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

In this paper, we present a new kind of superconducting inductor for the synchronous machine. This inductor is composed of a two superconducting coils having the same axis and fed by a currents with the same direction. A superconducting bulk is used in order to achieve a variation of the flux density in the air-gap. The superconducting bulk is surrounded by a ferromagnetic material in order to improve the radial component of the flux density in the air-gap. With the proposed superconducting inductor, we obtain a two-poles electrical machine with an important value of a magnetic field in the air-gap.

Study and test of a new superconducting inductor structure for a synchronous machine

This paper deals with electromagnetic and thermal modelling of wound rotor synchronous machine for automotive applications. Analytical electromagnetic model allows accurate and fast computations of machine performances compared to FE model. $3\mathrm{D}$ lumped parameters thermal model is constructed to evaluate transient and steady state machine temperatures. This model is also precise and fast compared to 3D FE computations.

Analytical Model of Wound Rotor Synchronous Machine for Electric Vehicle Traction

The construction and the tests of a superconducting machine using high and low temperature superconductors are described. The originality of the prototype concerns the design of the inductor. 
The inductor is composed of two coaxial superconducting solenoids made with NbTi wires separated by an YBCO superconducting plate . Both solenoids are fed by a direct current and each of them produces a magnetic field in the same direction.
An inclined superconducting bulk is placed between the two solenoids. It is used as superconducting magnetic barrier. The diamagnetic behavior of a superconducting bulk cooled under zero-field is used to obtain a variation of the magnetic flux density in the air-gap. This kind of inductor is original.
The superconducting motor consists of a 3-phase stator with copper windings and this new kind of inductor. This motor have been designed by 3D finite element computations. After this design, this motor have been built and tested.
The inductor has been immerged in a cryostat and cooled at 4.2 K in liquid Helium. Several tests have been carried out as follows
No-load and short-circuit tests allowed us to determine the equivalent circuit parameters,
Load tests in generator mode at rated conditions. 
Most of the measured external quantities have been checked by 3D finite element computations

A new kind of superconducting motor

This article presents a 3-D semi-analytical model of an axial-flux reluctance coupling. Thanks to the separation of variables method, Fourier series analysis and the convolution theorem (i.e., Cauchy's product), the salient-pole region is modelled by a spatially variable magnetic permeability. Additionally, an iterative algorithm is implemented to account for the magnetic saturation of the iron teeth. The results of the proposed model are compared with a previously published 2-D semi-analytical model, 3-D finite-element method and experimental results. The proposed method appears to be an appropriate tool for the design process of reluctance couplings in cases where the salient poles are saturated.

Non-Linear 3-D Semi-Analytical Model for an Axial-Flux Reluctance Magnetic Coupling

L'objectif de cet article concerne la comparaison de differentes approches analytiques permettant d'estimer le contenu spatio-temporel des forces radiales dans l'entrefer d'une machine asynchrone. En effet, lors d'une phase de conception integrant la problematique du bruit des machines electriques, il est interessant de predire les harmoniques de force d'origine magnetique qui pourraient solliciter la structure. Deux approches sont proposees, la premiere exploite un modele analytique simple reposant sur le calcul de la force magnetomotrice et de la permeance d'entrefer globale ; et la seconde repose sur la theorie des sous-domaines. Ces deux approches sont comparees avec la methode des elements finis et des mesures de vibration valident qualitativement le contenu spatio-temporel des forces radiales dans l'entrefer obtenu par les deux approches.

https://hal.archives-ouvertes.fr/hal-01910631/document

Approche « sous-domaine vs perméance analytique » en vue d’estimer le contenu spatio-temporel des harmoniques de forces radiales d’une machine asynchrone

Thierry Lubin

Papers

Study and test of a new superconducting inductor structure for a synchronous machine

Analytical Model of Wound Rotor Synchronous Machine for Electric Vehicle Traction

A new kind of superconducting motor

Non-Linear 3-D Semi-Analytical Model for an Axial-Flux Reluctance Magnetic Coupling

Approche « sous-domaine vs perméance analytique » en vue d’estimer le contenu spatio-temporel des harmoniques de forces radiales d’une machine asynchrone