Analytical investigation of sideband electromagnetic vibration in integral-slot PMSM drive with SVPWM technique

This paper provides a comprehensive investigation into the electromagnetic vibration associated with the sideband harmonic components introduced by space vector pulse width modulation applied in integral-slot permanent magnet synchronous machine drives. The critical permanent magnet, armature reaction, and sideband magnetic field components, which are the primary causes for sideband electromagnetic vibration in integral-slot permanent magnet synchronous machines, are identified. The analytical derivations of the magnetic field components are carried out, and amplitudes and frequencies of the resultant sideband radial electromagnetic force components are obtained. Furthermore, the proposed models of the sideband radial electromagnetic force components are incorporated into the vibration model to analytically evaluate the corresponding sideband electromagnetic vibrations of the machine. Experimental tests on an integral-slot permanent magnet synchronous machine drive are comprehensively performed to confirm the validity and accuracy of the analytical models. Not only can the validated analytical models offer insightful details in understanding the impacts of the key factors, such as operation conditions, machine geometry, electromagnetic and power converter parameters, on the sideband electromagnetic vibration, but also can be readily extended to assess and reduce noise in integral-slot permanent magnet synchronous machine drives

The investigation of electromagnetic radial force and associated vibration in permanent magnet synchronous machines

The rising public awareness of climate change and urban air pollution has been one of the key drivers for transport electrification. Such trend drastically accelerates the quest for high-power-and-torque-density electric drive systems. The rare-earth permanent magnet synchronous machine, with its excellent steady-state and dynamic characteristics, has been the ideal candidate for these applications. Specifically, the fractional-slot and concentrated-winding configuration is widely adopted due to its distinctive merits such as short end winding, low torque pulsation, and high efficiency. The vibration and the associated acoustic noise become one of the main parasitic issues of high-performance permanent magnet synchronous drives. These undesirable features mainly arise from mechanical connection failure, imperfect assembly, torque pulsation, and electromagnetic radial and axial force density waves. The high-power-and-torque-density requirement will only be ultimately fulfilled by the reduction of both electromagnetic active material and passive support structure. This results in inflated electromagnetic force density inside the electric machine. Besides, the sti.ness of the machine parts can be compromised and the resultant natural frequencies are significantly brought down. Therefore, the vibration and acoustic noise that are associated with the electromagnetic radial and axial force density waves become a burden for large deployment of these drives. This study is mainly dedicated to the investigation of the electromagnetic radial forced density and its associated vibration and acoustic noise in radial-flux permanent magnet synchronous machines. These machines are usually powered by voltage source inverter with pulse width modulation techniques and various control strategies. Consequently, the vibration problem not only lies on the permanent magnet synchronous machine but also highly relates to its drive and controller. Generally, the electromagnetic radial force density and its relevant vibration can be divided into low-frequency and high-frequency components based on their origins. The low-frequency electromagnetic radial force density waves stem from the magnetic field components by the permanent magnets and armature reaction of fundamental and phase-belt current harmonic components, while the high-frequency ones are introduced by the interactions between the main low-frequency and sideband highfrequency magnetic field components. Both permanent magnets and armature reaction current are the main sources of magnetic field in electric machines. Various drive-level modeling techniques are first reviewed, explored, and developed to evaluate the current harmonic components of the permanent magnet synchronous machine drive. Meanwhile, a simple yet e.ective analytical model is derived to promptly estimate the sideband current harmonic components in the drive with both sinusoidal and space-vector pulse width modulation techniques. An improved analytical method is also proposed to predict the magnetic field from permanent magnets in interior permanent magnet synchronous machines. Moreover, a universal permeance model is analytically developed to obtain the corresponding armature-reaction magnetic field components. With the permanent magnet and armature-reaction magnetic field components, the main electromagnetic radial force density components can be identified and estimated based on Maxwell stress tensor theory. The stator tooth structure has large impacts on both electromagnetic radial force density components and mechanical vibration behaviors. The stator tooth modulation e.ect has been comprehensively demonstrated and explained by both finite element analysis and experimental results. Analytical models of such e.ect are developed for prompt evaluation and insightful revelation. Based on the proposed models, multi-physics approaches are proposed to accurately predict low-frequency and high-frequency electromagnetic radial vibration. Such method is quite versatile and applicable for both integral-slot and fractional-slot concentrated-winding permanent magnet synchronous machines. Comprehensive experimental results are provided to underpin the validity of the proposed models and methods. This study commences on the derivations of the drive parameters such as torque angle, modulation index, and current harmonic components from circuit perspective and further progresses to evaluate and decouple the air-gap magnetic field components from field perspective. It carries on to dwell on the analytical estimations of the main critical electromagnetic radial force density components and stator tooth modulation e.ect. Based on the stator mechanical structure, the corresponding electromagnetic radial vibration and acoustic noise can be accurately predicted. Various analytical models have been developed throughout this study to provide a systematic tool for quick and e.ective investigation of electromagnetic radial force density, the associated vibration and acoustic noise in permanent magnet synchronous machine drive. They have all been rigorously validated by finite element analysis and experimental results. Besides, this study reveals not only a universal approach for electromagnetic radial vibration analysis but also insightful correlations from both machine and drive perspectives

