Low-speed brushless permanent magnet machines are ideal for use in gearless propulsion systems. It is important to provide a precise analytical model to determine the performance characteristics of these machines. One of the challenges in designing permanent magnet machines is the elimination of the pulsating torque due to the presence of cogging torque and torque ripple components. The use of dummy slots (auxiliary teeth) is one of the most common methods of reducing pulsating torque phenomenon. In this paper, an accurate two-dimensional analytical model for calculating the magnetic vector potential in brushless permanent magnet machines is presented, taking into account the effect of stator slots, stator dummy slots, the magnetic direction of permanent magnets and phase winding style. The proposed analytical method is based on solving the Laplace’s and Poisson’s equations using the separation of variables method for given regions in the subdomain approach. In the proposed method, in order to achieve a simpler analytical model, by changing the variable, the polar coordinate system is converted to a quasi-Cartesian coordinate system. Therefore, in mathematical terms, the hyperbolic functions are used instead of exponential ones. To validate the proposed model accuracy, the performance of a 14 kW low-speed brushless permanent magnet motor is calculated analytically and compared with the results of numerical method and the experimental tests. Comparison of the performance results of this motor shows the consistency of analytical, numerical and experimental results.
