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Synchronous Reluctance Machines (SRM’s) are gaining more and more importance in various fields of application thanks to their known merits like rugged construction, high efficiency, absence of field windings, no or reduced need for permanent magnets. Out of the possible design variants, in this paper SynRel motors with uniform mechanical air-gap and circularly-shaped flux barriers are taken into account and a conformal-mapping approach to their analytical modeling and simulation is proposed. A suitable conformal transformation is introduced to compute the reluctance of each rotor circularly-shaped flux barrier and the result is then used to analytically determine the air-gap flux density distribution and the electromagnetic torque of the machine in arbitrary operating conditions. The accuracy of the methodology proposed is assessed against finite element analysis.

An electric machine equipped with n stator phases is characterized by a set of n × n phase inductances as concerns the stator section. In the case of nonuniform air gap, these inductances vary as the rotor moves. For their numerical determination as functions of the rotor position an accurate computation algorithm is proposed in this paper based on winding function theory. For permeance function identification, a numerically efficient method is employed based on the magnetostatic finite-element analysis of only three appropriately simplified machine models. In the presence of a field circuit, computation of mutual inductances among it and stator phases is also covered with the same approach. An extension of the method to permanent-magnet machines is also presented. Results are assessed on a six-phase synchronous generator prototype equipped with either a salient-pole wound-field rotor or with an interior permanent-magnet rotor.

The computation of end-coil leakage inductances of electric machines is a challenging task due to the complicated leakage flux 3-D distribution in the winding overhang region. In this paper, the problem of computing the field-circuit leakage inductance of round-rotor synchronous machines is addressed. The proposed method is fully analytical and descends from the symbolical solution of Neumann integrals applied to the computation of self-inductance and mutual inductance combined with the method of mirror images to account for core effects. With respect to existing analytical approaches, the methodology requires neither numerical integral solutions nor discretizing the end-coil geometry into small straight elements. The accuracy of the proposed technique for computing the mutual inductance between two single-end turns is assessed against measurements on a dedicated experimental setup. The extension of the method to the computation of the entire field-circuit end-coil leakage inductance is assessed by comparing with the 3-D finite-element analysis.

The complex relative permeance function is a useful mathematical tool to study the magnetic field of electric machines with slotted air gap. In the literature, the complex permeance function is usually identified by means of numerical techniques based on conformal mapping. In this paper an alternative analytical approach is proposed. The method is based on solving the magnetostatic differential field equation over a portion of the slotted air gap by imposing suitable boundary conditions in the slot opening region. Such boundary conditions exploit the mathematical law which governs the divergence of the magnetic field in the neighborhood of corner-shaped ferromagnetic regions. Furthermore, the results of Carter theory on slot fringing effects on the air gap field are used. A simple easy-to-compute formula is obtained for the complex permeance function. Its accuracy is assessed by comparison with Finite Element Analysis (FEA).

Cogging torque is a known disadvantage of surface permanent magnet (SPM) machines, especially if equipped with open stator slots. A possible strategy to reduce the cogging torque is to use suitably designed non-isotropic magnetic wedges. The design of such wedges for cogging torque minimization requires a genetic optimization approach. This has been done in previous works using Finite Element Analysis (FEA) simulations to predict the cogging torque for each machine design being explored, leading to a very time consuming optimization process. In this paper, the same optimization is performed using an analytical method to compute the cogging torque. It is shown that the optimization process, based on the analytical formula for cogging torque prediction, leads to the same result as the FEA-based procedure, but with a significant reduction in the computational burden.

Round conductive bars embedded in semi-closed slots are frequently used in the construction of electric machinery, for instance in the squirrel cage of induction motors. Frequently, such as in the study of induction motor steady-state performance at rated slip, it is useful to estimate the slot leakage inductance of these conductors under the hypothesis of no eddy currents and no magnetic saturation. This is usually done through simple approximated analytical formulas available in the literature. In this paper, an improved explicit ready-to-use leakage inductance expression for circular bars embedded in semi-closed slots is derived by solving Poisson's equation in the slot domain. The precision of the proposed formulation is assessed against Finite Element Analysis (FEA) for various slot geometries and is shown to always give very accurate results, with errors below 2%. Conversely, approximated simplified formulas available from the literature are demonstrated to possibly give large errors, which exceed 20% for some explored slot geometries.

Squirrel-cage induction motors are the most widely used type of electric machinery in industrial applications thanks to their rugged, cheap and robust construction. For the fast prediction of induction motor steady-state performance without the need for time-consuming finite-element analyses, the equivalent circuit parameters of the machine need to be calculated, including rotor slot leakage inductances. This paper, in particular, proposes a new improved analytical formula to determine the rotor slot leakage inductance in squirrel-cage induction motors with rectangular-shaped bars. The formula is obtained by solving Poisson's equation in the slot domain. Results are assessed by comparison against Finite Element Analysis (FEA). The precision of the presented methodology is also compared to that of approximated analytical models available from the literature. The comparison shows that the accurate formula proposed is in excellent agreement with FEA with errors below 2%, while the simplified model generally leads to errors above 10% which increase as the height-to-width bar ratio decreases.

Slot leakage field accounts for an important quota of the total leakage flux in electric machines. The computation of unsaturated slot leakage inductances can rely on analytical formulas for simple open slot shapes, while the case of semiclosed slots is more critical and typically requires finite element analysis (FEA) or analytically solving the field over the whole machine domain. This paper sets forth an analytical procedure for computing the leakage field in semiclosed slots of unsaturated electric machines. The method is based on solving Maxwell's equations in the slot domain alone, which is made possible by appropriately defining boundary conditions in the slot opening region. The method proposed is assessed by comparison with FEA. Validations indicate that a good accuracy is achieved by the presented approach in predicting unsaturated leakage inductances, while FEA is required when magnetic saturation effects need to be taken into account.

Various analytical techniques have been proposed in the literature for cogging torque computation in Surface Permanent Magnet (SPM) machines. Among the various available methods, the ones found to be satisfactorily accurate are based on the Maxwell's stress tensor, which involves both normal and tangential air-gap field and lead to quite involved calculation formulas. In this paper, a relatively simple alternative is proposed where permanent magnets are modeled as equivalent field circuits to which a well defined winding function can be associated. The approach leads to a plain cogging torque formulation where only the normal no-load air-gap flux density appears. The accuracy of the method is assessed by Finite Element (FE) analysis on some sample SPM machine geometries. The results are shown to match FE simulations with a satisfactory accuracy compared to Maxwell-stress-tensor-based analytical techniques available from the literature.