Conference Agenda
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WP1B: Mathematical Modeling #3
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Semi-Analytical Modeling of an Equivalent Circuit for Multi-Turn Coils Considering Parasitic Capacitance and Eddy Current Loss 1Nagasaki University, Japan; 2Aoyama Gakuin University, Japan; 3Hokkaido University, Japan This paper presents a semi-analytical method for modeling equivalent circuits of multi-turn coils considering parasitic capacitance and eddy current loss. The proposed method incorporates complex resistances and inductances into an RLC circuit based on the winding structure of a multi-turn coil. This enables the analysis of the eddy current loss resulting from skin and proximity effects within circuit analysis. Circuit parameters are determined using electrostatic and homogenization-based finite element analyses. The results demonstrate a significant difference in inductive-capacitive behavior between the proposed and conventional RLC circuits, primarily due to the inclusion of eddy current losses.
Derivation of Novel Equivalent Circuit Considering Parasitic Capacitance of AFPM Motor Incheon National University, Korea, Republic of (South Korea) Space Vector Pulse Width Modulation (SVPWM), known for its superior voltage utilization, is widely adopted in motor control systems. However, the high-speed switching of inverters generates harmonics, which in turn lead to the occurrence of Common Mode Voltage (CMV). CMV induces shaft voltage, resulting in phenomena such as pitting and fluting that can damage the bearings. As a result, the motor shaft is not securely fixed, which can lead to mechanical and electrical failures. Therefore, analyzing the characteristics of shaft voltage is crucial for ensuring high reliability in motors. In the case of Interior Permanent Magnet Synchronous Motor (IPMSM), Surface Permanent Magnet Synchronous Motor (SPMSM), induction motor extensive research has been conducted on the shaft voltage characteristics. However, studies on Axial Flux Permanent Magnet (AFPM) motors remain relatively insufficient. In this paper derives the internal parasitic capacitance and a new equivalent circuit for AFPM motors, considering their structural and electromagnetic characteristics, and validates them through comparison using FEM.
Unified Model of Paramagnetic Particle Transport Florida State University, United States of America A general model for the transport of paramagnetic particles in liquid solutions is proposed. The model describes the magnetic particles and the solvent as two interpenetrating continua and takes into consideration magnetophoresis and Brownian motion of magnetic particles, inertial and gravitation effects for both particles and fluid, as well as interaction between the magnetic particles and solvent continua. After developing our model, we show how various approximations made to the model equations lead to simplified approaches, some of them currently being used in the literature. A comparison with experimental data, the conditions under which these approximations can be made, advantages and disadvantages of using various model derivations, and details about their numerical implementation will be discussed at the conference.
Radial cylindrical multipole expansion of the free-space Green function for the three-dimensional Laplace equation Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia Free-space Green function in cylindrical coordinates has multipole expansion containing improper integral of modified Bessel functions. In order to make multipole expansion convenient for analytical calculations, it should contain multiple sums instead of integrals. In this paper, we prove radial multipole expansion of free-space Green function in cylindrical coordinates, which does not contain any integrals. Presented expansion contains triple sum of Gaussian hypergeometric functions, powers and trigonometric functions. Radial multipole expansion can be employed to analytically calculate electrostatic and magnetostatic potentials, fields, forces and inductances in cylindrically symmetric systems.
A Study on Simplified Modeling Using Spatial Permeability for Analyzing the Effects of Degaussing of Warships 1Hanwha Ocean, Korea, Republic of (South Korea); 2Pusan National University, Busan, Republic of (South Korea); 3Hanwha Ocean, Korea, Republic of (South Korea); 4Hanwha Ocean, Korea, Republic of (South Korea); 5Hanwha Ocean, Korea, Republic of (South Korea); 6Hanwha Ocean, Korea, Republic of (South Korea); 7Hanwha Ocean, Korea, Republic of (South Korea); 8Hanwha Ocean, Korea, Republic of (South Korea) This study proposes the development of a simplified model for the efficient design of degaussing coils of war ships. The research focuses on the complex structure of the ship made of magnetic materials, including internal equipment and detailed models. To simplify modeling, a technique is explored that excludes components such as bulkheads, decks, and major equipment, while assigning uniform permeability values to specific spatial regions. To validate the proposed model, the detailed model is compared with the actual ship measurement results, and the simplified model is confirmed to be valid by comparing it with the analysis results of the detailed model.
Application of A-input Cauer Ladder Network Method to Model Order Reduction of Induction Motors Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan This article presents the application of the magnetic flux input (A-input) Cauer ladder network (CLN) method to the model order reduction (MOR) of induction motors. This study develops an A-input rotor CLN, and a hybrid stator CLN having the source currents and vector potential at airgap as input. The developed motor MOR of A-input type is applied to the transient analysis of a squirrel cage induction motor. The comparison with the finite element analysis shows that the proposed method successfully reproduces the motor property under a wide range of slips as well as the conventional H-input CLN.
