Algorithmic Design of Modular Two-Layer Multiphase Windings Based on Number Theory

Many electromechanical specialists have attempted to move away from the classical method of designing windings of electrical machines using the star of slot electromotive forces, but their approaches are not always simple or universal. This article proposes a straightforward algorithmic method of winding synthesis based on number theory, which makes it possible to compute the distribution table of symmetrical multiphase, multimodular windings. Analytical expressions are provided for determining the assignment of coils to the corresponding phases, phase zones, and winding modules by sampling coils from a closed-ring structure. The method allows one to determine the direction of coil connections within a phase and covers both overlapping and non-overlapping windings. Three characteristic cases of the relationship between the number of coils and the number of pole pairs in multiphase alternating-current electrical machines are analyzed from the perspective of number theory. Conditions for implementing symmetrical windings are presented. The distribution factors of modular windings for higher field harmonics are evaluated. To validate the approach, examples of application and experimental results are provided.