In this paper, several of analytical methods for modelling the magnetic field are described. These models are used in design routines of the rotating machines, linear motors as well as actuators. Thanks to their high accuracy and low requirements for computation power, they are successfully implemented in designing high precision machines. In order to enlarge the applicability of the methods it is a common practise to combine two or more model such as Magnetic Equivalent Circuit (MEC) and Harmonic Method (HM), Schwartz Christoffel (SC) mapping and Tooth Contour Method (TCM), those combinations turns into so called Hybrid Methods which are also intended to increase the computation speed and results precision.
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In this study, six different modelling methods for permanent magnet electric machines are compared in terms of their computational complexity and accuracy. The methods are based primarily on conformal mapping, mode matching, and harmonic modelling. In the case of conformal mapping, slotted air gap of a complex machine geometry is transformed to a smooth slotless air gap where analytical expression for field solution is available. The solution in the canonical domain is then mapped back to the original slotted air-gap domain. Mode matching or subdomain method, as it is called in different sources, is using a solution of Laplace's equation to model the slotted air gap. In harmonic modelling, the machine cross-section is divided into homogeneous regions that are represented using Fourier series and coupled with each other using boundary conditions. The boundary value problems in both the mode matching and harmonic models are solved to obtain the field solutions. The performance of the modelling methods are evaluated by comparing the global parameters such as cogging torque, electromagnetic torque, back-emf as well as the simulation time with the results of finite-element transient analysis.
This paper presents a comparison between two high-order modeling methods for solving magnetostatic problems under magnetic saturation, focused on the extraction of machine parameters. Two formulations are compared, the first is based on the Newton-Raphson approach, and the second successively iterates the local remanent magnetization and the incremental reluctivity of the nonlinear soft-magnetic material. The latter approach is more robust than the Newton-Raphson method, and uncovers useful properties for the fast and accurate calculation of incremental inductance. A novel estimate for the incremental inductance relying on a single additional computation is proposed to avoid multiple nonlinear simulations which are traditionally operated with finite difference linearization or spline interpolation techniques. Fast convergence and high accuracy of the presented methods are demonstrated for the force calculation, which demonstrates their applicability for the design and analysis of electromagnetic devices.
The short rise time observed in the PWM voltages generated by ultra-fast wide bandgap devices increases the amplitude of voltage harmonics at higher frequencies. These harmonics can excite the resonances of Medium-Frequency Transformers (MFTs), resulting in overvoltages inside the windings during continuous operation. Without further measures, these overvoltages can lead to unexpectedly high electric fields in the insulation material, which can result in partial discharge, accelerated ageing and possible failure of the MFT. To avoid these effects, the mechanism causing the overvoltages has to be understood and quantified during the design process. Based on this, the MFT can be designed in a way that the overvoltages vanish or are tolerable. Therefore, the voltage distribution inside the MFT windings is analysed by a fully-coupled multi-conductor transmission line model, which includes the damping effect of electromagnetic losses in the litz wire and in the core. This method is verified by measuring the transfer functions of the voltage to ground of individual turns and their voltage waveforms during continuous operation. The waveforms indicate repeating overvoltages inside the windings. A guideline for the design verification and a simplified approach to speed-up the modelling process are presented.
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