Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model

Schlesinger, Richard B.; Ewald, Thomas; Biela, J.

doi:10.1109/tpel.2022.3226240

Cited by 4 publications

(13 citation statements)

References 26 publications

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“…the maximal inductance value. At low frequency, inductance is maximal [27], [29], [30], and the iT2D model provides exactly that. • CWM transformers for HVPP applications always require a significant distance from top of the secondary winding to the inner winding to avoid dielectric breakdowns.…”

Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 87%

“…Where I ref is the current through the transformer side that the leakage inductance is referred to. The complete model derivations are given in the Appendices and a detailed derivation of the magnetic energy computed from the magnetic field can be found in [27].…”

Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 99%

“…3b. This leads to highly reduced computational effort while maintaining high accuracy in leakage inductance calculations [27], [28]. It is to be noted that the diameter of the field shape rings exceeds the diameter of the secondary winding turns by far.…”

Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 99%

“…Where i is the index of the original windings, k denotes the index of all windings N wdgs , including mirror image windings, Γ i,k is the antiderivate function (27), and a i & a k , and h i and h k are width and height of winding i and k, respectively. The derivation and all required equations leading to (3) are given in Appendix B.…”

Section: B Cone Winding Leakage Inductance Pulmentioning

confidence: 99%

“…In curved winding sections, the magnetic energy is curved and therefore, the scaling length of curved sections has to be radially energy weighted [17], [27]. In the corner length model of the iT2D model, the energy density is assumed to be constant within a rectangle that encloses the windings as provided in Appendix C. The resulting equation is given in (8).…”

Section: Partial Leakage Length Modelsmentioning

confidence: 99%

See 4 more Smart Citations

Improved Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers

Schlesinger¹,

Biela²

2023

IEEE Open J. Power Electron.

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The transformer leakage inductance is one of the limiting factors for pulse shape quality in high voltage pulsed power (HVPP) converters that are essential in applications such as cancer treatment, particle accelerators, and free electron lasers. Cone winding matrix (CWM) transformers are commonly used in HVPP converters as they offer low leakage inductance and high insulation distance. This paper proposes an improved Triple-2D (iT2D) leakage inductance model for CWM transformers. The iT2D model identifies three basic cross sections of CWM transformers and calculates their associated leakage inductance contributions. The paper proposes an accurate and compact analytical formula of the leakage inductance contribution resulting from the magnetic energy stored in between the magnetic cores. For cross sections with cone windings, an expression is presented that computes the leakage inductance per unit length of non-parallel windings. The iT2D model is verified with measurements and finite element simulations of three transformer prototypes. The analytical solutions used in the iT2D model ensure applicability to arbitrary geometric aspect ratios and designs. Furthermore, the iT2D model is rapidly executable enabling its time-efficient integration in converter optimisations.

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Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 87%

Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 99%

Section: B Triple-2d Modelling Of Matrix Transformersmentioning

confidence: 99%

Section: B Cone Winding Leakage Inductance Pulmentioning

confidence: 99%

Section: Partial Leakage Length Modelsmentioning

confidence: 99%

See 3 more Smart Citations

Improved Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers

Schlesinger¹,

Biela²

2023

IEEE Open J. Power Electron.

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An Analytical Method to Obtain a Wide Frequency Range Equivalent $\pi$-Model of a Two-Winding Medium/High-Frequency Transformer

Das,

Fernandes

2023

IEEE Trans. on Ind. Applicat.

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Multi-Step Approach for Fast Calculation of Magnetic Field in Transformer Tank Shields

Jurković,

Jurišić,

Župan

2024

Energies

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A multi-step approach for the fast calculation of the magnetic field inside transformer tank shields, based on the 2D FEM, is presented in the paper. Due to the limitations of the 2D FEM, the proposed approach utilizes several 2D FEM models and calculates the magnetic field in multiple steps to account for the 3D geometry of the problem. In the first step, a distribution of the magnetic flux density that enters the tank shields is calculated using the quasi-3D model of the transformer. This quasi-3D model is obtained by superimposing the solution of multiple axisymmetric 2D FEM models, and assumes a considerably simplified transformer geometry. To account for the tank shield geometry that is neglected in the quasi-3D FEM model, an additional 2D FEM model with tank shields is introduced. After the distribution of the magnetic flux density that enters the tank shields is calculated, it is imposed in the final 2D FEM model with a non-linear tank shield which is used to calculate the magnetic flux density distribution inside the tank shields. The proposed approach enables a fast calculation of magnetic field distributions, both in the vertical and horizontal directions. The results of the proposed approach are compared against the 3D FEM. The relative error of the maximum magnetic flux density is under 2%, while the NRMSE of the magnetic flux density distribution within the tank shields is under 10%. The key contribution of the proposed approach is a low computation time. In the presented case study, the total computation time of the proposed approach is ~30 s, while the computation time of the 3D FEM is ~1 h. As the computation time is significantly reduced, while the accuracy is acceptable, the proposed approach can be a good alternative to the 3D FEM for design purposes. Therefore, it has industrial value.

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Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model

Cited by 4 publications

References 26 publications

Improved Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers

Improved Analytical Triple-2D Leakage Inductance Model of Cone Winding Matrix Transformers

An Analytical Method to Obtain a Wide Frequency Range Equivalent $\pi$-Model of a Two-Winding Medium/High-Frequency Transformer

Multi-Step Approach for Fast Calculation of Magnetic Field in Transformer Tank Shields

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