Two-dimensional steady-state thermal analytical model of permanent-magnet synchronous machines operating in generator mode

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zakarya Djelloul Khedda ◽  
Kamel Boughrara ◽  
Frédéric Dubas ◽  
Baocheng Guo ◽  
El Hadj Ailam
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Permanent Magnet ◽  
Analytical Model ◽  
Electrical Machines ◽  
Synchronous Machines ◽  
Analytical Prediction ◽  
Two Dimensional ◽  
Content Type ◽  
Proposed Model

Purpose Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode. Design/methodology/approach The proposed model is based on the multi-layer models with the convolution theorem (i.e. Cauchy’s product theorem) by using complex Fourier’s series and the separation of variables method. This technique takes into the different thermal conductivities of the machine parts. The heat sources are determined by calculating the different power losses in the PMSM with the finite-element method (FEM). Findings To validate the proposed analytical model, the analytical results are compared with those obtained by thermal FEM. The comparisons show good results of the proposed model. Originality/value A new 2D analytical model based on the PDE in steady-state for full prediction of temperature distribution in the PMSM takes into account the heat transfer by conduction, convection and radiation.

Analytical calculations of electromagnetic quantities for wound rotor salient-pole synchronous machines

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zohreh Delirani ◽  
Akbar Rahideh ◽  
Mohammad Mardaneh
Keyword(s):  
Analytical Model ◽  
Synchronous Machines ◽  
Magnetic Flux Density ◽  
Two Dimensional ◽  
Element Analysis ◽  
Content Type ◽  
Electromagnetic Model ◽  
Salient Pole ◽  
Salient Pole Synchronous Machine ◽  
Electromagnetic Quantities

Purpose This paper aims to present an analytical electromagnetic model for wound rotor synchronous machines with a salient-pole rotor structure based on the two-dimensional subdomain technique. Design/methodology/approach The machine is divided into five active sub-regions: stator slots, stator slot openings, air gap, rotor slots and rotor slot openings. For each sub-region, the governing partial differential equations are derived and solved analytically. Findings The magnetic flux density distributions in all active sub-regions are analytically computed and other quantities such as back-emf, inductances, electromagnetic torque and unbalanced magnetic forces are also analytically calculated. The results of the analytical model are compared to those obtained from the finite element analysis to show the accuracy of the proposed model. Originality/value The two-dimensional analytical model of a wound rotor salient-pole synchronous machine using the sub-domain technique is the main contribution of the research.

Motion in frequency domain for harmonic balance simulation of electrical machines

2018 ◽  
Vol 37 (4) ◽  
pp. 1449-1460
Author(s):  
Markus Wick ◽  
Sebastian Grabmaier ◽  
Matthias Juettner ◽  
Wolfgang Rucker
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Efficient Method ◽  
Harmonic Balance ◽  
Eddy Currents ◽  
Computational Effort ◽  
Electrical Machines ◽  
Accurate Approximation ◽  
Content Type ◽  
Magnetic Devices

Purpose The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Design/methodology/approach The high computational effort of steady-state simulations limits the optimization of electrical machines. Stationary solvers calculate a fast but less accurate approximation without eddy-currents and hysteresis losses. The harmonic balance approach is known for efficient and accurate simulations of magnetic devices in the frequency domain. But it lacks an efficient method for the motion of the geometry. Findings The three-phase symmetry reduces the simulated geometry to the sixth part of one pole. The motion transforms to a frequency offset in the angular Fourier series decomposition. The calculation overhead of the Fourier integrals is negligible. The air impedance approximation increases the accuracy and yields a convergence speed of three iterations per decade. Research limitations/implications Only linear materials and two-dimensional geometries are shown for clearness. Researchers are encouraged to adopt recent harmonic balance findings and to evaluate the performance and accuracy of both formulations for larger applications. Practical implications This method offers fast-frequency domain simulations in the optimization process of rotating machines and so an efficient way to treat time-dependent effects such as eddy-currents or voltage-driven coils. Originality/value This paper proposes a new, efficient and accurate method to simulate a rotating machine in the frequency domain.

