Linear Magnetic Circuit Research Articles

CALCULATION OF POWER TRANSFORMER INDUCTANCE MATRIX

Practical calculations of electric equipment and electric networks are performed using equivalent circuits. Without taking into account saturation phenomena, electromagnetic processes in a power transformer are described by a system of linear equations, which can be represented in matrix form. The transformer inductance matrix contains self and mutual winding inductances, whose values for one phase are determined directly from the passport data containing the results of no-load and short circuit experiments. Mutual inductances between phases depending on the type and size of the magnetic core are not usually given in the transformer documentation. It does not allow to simulate the operating modes that differ from the steady state with uniform phase load.
 
 The purpose of the work is to develop an algorithm for calculating elements of the power transformer inductance matrix according to its passport data and magnetic circuit parameters.
 
 The scientific novelty lies in use of information about magnetic circuit type and size to determine elements of the inductance matrix.
 
 Materials and methods. Methods of linear electric and magnetic circuit theory are used in the work.
 
 Results. The proposed algorithm for calculation of power transformer inductance matrix includes three stages: calculation of self and mutual inductances for one phase; construction of an equivalent circuit for a magnetic circuit and calculation of magnetic fluxes in order to take into account the mutual influence of windings on various phases; assembly of the inductance matrix of three-phase transformer. A method is proposed for constructing the transformer inductance matrix with an arbitrary type of magnetic circuit, phases and windings quantity. The method involves preliminary calculation of the coefficient matrix that characterizes the magnetic circuit and depends mainly on its type and, to a less, on the ratio of geometric dimensions in rods and yokes. The coefficient matrix can be calculated in advance and used to determine the inductance matrix of a wide range of transformers.
 
 Conclusions. 1. The passport data of the transformer do not allow to model transformer operation at unbalanced load validly. 2. An algorithm for determining the inductance matrix of transformers has been developed. 3. A method for compilation of a transformer inductance matrix with an arbitrary type of magnetic circuit, the number of phases and windings is introduced. The practical significance of the algorithm is determined by the simplicity of algorithmizing, as well as by the possibility of using it in computer simulation of electrical circuits with transformers, for example, using the modified nodal analysis method.

Investigation of multi loop linear magnetic circuits of electromagnetic flow converters with ring channels

Mathematical models of single and multiloop magnetic circuits of electromagnetic flow transducers with an annular channel are designed taking into account the parameters of the magnetic circuit. The possibility of compensating the difference in magnetic resistances of coaxially located concentric ferromagnetic cores and the difference in their circumference by selecting the thickness of the cores is shown. It has been installed that the magnetic flux in ferromagnetic cores is distributed along the angular coordinate. The magnetic induction in the annular channel is unevenly distributed along the radial coordinates. It was found that with an increase in the value of the attenuation coefficient of the magnetic field in the magnetic circuit, the degree of magnetic induction in the annular channel increases along the angular coordinate, while it remains constant along the radial coordinate.

A Parameterized Linear 3D Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears–Part I: Implementation

Magnetic gears can perform the same function as mechanical gears with the added benefits inherent to contactless power transfer. However, quick and accurate analysis tools are required for magnetic gears to reach their full potential. As end effects can significantly impact the slip torque of a magnetic gear, 2D models often overestimate the slip torques, so 3D models are frequently required. Therefore, this paper proposes a 3D linear Magnetic Equivalent Circuit (MEC) or reluctance network model of radial flux magnetic gears with surface mounted magnets. This is an extension of a previously developed 2D MEC model, and, like the previous 2D model, it is thoroughly parametrized so that it can be directly applied to a wide range of parametric cases. This is Part I of a two-part paper and focuses on the implementation of the 3D MEC model. Part II compares the 3D MEC model against nonlinear finite element analysis (FEA) models to validate the MEC model's accuracy and to develop guidelines for discretizing the geometry.

A Parameterized Linear Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears—Part I: Implementation

This is Part II of a two part paper on the development of a parameterized linear magnetic equivalent circuit (MEC) for radial flux magnetic gears with surface permanent magnets. Part I describes the MEC implementation. This section, Part II, evaluates the MEC model's accuracy by comparing its results against those produced by a nonlinear finite-element analysis (FEA) model. Simulation results demonstrate that the linearity approximation does not prevent the MEC from accurately matching the torque and air-gap flux densities predicted by a nonlinear FEA model for three diverse magnetic gear base designs. The impacts of the MEC discretization parameters introduced in Part I are also investigated using the same base designs, and guidelines for those settings are developed. Additionally, single design parameter sweeps illustrate the MEC's ability to track these changes over most practical design ranges and reveal where the MEC's accuracy degrades due to the linearity approximation. Finally, the results of a 46,656 case parametric optimization study demonstrate the MEC's ability to match the nonlinear FEA model's torque predictions within a few percent over a wide range of designs while achieving average simulation speeds 44 to 271 times faster than those of the FEA model.

