An Analytical Subdomain Model for Dual-Rotor Permanent Magnet Motor With Halbach Array

Golovanov, Dmitry; Gerada, Chris

doi:10.1109/tmag.2019.2941699

Cited by 30 publications

(20 citation statements)

References 12 publications

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“…An ideal segmentation of Halbach array have been assumed for PMs region: in each segment of PM the DOM is constant in radial and tangential direction. The Fourier decomposition of the PM magnetization function is given in [14]. The equation (46) describes the distribution magnetic vector potential in PM region.…”

Section: Inductance Matrixmentioning

confidence: 99%

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Analytical Methodology for Modelling of Circulating Current Loss in Synchronous Electrical Machines With Permanent Magnets

Golovanov

Gerada

2022

IEEE Trans. Energy Convers.

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This paper describes a novel analytical methodology for modelling winding copper losses as a result of circulating currents (CC) in permanent magnet synchronous machines (PMSM). CCs are important to be considered at an early design stage especially in high frequency and high performance machines where sub-optimal design choices can lead to significant alternating current (AC) losses. Nowadays mainly FEM method is used for precise calculation of circulating currents. However, it suffers on significant computational time required for building models and simulation of circulating current effect that makes it inapplicable for optimization purpose. The paper demonstrates the computationally efficient methodology through comparison with FEM based models for high power density PMSM with concentrated winding and validation against experimental results for a stator section at the fundamental frequency from 500 Hz to 2000 Hz. The methodology allows simulation of CC and AC Ohmic losses when machine supplied by any current waveforms, for arbitrary size and location of the conductors in the slots. A key novelty of the proposed method is the utilization of subdomain (SDM) approach in conjunction with solution of a system of ordinary differential equations (ODE) for an equivalent electrical circuit of machine windings. This approach is precise and fast but has never been used before for circulating current loss evaluation in windings of electrical machines. The model is intended to be used at the design stage of an electrical machine where multiple geometric dimensions, winding configurations and conductor placement in the slot are considered towards an optimal design. Index Terms-Analytical model, circulating current loss, AC loss in electrical machines NOMENCLATURE ܴ ௌଵ , ܴ ௌଶ . . ܴ ௌ Strands resistance ‫ܮ‬ ௌଵ , ‫ܮ‬ ௌଶ . . ‫ܮ‬ ௌ Strands inductance ‫ܧ‬ ଵ , ‫ܧ‬ ଶ . . ‫ܧ‬ bEMFs induced in strands ‫ܯ[‬ ௦௧ ] Square n×n strands inductance matrix ൣ‫ܯ‬ ൧ Rectangular n×x matrix of mutual inductances between machine phases and each strand of investigated coil, x -number of phases [ܴ] Resistance matrix ‫ܫ‬ ଵ . . ‫ܫ‬ Current through each strand ‫ܫ‬ _ଵ . . ‫ܫ‬ _௫ Phase current ݊ Number of parallel strands per coil ܷ Voltage across the terminals of stranded coil ‫ܣ‬ Vector potential in the air gap ‫ܣ‬ ௦ Vector potential in the slot opening ‫ܣ‬ ௦ Vector potential in the slots with bulk coils ‫ܣ‬ ெ Vector potential in the PM subdomain ‫ܣ‬ ௧ , ‫ܣ‬ , ‫ܣ‬ ௧ Vector potentials in the slots with stranded coils ‫ܣ‬ ெ , ‫ܤ‬ ெ , ‫ܥ‬ ெ , ‫ܦ‬ ெ Coefficients for the function of vector potential in PM subdomain ‫ܣ‬ , ‫ܤ‬ , ‫ܥ‬ , ‫ܦ‬ Coefficients for the function of vector potential in the air gap ‫ܣ‬ ௦ , ‫ܤ‬ ௦ , ‫ܣ‬ , ‫ܤ‬ Coefficients for the function of vector potential in the slot opening ‫ܣ‬ ௦ , ‫ܤ‬ ௦ , ‫ܣ‬ , ‫ܤ‬ Coefficients for the function of vector potential in the slots with bulk coils

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Section: Inductance Matrixmentioning

confidence: 99%

“…Where ‫ܯ‬ ௦ , ‫ܯ‬ , ‫ܯ‬ ఏ௦ , ‫ܯ‬ ఏ are the expressions corresponding to sin and cos parts of the magnetization functions ‫ܯ‬ and ‫ܯ‬ ఏ of rotor -given in the Appendix of [14].…”

Section: Inductance Matrixmentioning

confidence: 99%

Analytical Methodology for Modelling of Circulating Current Loss in Synchronous Electrical Machines With Permanent Magnets

Golovanov

Gerada

2022

IEEE Trans. Energy Convers.