Dynamic and steady state modeling of permanent magnet induction machine

2018 ◽  
Vol 37 (1) ◽  
pp. 465-483
Author(s):  
Hamid Reza Izadfar ◽  
Hamid Naseri
Keyword(s):  
Steady State ◽  
Permanent Magnet ◽  
Dynamic Model ◽  
Reference Frame ◽  
Reference Frames ◽  
Induction Machine ◽  
Electric Machine ◽  
Dynamic Equations ◽  
Equivalent Circuits ◽  
Content Type

Purpose Modeling electric machines is one of the powerful approaches for analyzing their performance. A dynamic model and a steady-state model are introduced for each electric machine. Permanent magnet induction machine (PMIM) is a dual-rotor electric machine, which has various advantages such as high-power factor and low magnetizing current. Studying PMIM and its modeling might be valuable. The purpose of this paper is to introduce a simple and accurate method for dynamic and steady-state modeling of PMIM. Design/methodology/approach In this paper, arbitrary dqo reference frame is used to model PMIM. First, three-phase dynamic equations of stator and rotors are introduced. Then, they are transferred to an arbitrary reference frame. The voltage and magnetic flux equations aligned at dqo axes are obtained. These equations give the dynamic model. To investigate the results, PMIM simulation is performed according to obtained dynamic equations. Simulation results verify the analytic calculations. Findings In this paper, dynamic equations of PMIM are obtained. These equations are used to determine dynamic equivalent circuits of PMIM. Steady-state equations and one phase equivalent circuit of the PMIM using phasor relations are also extracted. Originality/value PMIM equations along dqo axes and their dynamic and steady-state equivalent circuits are determined. These equations and the equivalent circuits can be transformed to different reference frames and analyzed easily.

scholarly journals Exact Two-Dimensional Analytical Calculations for Magnetic Field, Electromagnetic Torque, UMF, Back-EMF, and Inductance of Outer Rotor Surface Inset Permanent Magnet Machines

2019 ◽  
Vol 24 (1) ◽  
pp. 24 ◽  
Author(s):  
AmirAbbas Vahaj ◽  
Akbar Rahideh ◽  
Hossein Moayed-Jahromi ◽  
AliReza Ghaffari
Keyword(s):  
Permanent Magnet ◽  
Analytical Model ◽  
Permanent Magnets ◽  
Optimization Problems ◽  
Magnetic Flux Density ◽  
Permanent Magnet Machines ◽  
Two Dimensional ◽  
Electromagnetic Torque ◽  
Outer Rotor ◽  
Rotor Surface

This paper presents a two-dimensional analytical model of outer rotor permanent magnet machines equipped with surface inset permanent magnets. To obtain the analytical model, the whole model is divided into the sub-domains, according to the magnetic properties and geometries. Maxwell equations in each sub-domain are expressed and analytically solved. By using the boundary/interface conditions between adjacent sub-regions, integral coefficients in the general solutions are obtained. At the end, the analytically calculated results of the air-gap magnetic flux density, electromagnetic torque, unbalanced magnetic force (UMF), back-electromotive force (EMF) and inductances are verified by comparing them with those obtained from finite element method (FEM). One of the merits of this method in comparison with the numerical model is the capability of rapid calculation with the highest precision, which made it suitable for optimization problems.

scholarly journals Two-dimensional hybrid model for magnetic field calculation in electrical machines: exact subdomain technique and magnetic equivalent circuit

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Brahim Ladghem Chikouche ◽  
Kamel Boughrara ◽  
Dubas Frédéric ◽  
Rachid Ibtiouen
Keyword(s):  
Magnetic Field ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Current Density Distribution ◽  
Electrical Machines ◽  
Field Calculation ◽  
Two Dimensional ◽  
Content Type ◽  
The Magnetic Field ◽  
Load Conditions

Purpose The purpose of this paper is to propose a two-dimensional (2-D) hybrid analytical model (HAM) in polar coordinates, combining a 2-D exact subdomain (SD) technique and magnetic equivalent circuit (MEC), for the magnetic field calculation in electrical machines at no-load and on-load conditions. Design/methodology/approach In this paper, the proposed technique is applied to dual-rotor permanent magnet (PM) synchronous machines. The magnetic field is computed by coupling an exact analytical model (AM), based on the formal resolution of Maxwell’s equations applied in subdomains, in regions at unitary relative permeability with a MEC, using a nodal-mesh formulation (i.e. Kirchhoff's current law), in ferromagnetic regions. The AM and MEC are connected in both directions (i.e. r- and theta-edges) of the (non-)periodicity direction (i.e. in the interface between teeth regions and all its adjacent regions as slots and/or air-gap). To provide accurate solutions, the current density distribution in slot regions is modeled by using Maxwell’s equations instead to MEC and characterized by an equivalent magnetomotive force (MMF) located in the slots, teeth and yoke. Findings It is found that whatever the iron core relative permeability, the developed HAM gives accurate results for both no-load and on-load conditions. Finite element analysis demonstrates the excellent results of the developed technique. Originality/value The main objective of this paper is to achieve a direct coupling between the AM and MEC in both directions (i.e. r- and theta-edges). The current density distribution is modeled by using Maxwell’s equations instead to MEC and characterized by an MMF.

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