There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Although the concept of variable-speed drives, based on utilization of multiphase machines, dates back to the late 1960s, it was not until the mid- to late 1990s that multiphase drives became serious contenders for various applications. These include electric ship propulsion, locomotive traction, electric and hybrid electric vehicles, ldquomore-electricrdquo aircraft, and high-power industrial applications. As a consequence, there has been a substantial increase in the interest for such drive systems worldwide, resulting in a huge volume of work published during the last ten years. An attempt is made in this paper to provide a brief review of the current state of the art in the area. After addressing the reasons for potential use of multiphase rather than three-phase drives and the available approaches to multiphase machine designs, various control schemes are surveyed. This is followed by a discussion of the multiphase voltage source inverter control. Various possibilities for the use of additional degrees of freedom that exist in multiphase machines are further elaborated. Finally, multiphase machine applications in electric energy generation are addressed.

Multiphase Electric Machines for Variable-Speed Applications

This paper proposes a general field modulation theory for electrical machines by introducing magnetomotive force modulation operator to characterize the influence of short-circuited coil, variable reluctance, and flux guide on the primitive magnetizing magnetomotive force distribution established by field winding function multiplied by field current along the airgap peripheral. Magnetically anisotropic stator and rotor behave like modulators to produce a spectrum of field harmonics and the armature winding plays the role of a spatial filter to extract effective field harmonics to contribute the corresponding flux linkage and induce the electromotive force. The developed field modulation theory not only unifies the principle analysis of a large variety of electrical machines, including conventional dc machine, induction machine, and synchronous machine which are just special cases of the general field modulated machines, thus eliminating the problem of the machine theory fragmentation, but also provides a powerful guidance for inventing new machine topologies.

General Airgap Field Modulation Theory for Electrical Machines

This paper presents an analytical subdomain model to compute the magnetic field distribution in surface-mounted permanent-magnet (PM) motors with semi-closed slots. The proposed model is sufficiently general to be used with any pole and slot combinations including fractional slot machines with distributed or concentrated windings. The model accurately accounts for armature reaction magnetic field and mutual influence between the slots. The analytical method is based on the resolution of two-dimensional Laplace's and Poisson's equations in polar coordinates (by the separation of variables technique) for each subdomain, i.e., magnet, air gap, slot-opening, and slots. Magnetic field distributions, back-EMF, and electromagnetic torque (including cogging torque) computed with the proposed analytical method are compared with those issued from finite-element analyses.

https://hal.archives-ouvertes.fr/hal-00558543/document

2-D Exact Analytical Model for Surface-Mounted Permanent-Magnet Motors With Semi-Closed Slots

Environmental protection and energy conservations are the main concern of 21st century which has now accelerated the pace to plan and develop electric vehicle technology. The electric vehicles (EVs) offer a zero emission, new automobile industry establishment, and economic development, efficient and smart transportation system. Also EVs equipped with artificial intelligence system will also improve the present traffic safety and road utilization. The EV system consist of energy storage devices such as various types of batteries, fuel cells, ultra-capacitors along with electric propulsion, body of the vehicle and energy management system with the diversified technology of electrical, electronics, mechanical, automotive and chemical engineering. The objective of electric vehicle is to produce commercial viable range, efficient performance, and comfort with safety and reliable operations at cheaper price than its counterpart the internal combustion EV. Currently the permanent magnet brushless direct current motors are the present choice of automobile industries and researchers because of its high power density, compact size, reliability, and noise free and minimum maintenance requirements. In this paper an overview of electric vehicle technology and key strategy is presented. The present state of art permanent magnet brushless DC motor drive for the electric vehicle application is also presented in this paper. In addition the energy storage devices, smart energy management system unit for EV and commercial aspects and benefits of EV are highlighted.

Development scheme and key technology of an electric vehicle: An overview

This paper deals with an analytical method for magnetic field calculation in the air gap of cylindrical electrical machines including slotting effects. The analytical method is based on the resolution of the two-dimensional Laplace's equation in polar coordinates by the separation of variables technique. The originality of the proposed model is to take into account the mutual influence of slots on the air-gap magnetic field. The proposed method is sufficiently general to be used as a tool for air-gap magnetic field calculation of slotted electrical machines as reluctance or permanent magnet motors or actuators. Magnetic field and electromagnetic torque computed with the proposed analytical method are validated through finite-element analysis.

/pdf/exact-analytical-method-for-magnetic-field-computation-in-4d4iudwha3.pdf

Exact Analytical Method for Magnetic Field Computation in the Air Gap of Cylindrical Electrical Machines Considering Slotting Effects

We propose an analytical computation of the magnetic field distribution in a magnetic gear. The analytical method is based on the resolution of Laplace's and Poisson's equations (by the separation of variables technique) for each subdomain, i.e., magnets, air gap, and slots. The global solution is obtained using boundary and continuity conditions. Our analytical model can be used as a tool for design optimization of a magnetic gear. Here, we compare magnetic field distributions and electromagnetic torque computed by the analytical method with those obtained from finite-element analyses.

/pdf/analytical-computation-of-the-magnetic-field-distribution-in-2h71wyvuud.pdf

Analytical Computation of the Magnetic Field Distribution in a Magnetic Gear

In this paper, a theoretical analysis of an axial magnetic coupling is presented, leading to new closed-form expressions for the magnetic axial force and torque. These expressions are obtained by using a 2-D approximation of the magnetic coupling geometry (mean radius model). The analytical method is based on the solution of Laplace's and Poisson's equations by the separation of variables method. The influence of geometrical parameters such as number of pole pairs and air-gap length is studied. Magnetic field distribution, axial force, and torque computed with the proposed 2-D analytical model are compared with those obtained from 3-D finite elements simulations and experimental results.

/pdf/simple-analytical-expressions-for-the-force-and-torque-of-2k00vetwqw.pdf

Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

This paper compares the prediction of two independent methods for calculating electromagnetic torque and inductances of a synchronous reluctance machine under linear condition. One method is based on winding function analysis (WFA) and the other on finite-element analysis (FEA). Both methods take into account the rotor geometry, the stator slot effects and the stator winding connections. The simulation results obtained by the WFA are compared with the ones obtained by two-dimensional FEA. It is shown that the two methods give approximately the same results but require different computation times.

/pdf/comparison-between-finite-element-analysis-and-winding-cppewq5ar6.pdf

Thierry Lubin

Papers

2-D Exact Analytical Model for Surface-Mounted Permanent-Magnet Motors With Semi-Closed Slots

Exact Analytical Method for Magnetic Field Computation in the Air Gap of Cylindrical Electrical Machines Considering Slotting Effects

Analytical Computation of the Magnetic Field Distribution in a Magnetic Gear

Simple Analytical Expressions for the Force and Torque of Axial Magnetic Couplings

Comparison Between Finite-Element Analysis and Winding Function Theory for Inductances and Torque Calculation of a Synchronous Reluctance Machine