A Parameterized Linear Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears–Part II: Evaluation

A Parameterized Linear Magnetic Equivalent Circuit for Analysis and Design of Radial Flux Magnetic Gears–Part II: Evaluation

Inverse design of a harmonic two-phase reluctance machine

A partial inverse design is introduced to derive a mutually coupled two-phase reluctance machine concept. The inverse design part begins with the torque as a function of inductance and current. For given torque characteristics the required inductance characteristics are calculated and including a m agnetic circuit yields required reluctance or permeance characteristics for the air gaps. Such inverse design focuses on possibilities of reluctance machines in general, independent of any machine geometry. The derived two-phase motor concept uses self and mutual inductance independently to obtain up to four shifted harmonic torque characteristics. This allows to generate a bidirectional torque at every rotor position. Thus, there is no self-start problem and reduced torque ripple. The theoretical operation is shown with a linear magnetic circuit model and non-linear FEM calculations for a 2D and a 3D machine design.

Nonlinear Modeling of Electromagnetic Forces for the Planar-Switched Reluctance Motor

Planar switched reluctance motors (PSRMs) have the merits of simple structure, low cost, low heat loss, high precision, ease of manufacture, and strong adaptability of harsh environment, which directly transform the mechanical energy to electromagnetic energy available to planar motions without mechanical transmissions. Therefore, PSRMs are an attractive candidate in high-precision two-dimensional positioning devices [1], [2]. For PSRMs, accurate modeling of electromagnetic forces is the theoretical foundation of the design and control. However, electromagnetic forces are highly nonlinear and hard to be accurately modeled due to the inherently complex magnetic characteristics of PSRMs. There are primarily three methods utilized to model electromagnetic forces of switched reluctance motors (SRMs) up to now, which are the equivalent magnetic circuit method, the Maxwell stress method, and the virtual work method [3]-[5]. Additionally, the neuron network is also employed to model electromagnetic forces for a SRM [6]. Nevertheless, the modeling of electromagnetic forces for SRMs cannot be directly applied to PSRMs owing to their unique structure of magnetic circuit. For linear switched reluctance motors (LSRMs) and PSRMs, electromagnetic forces including thrust force and normal force have been modeled under linear magnetic circuit [7], [8], but the modeling of electromagnetic forces has not been formulated so far with consideration of magnetic saturation. Furthermore, the finite-element method (FEM) is frequently used to establish electromagnetic force model for SRMs, LSRMs and PSRMs [9]-[11], whereas FEM takes a long calculating time. Based on aforementioned analysis, the nonlinear modeling of electromagnetic forces has not been built analytically for PSRMs. Hence, it is necessary to derive the nonlinear modeling of electromagnetic forces for deeper investigation of PSRMs.

MEC-Based Sizing of a Hybrid-Excited Claw Pole Alternator

The paper is aimed at a magnetic equivalent circuit (MEC)-based sizing of a novel hybrid-excited claw pole alternator. It consists in a claw pole concept with a NdFeB permanent magnet (PM) excitation in the rotor and a dc one in the stator, with the homopolar flux eradicated owing to a magnetic barrier inserted between the stator yoke and lamination. The proposed MEC considers both linear and saturated magnetic circuit, with a focus on the modeling of the leakage fluxes. The developed model is applied for the prediction of the no-load characteristic which is validated by 3-D finite-element analysis (FEA). Then, a dual FEA-experimental validation is carried out considering the case of a dc excitation. Moreover, the proposed MEC makes the investigation of the influent sizing parameters on the machine back-electromotive force (EMF) production capability easy. This latter is enhanced owing to the integration of two ring ferrite PMs linked to the stator, along with a reduction of the volume of the NdFeB PM in the rotor. It has been found that the gained improvement is better than the benefit yielded by as many pole number ferrite PMs inserted between the claws.