Armature MMF and electromagnetic performance analysis of dual three-phase 10-pole/24-slot permanent magnet synchronous machine

Fractional-slot concentrated-winding permanent magnet synchronous machines (FSCW-PMSMs) have a good prospect of application in the drive system of electric and hybrid electric vehicles. However, the armature magnetomotive force (MMF) of FSCWPMSM contains a large number of space harmonics, which induce large magnet eddycurrent loss (ECL). To solve this problem, a dual three-phase 10-pole and 24-slot winding layout is proposed.MMFharmonic analysis shows that the 1st, 7th and 17th space-harmonic winding factors of the proposed winding can be reduced by 100%, 87% and 87% respectively, compared with a dual three-phase 10-pole and 12-slot winding. Electromagnetic performances of the proposed machine under rated sinusoidal current supply and space vector pulse-width-modulated (SVPWM) voltage supply are investigated based on 2D finite-element analysis. It is shown that the proposed machine can meet the requirement of torque and efficiency in the full speed range. Especially, magnet ECL can be reduced greatly due to the reduction of the 7th and 17th space harmonics

Permanent Magnet Vernier Machine: A Review

Permanent magnet vernier machines (PMVMs) gained a lot of interest over the past couple of decades. This is mainly due to their high torque density enabled by the magnetic gearing effect. This study will provide a thorough review of recent advances in PMVMs. This review will cover the principle of operation and nature of magnetic gearing in PMVMs, and a better understanding of novel PMVM topologies using different winding configuration as well as different modulation poles and rotor structures. Detailed discussions on the choice of gear ratio, slot-pole combinations, design optimisation and role of advanced materials in PMVMs will be presented. This will provide an update on the current state-of-the art as well as future areas of research. Furthermore, the power factor issue, fault tolerance as well as cost reduction will be discussed highlighting the gap between the current state-of-the art and what is needed in practical applications

Development of a multidisciplinary and optimized design methodology for surface permanent magnets synchronous machines

Electric energy is one of the supports of modern civilization. In the actual context, the electrical machines are of capital importance since most of power plants, from nuclear plants to wind turbines, need an electrical machine working as a generator. Moreover, it is estimated that nowadays the 65% of the total energy supplied by the grid is consumed by electric motors working in an industrial environment. Electrical machines are complex systems where a great amount of physical phenomena are produced simultaneously; that is why a proper design requires detailed multidisciplinary models. However, most of the design methodologies and tools are only focused on machine electromagnetic performance in order to achieve power, efficiency and mass to volume ratio goals, performing an adequate more than an optimized design. In the best cases, the features related with other physical domains are taken into account through figures or merit or rules of the thumb based on designer particular experience (e.g. thermal sizing); or even they are treated as an afterthought if needed (typical case of the machine vibro-acoustic performance). These approaches are only suitable for very well-known applications where machine features are perfectly known and characterized. However, these methodologies are unsystematic by nature so they have serious difficulties in order to extrapolate the obtained results to a new set of specifications or to more challenging applications where not only electromagnetic criteria but other physical domains, such as vibro-acoustic, should be taken into account. More precisely, since the advent of neodymium iron boron (NdFeB) magnets, permanent magnets synchronous machines (PMSM) has become a suitable option both in industrial and domestic applications such as aircraft industry, elevation, electric vehicle or power generation. Due to their attractive features (e.g. high efficiency, compactness and power density) PMSMs are an emerging technology and an attractive field of study, as it is highlighted by the great amount of publications devoted to that topic in the last years. Therefore, the thesis main goal is the development of a pioneering PMSM design methodology based on a holistic, multidisciplinary and optimized approach. Moreover, this proposed methodology takes into account not only the electromagnetic and thermal conventional aspects but also the machine vibro-acoustic behaviour. In order to fulfil this aim, a complete multiphysical analytical model has been carried out, including a detailed study of the electromagnetic, thermal and vibro-acoustics PMSM features, paying a special attention to these physical domains interactions. The developed models have been used in order to implement a PMSM design optimized methodology based on an innovative heuristic algorithm labelled Direct Multisearch (DMS). In order to validate the physical models, a 75 kW PMSM prototype (IkerMAQ) has been designed and built. A huge amount of tests were carried out and the analytical models have been exhaustively validated, including electromagnetic, thermal and vibro-acoustic domains

