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Finite element analysis of electrical machines and transformers: State of the art and future trends

Erich Schmidt (Institute of Energy Systems and Electric Drives, Vienna University of Technology, Vienna, Austria)



The purpose of this paper is to discuss the state of the art of finite element analysis of electrical machines and transformers. Electrical machines and transformers are prime examples of multi‐physical systems involving electromagnetics, thermal issues, fluid dynamics, structural mechanics as well as acoustic phenomena. An accurate operational performance with different electrical and mechanical load situations is more and more evaluated using various numerical analysis methods including the couplings between the various physical domains. Therefore, numerical analysis methods are increasingly utilized not only for the verification of contractual values of existing machines, but also for the initial design process and for the design optimization of new machines.


The finite element method is the most powerful numerical analysis method for such multi‐physical devices. Since optimizations with respect to the overall performance and also the total manufacturing costs will become more important, the utilization of coupled multi‐physical analyses is of growing interest. For the fast and powerful application of this numerical analysis method, special attention should be given to the requirements of these electromagnetic devices.


Various methods of coupling the different physical domains of multi‐field finite element analyses are described. Thereby, weakly coupled cascade algorithms can be used with most problems in the field of electrical machines and transformers. On the other hand, a prime objective is to derive comprehensive, multi‐physical simulation models which are easily incorporated into design tools used by engineering professionals.

Research limitations/implications

The development of robust and reliable computer‐aided tools for an optimal design of multi‐physical devices such electrical machines and transformers has to argue about the best possible coupling of various simulation methods. Special consideration shall be paid more and more to a treatment of uncertainties and tolerances by means of statistical and probabilistic approaches.


The paper discusses state of the art of finite element analyses of the mentioned devices. Various optimized methods of modelling and analysis concerning the repetitive structure of electrical machines for electromagnetic analyses are compared with their advantages and drawbacks. Further, various methods of coupling the different domains of multi‐field analyses in case of electrical machines and transformers are described.



Schmidt, E. (2011), "Finite element analysis of electrical machines and transformers: State of the art and future trends", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 30 No. 6, pp. 1899-1913.



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