General modeling of the windings for multi-phase ac machines

This paper, which deals with the winding modeling of ac multi-phase machines with a regular distribution of the stator slots, details an original matrix modeling of the stator winding. First, the properties of the balanced multi-phase windings (with integral-slot and fractional-slot patterns) are analysed. The winding function approach, one of the most common way to model the winding distribution effects on the stator rotating field, is then introduced. For multi-phase machines, it will be shown that the pole number generated by the winding distribution depends on a new parameter: the circularity index. The discrete nature of the winding, imposed by the stator slots, leads to the development of a discrete modeling of the winding obtained from sampling the winding function: two matrices, the winding function matrix and the distribution function matrix, are introduced to characterize the multi-phase winding. This matrix approach is thus a concise way to calculate the winding factors and to estimate the set of self and mutual stator inductances for smooth air gap multi-phase machines. A particularly original method of obtaining an analytical expression for the leakage mutual inductance is described. The results are validated with two experimental 5-phase PM machines by using experimental measurements and numerical simulations

Comparizon of Conventional and Unconventional 5-phase PM Motor Structures for Naval Applications

Multi-phase motors are widely used in marine propulsion. In this paper, a Multi-machine modeling of Surface Mounted PM motors is presented and applied to a 5-phase one. The latter is proved to be equivalent to a set of two-phase fictitious machines each ones being characterized by a set of specific harmonic rank. A simple control consists in supplying each fictitious machine by a current which contains only one harmonic. A five phase machine is then supplied by currents with only both first and third harmonics. Considering this kind of control, it is proved that for given stator resistance and average torque the Joule losses and the torque ripple are minimized if a simple criterion on the harmonics of electromotive force at constant speed is fullfilled. Different structures of rotor are then compared to examine numerically which improvements can be practically obtaine

Investigations on the performances of the electrical generator of a rim-driven marine current turbine”

In this paper, the electrical generator of a rim-driven horizontal-axis current turbine is modeled in detail. Its main characteristics and performances are evaluated (efficiency, mass, cost, etc). This generator is of permanent magnet direct-driven synchronous type and is connected to a variable speed power electronics drive. It is then compared to a more traditional technology (a pod generator) in terms of mass and cost for a common set of specification. In addition, due to the specific geometry of the machine, the use of low-cost ferrite magnets is investigated in place of NdFeB magnets

A coupled electromagnetic / hydrodynamic model for the design of an integrated rim - driven naval propulsion system

This paper presents an analytical multi-physic modeling tool for the design optimization of a new kind of naval propulsion system. This innovative technology consists in an electrical permanent magnet motor that is integrated into a duct and surrounds a propeller. Compared with more conventional systems such as pods, the electrical machine and the propeller have the same diameter. Thus, their geometries, in addition to speed and torque, are closely related and a multidisciplinary design approach is relevant. Two disciplines are considered in this analytical model: electromagnetism and hydrodynamics. An example of systematic design for a typical application (a rim-driven thruster for a patrol boat) is then presented for a set of different design objectives (efficiency, mass, etc). The effects of each model are commente

General modeling of the windings for multi-phase ac machines

This paper, which deals with the winding modeling of ac multi-phase machines with a regular distribution of the stator slots, details an original matrix modeling of the stator winding. First, the properties of the balanced multi-phase windings (with integral-slot and fractional-slot patterns) are analysed. The winding function approach, one of the most common way to model the winding distribution effects on the stator rotating field, is then introduced. For multi-phase machines, it will be shown that the pole number generated by the winding distribution depends on a new parameter: the circularity index. The discrete nature of the winding, imposed by the stator slots, leads to the development of a discrete modeling of the winding obtained from sampling the winding function: two matrices, the winding function matrix and the distribution function matrix, are introduced to characterize the multi-phase winding. This matrix approach is thus a concise way to calculate the winding factors and to estimate the set of self and mutual stator inductances for smooth air gap multi-phase machines. A particularly original method of obtaining an analytical expression for the leakage mutual inductance is described. The results are validated with two experimental 5-phase PM machines by using experimental measurements and numerical simulations

A Connected Version of the Graph Coloring Game

The graph coloring game is a two-player game in which, given a graph G and a set of k colors, the two players, Alice and Bob, take turns coloring properly an uncolored vertex of G, Alice having the first move. Alice wins the game if and only if all the vertices of G are eventually colored. The game chromatic number of a graph G is then defined as the smallest integer k for which Alice has a winning strategy when playing the graph coloring game on G with k colors. In this paper, we introduce and study a new version of the graph coloring game by requiring that, after each player's turn, the subgraph induced by the set of colored vertices is connected. The connected game chromatic number of a graph G is then the smallest integer k for which Alice has a winning strategy when playing the connected graph coloring game on G with k colors. We prove that the connected game chromatic number of every outerplanar graph is at most 5 and that there exist outerplanar graphs with connected game chromatic number 4. Moreover, we prove that for every integer k ≥ 3, there exist bipartite graphs on which Bob wins the connected coloring game with k colors, while Alice wins the connected coloring game with two colors on every bipartite graph

Étude comparative de différents correcteurs pour la commande optimale avec défauts d’une machine pentaphasée

La version éditeur de cet article est accessible à l'adresse suivante : doi:10.3166/ejee.15.377-400The use of multiphase PM synchronous machines associated with VSI drives appears to be a very efficient solution when a high level of reliability, compactness and acoustic behaviour is required. This kind of solution is for example very useful in naval propulsion systems. The paper deals with the optimal control of a 5-phase PM machine associated with a VSI under fault conditions. This work focus on the use of such a system in normal and fault operations. The studied fault operations are open circuited phase fault conditions. Previous works have shown that, with this kind of 5-phase drive, it is possible to determine optimal currents references which maximize the torque density and reduce the torque pulsations of the machine when one or two phases are open circuited. In this fault case, classical linear controllers (as PID for example) cannot provide a correct tracking of these optimal reference currents because they have a highly dynamical behavior. Using this optimal reference current generation, we propose in this paper to compare classical PID controllers with fixed band and adaptive band hysteresis controllers. This comparison is done using Matlab/Simulink simulation in the case of a 5 phase surface mounted permanent magnet machine in normal and open-circuited fault operations. Study results show that adaptive band hysteresis control allows a good tracking of these unconventional reference currents with a fixed switching frequency for the VSI. In this case of adaptive s band hysteresis control appears to be particularly efficient

Commande avec prise en compte de défauts d’ouverture de phase d’une machine pentaphasée à aimants associée à un onduleur de tension MLI

Cet article est consacré à l’étude d’une méthode de commande d’une machine synchrone à aimant permanent à cinq phases associée à un onduleur de tension à MLI intersective. On s’intéresse au cas de la commande en mode normal et en mode dégradé. Les défauts étudiés sont liés à la déconnexion d’une phase ou de plusieurs phases. Dans ce cas la méthode étudiée, qui est basée sur une approche vectorielle, permet une détermination en ligne des courants de référence optimaux adaptés au défaut. De ce fait, cette méthode garantit un fonctionnement continu de la machine. L’approche de commande utilisée est basée sur le formalisme multimachine des machines polyphasées. Le contrôle des courants utilise des régulateurs PID qui seront comparés des régulateurs type hystérésis en mode normal et en mode de défaut. Les résultats de simulation effectués sur MATLAB / Simulink sont présentés et discutés afin de vérifier les performances de la stratégie et des régulateur étudiés. Ils montrent en particulier l'efficacité de la régulation de type PID en mode normal et de la régulation par hystérésis en mode de défau