Calculation of synchronous reactances of small permanent-magnet alternating-current motors: comparison of analytical approach and finite element method with measurements

The synchronous reactances of permanent magnet (PM) motors have been determined using: (1) analytical method, i.e., form factors of the stator field (armature reaction factors), (2) finite element method (FEM), and (3) experimental tests on a special machine set. The analytical method is widely used in calculations of synchronous reactances of salient pole synchronous machines with electromagnetic excitation. Rotors of PM synchronous machines have more complicated structures, hence it is more difficult to predict accurately the magnetic field distribution in their airgaps in order to find the form factors of the stator field. Numerical methods of field analysis can easily solve this problem. The FEM can predict both the synchronous and mutual (armature reaction) reactances in the d and q axes. The leakage reactance can then be evaluated as a difference between synchronous and mutual reactances. As an example, a small, three-phase, four-pole motor with SmCo surface mounted PM's (three parallel magnets per pole), and mild-steel pole shoes has been investigated. Such a complicated rotor structure has been intentionally designed in order to be able to compare the advantages and disadvantages of the analytical method and the FEM. In the FEM, the reactances have been calculated using both the flux linkage and current/energy perturbation method. Synchronous reactances as functions of the stator current and load angle obtained analytically from the FEM modeling and from measurements have been compared.