Eddy current losses that occur in permanent magnets of surface mounted permanent magnet brushless machines are potentially dangerous because they directly increase the temperature of the permanent magnets. Indeed, this led to the phenomenon analysis and the development of numerical as well as analytical methods aimed at estimating these losses, with diverse levels of accuracy. The aim of this thesis is the development of a technique for the estimation of eddy current losses in permanent magnets of these machines, as a tool to be used in the design process. In particular, the armature magnetic field is analysed as source of eddy currents, considering both time harmonics of stator currents and winding magnetomotive force space harmonics. The magnetic field is computed by a two-dimensional sub-domain field model in a circular geometric model of the machine, described by a polar coordinate system. The armature magnetic field and that relating to the eddy currents are evaluated separately, an iterative procedure is proposed to consider the modifying effect of the eddy currents on themselves. This simplifies the mathematical model of the phenomenon, espe cially to consider simultaneously the eddy current reaction magnetic field and insulation at the boundaries of the magnets. To compute the eddy current reaction field the eddy currents induced in the permanent magnets are substituted by a current sheet, placed at the interface between magnet region and air-gap. This inevitably reduces the proposed method accuracy but simplifies the eddy current reaction magnetic field computation. The proposed method is used to estimate the magnet eddy current losses of two different machines in terms of both winding configuration and working condition. The results are compared to those obtained by finite element analysis, to validate the ability of the developed method to estimate the magnet eddy current losses. Good agreement is achieved, also when the eddy currents are mainly limited by the magnetic field generated by them. This confirms the validity of the assumption made to describe the eddy current reaction field, for the estimation of these losses.
Le perdite per correnti parassite nei magneti permanenti di macchine brushless a magneti permanenti superficiali sono potenzialmente pericolose in quanto aumentano direttamente la temperatura di questi. Infatti, questo ha portato all'analisi del fenomeno ed allo sviluppo sia di metodi numerici che analitici per la stima di queste perdite, con differenti livelli di accuratezza. Lo scopo della tesi è quello di sviluppare un metodo per la stima di queste perdite, determinando uno strumento utilizzabile nella fase di progettazione della macchina. In particolare, si analizza come sorgente delle correnti parassite il campo magnetico di armatura, considerando sia le armoniche spaziali di forza magnetomotrice dell'avvolgimento che quelle temporali delle correnti di statore. Si valuta il campo magnetico in un modello geometrico bidimensionale circolare della macchina, descritto da un sistema di coordinate polari, tramite il metodo detto dei sottodomini. Il campo magnetico di armatura e quello generato dalle correnti parassite sono calcolati separatamente, una procedura iterativa è proposta per la valutazione dell'effetto modificante del campo magnetico generato dalle correnti indotte su di esse. Per semplificare la valutazione di questo, le correnti parassite indotte nella regione dei magneti sono sostituite da uno strato di corrente posto all'interfaccia fra i magneti ed il traferro. Questa assunzione riduce l'accuratezza del metodo proposto, tuttavia permette di semplificare notevolmente la descrizione matematica del fenomeno, in particolare considerando simultaneamente il campo magnetico generato dalle correnti parassite e l'isolamento ai bordi dei magneti. La tecnica proposta è utilizzata per la stima di queste perdite in due macchine differenti, sia per tipologia di avvolgimento che condizione di funzionamento. Per la validazione dei risultati, questi vengono confrontati con quelli ottenuti da analisi numerica tramite metodo degli elementi finiti. Una buona concordanza è ottenuta, anche quando le correnti parassite sono principalmente limitate dal campo magnetico da esse generato. Questo conferma la validità dell'assunzione per lo studio del campo magnetico generato dalle correnti indotte, nello stimare le perdite analizzate.
Estimation of eddy current losses in surface mounted permanent magnet brushless machines
Figoni, Isacco
2022/2023
Abstract
Eddy current losses that occur in permanent magnets of surface mounted permanent magnet brushless machines are potentially dangerous because they directly increase the temperature of the permanent magnets. Indeed, this led to the phenomenon analysis and the development of numerical as well as analytical methods aimed at estimating these losses, with diverse levels of accuracy. The aim of this thesis is the development of a technique for the estimation of eddy current losses in permanent magnets of these machines, as a tool to be used in the design process. In particular, the armature magnetic field is analysed as source of eddy currents, considering both time harmonics of stator currents and winding magnetomotive force space harmonics. The magnetic field is computed by a two-dimensional sub-domain field model in a circular geometric model of the machine, described by a polar coordinate system. The armature magnetic field and that relating to the eddy currents are evaluated separately, an iterative procedure is proposed to consider the modifying effect of the eddy currents on themselves. This simplifies the mathematical model of the phenomenon, espe cially to consider simultaneously the eddy current reaction magnetic field and insulation at the boundaries of the magnets. To compute the eddy current reaction field the eddy currents induced in the permanent magnets are substituted by a current sheet, placed at the interface between magnet region and air-gap. This inevitably reduces the proposed method accuracy but simplifies the eddy current reaction magnetic field computation. The proposed method is used to estimate the magnet eddy current losses of two different machines in terms of both winding configuration and working condition. The results are compared to those obtained by finite element analysis, to validate the ability of the developed method to estimate the magnet eddy current losses. Good agreement is achieved, also when the eddy currents are mainly limited by the magnetic field generated by them. This confirms the validity of the assumption made to describe the eddy current reaction field, for the estimation of these losses.File | Dimensione | Formato | |
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https://hdl.handle.net/10589/217313