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

Abstract

The leakage field in shell-type transformers is strongly affected by the boundary conditions introduced by the core walls and thus the effect of the core should be considered properly in the leakage inductance calculation. In this paper, a new method for accurate calculation of the leakage inductance of shell-type multi core-segment transformers with circular windings is presented. For this purpose, first, the expressions for self and mutual inductances are derived in cylindrical coordinates considering the core walls as the flux-normal boundary condition. Then, a new approach is proposed for calculating the leakage inductance considering the number and dimensions of the used core segments. The method is developed at first for single and double core-segment transformers (known also as E-core and U-core transformers) and then adopted for shell-type segmented-core transformers. The method is verified by 3-D FEM simulations. The comparisons with the previous analytical methods demonstrate the superiority of the proposed method. A transformer prototype has been built and verification tests have been conducted. The comparisons show that the leakage inductance can be estimated with an error less than 1%, demonstrating a very high accuracy with the proposed method.

Green Solution for Insulation System of a Medium Frequency High Voltage Transformer for an Offshore Wind Farm

“…Therefore, special care must be paid to these two contradicting requirements for the gap between the windings. The authors have presented an effective analytical method, for calculating the leakage inductance of shell-type transformers with circular windings in [24].…”

Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model

“…Based on this, δ max = 0.2 is set to model the OW cross section in the HQ3D model. Note that based on this finding, scaling window width and window height by a factor of c = 2 as done in [19] might not be sufficiently large to eliminate the influence of the core on the magnetic field to a satisfactory degree.…”

“…1b as they implicitly satisfy the imposed mirroring boundary conditions at all surrounding window edges. To use the model for the OW cross section in which the boundary conditions are different, a simple trick is applied: the windings are placed in an equivalent window whose width and height are significantly larger than the original window with the intention of representing an infinitely large window as also done in [19]. It is important to note that the windings are kept at center height.…”

“…Furthermore, it is restricted to cores with rectangular center leg. Some models use cylindrical coordinates to implicitly take into account the curvature of the field in curved winding sections [18], [19]. But these solutions are complex to derive and involve computationally effortful evaluations of Bessel integrals.…”

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“…In the last one, the magnetic field induction in airgaps can even reach the Tesla level [25,26]. The leakage flux in transformers (including highfrequency solid-state devices for traction or more electric aircraft applications) may reach up to hundreds of mT [27]. Such transformers for power electronics converters contain magnetic fluxes that penetrate their electrical insulation.…”