Analytical Solution Of Magnetic Field In Permanent Magent Machines:Theory And Application

Electrical machine is a kind of magnetic force transmission device for energy conversion, based on electromagnetic induction principle. There are mainly two viewpoints for the analysis of the physical object:from the view of circuit and from the view of field. From the viewpoint of circuit, it regards the field problem as the circuit problem, by taking the magnetomotive force, reluctance and flux as the electromotive force, resistance and current in the circuit through analogy, and builds the electrical machinery theory according to circuit theory. From the viewpoint of field, the focus is on the magnetic field variables based on Maxwell’s equations, such as flux density, magnetic field strength, current density, electric field strength and so on, the electromagnetic field on electric machines is set up on the basis of electromagnetic field theory. The work of this paper mainly addresses the analytical calculation of the machine electromagnetic field, including two types of problems:two dimensional (2D) static field and2D quasi-static magnetic field.For2D static field, on the basis of comprehensive statement about2D analytical solution for surface permanent manet (PM) machine, four types of accurate subdomain model for different machines are set up, that is, surface vernier PM machine with open slots, dual three-phase surface PM machine with semi-closed slots, suface vernier PM machine with flux-modulation-poles and surface-inset PM machine with open slots. The general solutions for different kinds of subdomains are deduced, the scaling of unknown Fourier coefficients is talked, and the periodic conditions is applied to improve the computational efficiency. Taking the prototypes as example, the air-gap magnetic field density and related electromagnetic performances is predicted by analytical model and validated by corresponding finite-element (FE) method, which provides a simple and convenient way to optimize machine design.For2D quasi-static magnetic field, the investigation is focused on one specific problem; that is, operational inductances in surface PM synchronous machine. Comprehensive statement about analytical models and FE methods for rotor eddy current loss in PM machines is reviewed and summarized. The resistance-limited eddy current and inductance-limited eddy current is discussed and compared. The inductance-limited eddy current model is extended to deal with the operational inductances of surface PM machines. Taking the static test method and steady-state asynchronous run test method as a starting point respectively, two analytical models for operational inductances of surface PM machines are set up by assuming the magnet as a uniform ring, based on complex power balance principle and flux linkage method separately. The FE results are given and transient parameters are studied.Finally the future research direction for the subject is put forward, on the basis of this paper.