Calculation approach of reluctance in the magnetic circuit of transformer employed to convert into equivalent electric circuit

Abstract

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.

CAD-based Design of Three Phase Transformer and Comprehensive Analysis for Wind Turbine Using Coupled Electromagnetic Field, Circuit and Thermal Model for 3.8 MVA Power

“…Symmetrical excitation currents are applied for the magneto motive forces (FLV_a = NLV ia, FLV_b = NLV ib and FLV_c = NLV ic) required to produce instantaneous values of fluxes (ɸa, ɸb and ɸc). The reluctance of a core section or air region as a limb of the magnetic circuit is obtained by magnetic energy and magnetic flux related to magnetic sections of the core [32]. It is clear from the Fig 4b that there is a natural asymmetry in the core as the length of magnetic path of phase B between the points P1 and P2 is less than that of phase A and C. Using the superposition theorem to equivalent magnetic circuit [35] of the transformer at no load, instantaneous values of fluxes (ɸa, ɸb and ɸc) in every limb can be figured out by Eqs.…”

A Novel Magnetic Equivalent Circuit Model for the Corner of Inductor Core

“…Both of the MEC Linc-i curves were compared with the measured data to calculate the relative error of each point, as shown in Figure 12b. The maximum relative error emax and average error eavg were calculated by Equations (11) and (12), and presented in Table 2. = 100 × max…”

“…The maximum relative error e max and average error e avg were calculated by Equations (11) and (12), and presented in Table 2.…”

“…On the other hand, a few institutions and individuals aimed at the main reluctance of the core, especially the corner. Except for the equivalent corner reluctance model established by the finite element method [12], the common method is to simplify the corner as a quarter-circle that has a fixed radius, replacing the original rectangular geometry, such as the IEC (International Electrotechnical Commission) 60205 [13] model, which has a radius equal to half the average length of the corners and is adopted in [9]. In the Snelling [14,15] model, the authors choose a quarter of the average length of the corner as the radius and this corner model is adopted in [5,6].…”