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Purpose The theoretical method of converting the magnetic circuit into an electric circuit is mature, but the way to determine the inductances in the electric circuit is not reliable, especially for the core working in saturation status, and it is impossible to determine the inductances by the transformer terminal measurements, as the measurement information is not enough to determine a number of inductances. This paper aims to propose an approach of calculating the reluctances.Design/methodology/approach In this paper, an approach of calculating the reluctances is proposed based on the numerical simulation of magnetic field in transformer with different values of current excitation. The reluctance of a core segment or air region as a branch of magnetic circuit is obtained by the magnetic energy and magnetic flux. By this way, all the reluctances as function of flux can be determined, and then the inductances can be determined. The reluctances and equivalent electric circuit of three-phase integrative transformer is determined, and its validation is proved in the paper.Findings The single phase example shows that the proposed method has a good performances on analysis of the inrush current in deep saturation. The peak value of the inrush current derived from the proposed approach matches well with the results obtained by coupled circuit-FEM analysis, and the difference is about 4.8 per cent. For studies on dual models of single phase transformers, the leakage inductances have important effects on the peak value of the inrush current. The reluctances of three-phase transformer are calculated, and the equivalent circuit simulation results are slightly smaller than the coupled circuit-FEM simulation results.Originality/value Approach of calculating the reluctances based on the numerical simulation of magnetic field in transformer is proposed. The magnetic core and air space are divided into several segments, and the reluctance for each segment is calculated based on the energy in the region and the flux of the cross-sectional area. By applying various excitation currents, all the reluctances as function of flux can be determined, and then all the non-linear inductances including the non-linear leakage inductances are obtained. The proposed approach is reliable to determine a number of inductances in the dual electric circuit, especially for deep saturation status. [ABSTRACT FROM AUTHOR]

Purpose This paper aims to study the influence of supply voltage variations on the external magnetic field emitted by grid-powered induction machines (IMs).Design/methodology/approach Two models are developed in the paper to analyse, for different supply voltage values, the influence of the variations of the magnetizing voltage for which there is a link with the tangential component of the external flux. The first is an analytical model based on the IM single-phase-equivalent circuit with variable magnetizing reactance to take into account the saturation of the magnetic circuit. The second is a numerical finite element simulation to model the same phenomenon. Results of both models are analysed with experimental measures of the external flux.Findings The study shows that the amplitude of the external field strongly depends on supply voltage values.Research limitations/implications The investigation is mainly focused on the tangential component of the external magnetic field which is of high importance concerning the applicability of non-invasive methods of diagnosis, as electromagnetic torque estimation developed by the authors or internal fault determination.Originality/value The originality of the paper concerns the characterization of the external flux with the supply voltage for IMs. It is shown that the magnetic circuit radiates external flux differently with the load and with the supply voltage. [ABSTRACT FROM AUTHOR]

Purpose Induction machines for traction applications are operated at working points of high ferromagnetic saturation. Depending on the working point, a broad spectrum of harmonic frequencies appears in the magnetic flux density of induction machines. Detailed loss analysis therefore requires local and temporal highly resolved nonlinear field computation. This loss analysis can be performed in the post processing of nonlinear transient finite element simulations of the magnetic circuit. However, it takes a large number of transient simulation time steps to build up the rotor flux of the machine.Design/methodology/approach In this paper, hybrid simulation approaches that couple static FEA, transient FEA and analytic formulations to significantly decrease the number of simulation time steps to calculate the magnetic field in steady state are discussed, analyzed and compared.Findings The proposed hybrid simulation approaches drastically decrease the simulation time by shortening the transient build-up of the rotor flux. Depending on the maximum error of the rotor flux linkage amplitude compared to the steady state value, a reduction of simulation time steps in the range of 55.5 to 98 per cent is found.Originality/value The presented hybrid simulation approaches allow efficient performing of the transient FE magnetic field simulations of induction machines operated as traction drives. [ABSTRACT FROM AUTHOR]