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Purpose – The purpose of this paper is to comparatively study a synchronous reluctance machine (SynRM) and a permanent magnet assisted synchronous reluctance machine (PMASynRM) as alternatives of the interior permanent magnet synchronous machine (IPMSM), and to investigate the performance and conclude both advantages and disadvantages. Design/methodology/approach – A unified mathematical model is established for the IPMSM, SynRM and PMASynRM. Then finite element method (FEM) is used to compare the electromagnetic performance. Permeability-frozen method is utilized to distinguish basic electromagnetic torque and reluctance torque. Findings – The PMASynRM can improve the power factor of the SynRM, overcome the drawback of the IPMSM in the high-speed flux-weakening region and is more proper to operate over a wide speed region. The SynRM is mechanically robust for lacking of the permanent magnets, and the PMASynRM can keep similar rotor stress as the SynRM by optimizing the magnets. Assembly of the SynRM is the simplest, and the economic performance of the SynRM and PMASynRM could be much better than the IPMSM which even uses ferrite magnets. Practical/implications – The SynRM can produce identical torque and efficiency compared with the IPMSM except the poor power factor. The poor power factor could be improved by adopting the PMASynRM, which is proved to be able to act as an alternative of the IPMSM for low-cost high-performance application. Originality/value – This paper provides the theoretical model of the IPMSM, SynRM and PMASynRM in a unified format. The electromagnetic, mechanical and economic performances of the three kinds of synchronous motors are compared comprehensively. Then, both the advantages and disadvantages are summarized. [ABSTRACT FROM AUTHOR]