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This paper presents a fast analytical model for estimating the components of the PM flux density distribution in the air-gap for a number of interior permanent magnet synchronous machines (IPMSMs). Deriving the two-dimensional (2-D) analytical model for IPMSMs is more challenging compared to that of surface-mounted permanent magnet synchronous machines (SPMSMs) due to the inconsistent geometry of the rotor in polar coordinates. IPMSMs are usually modeled by using 0-D or 1-D methods such as the magnetic equivalent circuit (MEC); however, the MEC method is unable to take into account the tangential component of the magnetic flux density vector. In this paper, a 2-D analytical no-load electromagnetic model for five rotor topologies of IPMSMs is proposed. The effects of the stator slots on the radial component of the PM flux density distribution in the air-gap are then included by defining an air-gap function. The effects of the stator slots on the tangential components of the PM flux density distribution in the air-gap are also considered by injecting virtual surface currents (VSCs) or virtual permanent magnets (VPMs). For verification purposes, the analytical results are compared with those of the finite element method (FEM) and the experimental results of one of the cases. [ABSTRACT FROM AUTHOR]

In this paper, by solving the Maxwell's equations, an analytical model is developed for the prediction of the air gap flux density in the eccentric permanent magnet (PM)-inset machines at no-load and on-load conditions. Since in this model neither Schwartz–Christoffel transformation nor perturbation analysis is used, it is fast and accurate. In the modeling process, the stator of the eccentric machine is replaced with an equivalent surface current (ESC), which is injected at the stator bore. Distribution of the ESC is unknown and must be selected, such that the resultant tangential field satisfies the boundary condition at the stator bore contour. To apply this condition, the flux density of the PMs, armature current, and the ESC are obtained by applying the subdomain analysis and using a conformal transformation. The armature current and ESC are considered as a surface current sheet at the stator bore. The back electromotive force and inductances of the eccentric machine are obtained in the proposed model. In addition, using the Maxwell stress tensor, the unbalanced magnetic force, and the electromagnetic torque are computed. Finally, the model is verified by means of finite element analysis. [ABSTRACT FROM AUTHOR]

In this work, an analytical technique is developed for modeling of the air gap flux density in the slotless eccentric surface-mounted permanent magnet (PM) machines. In the developed model, a 2-D solution for the Poisson equation is provided. In the modeling process, the eccentric stator is replaced with an equivalent current sheet at the stator bore. This current sheet is selected such that the overall tangential flux density caused by the PMs and the current sheet at the removed stator bore is zero. To find the contribution of current sheet on the air gap flux density, a conformal transformation is applied. The obtained exact values of the instantaneous air gap flux density components are used to compute the variables of the eccentric machine such as the back-EMF, the electromagnetic torque, and the unbalanced magnetic force. The provided model is valid for static, dynamic, and even mixed rotor eccentricity conditions. Finally, finite-element analysis is applied to verify the proposed model. [ABSTRACT FROM PUBLISHER]