted research, the mathematical model of the pre-magnetized three-phase Dy transformer is modified. Particular attention is paid to the issue of residual magnetism of the transformer core and its consideration in further research. The original strategy for energizing a three-column three-phase Dy transformer with a suitable pre-magnetization of its columns and original control switching system with a given/set value of the initial phase in the supply voltage is put to the test. The evolution of the induced inrush phenomenon up to the quasi-steady state under given (forced) conditions is documented (currents, voltages and the dynamics of changes taking place in the core (hysteresis loops)). This article represents a continuation of ongoing work on the study of transient states (dynamics of transformer inrush currents). At present, the Dy three-phase transformer is analyzed because of the requirements of industrial operators.

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“…One important issue is the correct selection of the mathematical description of the model (i.e., the choice of differential equations that define its dynamics) and method necessary to solve it [3,[22][23][24][25][26]. In fact, this is a research matter, which leads to understanding the different phenomena involved and making suitable assumptions.…”

Section: Introductionmentioning

confidence: 99%

Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching

et al. 2023

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The methodology and test results of a three-phase three-column transformer with a Dy connection group are presented in this paper. This study covers the dynamics of events that took place in the first period of the transient state caused by the energizing of the transformer under no-load conditions. The origin of inrush currents was analyzed. The influence of factors accompanying the switch-on and the impact of the model parameters on the distribution and maximum values of these currents was studied. In particular, the computational methods of taking into account the influence of residual magnetism in different columns of the transformer core, as well as the impact of the time instant determined in the voltage waveform at which the indicated voltage is supplied to a given transformer winding, were examined. The study was carried out using a nonlinear model constructed on the basis of classical modeling, in which hysteresis is not taken into account. Such a formulated model requires simplification, which is discussed in this paper. The model is described using a system of stiff nonlinear ordinary differential equations. In order to solve the stiff differential state equations set for the transient states of a three-phase transformer in a no-load condition, a Runge–Kutta method, namely the Radau IIA method, with ninth-order quadrature formulas was applied. All calculations were carried out using the authors’ own software, written in C#. A ready-made strategy for energizing a three-column three-phase transformer with a suitable pre-magnetization of its columns is given.

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Ferromagnetic coil frequency response and dynamics modeling with fractional elements

Cited by 7 publications

References 41 publications

Generalized Fractional-order Electrical Element: Modeling, Response Characteristic Analysis and Circuit Simulation

Generalized Fractional-order Electrical Element: Modeling, Response Characteristic Analysis and Circuit Simulation

Practical Experiments with a Ready-Made Strategy for Energizing a Suitable Pre-Magnetized Three-Column Three-Phase Dy Transformer in Unloaded State for Inrush Current Computations

Inrush Current Reduction Strategy for a Three-Phase Dy Transformer Based on Pre-Magnetization of the Columns and Controlled Switching

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