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In the optimisation of electrical drives, the required degree of detail in the simulation increases constantly. Especially, the industrial demand on multi‐objective optimisation craves for highly efficient models. The purpose of this paper is to propose a hybrid model for the computation of the air‐gap field of a permanent magnet synchronous motor (PMSM) combining analytic and numeric methods.

The classic conformal mapping (CM) approach is improved by the numeric approximation of the required ansatz‐functions. This approach allows to consider the non‐linear permeability of the applied materials and complex geometries. The non‐linear permeance‐function is described by a one‐dimensional wave varying in time and space.

The permeance‐function has to be derived for different load cases at the actual stage.

A physical motivated modelling allowing for an appropriate interpolation between different load cases is planned in further research.

The proposed approach is applied to a surface mounted PMSM. It is validated by means of a non‐linear finite element analysis.

The hybrid model offers to consider rotors with buried magnets using the CM approach. It is possible to either use analytic or numeric modelling of rotor ansatz‐function, stator current ansatz‐function and permeance‐function with the proposed approach. Non‐linear permeability of iron is modelled by means of a wave representation of the permeance‐function. This can significantly reduce the computational cost in the design and optimisation stage of electrical machines.

This paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap.

The superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP.

The radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results.

This paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method.

When solving the cogging torque of complex electromagnetic structures, such as consequent pole hybrid excitation synchronous (CPHES) machine, traditional methods have a huge computational complexity. The notable feature of CPHES machine is the symmetric range of field-strengthening and field-weakening, but this type of machine is destined to be equipped with a complex electromagnetic structure. The purpose of this paper is to propose a hybrid analysis method to quickly and accurately solve the cogging torque of complex 3D electromagnetic structure, which is applicable to CPHES machine with different magnetic pole shapings.

In this paper, a hybrid method for calculating the cogging torque of CPHES machine is proposed, which considers three commonly used pole shapings. Firstly, through magnetic field analysis, the complex 3D finite element analysis (FEA) is simplified to 2D field computing. Secondly, the discretization method is used to obtain the distribution of permeance and permeance differential along the circumference of the air-gap, taking into account the effect of slots. Finally, the cogging torque of the whole motor is obtained by using the idea of modular calculation and the symmetry of the rotor structure.

This method is applicable to different pole shapings. The experimental results show that the proposed method is consistent with 3D FEA and experimental measured results, and the average calculation time is reduced from 8 h to 4 min.

This paper proposes a new concept for calculating cogging torque, which is a hybrid calculation of dimension reduction and discretization modules. Based on magnetic field analysis, the 3D problem is simplified into a 2D issue, reducing computational complexity. Based on the symmetry of the machine structure, a modeling method for discretized analytical models is proposed to calculate the cogging torque of the machine.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to present an improved conformal mapping (ICM) method that simultaneously considers the influence of relative recoil permeability of PMs, the armature reaction, the stator slotting, and the magnetic saturation on determination of the PM operating point in its different parts.

The ICM method is a time-effective method that considers the magnetic saturation by suitable increments in air-gap length under each tooth and also the width of slot openings. In this paper, the analytical and numerical conformal mappings such as the Schwarz-Christoffel (SC) mapping are used for magnetic field analysis due to the permanent magnets and the armature reaction in one slotted air gap. The field solution in the slotted air gap is obtained through the modulation of field solution in one slotless air-gap using the complex air-gap permeance.

The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts.

The ICM method is applied to one surface mounted permanent magnet (SMPM) motor and is verified by comparing with the corresponding results obtained through finite element method (FEM), and frozen permeability finite element method (FP-FEM).

This paper presents an ICM method with a new technique for saturation effect modeling, which can be used to separate and calculate the on-load components of air-gap field and torque.

The purpose of this paper is to present an improved winding function theory (IWFT) for performance analysis of surface mounted permanent magnet (SMPM) motors, which can precisely and simultaneously consider the impacts of stator slotting, the winding distribution, the magnetic flux density within PMs because of the armature reaction, the PM magnetization angle and the magnetic saturation,.

To obtain this improved analytical model, the conformal mappings (CMs) are introduced to calculate the relative complex permeance of slotted air-gap, which is used to obtain the function of slotted air-gap length. The equivalent magnetizing current model is used to extract the equivalent winding function for each PM pole. For retaining the basic assumption of WFT, the magnetic saturation is also considered by a proper increase in the air-gap length in the front of the stator teeth.

A new hybrid analytical model (HAM) based on WFT is presented in this paper, which can simultaneously and accurately consider the effects of slotting, the magnetic saturation, the variation of PM operating point and the winding distribution. In fact, IWFT removes all the drawbacks of the conventional WFT. Moreover, IWFT is more user-friendly and faster than other analytical and numerical techniques.

The obtained HAM can be used for design, optimization and fault diagnosis in electric machines.

This paper presents a new HAM for accurate modeling the SMPM motors, which includes different considerations of electromagnetic modeling. This new HAM can also be used for modeling the other electric motors.