Mathematical Models for the Design of Electrical Machines

This book is a comprehensive set of articles reflecting the latest advances and developments in mathematical modeling and the design of electrical machines for different applications. The main models discussed are based on the: i) Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by using the separation of variables method and the Fourier’s series in 2-D or 3-D with a quasi-Cartesian or polar coordinate system); ii) electrical, thermal and magnetic equivalent circuit; iii) hybrid model. In these different papers, the numerical method and the experimental tests have been used as comparisons or validations

Multi-level-objective design optimization of permanent magnet synchronous wind generator and solar photovoltaic system for an urban environment application

This Ph.D. thesis illustrates a novel study on the analytical and numerical design optimization of radial-flux permanent magnet synchronous wind generators (PMSGs) for small power generation in an urban area, in which an outer rotor topology with a closed-slot stator is employed. The electromagnetic advantages of a double-layer fractional concentration non-overlapping winding configuration are discussed. The analytical behavior of a PMSG is studied in detail; especially for magnetic flux density distribution, time and space harmonics, flux linkages, back-EMF, cogging torque, torque, output power, efficiency, and iron losses computation. The electromagnetic behavior of PMSGs are evaluated when a number of various Halbach array magnetization topologies are presented to maximize the generator’s performance. In addition, the thermal behavior of the PMSG is improved using an innovative natural air-cooling system for rated speed and higher to decrease the machine’s heat mainly at the stator teeth. The analytical investigation is verified via 2-D and 3-D finite element analysis along with a good experimental agreement. Design optimization of electrical machines plays the deterministic role in performance improvements such as the magnetization pattern, output power, and efficiency maximization, as well as losses and material cost minimization. This dissertation proposes a novel multi-objective design optimization technique using a dual-level response surface methodology (D-RSM) and Booth’s algorithm (coupled to a memetic algorithm known as simulated annealing) to maximize the output power and minimize material cost through sizing optimization. Additionally, the efficiency maximization by D-RSM is investigated while the PMSG and drive system are on duty as the whole. It is shown that a better fit is available when utilizing modern design functions such as mixed-resolution central composite (MR-CCD) and mixed-resolution robust (MR-RD), due to controllable and uncontrollable design treatments, and also a Window-Zoom-in approach. The proposed design optimization was verified by an experimental investigation. Additionally, there are several novel studies on vibro-acoustic design optimization of the PMSGs with considering variable speed analysis and natural frequencies using two techniques to minimize the magnetic noise and vibrations. Photovoltaic system design optimization considered of 3-D modeling of an innovative application-oriented urban environment structure, a smart tree for small power generation. The horizon shading is modeled as a broken line superimposed onto the sun path diagram, which can hold any number of height/azimuth points in this original study. The horizon profile is designed for a specific location on the Barcelona coast in Spain and the meteorological data regarding the location of the project was also considered. Furthermore, the input weather data is observed and stored for the whole year (in 2016). These data include, ambient temperature, module’s temperature (open and closed circuits tests), and shading average rate. A novel Pareto-based 3-D analysis was used to identify complete and partial shading of the photovoltaic system. A significant parameter for a photovoltaic (PV) module operation is the nominal operating cell temperature (NOCT). In this research, a glass/glass module has been referenced to the environment based on IEC61215 via a closed-circuit and a resistive load to ensure the module operates at the maximum power point. The proposed technique in this comparative study attempts to minimize the losses in a certain area with improved output energy without compromising the overall efficiency of the system. A Maximum Power Point Track (MPPT) controller is enhanced by utilizing an advanced perturb & observe (P&O) algorithm to maintain the PV operating point at its maximum output under different temperatures and insolation. The most cost-effective design of the PV module is achieved via optimizing installation parameters such as tilt angle, pitch, and shading to improve the energy yield. The variation of un-replicated factorials using a Window-Zoom-in approach is examined to determine the parameter settings and to check the suitability of the design. An experimental investigation was carried out to verify the 3-D shading analysis and NOCT technique for an open-circuit and grid-connected PV module.Esta tesis muestra un novedoso estudio referente al diseño optimizado de forma analítica y numérica de un generador síncrono de imanes permanentes (PMSGs) para una aplicación de microgeneración eólica en un