An Accurate Analytical Method for Leakage Inductance Calculation of Shell-Type Transformers With Rectangular Windings

Abstract

This paper presents an accurate analytical method for calculating the leakage inductance of shell-type E-core transformers with rectangular windings. For this purpose, first, an expression for calculating the leakage inductance per unit length inside the core window considering the core walls as the flux-normal boundary condition is derived. Then, a new accurate method for determining the Mean Length of Turns (MLT) based on the total stored energy is presented. The MLT is needed for the leakage inductance calculation using 2-D methods. By dividing the MLT into three partial lengths and calculating the corresponding leakage inductances using three different core window arrangements, the effect of core structure on the total leakage inductance is considered. The method is verified by 3-D FEM simulations as well as the leakage inductance measurements on two different fabricated transformer prototypes. The superiority of the method is also confirmed by comparisons with the previous analytical approaches. The proposed method enables the leakage inductance calculation with an error less than 1%, compared to the 3-D FEM results. Using the presented method, the leakage inductance calculations can be performed rapidly and accurately in the design stage without the need for time-consuming 3-D FEM simulations.

An Accurate Method for Leakage Inductance Calculation of Shell-Type Multi Core-Segment Transformers With Circular Windings

“…The mean length of turns (MLT) is of great importance in the determination of the leakage inductance for planar windings since the total leakage inductance is obtained by multiplying the leakage inductance per unit length by MLT [16]. According to the relations derived in the previous section, there is no need to scale the calculated leakage inductance since the self and mutual inductances are calculated in H rather than H/m in cylindrical coordinates.…”

“…However, in order to find the portion of the windings which is surrounded by the core segments, a method for determination of MLT in cylindrical coordinates is developed in this section. The method is similar to the one presented by the authors in [16] but it is adopted for circular windings. The method is based on the total energy stored in the axial leakage field.…”

“…The method presented in this section can be developed for the cases where each winding needs to be modeled layer-by-layer. The method has been discussed in [16] for planar windings which can be extended for axisymmetric windings considering the approach provided in this section.…”

“…The behavior of the leakage inductance with respect to frequency in high frequency transformers (HFT) is studied up to 2 MHz in [5], [11], [12], [13], using Dowell method [14] or its improved form [15]. For high-power MFTs with rated frequencies less than 20 kHz, if Litz wire is used, the change of leakage inductance due to the frequency variation is almost negligible [16].…”

“…In the previously published article [16], the authors focused on the leakage inductance calculation of shell-type MFTs with rectangular windings. The leakage inductance per unit length is calculated by a double Fourier series analysis in 2-D planar coordinates.…”