Purpose 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,. Design/methodology/approach 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. Findings 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. Practical implications The obtained HAM can be used for design, optimization and fault diagnosis in electric machines. Originality/value 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.
Purpose 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. Design/methodology/approach 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). Findings 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. Practical implications The obtained optimal design is completely practical and is validated by comparing with the corresponding results obtained through finite element method. Originality/value 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.
An enhanced analytical technique based on winding function theory (WFT) is developed in this paper, which can be used for accurate electromagnetic modeling of the induction motors. The enhanced winding function theory (EWFT) acts based on the calculation of inductance matrix of stator and rotor windings while accurately consider the air-gap length function and the magnetic saturation in iron parts, simultaneously. By using the conformal mappings (CMs), a modified air-gap length function is presented for a typical wound rotor induction motor (WRIM), which considers the slot effect on flux tubes in slotted air-gap. The finite element method (FEM) is used to confirm the accuracy of air-gap length function obtained through EWFT. Compared to conventional WFT, EWFT is also redefined to consider the magnetic saturation by using the equivalent virtual winding functions. In real, the magneto motive force (MMF) drops in iron parts of stator and rotor obtained through magnetic equivalent circuit (MEC) are replaced with a virtual winding. In this paper, by using EWFT, a 3-D lookup table is prepared in advance for elements of inductance matrix and their derivative, and it is then used to model the startup and steady-state conditions of WRIM under different load torques. To confirm the accuracy of EWFT, the some corresponding results of EWFT, FEM, and experiment setup are finally compared.
A new hybrid analytical model (HAM) based on conformal mapping (CM) method and magnetic equivalent circuit (MEC) model is presented in this paper for electromagnetic modelling of cage rotor induction motors (CRIMs) used in electric submersible pumps (ESPs). For every operating point, the iron parts are modelled with a non-linear MEC model to calculate the equivalent virtual currents, which represent the influence of magneto motive force (MMF) drops and MMF sources in stator and rotor cores. The effects of the equivalent virtual currents on the air-gap magnetic field are then considered using the CM method and Hague's solution. This approach for calculating the air-gap field is also used to prepare a 3-D lookup table (3-D LUT) for each element of inductance matrix and derivative of inductance matrix in terms of rotor position. These LUTs are then used for transient modelling and analysis of CRIM under no-load and loading conditions. The accuracy of proposed HAM is validated by comparing the results obtained through HAM with corresponding results obtained from finite element method and experiment set-up. K E Y W O R D S conformal mapping (CM), hybrid analytical model (HAM), inductance, magnetic equivalent circuit (MEC) model, magnetic field, magnetic saturation This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Purpose 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. Design/methodology/approach 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. Findings The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts. Practical implications 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). Originality/value 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.
Accurate modeling of slotting and magnetic saturation effects has been two main challenges for analytical modeling of electric machines. In this article, first, different techniques such as sub-domain (S-D) model, winding function theory, magnetic equivalent circuit (MEC) model, and conformal mapping (CM) method are introduced to analytical model and analysis of electric machines. These techniques are also compared in terms of their accuracy, and computational complexity. Second, with respect to the comparison results, a new hybrid analytical model is presented for electromagnetic modeling of wound rotor induction motors, which consider the modeling accuracy of slotting and magnetic saturation effect, simultaneously. In this way, the air-gap region is modeled by using S-D model, and the iron parts are considered by using MEC model assisted by CMs. In final, the analytical results are verified by comparing with corresponding results obtained through finite element method and experiment set-up.
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