MEC-Based Modeling and Sizing of a Tubular Linear PM Synchronous Machine

Linear machines are currently considered as viable candidates for direct-drive wave and free-piston energy converters. This paper is devoted to an approach based on a magnetic equivalent circuit (MEC), which is also called lumped circuit, dedicated to the modeling and sizing of a tubular linear permanent-magnet synchronous machine (T-LPMSM). The proposed approach considers, in a first step, the cancelation of the end-effect phenomenon. To do so, a dedicated design procedure, consisting in achieving a $2pi/3$-shift between the armature phase flux linkages by selecting a fractional ratio of the stator pole pitch to the mover one and balancing the amplitudes of the phase flux linkages by extending the stator magnetic circuit with teeth of appropriate dimensions, is firmly applied on two basic T-LPMSM topologies using a dedicated MEC. Then, an investigation of the influent sizing parameters on the force production capability of the initial concept is carried out. The MEC-based prediction of the force requires the incorporation of the mover displacement, yielding the so-called “position varying MEC” on one hand and the armature magnetic reaction on the other hand. The finite-element analysis of the armature phase flux linkages and the developed force enable the validation of the results yielded by the established MECs.