entorno urbano, donde se ha escogido una topología de rotor exterior con un estator de ranuras cerradas. Las ventajas electromagnéticas de los arrollamientos fraccionarios de doble capa, con bobinas concentradas se discuten ampliamente en la parte inicial del diseño del mismo, así como las características de distribución de la inducción, los armónicos espaciales y temporales, la fem generada, el par de cogging así como las características de salida (par, potencia generada, la eficiencia y la distribución y cálculo de las pérdidas en el hierro que son analizadas detalladamente) Posteriormente se evalúan diferentes configuraciones de estructuras de imanes con magnetización Halbach con el fin de maximizar las prestaciones del generador. Adicionalmente se analiza la distribución de temperaturas y su mejora mediante el uso de un novedoso diseño mediante el uso de ventilación natural para velocidades próximas a la nominal y superiores con el fin de disminuir la temperatura de la máquina, principalmente en el diente estatórico. El cálculo analítico se completa mediante simulaciones 2D y 3D utilizando el método de los elementos finitos así como mediante diversas experiencias que validan los modelos y aproximaciones realizadas. Posteriormente se desarrollan algoritmos de optimización aplicados a variables tales como el tipo de magnetización, la potencia de salida, la eficiencia así como la minimización de las pérdidas y el coste de los materiales empleados. En la tesis se proponen un nuevo diseño optimizado basado en una metodología multinivel usando la metodología de superficie de respuesta (D-RSM) y un algoritmo de Booth (maximizando la potencia de salida y minimizando el coste de material empleado) Adicionalmente se investiga la maximización de la eficiencia del generador trabajando conjuntamente con el circuito de salida acoplado. El algoritmo utilizado queda validado mediante la experimentación desarrollada conjuntamente con el mismo. Adicionalmente, se han realizado diversos estudios vibroacústicos trabajando a velocidad variable usando dos técnicas diferentes para reducir el ruido generado y las vibraciones producidas. Posteriormente se considera un sistema fotovoltaico orientado a aplicaciones urbanas que hemos llamado “Smart tree for small power generation” y que consiste en un poste con un generador eólico en la parte superior juntamente con uno o más paneles fotovoltaicos. Este sistema se ha modelado usando metodologías en 3D. Se ha considerado el efecto de las sombras proyectadas por los diversos elementos usando datos meteorológicos y de irradiación solar de la propia ciudad de Barcelona. Usando una metodología basada en un análisis 3D y Pareto se consigue identificar completamente el sistema fotovoltaico; para este sistema se considera la temperatura de la célula fotovoltaica y la carga conectada con el fin de generar un algoritmo de control que permita obtener el punto de trabajo de máxima potencia (MPPT) comprobándose posteriormente el funcionamiento del algoritmo para diversas situaciones de funcionamiento del sistemaLa tesis desenvolupa un nou estudi per al disseny optimitzat, analític i numèric, d’un generador síncron d’imants permanents (PMSGs) per a una aplicació de microgeneració eòlica en aplicacions urbanes, on s’ha escollit una configuració amb rotor exterior i estator amb ranures tancades. Es discuteixen de forma extensa els avantatges electromagnètics dels bobinats fraccionaris de doble capa així com les característiques resultats vers la distribució de les induccions, els harmònics espacials i temporals, la fem generada, el parell de cogging i les característiques de sortida (parell, potencia, eficiència i pèrdues) Tanmateix s’afegeix l’estudi de diferents estructures Halbach per als imants permanents a fi i efecte de maximitzar les característiques del generador. Tot seguit s’analitza la distribució de temperatures i la seva reducció mitjançant la utilització d’una nova metodologia basada en la ventilació natural. Els càlculs analítics es complementen mitjançant anàlisi en 2 i 3 dimensions utilitzant elements finits i diverses experiències que validen els models i aproximacions emprades. Una vegada fixada la geometria inicial es desenvolupen algoritmes d’optimització per a diverses variables (tipus de magnetització dels imants, potencia de sortida, eficiència, minimització de pèrdues i cost dels materials) La tesi planteja una optimització multinivell emprant la metodologia de superfície de resposta i un algoritme de Booth; a més, es realitza la optimització considerant el circuit de sortida. L’algoritme resta validat per la experimentació realitzada. Finalment, s’han considerat diversos estudis vibroacústic treballant a velocitat variable, emprant dues tècniques diferents per a reduir el soroll i les vibracions desenvolupades. Per a finalitzar l’estudi es considera un sistema format per una turbina eòlica instal·lada sobre un pal de llum autònom, els panells fotovoltaics corresponents i el sistema de càrrega. Per a modelitzar l’efecte de l’ombrejat s’ha emprat un model en 3D i les dades del temps i d’irradiació solar de la ciutat de Barcelona. El model s’ha identificat completament i s’ha generat un algoritme de control que considera, a més, l’efecte de la temperatura de la cèl·lula fotovoltaica y la càrrega connectada al sistema per tal d’aconseguir el seguiment del punt de màxima potenciaPostprint (published version