This paper presents a nonlinear analytical (NA) solution based on subdomains for predicting magnetic field and performances of a spoke array vernier permanent magnet (SAVPM) machine which has spoke array type permanent magnet (PM) excitation. On one hand, equivalent current sheets replace tangentially magnetized PMs to make the magnetic vector potential in the region with PMs satisfy a Laplace's equation, which simplifies the problem and reduces the workload of numerical calculation. On the other hand, in contrast to the existing literature, regions of soft-magnetic material such as a tooth and a rotor pole are subdivided into small pieces, and are no longer a whole with a single permeability for considering local magnetic saturation. Poisson's and Laplace's equations with the given permeability of soft-magnetic material are analytically solved by separation technique of variables in seven subdomains, and nonlinear iteration is used to determine the solution of NA and update soft-magnetic material permeability. NA solves the magnetic field and performances of a SAVPM machine. Frozen permeability method (FPM) is used to determine PM flux linkage and d-axis inductance under load. Results from the NA model have been compared with those from FEA and experiments.

This study presents an analytical model (ANA) for predicting magnetic field and performances of a fractional slot (FS) double‐layer‐winding (DLW) vernier permanent magnet (VPM) machine. Magnetic vector potential equations of a FS DLW VPM machine are analytically solved by the technique of variable separation in three subdomains, that is, regions of permanent magnets (PM), air‐gap, and slots in 2‐D polar coordinate system. Field distributions and performances, such as flux linkage, electromotive force (EMF), torque and inductance of a FS DLW VPM machine are developed. Results from ANA of an 18‐slot/2‐stator‐pole‐pair FS DLW VPM machine prototype have been compared with those from finite element analysis (FEA), which indicates that ANA has a huge advantage in the computing speed in addition to a good accuracy. In the end, a prototype is built and its EMF and torque are tested in experiment platforms in which the results verify ANA. The necessity and importance of the research is that the model is an analytical method which provides a close solution of magnetic field and performances of a FS DLW VPM machine and its calculation time is much less than FEA on the base of a good precision.