Effect of Magnetic Anisotropy Property of Non-Oriented Electrical Steel on SPMSM Cogging Torque 1Yeungnam University, Korea, Republic of (South Korea); 2Hanyang University, Korea, Republic of (South Korea); 3Dongguk University, Korea, Republic of (South Korea) Cogging torque in surface-mounted permanent magnet synchronous motors (SPMSMs) is an important design criterion for applications such as reaction force actuators in steer-by-wire systems and robotics. Ideally, the cogging torque in SPMSMs can be minimized by applying a skew with an appropriate angle, considering the pole-slot combination. However, due to manufacturing tolerances (MTs), additional cogging torque harmonics may occur, which cannot be disregarded. Similarly, differences in the saturation magnetic flux density between the rolling and counter rolling directions of non-oriented electrical steel can generate additional cogging torque harmonics. In this study, we investigated the effect of the anisotropic properties of non-oriented electrical steel on cogging torque. To differentiate the additional cogging torque caused by stator and rotor MTs from that caused by the anisotropic properties of non-oriented electrical steel, the effects of stator and rotor MTs were analyzed using 2D finite element analysis (FEA). Subsequently, 2D FEA was conducted by considering the anisotropic properties of non-oriented electrical steel. This analysis results confirmed that additional cogging torque harmonics, distinct from those caused by stator and rotor MTs, were generated.
Identification of B-dependent Coefficient for Excess Eddy-current Field Graduate School of Engineering, Kyoto University, Japan An accurate excess eddy-current loss modeling is vital for the iron loss evaluation of core materials. Bertotti’s excess eddy-current loss model has good accuracy for silicon steel sheet, which gives the excess eddy-current field as gex(dB/dt)1/2. In previous research, the coefficient gex is often treated as independent of magnetic flux-density, which is not always true for real materials. In this research, we developed a method for identifing the magnetic flux-density dependence of the coefficient from measured excess eddy-current loss. The proposed method improves the iron loss evaluation for the silicon steel sheet under compressive stress.
Design and Thermal Analysis of a Heat Pipe for High-Temperature Stability in a Dy-Free Permanent Magnet Motor Wonkwang University, Korea, Republic of (South Korea) With the rapid growth of the electric vehicle (EV) market, the demand for high-efficiency and high-power motors has steadily increased. Consequently, the use of rare-earth materials such as neodymium (Nd) permanent magnets has also risen. However, the monopolistic supply chain and price volatility of rare-earth elements limit their wide adoption. In this study, we propose a motor structure that eliminates the use of dysprosium (Dy)—a rare-earth element critical for maintaining coercivity in high-temperature environments—to address concerns related to supply instability and cost escalation. While Dy plays a key role in preventing irreversible demagnetization by preserving magnet coercivity under elevated temperatures, this research demonstrates that stable performance can still be achieved at high temperatures without Dy by integrating a heat pipe into the motor design. The heat pipe effectively reduces the temperature of the permanent magnets; however, poor structural design may exacerbate eddy current losses, leading to further temperature increases. Hence, we conducted a thermal equivalent circuit analysis to verify that the heat pipe successfully controls magnet temperature rise and prevents irreversible demagnetization. The proposed structure is expected to reduce the consumption of rare-earth materials while enhancing both the efficiency and reliability of the motor.
A Semi-Analytical Method for the Analysis of Electrical Machines with Complex 3D Salient Geometries Eindhoven University of Technology, Netherlands, The This research presents a Semi-Analytical method to analyze air gap fields of electrical machines with complex salient geometries and that, a priori, require a 3-dimensional (3D) approach. When comparing the performance of a Radial Variable Flux Reluctance Machine (RVFRM) to that of an Axial Variable Flux Reluctance Machine (AVFRM), the computational cost of the process is increased due to the 3D nature of the latter machine. Approximations of radial flux machines with a 2-dimensional (2D) cross section are a standard procedure, and have further been combined with analytical methods based on conformal mapping. Consequently, this research establishes an equivalent procedure for axial flux machines based on applying a semi-analytical method on already researched 2D slicing of axial flux Permanent Magnet (PM) based machines.
Incomplete Balancing Domain Decomposition Methods for Magnetostatic Problems Based on Discrete de Rham Sequences Kyushu University, Japan A Balancing Domain Decomposition (BDD) method is considered as the preconditioner of an iterative Domain Decomposition Method (DDM) for perturbed magnetostatic problems, where the magnetic vector potential is regarded as an unknown function. To reduce the number of the Degrees Of Freedom (DOF) of coarse spaces in BDD methods, Polytopal Element Methods (PEMs) are introduced, which are originally proposed by Di Pietro, et al. The PEMs can constract any order elements, satisfying Discrete de Rham Sequences. Owing to the introduction of PEMs and the result of BDD method originally proposed by Mandel, the condition number of coefficient matrices derived from the iterative DDM is evaluated. Therefore, the number of iterations of the iterative DDM can be kept even when the number of the subdomains becomes larger. Moreover, the approximate coarse space by PEMs can admit that each subdomain becomes more general polyhedron. The results in case of higher order PEMs are also shown.
An Efficient Architecture Selection Approach for PINNs Applied to Electromagnetic Problems Technische Universität Berlin, Germany Physics-Informed Neural Networks (PINNs) can mitigate the difficulty that arises when using mesh-based approaches, such as finite difference methods, regarding the scalability of the model with bigger meshes. Since PINNs are mesh-free they do not suffer from the same problems as mesh-based methods. However, choosing the PINNs’ parameter is cumbersome. We propose a bottom-to-top method to compute the parameters of the PINNs in a faster way than random or surrogate-based optimization strategies do.
Finite Element Method with Unbounded Approach USP, Brazil This paper aims to describe the Finite Element Method (FEM) using a mapping technique. FEM is a numerical method for solving partial differential equations with boundary value problems. As the name suggests, the method truncates the domain into a finite region in space. However, this truncation can lead to inaccuracies in the calculation results. To address this issue, a mapping method, referred in this paper as the Unbounded Approach, will be used. The method will be applied in the Laplace's Equation to solve electrokinetic problems.
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