Particular Reduced Scalar Potential Formulation for End Winding Magnetic Circuits modeling enabling increased Field Weakening in PM motors

Abstract

Permanent magnet machines are now-a-days very popular in electric traction applications requiring a wide constant-power speed range. However, the field weakening action, necessary in higher speeds creates important air gap field distribution distortion and increased losses leading to particular configurations search, such as conjunction with variable reluctance rotors [1], pole shoe configurations [2], flat embedded magnet topologies [3], convenient stator windings and permanent magnet arrangements [4], axial flux topologies [5]. In the present paper a convenient configuration of stator windings in permanent magnet motors is proposed involving appropriate additional end winding magnetic circuits in order to achieve inductance management. Such a technique can be applied in all permanent magnet motor configuration cases and enables increased flux weakening capability in high rotor speeds, resulting in substantial efficiency improvements. The optimal design of these extra iron cores can be modeled by adopting a particular reduced scalar potential formulation and the resulting finite element model can be facilitated considering appropriate two dimensional configurations. The overall analysis is performed through co-simulation of the additional magnetic circuits simultaneously with the permanent magnet synchronous machine active part. The proposed methodology enables appropriate handling of increased flux weakening effects in traditional surface mounted permanent magnet motors. It exploits the end zone part of the windings, which does not contribute in the machine torque and performance. The main concept involves introduction of convenient magnetic circuits in the end zone parts of stator coils. These magnetic circuits enable magnetic coupling with auxiliary windings which are connected to appropriate varistors and are energized in desired electromotive force values developed at specific speed ranges through convenient selection of turns ratios. The magnetic material proposed for the additional magnetic circuits is a particular Ferrite ensuring low losses in order not to compromise the machine efficiency. Moreover, the increase of the stator windings leakage inductance is reduced when the auxiliary windings are not energized and is greatly increased when the varistors are activating them. The representation of such configurations necessitates in general a 3D finite element modeling of the whole machine, which is very demanding in computational means. However, an important reduction in computation requirements can be achieved by adopting an appropriate reduced scalar potential formulation, involving one unknown per node. A further calculation simplification can be obtained by implementing an appropriate two dimensional axisymmetric representation for the additional magnetic circuits in conjunction with a two dimensional Cartesian representation of the motor active part and by adopting a direct coupling of field and circuit equations [6]. The methodology developed has been applied in a permanent magnet synchronous machine case with surface permanent magnet rotor configuration and rated power of 100 kW. The motor end winding geometry for one pole part illustrating the additional ferrite toroidal magnetic circuits positioning is shown in Fig. 1. The obtained efficiency maps in cases without and with the additional magnetic circuits are shown in Figs. 2a and 2b, respectively, illustrating the important efficiency improvement resulting in high speed ranges. It may be noted that the proposed technique can offer great services in field weakening action and respective efficiency improvements at high speed ranges of all permanent magnet machine configurations implemented in electric traction applications. **