###### Abstract
What is more, the sub-circuit division needs to be more detailed in order to improve the calculation accuracy, and the amount of computation would be greatly increased [17]. For the subdomain modeling method, this was adopted to model the rotor magnetic field under no-load and under-load conditions in [18], in which the effect of saturation in iron core was taken into account. In [19], the subdomain model method was used to analyze the air-gap magnetic fields of the permanent magnet motor under no-load and load conditions. In this study, in order to calculate the influence of the saturation effect of the rotor iron core, the saturation effect is equivalent to the sector-shaped saturation region. In [20], the subdomain modeling method was used to analyze the distribution of the air-gap magnetic field of surface-mounted permanent magnet synchronous motors with different slot structures. In [21], the subdomain modeling method was used to model the armature reaction magnetic field of the PMSM, and the inductance parameters were identified. In this study, the effect of saturation in iron core was ignored. For the subdomain method, the mutual influence of the slots can be considered, but it is required to solve the partial differential equation and solve the undetermined coefficient through boundary conditions, which lead to a large amount of calculation. The most important thing for the subdomain method is that the effect of saturation in iron core on the air-gap magnetic field of the motor cannot be calculated directly. The magneto-motive force-magnetic permeability method [22; 23; 24; 25; 26] generally assumes that the magnetic permeability of the rotor core is infinite, so the nonlinear effect of saturation in the iron core on the air-gap magnetic field cannot be considered. At the same time, although the spatial distribution of the armature reaction magnetic field can be calculated by vector superposition, the effect of magnetic saturation is ignored [27; 28]. We can conclude from the above analysis that, in the analytical modeling of air-gap magnetic field of the PMSM, a high-dimensional model and complex boundary conditions will be introduced due to the magnetic saturation in iron core. As a result, the influence of magnetic saturation in iron core has been ignored in the single analytical modeling method, which makes it difficult to accurately reflect the magnetic field distribution. In view of the existing problems in the current analytical methods and in order to accurately calculate the air-gap magnetic field distribution in IPMSMs with mixed eccentricity, an analytical model that accounts for the influence of magnetic saturation in the bridge regions was established by combining the equivalent magnetic circuit network method and the subdomain method. This analytical model shows high accuracy, which has been verified by finite element simulation. Then, using the established model, the distribution of the air-gap magnetic field of the IPMSM with mixed eccentricity values of different severity was calculated, and features reflecting the eccentricity were extracted. The results of this study lay a foundation for developing early identification and diagnosis methods for eccentricity faults in IPMSMs.