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Numerical verification of Turowski’s coefficient

Hugo Rodriguez-Ignacio (Department of Electrical Engineering, Universidade de Vigo, Vigo, Spain)
Xose M. Lopez-Fernandez (Department of Electrical Engineering, Universidade de Vigo, Vigo, Spain)



The purpose of this paper is the numerical verification of the linearization coefficient ap proposed by Turowski for the calculation of the electromagnetic field distribution and therefore the stray losses inside magnetically saturated solid steel conductors.


The numerical verification is performed on a case study consisting of a simple current conductor sheet parallel to a solid steel plate. Numerical computations are compared with analytical calculations with and without inclusion of the semi-empirical Turowski’s coefficient.


Results confirm a good agreement between numerical values for steel with non-linear permeability and analytical ones applying Turowski’s coefficient. This is particularly powerful in the case of analytical calculation of the magnetic surface impedance (SI) to increase precision when hybrid methods are used. The concept of SI enables the establishment of hybrid approaches for the calculation of stray losses, combining the numerical methods (finite difference method, finite element method (FEM), etc.) together with the analytical formulation, gaining from the advantages of both methods.


Previous numerical analysis was focused on the field dependence on time for several depths inside solid steel. The aim of this paper is to investigate the electromagnetic field distribution inside solid steel on a representative FEM model and verify how the linearization coefficient ap proposed by Turowski works.



Professor Xose M. Lopez-Fernandez would like to thank Professor Janusz Turowski, who retired from the Institute of Electrical Machines and Transformers, Lodz, Poland, for the invaluable support and collaboration over the years not only at a technical level, but also at a personal level, which was very enriching. His constructive comments and devoted expertise have undoubtedly had a powerful impact on the quality of the joint results. Xose M. Lopez-Fernandez is indebted to him for this, for his passion, for his ideas and for the endless lines of conversations Xose M. Lopez-Fernandez and Janusz Turowski have shared.


Rodriguez-Ignacio, H. and Lopez-Fernandez, X.M. (2016), "Numerical verification of Turowski’s coefficient", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 35 No. 6, pp. 1965-1972.



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