The paper presents a mathematical base modeling combined to Modified-Winding -Function-Approach (MWFA) for eccentricity fault detection of a round-rotor synchronous machine. For this aim, a 6-polemachine is considered, and the machine inductances are computed byMWFA in healthy and also under eccentricity fault. A numerical discrete-time method has been proposed to machine modeling in voltage-fed case, and an exact analytical method is proposed to calculate the machine'scurrents and torque. A method is introduced for both static and dynamic eccentricity fault diagnosis, which is proposed for first time. A mathematical base method is introduced for machine modeling, and new results are obtained to a novel method addressing for eccentricity fault diagnosis. The method is validated by Finite-Element-Method (FEM) so accuracy of theproposed method is proofed. Manuscript profile