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“…The second stage of optimisation is performed by using a subdomain analytical modelling technique (SDM) [26], [27], [28]. The SDM model is based on the direct solution of Laplace's and Poisson's equations within the four domains of the machine, as shown in Fig.…”

Section: B Second Stage Of Optimizationmentioning

confidence: 99%

“…The SDM model is based on the direct solution of Laplace's and Poisson's equations within the four domains of the machine, as shown in Fig. 10 The detailed solution of ( 2) -( 4) is described in [26], [28]. The set of input variables for this second stage optimisation are listed in Table 3.…”

Section: B Second Stage Of Optimizationmentioning

confidence: 99%

4-MW Class High-Power-Density Generator for Future Hybrid-Electric Aircraft

Golovanov

Gerada

Sala

et al. 2021

IEEE Trans. Transp. Electrific.

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This paper describes the underpinning research, development, construction and testing of a 4MW multi-three phase generator designed for a hybrid-electric aircraft propulsion system demonstrator. The aim of the work is to demonstrate gravimetric power densities around 20 kW/kg, as required for multi-MW aircraft propulsion systems. The key design choices, development procedures and trade-offs, together with the experimental testing of this electrical machine connected to an active rectifier are presented. A time-efficient analytical approach to the down-selection of various machine configurations, geometrical variables, different active and passive materials and different thermal management options is first presented. A detailed design approach based on 3D Finite Element Analysis (FEA) is then presented for the final design. Reduced power tests are carried out on a full scale 4 MW machine prototype, validating the proposed design. The experimental results are in good agreement with simulation and show significant progress in the field of high power density electrical machines at the targeted power rating.

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“…The chamfered pole is a simple and effective method to improve the air-gap flux density waveform, which is widely used in practice, and it is easy to install and fix [15][16][17]. In [18][19][20], analytical models have been carried out, such as sinusoidal PM shape, segmented pole and Halbach PM array etc. However, the analytical model of SPMSM with the chamfered pole is not studied to reduce the harmonic content of air-gap flux density and suppress the torque ripple.…”

Section: Model Of Chamfered Polementioning

confidence: 99%

Analytical model for magnetic field calculation of SPMSM with chamfered pole considering iron core saturation

Jing

et al. 2020

IET Electric Power Applications

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To effectively optimise pole shape for surface‐mounted permanent magnet synchronous machine (SPMSM), an analytical model of SPMSM with the chamfered pole is proposed for no‐load and on‐load magnetic field calculation. In this model, the pole of SPMSM is approximately segmented into pieces with regular shape and uniform magnet property, and magnetic field parameters can be obtained by subdomain superposition. Meanwhile, iron core saturation is considered to get a correction coefficient to revise air‐gap flux density, inducing flux linkage, line no‐load back electromotive force (EMF) and electromagnetic torque. Based on this analytical model, the geometry optimisation of PM can be optimised by end thickness of pole, pole‐arc coefficient of cutting and remanence, and the waveform total harmonic distortion of air‐gap flux density and no‐load back EMF are greatly reduced. To verify the analytical model, an outer rotor type SPMSM with 20‐poles and 72‐slots for tractor application is designed and manufactured. Finally, the effectiveness of the improved method is validated by the finite‐element method and experimental test.

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An Analytical Subdomain Model for Dual-Rotor Permanent Magnet Motor With Halbach Array

Cited by 30 publications

References 12 publications

Analytical Methodology for Modelling of Circulating Current Loss in Synchronous Electrical Machines With Permanent Magnets

Analytical Methodology for Modelling of Circulating Current Loss in Synchronous Electrical Machines With Permanent Magnets

4-MW Class High-Power-Density Generator for Future Hybrid-Electric Aircraft

Analytical model for magnetic field calculation of SPMSM with chamfered pole considering iron core saturation

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