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Analysis of electromagnetic phenomena in electromechanical converters using field approach two and three-dimensional models abstract
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Abstrakty
W pracy przedstawiono zarys historii stosowania numerycznych metod analizy pola elektromagnetycznego w obliczeniach przetworników elektromechanicznych. Zwrócono uwagę na dwa główne nurty prac wykorzystujących te metody: (a) prace polegające na stosowaniu metod polowych do obliczania parametrów schematów zastępczych przetworników, (b) prace nad modelami polowo-obwodowymi i algorytmami, w których równania pola są rozwiązywane równocześnie z równaniami stanu przetwornika. Omówiono badania nad dwuwymiarowymi modelami polowo-obwodowymi. Przedstawiono ogólną postać równań modeli trójwymiarowych.
The paper presents shortly the history of the applications of the numerical methods of electromagnetic field analysis in the electromechanical converter calculations. Attention is paid to the finite difference (FD) and finite element (FE) methods. It has been shown that there are two main lines of the application of these method: (a) the methods are applied in the calculations of integral parameters of the equivalent electric and magnetic circuits, and (b) the equations of FD or FE method are combined with the circuit equations of converter windings and with circuit equations of supply system (the circuit and field equations create the so called coupled field-circuit model of the converter). Summarily, the research works in relation to the 2D field-circuit models are discussed in the section 2. The 3D field-circuit models are presented in the section 3. In the considered models, the magnetic vector potential formulation is applied. First, the equations for the models with the edge element (EE) are presented. The finite elements are assumed to be edge elements in relation to magnetic vector potential A. The EE equations of the magnetic field are combined with the equations that describe the distribution of the electric field of conducting currents. In the case of the region with filamentary conductors, the EE equations are combined with the voltage equations which describe the winding currents i(c), see Eq. (1). These currents represent the edge values of current vector potential T. However, for the regions with solid conductors, the electric scalar potential V formulation is applied, see Eq. (3). Matrix equation (3) can be represented by the equations of the reluctance-conductance network. The network representation of tetrahedron is shown in Fig. 1 (reluctance network - Fig. 1a), conductance network - Fig. 1b). The edge element method has been compared with the classical nodal element method for the magnetic vector potential formulation. Finally, the unifed matrix of the equations for the 3D field models have been proposed, see Eq. (6). Equations (6a), (6b) are related to A-T formulation and A-V formulation, respectively. In the case of A-T formulation the finite elements are assumed to be nodal or edge elements in relation to A and T. However, for A-V formulation the finite elements are assumed be nodal in relation to V and are assumed to be nodal or edge elements in relation to A.
Czasopismo
Rocznik
Tom
Strony
61-73
Opis fizyczny
Bibliogr. 37 poz., rys.
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autor
autor
autor
- Politechnika Poznańska, Instytut Elektrotechniki Przemysłowej
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Bibliografia
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bwmeta1.element.baztech-article-BPS2-0014-0042