In the electromagnetic field simulation of modern servo drives, the computation of higher time and space harmonics is essential to consider appearing torque pulsations, radial forces and ripple torques. The purpose of this paper is to propose a method to cover the effect of saturation on the armature flux density within conformal mapping (CM) by an finite element (FE) re‐parameterization.

Field computation by CM techniques is a time‐effective method to compute the radial and tangential field components, but it generally neglects the effect of saturation.

This paper presents a method to re‐parameterize the CM approach by single FE computations so as to consider saturation in the model over a wide operation range of the electrical drive.

The proposed method is applied to a surface permanent magnet synchronous machine, and compared to numerical results obtained by finite element analysis (FEA).

The paper shows that an accuracy similar to that of FE simulations can be obtained with still the low‐computation time that is the characteristic of analytical models.

This paper aims to reviewed analytical methodologies, i.e. lumped parameter magnetic equivalent circuit (LPMEC), magnetic co-energy (MCE), Laplace equations (LE), Maxwell stress tensor (MST) method and sub-domain modelling for design of segmented PM(SPM) consequent pole flux switching machine (SPMCPFSM). Electric machines, especially flux switching machines (FSMs), are accurately modeled using numerical-based finite element analysis (FEA) tools; however, despite of expensive hardware setup, repeated iterative process, complex stator design and permanent magnet (PM) non-linear behavior increases computational time and complexity.

This paper reviews various alternate analytical methodologies for electromagnetic performance calculation. In above-mentioned analytical methodologies, no-load phase flux linkage is performed using LPMEC, magnetic co-energy for cogging torque, LE for magnetic flux density (MFD) components, i.e. radial and tangential and MST for instantaneous torque. Sub-domain model solves electromagnetic performance, i.e. MFD and torque behaviour.

The reviewed analytical methodologies are validated with globally accepted FEA using JMAG Commercial FEA Package v. 18.1 which shows good agreement with accuracy. In comparison of analytical methodologies, analysis reveals that sub-domain model not only get rid of multiples techniques for validation purpose but also provide better results by accounting influence of all machine parts which helps to reduce computational complexity, computational time and drive storage with overall accuracy of ∼99%. Furthermore, authors are confident to recommend sub-domain model for initial design stage of SPMCPFSM when higher accuracy and low computational cost are primal requirements.

The model is developed for high-speed brushless AC applications.

The SPMCPFSM enhances electromagnetic performance owing to segmented PMs configuration which makes it different than conventional designs. Moreover, developed analytical methodologies for SPMCPFSM reduce computational time compared with that of FEA.

The purpose of this paper is to present a new optimal design for integral slot permanent magnet synchronous motors (PMSMs) to shape the air-gap magnetic field in sinusoidal and to reduce the cogging torque, simultaneously.

For obtaining this new optimal design, the influence of different magnetizations of permanent magnets (PMs), including radial, parallel and halbach magnetization is investigated on the performance of one typical PMSM by using the conformal mapping (CM) method. To reduce the cogging torque even more, the technique of slot opening shift is also implemented on the stator slots of analyzed PMSM without reduction in the main performance, including the air-gap magnetic field, the average torque and back-electromotive force (back-EMF).

Finally, an optimal configuration including the Hat-type magnet poles with halbach magnetization on the rotor and shifted slot openings on the stator is obtained through the CM method, which shows the main reduction in cogging torque and the harmonic content of air-gap magnetic field.

The obtained optimal design is completely practical and is validated by comparing with the corresponding results obtained through finite element method.

This paper presents a new optimal design for integral slot PMSMs, which can include different design considerations, such as the reduction of cogging torque and the total harmonic distortion of air-gap magnetic field by using the CM method.

The purpose of this paper is to study the effect of curvature on the magnetic field distribution and no-load rotor eddy current losses in electric machines, particularly in high-speed permanent magnet (PM) machines.

The magnetic field distribution is obtained using conformal mapping, and the eddy current losses are obtained using a cylindrical multilayer model. The analytical results are validated using a two-dimensional finite element analysis. The analytical method is based on a proportional-logarithmic conformal transformation that maps the cylindrical geometry of a rotating electric machine into a rectangular configuration without modifying the length scale. In addition, the appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. Based on this conformal transformation, a coefficient to quantify the effect of curvature is proposed.

Neglecting the effect of curvature can produce significant errors in the calculation of no-load rotor losses when the ratio between the air-gap length and the rotor diameter is large.

The appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. The proportional-logarithmic transformation proposed provides an insight into the effect of curvature on the magnetic field distribution in the air-gap and no-load rotor losses. Furthermore, the proposed curvature coefficient gives a notion of the effect of curvature for any particular geometry without the necessity of any complicated calculation. The case study shows that neglecting the effect of curvature underestimates the rotor eddy-current losses significantly in machines with large gap-to-rotor diameter ratios.