Linear Model of a Novel 5-Phase Segment Type Switched Reluctance Motor

This paper introduces the general linear magnetic circuit model of a novel 5-phase segment type switched reluctance motor (ST-SRM) of which rotor cores are embedded in an aluminum block as well as to improve the performance characteristics under simultaneous two-phase (bipolar) excitation of windings. The developed model implements the magneto motor force (mmf) that is necessary to produce short and exclusive magnetic flux paths minimizing the commutation switching and eddy current losses in the laminations. For this purpose, an equivalent magnetic circuit for newly developed ST-SRM and the underlying assumptions are given. The concept of apparent inductance and torque equations of two-phase simultaneously excited ST-SRM is introduced and the effectiveness and deficiencies of the linear model are given. DOI: http://dx.doi.org/10.5755/j01.eee.20.1.6159

An Analysis of kii Coupling Coefficients

The mutual inductance and the coupling coefficient for a couple of coils are usually described by simple parameters M and K respectively, instead of M12, M21 and k12 and k21. Many electric circuits theory books present at least a chapter about mutual inductance, in which a proof of M12 = M21 = M is usually described. Since most applications of M aim to transfer energy between coils, a coupling coefficient K is usually assumed without the rigorous analysis of k12 and k21. This paper presents an analysis of the mutual inductance between two coupled coils based on the linear magnetic circuit theory and a theoretical proof that it is not necessarily the case that k12 = k21 as many books assume. Finally, a practical experiment is presented to confirm the theoretical analysis.

Loss Analysis of Permanent-Magnet Motors With Concentrated Windings—Variation of Magnet Eddy-Current Loss Due to Stator and Rotor Shapes

In this paper, we investigate losses, including magnet eddy-current loss of permanent-magnet synchronous motors with concentrated windings. A 3-D finite-element method that considers carrier harmonics of pulsewidth modulation inverters is utilized to calculate the losses in each part of the motor separately. A simple linear magnetic circuit model is also introduced in order to understand the mechanism of eddy-current loss generation in the magnet. First, the measured and calculated results are compared to verify the validity of the analysis. Next, the variation of the losses due to the stator and rotor shapes is investigated, for instance, concentrated and distributed stator windings and interior and surface-mounted permanent magnets. It is clarified that the eddy-current loss of the permanent magnet in the concentrated winding motor is much larger than that in the distributed winding motor. The difference of the loss generation mechanism due to the rotor shape is also clarified.

The design and analysis of a novel brushless dc linear motor

A novel brushless dc linear motor was designed, with two armature cores and seven high energy product magnets. It was then built and tested. Both the design and the analysis were carried out assuming a linear magnetic circuit. The design procedure and the test results are presented and discussed in this paper. The new motor can also be used as a slotless linear stepping motor.

Linear AC magnetic circuit theory

A theory is presented for linear, AC magnetic circuits. The theory develops real and imaginary reluctance terms, which are used in the same manner as real and imaginary impedance terms in linear, AC electrical circuit theory. The reluctance terms can be manipulated through coil-coupled resistances and capacitances. The theory is applied to a parallel magnetic-circuit configuration to show the limits of applicability for the particular materials from which the circuit is constructed. >

Adaptive input-output linearizing control of induction motors

A nonlinear adaptive state feedback input-output linearizing control is designed for a fifth-order model of an induction motor which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The control algorithm contains a nonlinear identification scheme which asymptotically tracks the true values of the load torque and rotor resistance which are assumed to be constant but unknown. Once those parameters are identified, the two control goals of regulating rotor speed and rotor flux amplitude are decoupled, so that power efficiency can be improved without affecting speed regulation. Full state measurements are required.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The general equations of 3-phase transformers with a symmetrical and linear magnetic circuit for use in network calculations

In this paper general differential equations are derived for the 3-phase transformer with the help of the symmetrical component transformation. With respect to their phase shifting properties the 3-phase transformers can be divided into two basic groups, depending on whether or not the phase displacement is an even multiple of π/6. This holds for both the steady state and for the transients. Only the appearance of a zero sequence component system may introduced differences. The derivation of the equations gives a clear insight into the internal behaviour of the transformer. The applicability of the general equations is demonstrated in an example.

CALCULATION OF THE PULL-OUT TORQUE OF HYBRID STEPPING MOTORS IN THE HALF-STEP MODE

ABSTRACT A method is described for predicting the pull-out torque/speed characteristics of hybrid stepping motors operating in the half-step excitation mode. The analysis assumes initially a linear magnetic circuit in order to derive an expression for the pull-out torque. Subsequently, the important effect of magnetic non-linearity is introduced into the calculation method by appropriate adjustment of the flux-linkage coefficients using an iterative computational routine. A comparison of experimental and predicted results is presented for a commercial 1.8°(200 step/revolution) stepping motor