[Objective] This study aims to explore the efficiency and accuracy of distribution coefficient calculations for fractional-slot concentrated winding (FSCW) to further propose universally applicable calculation formulae. [Methods] Focusing on the distribution coefficients of FSCW

three innovative methods for calculating the distribution coefficient were proposed and comprehensively compared. The definition method

based on the classical theory of winding coefficients

derived the calculation formula through Fourier decomposition and the fundamental definition of the distribution coefficient. The harmonic synthesis method

utilizing the superposition principle of spatial magnetomotive force vectors

established a vector superposition model in a multi-pole-pair coordinate system. The phasor synthesis method incorporated the concept of time-domain phasors into spatial harmonic analysis to develop a winding distribution characterization method in the complex domain. Using theoretical analysis and numerical calculations as the basis

combined with analysis of case studies

the principles

applicability

and calculation characteristics of each method were summarized. [Results] Precise calculations for three typical slot-pole combinations were conducted. The results showed that the numerical values obtained from all three calculation methods were identical. [Conclusion] The definition method considers only the harmonic magnetomotive force amplitudes

but fails to effectively analyze the peak and valley distribution of the synthesized magnetomotive force along the axis. The harmonic synthesis method and phasor synthesis method incorporate both the amplitude and direction of the synthesized magnetomotive force phasors

thereby making them suitable for accurately determining the peak and valley distributions in the synthesized magnetomotive force harmonic. Derived from different perspectives

the three methods provide three distinct calculation formulae applicable to various distribution coefficient calculations

providing a theoretical basis for optimizing the design of FSCW.